{
  "schema": "ferrofinder.endpoint_parent_recovery.v4_variable_cell",
  "status": "complete",
  "input_atom_count": 8,
  "input_formula": "K2N2O4",
  "input_spacegroup": "Cm",
  "input_pointgroup": "m",
  "input_is_polar_point_group": true,
  "input_energy_eV": -45.28415291900953,
  "input_cartesian_polarization_e_A2": [
    -0.0018579763865118483,
    -4.11534425454891e-18,
    -0.0009669751479724851
  ],
  "input_reduced_polarization": [
    -0.051301107735234636,
    -1.1172357382197103e-16,
    -0.04100318391208321
  ],
  "input_formal_targets": [
    {
      "orbit_id": 0,
      "representative_formal_class": [
        0.0,
        0.0,
        0.0
      ],
      "target_reduced_polarization": [
        0.0,
        0.0,
        0.0
      ]
    },
    {
      "orbit_id": 1,
      "representative_formal_class": [
        0.5,
        0.0,
        0.0
      ],
      "target_reduced_polarization": [
        -0.5,
        0.0,
        0.0
      ]
    },
    {
      "orbit_id": 2,
      "representative_formal_class": [
        0.0,
        0.0,
        0.5
      ],
      "target_reduced_polarization": [
        0.0,
        0.0,
        -0.5
      ]
    },
    {
      "orbit_id": 3,
      "representative_formal_class": [
        0.0,
        0.5,
        0.0
      ],
      "target_reduced_polarization": [
        0.0,
        -0.5,
        0.0
      ]
    },
    {
      "orbit_id": 4,
      "representative_formal_class": [
        0.5,
        0.0,
        0.5
      ],
      "target_reduced_polarization": [
        -0.5,
        0.0,
        -0.5
      ]
    },
    {
      "orbit_id": 5,
      "representative_formal_class": [
        0.5,
        0.5,
        0.0
      ],
      "target_reduced_polarization": [
        -0.5,
        -0.5,
        0.0
      ]
    },
    {
      "orbit_id": 6,
      "representative_formal_class": [
        0.0,
        0.5,
        0.5
      ],
      "target_reduced_polarization": [
        0.0,
        -0.5,
        -0.5
      ]
    },
    {
      "orbit_id": 7,
      "representative_formal_class": [
        0.5,
        0.5,
        0.5
      ],
      "target_reduced_polarization": [
        -0.5,
        -0.5,
        -0.5
      ]
    }
  ],
  "parent_candidates": [
    {
      "candidate_id": "inversion_parent_endpoint_00",
      "source": "same_species_inversion_center_projection_from_endpoint",
      "spacegroup": "C2/m",
      "spacegroup_number": 12,
      "pointgroup": "2/m",
      "has_inversion": true,
      "is_polar_point_group": false,
      "nonpolar_parent_hypothesis": true,
      "symmetry_tolerance_A": null,
      "target_reduced_polarization": [
        0.0,
        0.0,
        0.0
      ],
      "formal_class": [
        0.0,
        0.0,
        0.0
      ],
      "target_residual": 3.1637788234913204e-16,
      "parent_symmetrization_rmsd_A": 0.3641878565555496,
      "parent_cell_rmsd_A": 0.0,
      "energy_eV": -36.2918145715905,
      "reduced_polarization": [
        -6.59372601811935e-17,
        2.608896426545486e-16,
        -1.6638460420093191e-16
      ],
      "cartesian_polarization_e_A2": [
        -8.081437726684733e-19,
        9.609884961973672e-18,
        -3.923836198001369e-18
      ],
      "ranking_score": 0.3641878565555502
    },
    {
      "candidate_id": "bec_projection_00",
      "source": "MACEField_BEC_backprojection",
      "spacegroup": "Cm",
      "spacegroup_number": 8,
      "pointgroup": "m",
      "has_inversion": false,
      "is_polar_point_group": true,
      "nonpolar_parent_hypothesis": false,
      "symmetry_tolerance_A": null,
      "target_reduced_polarization": [
        0.0,
        0.0,
        0.0
      ],
      "formal_class": [
        0.0,
        0.0,
        0.0
      ],
      "target_residual": 0.0003122601609127391,
      "parent_symmetrization_rmsd_A": 0.09160132845627864,
      "parent_cell_rmsd_A": 0.07558508367349794,
      "energy_eV": -45.00046582492504,
      "reduced_polarization": [
        -0.0002815320957919248,
        8.28639211027957e-16,
        -0.00013507807791146635
      ],
      "cartesian_polarization_e_A2": [
        -1.1525271444262979e-05,
        3.0634937163843476e-17,
        -3.368965610748936e-06
      ],
      "ranking_score": 0.6111221196964786
    },
    {
      "candidate_id": "inversion_parent_bec_00_00",
      "source": "same_species_inversion_center_projection_after_BEC",
      "spacegroup": "C2/m",
      "spacegroup_number": 12,
      "pointgroup": "2/m",
      "has_inversion": true,
      "is_polar_point_group": false,
      "nonpolar_parent_hypothesis": true,
      "symmetry_tolerance_A": null,
      "target_reduced_polarization": [
        0.0,
        0.0,
        0.0
      ],
      "formal_class": [
        0.0,
        0.0,
        0.0
      ],
      "target_residual": 2.402008833452568e-15,
      "parent_symmetrization_rmsd_A": 0.36482939244679163,
      "parent_cell_rmsd_A": 0.07558508367349794,
      "energy_eV": -33.38130821480456,
      "reduced_polarization": [
        -1.0792805391389729e-15,
        -4.8669720728947886e-17,
        -2.1453277633276043e-15
      ],
      "cartesian_polarization_e_A2": [
        -2.212260925412004e-17,
        -1.7708056164071373e-18,
        -5.094262375194133e-17
      ],
      "ranking_score": 0.38372566336517094
    },
    {
      "candidate_id": "bec_projection_01",
      "source": "MACEField_BEC_backprojection",
      "spacegroup": "Cm",
      "spacegroup_number": 8,
      "pointgroup": "m",
      "has_inversion": false,
      "is_polar_point_group": true,
      "nonpolar_parent_hypothesis": false,
      "symmetry_tolerance_A": null,
      "target_reduced_polarization": [
        -0.5,
        0.0,
        0.0
      ],
      "formal_class": [
        0.5,
        0.0,
        0.0
      ],
      "target_residual": 0.21300933054527255,
      "parent_symmetrization_rmsd_A": 0.5971916181678212,
      "parent_cell_rmsd_A": 0.3724900867909749,
      "energy_eV": -40.494523189753025,
      "reduced_polarization": [
        -0.2953313765883656,
        2.0657943465767783e-14,
        -0.059023126739709046
      ],
      "cartesian_polarization_e_A2": [
        -0.01376252294880844,
        -3.4753375808104754e-16,
        -0.0004038356563199225
      ],
      "ranking_score": 1.61633280095611
    },
    {
      "candidate_id": "bec_projection_02",
      "source": "MACEField_BEC_backprojection",
      "spacegroup": "Cm",
      "spacegroup_number": 8,
      "pointgroup": "m",
      "has_inversion": false,
      "is_polar_point_group": true,
      "nonpolar_parent_hypothesis": false,
      "symmetry_tolerance_A": null,
      "target_reduced_polarization": [
        0.0,
        0.0,
        -0.5
      ],
      "formal_class": [
        0.0,
        0.0,
        0.5
      ],
      "target_residual": 0.06197481015677485,
      "parent_symmetrization_rmsd_A": 0.7082480131638751,
      "parent_cell_rmsd_A": 0.24630717120609466,
      "energy_eV": -42.87224777893235,
      "reduced_polarization": [
        -0.0021120742029668333,
        -4.380445456599932e-14,
        -0.4380611895777014
      ],
      "cartesian_polarization_e_A2": [
        0.005505988909076844,
        -5.439297253775007e-16,
        -0.010397361968807412
      ],
      "ranking_score": 1.3937744262789484
    },
    {
      "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": [
        0.0,
        -0.5,
        0.0
      ],
      "formal_class": [
        0.0,
        0.5,
        0.0
      ],
      "target_residual": 0.00014400091040324685,
      "parent_symmetrization_rmsd_A": 0.18480736286620233,
      "parent_cell_rmsd_A": 0.16200685399198483,
      "energy_eV": -22.903930535173465,
      "reduced_polarization": [
        9.099210629514173e-05,
        -0.5000122423754171,
        0.00011093612140815447
      ],
      "cartesian_polarization_e_A2": [
        -0.00042725174181179213,
        -0.018485250102102484,
        -0.0004099157576743037
      ],
      "ranking_score": 0.7255970781850051
    },
    {
      "candidate_id": "bec_projection_04",
      "source": "MACEField_BEC_backprojection",
      "spacegroup": "Cm",
      "spacegroup_number": 8,
      "pointgroup": "m",
      "has_inversion": false,
      "is_polar_point_group": true,
      "nonpolar_parent_hypothesis": false,
      "symmetry_tolerance_A": null,
      "target_reduced_polarization": [
        -0.5,
        0.0,
        -0.5
      ],
      "formal_class": [
        0.5,
        0.0,
        0.5
      ],
      "target_residual": 0.032480316456082,
      "parent_symmetrization_rmsd_A": 0.5990942888935772,
      "parent_cell_rmsd_A": 0.4248794940632923,
      "energy_eV": -36.15135920996109,
      "reduced_polarization": [
        -0.47603470222299143,
        3.185188352549645e-14,
        -0.47807660018276044
      ],
      "cartesian_polarization_e_A2": [
        -0.01468612912940743,
        -1.9181931507631617e-15,
        -0.009772478936886457
      ],
      "ranking_score": 1.2702747953215643
    },
    {
      "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,
        -0.5,
        0.0
      ],
      "formal_class": [
        0.5,
        0.5,
        0.0
      ],
      "target_residual": 0.3436759977115776,
      "parent_symmetrization_rmsd_A": 0.6107770464594865,
      "parent_cell_rmsd_A": 0.42143094850996643,
      "energy_eV": -40.17950072095579,
      "reduced_polarization": [
        -0.28061982214056413,
        -0.23907731218526354,
        -0.04364493039224772
      ],
      "cartesian_polarization_e_A2": [
        -0.013311195291847324,
        -0.00950743806139494,
        -7.6816855559005e-05
      ],
      "ranking_score": 1.9034867790101333
    },
    {
      "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": [
        0.0,
        -0.5,
        -0.5
      ],
      "formal_class": [
        0.0,
        0.5,
        0.5
      ],
      "target_residual": 0.017250653601939118,
      "parent_symmetrization_rmsd_A": 0.6585390053247627,
      "parent_cell_rmsd_A": 0.2973057965439509,
      "energy_eV": -37.41095385519867,
      "reduced_polarization": [
        0.005932512506080512,
        -0.49740899539887345,
        -0.4840100956783277
      ],
      "cartesian_polarization_e_A2": [
        0.006312073514037448,
        -0.018617248763565398,
        -0.011801058543132712
      ],
      "ranking_score": 1.2673667616646287
    },
    {
      "candidate_id": "bec_projection_07",
      "source": "MACEField_BEC_backprojection",
      "spacegroup": "P1",
      "spacegroup_number": 1,
      "pointgroup": "1",
      "has_inversion": false,
      "is_polar_point_group": true,
      "nonpolar_parent_hypothesis": false,
      "symmetry_tolerance_A": null,
      "target_reduced_polarization": [
        -0.5,
        -0.5,
        -0.5
      ],
      "formal_class": [
        0.5,
        0.5,
        0.5
      ],
      "target_residual": 0.33078958095414257,
      "parent_symmetrization_rmsd_A": 0.6038810117908464,
      "parent_cell_rmsd_A": 0.5026090351678443,
      "energy_eV": -38.45568692629783,
      "reduced_polarization": [
        -0.35140772910104,
        -0.2542954077934413,
        -0.3357704738315427
      ],
      "cartesian_polarization_e_A2": [
        -0.011663792241011519,
        -0.011070406693726682,
        -0.007365631984039363
      ],
      "ranking_score": 1.8911124324910926
    }
  ],
  "formal_branches": [
    {
      "orbit_id": 0,
      "formal_class": [
        0.0,
        0.0,
        0.0
      ],
      "formal_classes_in_orbit": [
        [
          0.0,
          0.0,
          0.0
        ]
      ],
      "target_reduced_polarization": [
        0.0,
        0.0,
        0.0
      ],
      "bec_backprojection": {
        "converged_to_target": true,
        "history": [
          {
            "iteration": 0,
            "reduced_polarization": [
              -0.051301107735234636,
              -1.1172357382197103e-16,
              -0.04100318391208321
            ],
            "branch_aligned_reduced_polarization": [
              -0.051301107735234636,
              -1.1172357382197103e-16,
              -0.04100318391208321
            ],
            "target_residual": 0.06567392744301402,
            "energy_eV": -45.28415291900953,
            "max_atomic_step_A": 0.07014607723582375,
            "max_log_strain_component": 0.014401440624826907,
            "step_scale": 1.0,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 1.9408351085199815,
            "cell_principal_stretches": [
              1.020139281491951,
              0.9934663110348941,
              0.9911162879060845
            ],
            "cell_volume_ratio": 1.0044705974174115,
            "cell_rmsd_from_input_A": 0.06772550817393695
          },
          {
            "iteration": 1,
            "reduced_polarization": [
              -0.004637663766799227,
              6.589910466067947e-16,
              -0.005081324647626635
            ],
            "branch_aligned_reduced_polarization": [
              -0.004637663766799227,
              6.589910466067947e-16,
              -0.005081324647626635
            ],
            "target_residual": 0.006879519270156916,
            "energy_eV": -45.04217448923005,
            "max_atomic_step_A": 0.007144652699832759,
            "max_log_strain_component": 0.0015508008719083114,
            "step_scale": 1.0,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 1.9408351085199815,
            "cell_principal_stretches": [
              1.0223980427101511,
              0.9926684612998782,
              0.9902145535445537
            ],
            "cell_volume_ratio": 1.004971019858263,
            "cell_rmsd_from_input_A": 0.07558508367349794
          },
          {
            "iteration": 2,
            "reduced_polarization": [
              -0.0002815320957919248,
              8.28639211027957e-16,
              -0.00013507807791146635
            ],
            "branch_aligned_reduced_polarization": [
              -0.0002815320957919248,
              8.28639211027957e-16,
              -0.00013507807791146635
            ],
            "target_residual": 0.0003122601609127391,
            "energy_eV": -45.00046582492504
          }
        ],
        "iterations": 2
      },
      "parent": {
        "candidate_id": "inversion_parent_endpoint_00",
        "source": "same_species_inversion_center_projection_from_endpoint",
        "spacegroup": "C2/m",
        "spacegroup_number": 12,
        "pointgroup": "2/m",
        "has_inversion": true,
        "is_polar_point_group": false,
        "nonpolar_parent_hypothesis": true,
        "symmetry_tolerance_A": null,
        "target_reduced_polarization": [
          0.0,
          0.0,
          0.0
        ],
        "formal_class": [
          0.0,
          0.0,
          0.0
        ],
        "target_residual": 3.1637788234913204e-16,
        "parent_symmetrization_rmsd_A": 0.3641878565555496,
        "parent_cell_rmsd_A": 0.0,
        "energy_eV": -36.2918145715905,
        "reduced_polarization": [
          -6.59372601811935e-17,
          2.608896426545486e-16,
          -1.6638460420093191e-16
        ],
        "cartesian_polarization_e_A2": [
          -8.081437726684733e-19,
          9.609884961973672e-18,
          -3.923836198001369e-18
        ],
        "ranking_score": 0.3641878565555502
      },
      "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": [
          -45.28415291900953,
          -45.08108331818531,
          -44.26613151545118,
          -42.83321172516358,
          -40.945456634278855,
          -39.015630413877645,
          -37.48666166586186,
          -36.579895881559054,
          -36.29181457159051
        ],
        "cartesian_polarizations_e_A2": [
          [
            -0.0018579763865118504,
            -6.629041015435542e-18,
            -0.0009669751479724801
          ],
          [
            -0.00147040281871342,
            -1.5949739624386856e-17,
            -0.0007016661819740481
          ],
          [
            -0.001547158556449101,
            -2.8696184261449157e-18,
            -0.0008896889857201778
          ],
          [
            -0.0018533828754653942,
            -1.4370337234803222e-17,
            -0.001284847587183655
          ],
          [
            -0.0019782477906333355,
            -8.175075748901213e-18,
            -0.0014092610474314151
          ],
          [
            -0.0018342192957488165,
            -2.718351718410145e-17,
            -0.0011702025885906102
          ],
          [
            -0.0014885668706751366,
            -1.9575691589205626e-18,
            -0.0008102790623732042
          ],
          [
            -0.000864923552042125,
            7.118433305165682e-19,
            -0.00041647223885806406
          ],
          [
            -1.525552731239858e-17,
            -2.1177339082867906e-17,
            7.770985909573083e-18
          ]
        ],
        "raw_reduced_polarization": [
          [
            -0.051301107735234615,
            -1.7996554053485066e-16,
            -0.041003183912083005
          ],
          [
            -0.039807763091616745,
            -4.3300433746136883e-16,
            -0.029753140569016772
          ],
          [
            -0.043770967933685435,
            -7.790454607045548e-17,
            -0.03772597587696975
          ],
          [
            -0.05516228377194187,
            -3.901266415621259e-16,
            -0.054482105384767186
          ],
          [
            -0.05934997984038365,
            -2.2193736961932084e-16,
            -0.05975767839444987
          ],
          [
            -0.05332975424867704,
            -7.379794984348574e-16,
            -0.04962074987654383
          ],
          [
            -0.04154405837044626,
            -5.31441864666673e-17,
            -0.03435871282138082
          ],
          [
            -0.02346233876508669,
            1.9325158715151747e-17,
            -0.01765990350422135
          ],
          [
            -2.2559104719628544e-16,
            -5.749234717757645e-16,
            3.29517428753504e-16
          ]
        ],
        "unwrapped_reduced_polarization": [
          [
            -0.051301107735234615,
            -1.7996554053485066e-16,
            -0.041003183912083005
          ],
          [
            -0.039807763091616745,
            -4.3300433746136883e-16,
            -0.029753140569016772
          ],
          [
            -0.043770967933685435,
            -7.790454607045547e-17,
            -0.03772597587696975
          ],
          [
            -0.05516228377194187,
            -3.901266415621259e-16,
            -0.054482105384767186
          ],
          [
            -0.05934997984038365,
            -2.2193736961932084e-16,
            -0.05975767839444987
          ],
          [
            -0.05332975424867704,
            -7.379794984348574e-16,
            -0.04962074987654383
          ],
          [
            -0.04154405837044626,
            -5.31441864666673e-17,
            -0.03435871282138082
          ],
          [
            -0.02346233876508669,
            1.9325158715151744e-17,
            -0.01765990350422135
          ],
          [
            -2.255140518769849e-16,
            -5.749234717757645e-16,
            3.2959746043559335e-16
          ]
        ],
        "berry_integer_shifts": [
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ]
        ],
        "folded_reduced_polarization": [
          [
            -0.05130110773523461,
            -1.6653345369377348e-16,
            -0.04100318391208302
          ],
          [
            -0.039807763091616766,
            -4.440892098500626e-16,
            -0.02975314056901679
          ],
          [
            -0.043770967933685456,
            -5.551115123125783e-17,
            -0.03772597587696974
          ],
          [
            -0.05516228377194188,
            -3.885780586188048e-16,
            -0.054482105384767165
          ],
          [
            -0.05934997984038365,
            -2.220446049250313e-16,
            -0.0597576783944499
          ],
          [
            -0.05332975424867703,
            -7.216449660063518e-16,
            -0.04962074987654386
          ],
          [
            -0.04154405837044628,
            -5.551115123125783e-17,
            -0.03435871282138081
          ],
          [
            -0.023462338765086688,
            0.0,
            -0.017659903504221364
          ],
          [
            -2.220446049250313e-16,
            -5.551115123125783e-16,
            3.3306690738754696e-16
          ]
        ]
      },
      "reflected": {
        "reached": true,
        "construction": "reflect_displacements_about_reconstructed_parent",
        "energies_eV": [
          -36.29181457159051,
          -36.57989588155906,
          -37.48666166586187,
          -39.01563041387765,
          -40.94545663427884,
          -42.83321172516358,
          -44.26613151545118,
          -45.0810833181853,
          -45.28415291900952
        ],
        "cartesian_polarizations_e_A2": [
          [
            2.6350421541584016e-17,
            -1.1389493288265091e-17,
            3.482795341977452e-18
          ],
          [
            0.0008649235520421074,
            -1.2546238700354514e-17,
            0.00041647223885808113
          ],
          [
            0.0014885668706751268,
            -9.698865378288242e-18,
            0.0008102790623731848
          ],
          [
            0.0018342192957488148,
            -2.091039783392419e-18,
            0.001170202588590553
          ],
          [
            0.0019782477906333147,
            -1.0154890011900418e-17,
            0.0014092610474314019
          ],
          [
            0.0018533828754653916,
            -2.567085010675374e-17,
            0.0012848475871836574
          ],
          [
            0.0015471585564491106,
            -1.4459317651117791e-18,
            0.0008896889857201997
          ],
          [
            0.0014704028187133642,
            -1.2457258284039944e-17,
            0.0007016661819739956
          ],
          [
            0.0018579763865118342,
            -6.273119350177257e-18,
            0.0009669751479724734
          ]
        ],
        "raw_reduced_polarization": [
          [
            6.00167545172325e-16,
            -3.0920253944242795e-16,
            1.476829039863925e-16
          ],
          [
            0.02346233876508653,
            -3.4060592235454955e-16,
            0.017659903504222075
          ],
          [
            0.04154405837044581,
            -2.633052874939426e-16,
            0.03435871282138
          ],
          [
            0.05332975424867629,
            -5.676765372575825e-17,
            0.0496207498765414
          ],
          [
            0.059349979840383045,
            -2.7568546729583666e-16,
            0.05975767839444931
          ],
          [
            0.05516228377194184,
            -6.969135361651599e-16,
            0.05448210538476728
          ],
          [
            0.04377096793368591,
            -3.925422864015198e-17,
            0.03772597587697068
          ],
          [
            0.03980776309161491,
            -3.381902775151556e-16,
            0.029753140569014545
          ],
          [
            0.051301107735234185,
            -1.7030296117727478e-16,
            0.041003183912082714
          ]
        ],
        "unwrapped_reduced_polarization": [
          [
            6.00167545172325e-16,
            -3.0920253944242795e-16,
            1.476829039863925e-16
          ],
          [
            0.02346233876508653,
            -3.4060592235454955e-16,
            0.017659903504222075
          ],
          [
            0.04154405837044581,
            -2.633052874939426e-16,
            0.03435871282138
          ],
          [
            0.05332975424867629,
            -5.676765372575827e-17,
            0.0496207498765414
          ],
          [
            0.059349979840383045,
            -2.7568546729583666e-16,
            0.05975767839444931
          ],
          [
            0.05516228377194184,
            -6.969135361651599e-16,
            0.05448210538476728
          ],
          [
            0.04377096793368591,
            -3.925422864015193e-17,
            0.03772597587697068
          ],
          [
            0.03980776309161491,
            -3.381902775151556e-16,
            0.029753140569014545
          ],
          [
            0.051301107735234185,
            -1.7030296117727478e-16,
            0.041003183912082714
          ]
        ],
        "gauge_integer_shift": [
          0,
          0,
          0
        ],
        "expected_opposite_endpoint_reduced_polarization": [
          0.05130110773523417,
          -9.698814030166783e-16,
          0.04100318391208366
        ],
        "actual_opposite_endpoint_branch_residual": 1.2369592895214559e-15
      },
      "pnp_branch": {
        "construction": "incoming_path_concatenated_with_parent_reflection",
        "reduced_polarization": [
          [
            -0.051301107735234615,
            -1.7996554053485066e-16,
            -0.041003183912083005
          ],
          [
            -0.039807763091616745,
            -4.3300433746136883e-16,
            -0.029753140569016772
          ],
          [
            -0.043770967933685435,
            -7.790454607045548e-17,
            -0.03772597587696975
          ],
          [
            -0.05516228377194187,
            -3.901266415621259e-16,
            -0.054482105384767186
          ],
          [
            -0.05934997984038365,
            -2.2193736961932084e-16,
            -0.05975767839444987
          ],
          [
            -0.05332975424867704,
            -7.379794984348574e-16,
            -0.04962074987654383
          ],
          [
            -0.04154405837044626,
            -5.31441864666673e-17,
            -0.03435871282138082
          ],
          [
            -0.02346233876508669,
            1.9325158715151747e-17,
            -0.01765990350422135
          ],
          [
            -2.2559104719628544e-16,
            -5.749234717757645e-16,
            3.29517428753504e-16
          ],
          [
            0.02346233876508653,
            -3.4060592235454955e-16,
            0.017659903504222075
          ],
          [
            0.04154405837044581,
            -2.633052874939426e-16,
            0.03435871282138
          ],
          [
            0.05332975424867629,
            -5.676765372575825e-17,
            0.0496207498765414
          ],
          [
            0.059349979840383045,
            -2.7568546729583666e-16,
            0.05975767839444931
          ],
          [
            0.05516228377194184,
            -6.969135361651599e-16,
            0.05448210538476728
          ],
          [
            0.04377096793368591,
            -3.925422864015198e-17,
            0.03772597587697068
          ],
          [
            0.03980776309161491,
            -3.381902775151556e-16,
            0.029753140569014545
          ],
          [
            0.051301107735234185,
            -1.7030296117727478e-16,
            0.041003183912082714
          ]
        ],
        "unwrapped_reduced_polarization": [
          [
            -0.051301107735234615,
            -1.7996554053485066e-16,
            -0.041003183912083005
          ],
          [
            -0.039807763091616745,
            -4.3300433746136883e-16,
            -0.029753140569016772
          ],
          [
            -0.043770967933685435,
            -7.790454607045547e-17,
            -0.03772597587696975
          ],
          [
            -0.05516228377194187,
            -3.901266415621259e-16,
            -0.054482105384767186
          ],
          [
            -0.05934997984038365,
            -2.2193736961932084e-16,
            -0.05975767839444987
          ],
          [
            -0.05332975424867704,
            -7.379794984348574e-16,
            -0.04962074987654383
          ],
          [
            -0.04154405837044626,
            -5.31441864666673e-17,
            -0.03435871282138082
          ],
          [
            -0.02346233876508669,
            1.9325158715151744e-17,
            -0.01765990350422135
          ],
          [
            -2.255140518769849e-16,
            -5.749234717757645e-16,
            3.2959746043559335e-16
          ],
          [
            0.02346233876508653,
            -3.4060592235454955e-16,
            0.017659903504222075
          ],
          [
            0.04154405837044581,
            -2.633052874939426e-16,
            0.03435871282138
          ],
          [
            0.05332975424867629,
            -5.676765372575827e-17,
            0.0496207498765414
          ],
          [
            0.059349979840383045,
            -2.7568546729583666e-16,
            0.05975767839444931
          ],
          [
            0.05516228377194184,
            -6.969135361651599e-16,
            0.05448210538476728
          ],
          [
            0.04377096793368591,
            -3.925422864015193e-17,
            0.03772597587697068
          ],
          [
            0.03980776309161491,
            -3.381902775151556e-16,
            0.029753140569014545
          ],
          [
            0.051301107735234185,
            -1.7030296117727478e-16,
            0.041003183912082714
          ]
        ],
        "berry_integer_shifts": [
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ]
        ],
        "folded_reduced_polarization": [
          [
            -0.05130110773523461,
            -1.6653345369377348e-16,
            -0.04100318391208302
          ],
          [
            -0.039807763091616766,
            -4.440892098500626e-16,
            -0.02975314056901679
          ],
          [
            -0.043770967933685456,
            -5.551115123125783e-17,
            -0.03772597587696974
          ],
          [
            -0.05516228377194188,
            -3.885780586188048e-16,
            -0.054482105384767165
          ],
          [
            -0.05934997984038365,
            -2.220446049250313e-16,
            -0.0597576783944499
          ],
          [
            -0.05332975424867703,
            -7.216449660063518e-16,
            -0.04962074987654386
          ],
          [
            -0.04154405837044628,
            -5.551115123125783e-17,
            -0.03435871282138081
          ],
          [
            -0.023462338765086688,
            0.0,
            -0.017659903504221364
          ],
          [
            -2.220446049250313e-16,
            -5.551115123125783e-16,
            3.3306690738754696e-16
          ],
          [
            0.02346233876508652,
            -3.3306690738754696e-16,
            0.017659903504222085
          ],
          [
            0.041544058370445835,
            -2.7755575615628914e-16,
            0.03435871282138003
          ],
          [
            0.05332975424867625,
            -5.551115123125783e-17,
            0.049620749876541415
          ],
          [
            0.05934997984038304,
            -2.7755575615628914e-16,
            0.05975767839444934
          ],
          [
            0.05516228377194188,
            -7.216449660063518e-16,
            0.054482105384767276
          ],
          [
            0.043770967933685956,
            -5.551115123125783e-17,
            0.037725975876970685
          ],
          [
            0.039807763091614934,
            -3.3306690738754696e-16,
            0.02975314056901457
          ],
          [
            0.05130110773523422,
            -1.6653345369377348e-16,
            0.041003183912082686
          ]
        ]
      },
      "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": [
        0.5,
        0.0,
        0.0
      ],
      "formal_classes_in_orbit": [
        [
          0.5,
          0.0,
          0.0
        ]
      ],
      "target_reduced_polarization": [
        -0.5,
        0.0,
        0.0
      ],
      "bec_backprojection": {
        "converged_to_target": false,
        "history": [
          {
            "iteration": 0,
            "reduced_polarization": [
              -0.051301107735234636,
              -1.1172357382197103e-16,
              -0.04100318391208321
            ],
            "branch_aligned_reduced_polarization": [
              -0.05130110773523466,
              -1.1172357382197103e-16,
              -0.04100318391208321
            ],
            "target_residual": 0.45056848204302485,
            "energy_eV": -45.28415291900953,
            "max_atomic_step_A": 0.11929720676800173,
            "max_log_strain_component": 0.019999999999999997,
            "step_scale": 0.13121995314934212,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 1.9408351085199815,
            "cell_principal_stretches": [
              1.0139757706713322,
              1.0066177611257343,
              0.9741268038015987
            ],
            "cell_volume_ratio": 0.9942776104536739,
            "cell_rmsd_from_input_A": 0.08548916340941828
          },
          {
            "iteration": 1,
            "reduced_polarization": [
              -0.1139790356400854,
              7.972844150424529e-15,
              -0.04305313066381589
            ],
            "branch_aligned_reduced_polarization": [
              -0.11397903564008538,
              7.972844150424529e-15,
              -0.04305313066381589
            ],
            "target_residual": 0.38841441397728027,
            "energy_eV": -45.10248810881821,
            "max_atomic_step_A": 0.12,
            "max_log_strain_component": 0.018233853786050254,
            "step_scale": 0.14834860008563924,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 1.9408351085199815,
            "cell_principal_stretches": [
              1.0275236945870279,
              1.011762050891057,
              0.9515629167868711
            ],
            "cell_volume_ratio": 0.9892538296547776,
            "cell_rmsd_from_input_A": 0.16271729605639698
          },
          {
            "iteration": 2,
            "reduced_polarization": [
              -0.17450826492074833,
              2.032856978798264e-14,
              -0.048519290569822696
            ],
            "branch_aligned_reduced_polarization": [
              -0.17450826492074833,
              2.032856978798264e-14,
              -0.048519290569822696
            ],
            "target_residual": 0.3290881206642085,
            "energy_eV": -44.573013699995116,
            "max_atomic_step_A": 0.12,
            "max_log_strain_component": 0.01838979056660751,
            "step_scale": 0.15869250770626192,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 1.9408351085199815,
            "cell_principal_stretches": [
              1.0423058725609575,
              1.0157063175321432,
              0.9298745968089235
            ],
            "cell_volume_ratio": 0.9844365319603193,
            "cell_rmsd_from_input_A": 0.24280214124077718
          },
          {
            "iteration": 3,
            "reduced_polarization": [
              -0.22613698788975042,
              3.4382966392551793e-14,
              -0.05768915180390283
            ],
            "branch_aligned_reduced_polarization": [
              -0.22613698788975045,
              3.4382966392551793e-14,
              -0.05768915180390283
            ],
            "target_residual": 0.2798731634829471,
            "energy_eV": -43.769031922259174,
            "max_atomic_step_A": 0.10697461512759598,
            "max_log_strain_component": 0.019999999999999997,
            "step_scale": 0.13880036779676297,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 1.9408351085199815,
            "cell_principal_stretches": [
              1.060011914990251,
              1.0182850008886049,
              0.9074775472735269
            ],
            "cell_volume_ratio": 0.9795260318279974,
            "cell_rmsd_from_input_A": 0.3373442558798842
          },
          {
            "iteration": 4,
            "reduced_polarization": [
              -0.2639047745701389,
              4.226421682105578e-14,
              -0.07050790844691897
            ],
            "branch_aligned_reduced_polarization": [
              -0.2639047745701389,
              4.226421682105578e-14,
              -0.07050790844691897
            ],
            "target_residual": 0.2463987025622011,
            "energy_eV": -42.71442968394072,
            "max_atomic_step_A": 0.0663015262292373,
            "max_log_strain_component": 0.02,
            "step_scale": 0.1428529878459298,
            "strain_jacobian_refreshed": true,
            "strain_jacobian_frobenius_norm": 2.401755895332643,
            "cell_principal_stretches": [
              1.063086377187849,
              0.9981216069191787,
              0.9058153894626884
            ],
            "cell_volume_ratio": 0.9611511833823083,
            "cell_rmsd_from_input_A": 0.3724900867909749
          },
          {
            "iteration": 5,
            "reduced_polarization": [
              -0.2953313765883656,
              2.0657943465767783e-14,
              -0.059023126739709046
            ],
            "branch_aligned_reduced_polarization": [
              -0.2953313765883656,
              2.0657943465767783e-14,
              -0.059023126739709046
            ],
            "target_residual": 0.21300933054527255,
            "energy_eV": -40.494523189753025
          }
        ],
        "iterations": 5
      },
      "parent": {
        "candidate_id": "inversion_parent_endpoint_00",
        "source": "same_species_inversion_center_projection_from_endpoint",
        "spacegroup": "C2/m",
        "spacegroup_number": 12,
        "pointgroup": "2/m",
        "has_inversion": true,
        "is_polar_point_group": false,
        "nonpolar_parent_hypothesis": true,
        "symmetry_tolerance_A": null,
        "target_reduced_polarization": [
          -0.5,
          0.0,
          0.0
        ],
        "formal_class": [
          0.5,
          0.0,
          0.0
        ],
        "target_residual": 0.49999999999999994,
        "parent_symmetrization_rmsd_A": 0.3641878565555496,
        "parent_cell_rmsd_A": 0.0,
        "energy_eV": -36.2918145715905,
        "reduced_polarization": [
          -6.59372601811935e-17,
          2.608896426545486e-16,
          -1.6638460420093191e-16
        ],
        "cartesian_polarization_e_A2": [
          -8.081437726684733e-19,
          9.609884961973672e-18,
          -3.923836198001369e-18
        ],
        "ranking_score": 1.3641878565555494
      },
      "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,
        0.0,
        -0.5
      ],
      "bec_backprojection": {
        "converged_to_target": false,
        "history": [
          {
            "iteration": 0,
            "reduced_polarization": [
              -0.051301107735234636,
              -1.1172357382197103e-16,
              -0.04100318391208321
            ],
            "branch_aligned_reduced_polarization": [
              -0.051301107735234636,
              -1.1172357382197103e-16,
              -0.04100318391208324
            ],
            "target_residual": 0.4618548265783384,
            "energy_eV": -45.28415291900953,
            "max_atomic_step_A": 0.12,
            "max_log_strain_component": 0.008342948645937024,
            "step_scale": 0.17563697540459558,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 1.9408351085199815,
            "cell_principal_stretches": [
              1.0099695900051773,
              1.0004017572902895,
              0.9915347989332676
            ],
            "cell_volume_ratio": 1.0018223221378717,
            "cell_rmsd_from_input_A": 0.04883880145216067
          },
          {
            "iteration": 1,
            "reduced_polarization": [
              -0.043229154178989614,
              -2.027708498010326e-15,
              -0.1240071908399015
            ],
            "branch_aligned_reduced_polarization": [
              -0.043229154178989614,
              -2.027708498010326e-15,
              -0.12400719083990153
            ],
            "target_residual": 0.37846975085353,
            "energy_eV": -45.21713398275616,
            "max_atomic_step_A": 0.12,
            "max_log_strain_component": 0.008674935413157205,
            "step_scale": 0.21672459725280271,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 1.9408351085199815,
            "cell_principal_stretches": [
              1.0204814071955288,
              1.0005563239679915,
              0.9830758198623102
            ],
            "cell_volume_ratio": 1.0037687061325047,
            "cell_rmsd_from_input_A": 0.09690591682154326
          },
          {
            "iteration": 2,
            "reduced_polarization": [
              -0.03504588685725542,
              -5.6739063825745886e-15,
              -0.20655852745886005
            ],
            "branch_aligned_reduced_polarization": [
              -0.03504588685725542,
              -5.6739063825745886e-15,
              -0.20655852745886005
            ],
            "target_residual": 0.2955268380244409,
            "energy_eV": -45.06383639280441,
            "max_atomic_step_A": 0.12000000000000001,
            "max_log_strain_component": 0.008752415057557916,
            "step_scale": 0.2716025668253892,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 1.9408351085199815,
            "cell_principal_stretches": [
              1.0311921519921663,
              1.000754915458843,
              0.9745708885208649
            ],
            "cell_volume_ratio": 1.0057285190795453,
            "cell_rmsd_from_input_A": 0.1450703915145997
          },
          {
            "iteration": 3,
            "reduced_polarization": [
              -0.02627586606369479,
              -8.787062647057318e-15,
              -0.2852498439762714
            ],
            "branch_aligned_reduced_polarization": [
              -0.02627586606369479,
              -8.787062647057318e-15,
              -0.2852498439762714
            ],
            "target_residual": 0.21635168279820013,
            "energy_eV": -44.780949178710515,
            "max_atomic_step_A": 0.12,
            "max_log_strain_component": 0.00827205275232354,
            "step_scale": 0.3601672628486037,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 1.9408351085199815,
            "cell_principal_stretches": [
              1.0413331581925547,
              1.0014774139134768,
              0.9660694670827316
            ],
            "cell_volume_ratio": 1.0074864478375816,
            "cell_rmsd_from_input_A": 0.19381797630599967
          },
          {
            "iteration": 4,
            "reduced_polarization": [
              -0.016839910850123038,
              -1.4744100888370387e-14,
              -0.35946014592676484
            ],
            "branch_aligned_reduced_polarization": [
              -0.016839910850123038,
              -1.4744100888370387e-14,
              -0.35946014592676484
            ],
            "target_residual": 0.14154516304122272,
            "energy_eV": -44.23161493333761,
            "max_atomic_step_A": 0.12,
            "max_log_strain_component": 0.015009257692727292,
            "step_scale": 0.6125716648655037,
            "strain_jacobian_refreshed": true,
            "strain_jacobian_frobenius_norm": 2.002930148072852,
            "cell_principal_stretches": [
              1.0498578040776456,
              0.9865582243937887,
              0.9571302931943931
            ],
            "cell_volume_ratio": 0.9913437300968754,
            "cell_rmsd_from_input_A": 0.24630717120609466
          },
          {
            "iteration": 5,
            "reduced_polarization": [
              -0.0021120742029668333,
              -4.380445456599932e-14,
              -0.4380611895777014
            ],
            "branch_aligned_reduced_polarization": [
              -0.0021120742029668333,
              -4.380445456599932e-14,
              -0.4380611895777014
            ],
            "target_residual": 0.06197481015677485,
            "energy_eV": -42.87224777893235
          }
        ],
        "iterations": 5
      },
      "parent": {
        "candidate_id": "inversion_parent_endpoint_00",
        "source": "same_species_inversion_center_projection_from_endpoint",
        "spacegroup": "C2/m",
        "spacegroup_number": 12,
        "pointgroup": "2/m",
        "has_inversion": true,
        "is_polar_point_group": false,
        "nonpolar_parent_hypothesis": true,
        "symmetry_tolerance_A": null,
        "target_reduced_polarization": [
          0.0,
          0.0,
          -0.5
        ],
        "formal_class": [
          0.0,
          0.0,
          0.5
        ],
        "target_residual": 0.49999999999999983,
        "parent_symmetrization_rmsd_A": 0.3641878565555496,
        "parent_cell_rmsd_A": 0.0,
        "energy_eV": -36.2918145715905,
        "reduced_polarization": [
          -6.59372601811935e-17,
          2.608896426545486e-16,
          -1.6638460420093191e-16
        ],
        "cartesian_polarization_e_A2": [
          -8.081437726684733e-19,
          9.609884961973672e-18,
          -3.923836198001369e-18
        ],
        "ranking_score": 1.3641878565555492
      },
      "branch_status": "awaiting_branch_sampling"
    },
    {
      "orbit_id": 3,
      "formal_class": [
        0.0,
        0.5,
        0.0
      ],
      "formal_classes_in_orbit": [
        [
          0.0,
          0.5,
          0.0
        ]
      ],
      "target_reduced_polarization": [
        0.0,
        -0.5,
        0.0
      ],
      "bec_backprojection": {
        "converged_to_target": true,
        "history": [
          {
            "iteration": 0,
            "reduced_polarization": [
              -0.051301107735234636,
              -1.1172357382197103e-16,
              -0.04100318391208321
            ],
            "branch_aligned_reduced_polarization": [
              -0.051301107735234636,
              -1.1102230246251565e-16,
              -0.04100318391208321
            ],
            "target_residual": 0.5042946209764587,
            "energy_eV": -45.28415291900953,
            "max_atomic_step_A": 0.12000000000000001,
            "max_log_strain_component": 0.012367435788272919,
            "step_scale": 0.5226473157584641,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 1.9408351085199815,
            "cell_principal_stretches": [
              1.0222144167562788,
              0.9953489245772426,
              0.9851336052097134
            ],
            "cell_volume_ratio": 1.0023340580590312,
            "cell_rmsd_from_input_A": 0.0924197191921154
          },
          {
            "iteration": 1,
            "reduced_polarization": [
              -0.0004823844018056111,
              -0.26935188656863746,
              -0.0005085661347540726
            ],
            "branch_aligned_reduced_polarization": [
              -0.0004823844018056111,
              -0.26935188656863746,
              -0.0005085661347540726
            ],
            "target_residual": 0.23064917854540737,
            "energy_eV": -40.95303263207283,
            "max_atomic_step_A": 0.10349469519639236,
            "max_log_strain_component": 0.011421314921959197,
            "step_scale": 1.0,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 1.9408351085199815,
            "cell_principal_stretches": [
              1.032353759150636,
              1.0015386012186547,
              0.9662820757065119
            ],
            "cell_volume_ratio": 0.9990797571054674,
            "cell_rmsd_from_input_A": 0.163204207229616
          },
          {
            "iteration": 2,
            "reduced_polarization": [
              0.0234273536512572,
              -0.5346194828867731,
              0.033097745318459444
            ],
            "branch_aligned_reduced_polarization": [
              0.0234273536512572,
              -0.5346194828867731,
              0.033097745318459444
            ],
            "target_residual": 0.05331801046189038,
            "energy_eV": -19.779958853696026,
            "max_atomic_step_A": 0.015269786448334993,
            "max_log_strain_component": 0.000499616795455873,
            "step_scale": 1.0,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 1.9408351085199815,
            "cell_principal_stretches": [
              1.031911016840416,
              1.0016396393910154,
              0.9664585679915255
            ],
            "cell_volume_ratio": 0.9989344547547534,
            "cell_rmsd_from_input_A": 0.16165410519031204
          },
          {
            "iteration": 3,
            "reduced_polarization": [
              0.002026870037446178,
              -0.49931618197197,
              0.0025246000563001144
            ],
            "branch_aligned_reduced_polarization": [
              0.002026870037446178,
              -0.49931618197197,
              0.0025246000563001144
            ],
            "target_residual": 0.0033089899801036697,
            "energy_eV": -23.080735302889472,
            "max_atomic_step_A": 0.0015800980848714931,
            "max_log_strain_component": 9.943878987781228e-05,
            "step_scale": 1.0,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 1.9408351085199815,
            "cell_principal_stretches": [
              1.0319422307519865,
              1.001695093214614,
              0.9663440621331638
            ],
            "cell_volume_ratio": 0.9989016131702166,
            "cell_rmsd_from_input_A": 0.16200685399198483
          },
          {
            "iteration": 4,
            "reduced_polarization": [
              9.099210629514173e-05,
              -0.5000122423754171,
              0.00011093612140815447
            ],
            "branch_aligned_reduced_polarization": [
              9.099210629514173e-05,
              -0.5000122423754171,
              0.00011093612140815447
            ],
            "target_residual": 0.00014400091040324685,
            "energy_eV": -22.903930535173465
          }
        ],
        "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": [
          0.0,
          -0.5,
          0.0
        ],
        "formal_class": [
          0.0,
          0.5,
          0.0
        ],
        "target_residual": 0.00014400091040324685,
        "parent_symmetrization_rmsd_A": 0.18480736286620233,
        "parent_cell_rmsd_A": 0.16200685399198483,
        "energy_eV": -22.903930535173465,
        "reduced_polarization": [
          9.099210629514173e-05,
          -0.5000122423754171,
          0.00011093612140815447
        ],
        "cartesian_polarization_e_A2": [
          -0.00042725174181179213,
          -0.018485250102102484,
          -0.0004099157576743037
        ],
        "ranking_score": 0.7255970781850051
      },
      "branch_status": "awaiting_branch_sampling"
    },
    {
      "orbit_id": 4,
      "formal_class": [
        0.5,
        0.0,
        0.5
      ],
      "formal_classes_in_orbit": [
        [
          0.5,
          0.0,
          0.5
        ]
      ],
      "target_reduced_polarization": [
        -0.5,
        0.0,
        -0.5
      ],
      "bec_backprojection": {
        "converged_to_target": false,
        "history": [
          {
            "iteration": 0,
            "reduced_polarization": [
              -0.051301107735234636,
              -1.1172357382197103e-16,
              -0.04100318391208321
            ],
            "branch_aligned_reduced_polarization": [
              -0.05130110773523466,
              -1.1172357382197103e-16,
              -0.04100318391208324
            ],
            "target_residual": 0.6418790953898346,
            "energy_eV": -45.28415291900953,
            "max_atomic_step_A": 0.09933328297382607,
            "max_log_strain_component": 0.02,
            "step_scale": 0.1676218452719602,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 1.9408351085199815,
            "cell_principal_stretches": [
              1.012061795861381,
              1.0099571276775998,
              0.9721565037761355
            ],
            "cell_volume_ratio": 0.9936791003147936,
            "cell_rmsd_from_input_A": 0.09498149880831248
          },
          {
            "iteration": 1,
            "reduced_polarization": [
              -0.13360298688252156,
              9.474028507508142e-15,
              -0.1252032622241523
            ],
            "branch_aligned_reduced_polarization": [
              -0.1336029868825216,
              9.474028507508142e-15,
              -0.1252032622241523
            ],
            "target_residual": 0.5241367816408491,
            "energy_eV": -44.861830804072945,
            "max_atomic_step_A": 0.1042189246735886,
            "max_log_strain_component": 0.02,
            "step_scale": 0.26442788635854636,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 1.9408351085199815,
            "cell_principal_stretches": [
              1.024475313368452,
              1.0195893522908963,
              0.9453624629483469
            ],
            "cell_volume_ratio": 0.9874728030714554,
            "cell_rmsd_from_input_A": 0.1847718851304791
          },
          {
            "iteration": 2,
            "reduced_polarization": [
              -0.2363055880721968,
              3.5103382610256315e-14,
              -0.23084143621292286
            ],
            "branch_aligned_reduced_polarization": [
              -0.23630558807219681,
              3.5103382610256315e-14,
              -0.23084143621292286
            ],
            "target_residual": 0.3768037623775432,
            "energy_eV": -43.13798829067797,
            "max_atomic_step_A": 0.0994818788204658,
            "max_log_strain_component": 0.02,
            "step_scale": 0.38737580312494874,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 1.9408351085199815,
            "cell_principal_stretches": [
              1.0374281497691797,
              1.0285496913450698,
              0.9197704093371237
            ],
            "cell_volume_ratio": 0.9814377070877158,
            "cell_rmsd_from_input_A": 0.2690751125741015
          },
          {
            "iteration": 3,
            "reduced_polarization": [
              -0.3369939993251768,
              6.595844692560282e-14,
              -0.3345519306033399
            ],
            "branch_aligned_reduced_polarization": [
              -0.3369939993251768,
              6.595844692560282e-14,
              -0.3345519306033399
            ],
            "target_residual": 0.23225851959203245,
            "energy_eV": -40.24856768096924,
            "max_atomic_step_A": 0.09310299649271155,
            "max_log_strain_component": 0.02,
            "step_scale": 0.5275740546248855,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 1.9408351085199815,
            "cell_principal_stretches": [
              1.050679180782862,
              1.0373491644331347,
              0.8950009246095061
            ],
            "cell_volume_ratio": 0.9754804551452665,
            "cell_rmsd_from_input_A": 0.3510463431745917
          },
          {
            "iteration": 4,
            "reduced_polarization": [
              -0.4164937367565516,
              7.70080907320116e-14,
              -0.4172039136419953
            ],
            "branch_aligned_reduced_polarization": [
              -0.4164937367565516,
              7.70080907320116e-14,
              -0.4172039136419953
            ],
            "target_residual": 0.11759459135983368,
            "energy_eV": -37.1357659006533,
            "max_atomic_step_A": 0.0597836924847971,
            "max_log_strain_component": 0.02,
            "step_scale": 0.6415582454862301,
            "strain_jacobian_refreshed": true,
            "strain_jacobian_frobenius_norm": 1.9450255178471778,
            "cell_principal_stretches": [
              1.0652122678527356,
              1.041506677217876,
              0.8718279091115303
            ],
            "cell_volume_ratio": 0.9672282792986561,
            "cell_rmsd_from_input_A": 0.4248794940632923
          },
          {
            "iteration": 5,
            "reduced_polarization": [
              -0.47603470222299143,
              3.185188352549645e-14,
              -0.47807660018276044
            ],
            "branch_aligned_reduced_polarization": [
              -0.47603470222299143,
              3.185188352549645e-14,
              -0.47807660018276044
            ],
            "target_residual": 0.032480316456082,
            "energy_eV": -36.15135920996109
          }
        ],
        "iterations": 5
      },
      "parent": {
        "candidate_id": "bec_projection_04",
        "source": "MACEField_BEC_backprojection",
        "spacegroup": "Cm",
        "spacegroup_number": 8,
        "pointgroup": "m",
        "has_inversion": false,
        "is_polar_point_group": true,
        "nonpolar_parent_hypothesis": false,
        "symmetry_tolerance_A": null,
        "target_reduced_polarization": [
          -0.5,
          0.0,
          -0.5
        ],
        "formal_class": [
          0.5,
          0.0,
          0.5
        ],
        "target_residual": 0.032480316456082,
        "parent_symmetrization_rmsd_A": 0.5990942888935772,
        "parent_cell_rmsd_A": 0.4248794940632923,
        "energy_eV": -36.15135920996109,
        "reduced_polarization": [
          -0.47603470222299143,
          3.185188352549645e-14,
          -0.47807660018276044
        ],
        "cartesian_polarization_e_A2": [
          -0.01468612912940743,
          -1.9181931507631617e-15,
          -0.009772478936886457
        ],
        "ranking_score": 1.2702747953215643
      },
      "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,
        -0.5,
        0.0
      ],
      "bec_backprojection": {
        "converged_to_target": false,
        "history": [
          {
            "iteration": 0,
            "reduced_polarization": [
              -0.051301107735234636,
              -1.1172357382197103e-16,
              -0.04100318391208321
            ],
            "branch_aligned_reduced_polarization": [
              -0.05130110773523466,
              -1.1102230246251565e-16,
              -0.04100318391208321
            ],
            "target_residual": 0.6730616294296946,
            "energy_eV": -45.28415291900953,
            "max_atomic_step_A": 0.11999222338986348,
            "max_log_strain_component": 0.02,
            "step_scale": 0.13121995314935084,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 1.9408351085199815,
            "cell_principal_stretches": [
              1.0139841908826257,
              1.007165809244662,
              0.973588648989156
            ],
            "cell_volume_ratio": 0.9942776104536757,
            "cell_rmsd_from_input_A": 0.08799477818343132
          },
          {
            "iteration": 1,
            "reduced_polarization": [
              -0.11245110241984228,
              -0.06321266124156569,
              -0.04161582803357806
            ],
            "branch_aligned_reduced_polarization": [
              -0.1124511024198423,
              -0.06321266124156566,
              -0.04161582803357806
            ],
            "target_residual": 0.5854137036815855,
            "energy_eV": -44.98362487145652,
            "max_atomic_step_A": 0.11999999999999998,
            "max_log_strain_component": 0.01864492290465564,
            "step_scale": 0.1456120729809895,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 1.9408351085199815,
            "cell_principal_stretches": [
              1.0277082256456098,
              1.0137783914262755,
              0.9493529556362981
            ],
            "cell_volume_ratio": 0.9891008371873642,
            "cell_rmsd_from_input_A": 0.17168253669545644
          },
          {
            "iteration": 2,
            "reduced_polarization": [
              -0.16910403246951683,
              -0.12049111644101312,
              -0.04217644417864326
            ],
            "branch_aligned_reduced_polarization": [
              -0.16910403246951683,
              -0.12049111644101312,
              -0.04217644417864326
            ],
            "target_residual": 0.5052702113440662,
            "energy_eV": -44.2080450577396,
            "max_atomic_step_A": 0.11560856847037491,
            "max_log_strain_component": 0.02,
            "step_scale": 0.15610765272407132,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 1.9408351085199815,
            "cell_principal_stretches": [
              1.0429772102638228,
              1.021228850187162,
              0.9235157244485899
            ],
            "cell_volume_ratio": 0.983653606692432,
            "cell_rmsd_from_input_A": 0.2647087823842206
          },
          {
            "iteration": 3,
            "reduced_polarization": [
              -0.21537625343981168,
              -0.17126208602216184,
              -0.04217698860422464
            ],
            "branch_aligned_reduced_polarization": [
              -0.2153762534398117,
              -0.17126208602216186,
              -0.04217698860422464
            ],
            "target_residual": 0.43687319849148415,
            "energy_eV": -43.03553990749154,
            "max_atomic_step_A": 0.08541491186300365,
            "max_log_strain_component": 0.020000000000000004,
            "step_scale": 0.13148101619608113,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 1.9408351085199815,
            "cell_principal_stretches": [
              1.0587021829904004,
              1.0287928014070375,
              0.8981798339991085
            ],
            "cell_volume_ratio": 0.97828416838314,
            "cell_rmsd_from_input_A": 0.35973016087073784
          },
          {
            "iteration": 4,
            "reduced_polarization": [
              -0.24752700736435118,
              -0.20327257136589885,
              -0.046986919037472784
            ],
            "branch_aligned_reduced_polarization": [
              -0.24752700736435118,
              -0.20327257136589882,
              -0.046986919037472784
            ],
            "target_residual": 0.39242521513638745,
            "energy_eV": -41.73391781014267,
            "max_atomic_step_A": 0.08949591810896769,
            "max_log_strain_component": 0.02,
            "step_scale": 0.139935748764787,
            "strain_jacobian_refreshed": true,
            "strain_jacobian_frobenius_norm": 2.3396915762813504,
            "cell_principal_stretches": [
              1.074300128398253,
              1.0096864973376922,
              0.8717190879928934
            ],
            "cell_volume_ratio": 0.945559215980856,
            "cell_rmsd_from_input_A": 0.42143094850996643
          },
          {
            "iteration": 5,
            "reduced_polarization": [
              -0.28061982214056413,
              -0.23907731218526354,
              -0.04364493039224772
            ],
            "branch_aligned_reduced_polarization": [
              -0.28061982214056413,
              -0.2390773121852635,
              -0.04364493039224772
            ],
            "target_residual": 0.3436759977115776,
            "energy_eV": -40.17950072095579
          }
        ],
        "iterations": 5
      },
      "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,
          -0.5,
          0.0
        ],
        "formal_class": [
          0.5,
          0.5,
          0.0
        ],
        "target_residual": 0.4999090203526708,
        "parent_symmetrization_rmsd_A": 0.18480736286620233,
        "parent_cell_rmsd_A": 0.16200685399198483,
        "energy_eV": -22.903930535173465,
        "reduced_polarization": [
          9.099210629514173e-05,
          -0.5000122423754171,
          0.00011093612140815447
        ],
        "cartesian_polarization_e_A2": [
          -0.00042725174181179213,
          -0.018485250102102484,
          -0.0004099157576743037
        ],
        "ranking_score": 1.7251271170695401
      },
      "branch_status": "awaiting_branch_sampling"
    },
    {
      "orbit_id": 6,
      "formal_class": [
        0.0,
        0.5,
        0.5
      ],
      "formal_classes_in_orbit": [
        [
          0.0,
          0.5,
          0.5
        ]
      ],
      "target_reduced_polarization": [
        0.0,
        -0.5,
        -0.5
      ],
      "bec_backprojection": {
        "converged_to_target": false,
        "history": [
          {
            "iteration": 0,
            "reduced_polarization": [
              -0.051301107735234636,
              -1.1172357382197103e-16,
              -0.04100318391208321
            ],
            "branch_aligned_reduced_polarization": [
              -0.051301107735234636,
              -1.1102230246251565e-16,
              -0.04100318391208324
            ],
            "target_residual": 0.6806687012296856,
            "energy_eV": -45.28415291900953,
            "max_atomic_step_A": 0.12000000000000001,
            "max_log_strain_component": 0.008257952071933023,
            "step_scale": 0.17384761509427002,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 1.9408351085199815,
            "cell_principal_stretches": [
              1.0124683190379922,
              0.99807543167299,
              0.9913747211271255
            ],
            "cell_volume_ratio": 1.0018037398892774,
            "cell_rmsd_from_input_A": 0.05602679818596174
          },
          {
            "iteration": 1,
            "reduced_polarization": [
              -0.04038179100702366,
              -0.08757798442776782,
              -0.12172125707956759
            ],
            "branch_aligned_reduced_polarization": [
              -0.04038179100702366,
              -0.08757798442776782,
              -0.1217212570795676
            ],
            "target_residual": 0.5610859250765965,
            "energy_eV": -44.92810290809818,
            "max_atomic_step_A": 0.12,
            "max_log_strain_component": 0.0069164734208354796,
            "step_scale": 0.2311466421675071,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 1.9408351085199815,
            "cell_principal_stretches": [
              1.0231461815442466,
              0.9969393102686375,
              0.9835165290744495
            ],
            "cell_volume_ratio": 1.0032012667299872,
            "cell_rmsd_from_input_A": 0.10723381664358764
          },
          {
            "iteration": 2,
            "reduced_polarization": [
              -0.02558548206993669,
              -0.18718536701124264,
              -0.20980388868565514
            ],
            "branch_aligned_reduced_polarization": [
              -0.02558548206993669,
              -0.18718536701124266,
              -0.20980388868565514
            ],
            "target_residual": 0.4274592314205059,
            "energy_eV": -43.81295446325863,
            "max_atomic_step_A": 0.12,
            "max_log_strain_component": 0.005538764961118411,
            "step_scale": 0.35886769946910996,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 1.9408351085199815,
            "cell_principal_stretches": [
              1.029840279072225,
              0.9970504349957516,
              0.9771779477588293
            ],
            "cell_volume_ratio": 1.0033689534048396,
            "cell_rmsd_from_input_A": 0.15246504304419492
          },
          {
            "iteration": 3,
            "reduced_polarization": [
              -0.006769173519847442,
              -0.30424903484542154,
              -0.3078777134141967
            ],
            "branch_aligned_reduced_polarization": [
              -0.006769173519847442,
              -0.30424903484542154,
              -0.3078777134141967
            ],
            "target_residual": 0.2743633267622485,
            "energy_eV": -41.8402505584432,
            "max_atomic_step_A": 0.12,
            "max_log_strain_component": 0.008685523561567309,
            "step_scale": 0.6054601849806833,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 1.9408351085199815,
            "cell_principal_stretches": [
              1.035854181617452,
              0.9958761456175302,
              0.9708342856145729
            ],
            "cell_volume_ratio": 1.0014956301314684,
            "cell_rmsd_from_input_A": 0.20676950529692276
          },
          {
            "iteration": 4,
            "reduced_polarization": [
              0.007865421608078673,
              -0.41784451409670315,
              -0.4066824111291431
            ],
            "branch_aligned_reduced_polarization": [
              0.007865421608078673,
              -0.41784451409670315,
              -0.4066824111291431
            ],
            "target_residual": 0.12457753053319813,
            "energy_eV": -39.339863289354085,
            "max_atomic_step_A": 0.08910225989910561,
            "max_log_strain_component": 0.01364310835873117,
            "step_scale": 1.0,
            "strain_jacobian_refreshed": true,
            "strain_jacobian_frobenius_norm": 2.110956986949169,
            "cell_principal_stretches": [
              1.022825325882829,
              1.0072499739027625,
              0.9514117057631452
            ],
            "cell_volume_ratio": 0.980183140512945,
            "cell_rmsd_from_input_A": 0.2973057965439509
          },
          {
            "iteration": 5,
            "reduced_polarization": [
              0.005932512506080512,
              -0.49740899539887345,
              -0.4840100956783277
            ],
            "branch_aligned_reduced_polarization": [
              0.005932512506080512,
              -0.49740899539887345,
              -0.4840100956783277
            ],
            "target_residual": 0.017250653601939118,
            "energy_eV": -37.41095385519867
          }
        ],
        "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": [
          0.0,
          -0.5,
          -0.5
        ],
        "formal_class": [
          0.0,
          0.5,
          0.5
        ],
        "target_residual": 0.017250653601939118,
        "parent_symmetrization_rmsd_A": 0.6585390053247627,
        "parent_cell_rmsd_A": 0.2973057965439509,
        "energy_eV": -37.41095385519867,
        "reduced_polarization": [
          0.005932512506080512,
          -0.49740899539887345,
          -0.4840100956783277
        ],
        "cartesian_polarization_e_A2": [
          0.006312073514037448,
          -0.018617248763565398,
          -0.011801058543132712
        ],
        "ranking_score": 1.2673667616646287
      },
      "branch_status": "awaiting_branch_sampling"
    },
    {
      "orbit_id": 7,
      "formal_class": [
        0.5,
        0.5,
        0.5
      ],
      "formal_classes_in_orbit": [
        [
          0.5,
          0.5,
          0.5
        ]
      ],
      "target_reduced_polarization": [
        -0.5,
        -0.5,
        -0.5
      ],
      "bec_backprojection": {
        "converged_to_target": false,
        "history": [
          {
            "iteration": 0,
            "reduced_polarization": [
              -0.051301107735234636,
              -1.1172357382197103e-16,
              -0.04100318391208321
            ],
            "branch_aligned_reduced_polarization": [
              -0.05130110773523466,
              -1.1102230246251565e-16,
              -0.04100318391208324
            ],
            "target_residual": 0.8136392155608482,
            "energy_eV": -45.28415291900953,
            "max_atomic_step_A": 0.10069003214110345,
            "max_log_strain_component": 0.02,
            "step_scale": 0.16762184527197438,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 1.9408351085199815,
            "cell_principal_stretches": [
              1.0120846894231579,
              1.010716795495587,
              0.9714038445223843
            ],
            "cell_volume_ratio": 0.9936791003147959,
            "cell_rmsd_from_input_A": 0.0986203345593085
          },
          {
            "iteration": 1,
            "reduced_polarization": [
              -0.13094983305741587,
              -0.07964379468838775,
              -0.12299542130931795
            ],
            "branch_aligned_reduced_polarization": [
              -0.13094983305741587,
              -0.07964379468838778,
              -0.12299542130931795
            ],
            "target_residual": 0.6745589799402764,
            "energy_eV": -44.71652639365996,
            "max_atomic_step_A": 0.11438185916985334,
            "max_log_strain_component": 0.02,
            "step_scale": 0.23825980635181343,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 1.9408351085199815,
            "cell_principal_stretches": [
              1.024573055724861,
              1.02274013842725,
              0.9423583091046231
            ],
            "cell_volume_ratio": 0.9874708755621856,
            "cell_rmsd_from_input_A": 0.1994086367952186
          },
          {
            "iteration": 2,
            "reduced_polarization": [
              -0.21391099399152172,
              -0.1608726558123168,
              -0.2048728956400084
            ],
            "branch_aligned_reduced_polarization": [
              -0.2139109939915217,
              -0.1608726558123168,
              -0.20487289564000843
            ],
            "target_residual": 0.5328736085251584,
            "energy_eV": -42.92622147331874,
            "max_atomic_step_A": 0.09902958253623366,
            "max_log_strain_component": 0.02,
            "step_scale": 0.24368155597581934,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 1.9408351085199815,
            "cell_principal_stretches": [
              1.0399574643016896,
              1.036858648336599,
              0.9100767532688553
            ],
            "cell_volume_ratio": 0.9813256527918364,
            "cell_rmsd_from_input_A": 0.31738420375829207
          },
          {
            "iteration": 3,
            "reduced_polarization": [
              -0.27125387861580874,
              -0.18449192280203605,
              -0.2628125503353341
            ],
            "branch_aligned_reduced_polarization": [
              -0.27125387861580874,
              -0.18449192280203608,
              -0.2628125503353341
            ],
            "target_residual": 0.45621050086982423,
            "energy_eV": -40.74812590063324,
            "max_atomic_step_A": 0.08720320943505037,
            "max_log_strain_component": 0.02,
            "step_scale": 0.25848275792439085,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 1.9408351085199815,
            "cell_principal_stretches": [
              1.0624970930734898,
              1.0473733617566205,
              0.8772545828013678
            ],
            "cell_volume_ratio": 0.9762362281770334,
            "cell_rmsd_from_input_A": 0.4484826001660367
          },
          {
            "iteration": 4,
            "reduced_polarization": [
              -0.32246795975415254,
              -0.1903623210864988,
              -0.3064282698888
            ],
            "branch_aligned_reduced_polarization": [
              -0.32246795975415254,
              -0.1903623210864988,
              -0.3064282698888
            ],
            "target_residual": 0.4060334126830413,
            "energy_eV": -41.28146875402449,
            "max_atomic_step_A": 0.10510425937095091,
            "max_log_strain_component": 0.02,
            "step_scale": 0.22833070356539412,
            "strain_jacobian_refreshed": true,
            "strain_jacobian_frobenius_norm": 1.9594596464300928,
            "cell_principal_stretches": [
              1.0609235032268616,
              1.0568007269772037,
              0.8530202888174127
            ],
            "cell_volume_ratio": 0.9563933217564412,
            "cell_rmsd_from_input_A": 0.5026090351678443
          },
          {
            "iteration": 5,
            "reduced_polarization": [
              -0.35140772910104,
              -0.2542954077934413,
              -0.3357704738315427
            ],
            "branch_aligned_reduced_polarization": [
              -0.35140772910104,
              -0.2542954077934413,
              -0.3357704738315427
            ],
            "target_residual": 0.33078958095414257,
            "energy_eV": -38.45568692629783
          }
        ],
        "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,
          -0.5,
          -0.5
        ],
        "formal_class": [
          0.5,
          0.5,
          0.5
        ],
        "target_residual": 0.33078958095414257,
        "parent_symmetrization_rmsd_A": 0.6038810117908464,
        "parent_cell_rmsd_A": 0.5026090351678443,
        "energy_eV": -38.45568692629783,
        "reduced_polarization": [
          -0.35140772910104,
          -0.2542954077934413,
          -0.3357704738315427
        ],
        "cartesian_polarization_e_A2": [
          -0.011663792241011519,
          -0.011070406693726682,
          -0.007365631984039363
        ],
        "ranking_score": 1.8911124324910926
      },
      "branch_status": "awaiting_branch_sampling"
    }
  ],
  "sampled_polarization_branches": [
    {
      "orbit_id": 0,
      "candidate_id": "inversion_parent_endpoint_00",
      "formal_class": [
        0.0,
        0.0,
        0.0
      ],
      "construction": "MACEField-BEC-parent plus variable-cell P-N-P path and symmetric log-strain continuation beyond both polar endpoints",
      "geometry_diagnostics": {
        "collision_aware": false,
        "permutations_tested": 1,
        "selected_order": [
          0,
          1,
          2,
          3,
          4,
          5,
          6,
          7
        ],
        "endpoint_rmsd_A": 0.3641878565555496,
        "minimum_distance_A_by_image": [
          1.273863539552552,
          1.230147404948503,
          1.1909627963689822,
          1.1567703102612137,
          1.12802399930229,
          1.1051489307941038,
          1.0885153188642214,
          1.078412010088034,
          1.0750231399999997
        ],
        "minimum_distance_A": 1.0750231399999997,
        "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": [
          155.96451874030947,
          155.96451874030947,
          155.96451874030947,
          155.96451874030947,
          155.96451874030947,
          155.96451874030947,
          155.96451874030947,
          155.96451874030947,
          155.96451874030947
        ],
        "cell_deformation_log_strain_norm": 0.0
      },
      "parent_reduced_polarization": [
        -2.2559104719628544e-16,
        -5.749234717757645e-16,
        3.29517428753504e-16
      ],
      "incoming": {
        "reached": true,
        "construction": "variable_cell_linear_interpolation",
        "continuation_fractions": [
          0.0,
          0.125,
          0.25,
          0.375,
          0.5,
          0.625,
          0.75,
          0.875,
          1.0
        ],
        "energies_eV": [
          -45.28415291900953,
          -45.08108331818531,
          -44.26613151545118,
          -42.83321172516358,
          -40.945456634278855,
          -39.015630413877645,
          -37.48666166586186,
          -36.579895881559054,
          -36.29181457159051
        ],
        "cartesian_polarizations_e_A2": [
          [
            -0.0018579763865118504,
            -6.629041015435542e-18,
            -0.0009669751479724801
          ],
          [
            -0.00147040281871342,
            -1.5949739624386856e-17,
            -0.0007016661819740481
          ],
          [
            -0.001547158556449101,
            -2.8696184261449157e-18,
            -0.0008896889857201778
          ],
          [
            -0.0018533828754653942,
            -1.4370337234803222e-17,
            -0.001284847587183655
          ],
          [
            -0.0019782477906333355,
            -8.175075748901213e-18,
            -0.0014092610474314151
          ],
          [
            -0.0018342192957488165,
            -2.718351718410145e-17,
            -0.0011702025885906102
          ],
          [
            -0.0014885668706751366,
            -1.9575691589205626e-18,
            -0.0008102790623732042
          ],
          [
            -0.000864923552042125,
            7.118433305165682e-19,
            -0.00041647223885806406
          ],
          [
            -1.525552731239858e-17,
            -2.1177339082867906e-17,
            7.770985909573083e-18
          ]
        ],
        "raw_reduced_polarization": [
          [
            -0.051301107735234615,
            -1.7996554053485066e-16,
            -0.041003183912083005
          ],
          [
            -0.039807763091616745,
            -4.3300433746136883e-16,
            -0.029753140569016772
          ],
          [
            -0.043770967933685435,
            -7.790454607045548e-17,
            -0.03772597587696975
          ],
          [
            -0.05516228377194187,
            -3.901266415621259e-16,
            -0.054482105384767186
          ],
          [
            -0.05934997984038365,
            -2.2193736961932084e-16,
            -0.05975767839444987
          ],
          [
            -0.05332975424867704,
            -7.379794984348574e-16,
            -0.04962074987654383
          ],
          [
            -0.04154405837044626,
            -5.31441864666673e-17,
            -0.03435871282138082
          ],
          [
            -0.02346233876508669,
            1.9325158715151747e-17,
            -0.01765990350422135
          ],
          [
            -2.2559104719628544e-16,
            -5.749234717757645e-16,
            3.29517428753504e-16
          ]
        ],
        "unwrapped_reduced_polarization": [
          [
            -0.051301107735234615,
            -1.7996554053485066e-16,
            -0.041003183912083005
          ],
          [
            -0.039807763091616745,
            -4.3300433746136883e-16,
            -0.029753140569016772
          ],
          [
            -0.043770967933685435,
            -7.790454607045547e-17,
            -0.03772597587696975
          ],
          [
            -0.05516228377194187,
            -3.901266415621259e-16,
            -0.054482105384767186
          ],
          [
            -0.05934997984038365,
            -2.2193736961932084e-16,
            -0.05975767839444987
          ],
          [
            -0.05332975424867704,
            -7.379794984348574e-16,
            -0.04962074987654383
          ],
          [
            -0.04154405837044626,
            -5.31441864666673e-17,
            -0.03435871282138082
          ],
          [
            -0.02346233876508669,
            1.9325158715151744e-17,
            -0.01765990350422135
          ],
          [
            -2.255140518769849e-16,
            -5.749234717757645e-16,
            3.2959746043559335e-16
          ]
        ],
        "berry_integer_shifts": [
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ]
        ],
        "folded_reduced_polarization": [
          [
            -0.05130110773523461,
            -1.6653345369377348e-16,
            -0.04100318391208302
          ],
          [
            -0.039807763091616766,
            -4.440892098500626e-16,
            -0.02975314056901679
          ],
          [
            -0.043770967933685456,
            -5.551115123125783e-17,
            -0.03772597587696974
          ],
          [
            -0.05516228377194188,
            -3.885780586188048e-16,
            -0.054482105384767165
          ],
          [
            -0.05934997984038365,
            -2.220446049250313e-16,
            -0.0597576783944499
          ],
          [
            -0.05332975424867703,
            -7.216449660063518e-16,
            -0.04962074987654386
          ],
          [
            -0.04154405837044628,
            -5.551115123125783e-17,
            -0.03435871282138081
          ],
          [
            -0.023462338765086688,
            0.0,
            -0.017659903504221364
          ],
          [
            -2.220446049250313e-16,
            -5.551115123125783e-16,
            3.3306690738754696e-16
          ]
        ]
      },
      "reflected": {
        "reached": true,
        "construction": "reflect_displacements_about_reconstructed_parent",
        "energies_eV": [
          -36.29181457159051,
          -36.57989588155906,
          -37.48666166586187,
          -39.01563041387765,
          -40.94545663427884,
          -42.83321172516358,
          -44.26613151545118,
          -45.0810833181853,
          -45.28415291900952
        ],
        "cartesian_polarizations_e_A2": [
          [
            2.6350421541584016e-17,
            -1.1389493288265091e-17,
            3.482795341977452e-18
          ],
          [
            0.0008649235520421074,
            -1.2546238700354514e-17,
            0.00041647223885808113
          ],
          [
            0.0014885668706751268,
            -9.698865378288242e-18,
            0.0008102790623731848
          ],
          [
            0.0018342192957488148,
            -2.091039783392419e-18,
            0.001170202588590553
          ],
          [
            0.0019782477906333147,
            -1.0154890011900418e-17,
            0.0014092610474314019
          ],
          [
            0.0018533828754653916,
            -2.567085010675374e-17,
            0.0012848475871836574
          ],
          [
            0.0015471585564491106,
            -1.4459317651117791e-18,
            0.0008896889857201997
          ],
          [
            0.0014704028187133642,
            -1.2457258284039944e-17,
            0.0007016661819739956
          ],
          [
            0.0018579763865118342,
            -6.273119350177257e-18,
            0.0009669751479724734
          ]
        ],
        "raw_reduced_polarization": [
          [
            6.00167545172325e-16,
            -3.0920253944242795e-16,
            1.476829039863925e-16
          ],
          [
            0.02346233876508653,
            -3.4060592235454955e-16,
            0.017659903504222075
          ],
          [
            0.04154405837044581,
            -2.633052874939426e-16,
            0.03435871282138
          ],
          [
            0.05332975424867629,
            -5.676765372575825e-17,
            0.0496207498765414
          ],
          [
            0.059349979840383045,
            -2.7568546729583666e-16,
            0.05975767839444931
          ],
          [
            0.05516228377194184,
            -6.969135361651599e-16,
            0.05448210538476728
          ],
          [
            0.04377096793368591,
            -3.925422864015198e-17,
            0.03772597587697068
          ],
          [
            0.03980776309161491,
            -3.381902775151556e-16,
            0.029753140569014545
          ],
          [
            0.051301107735234185,
            -1.7030296117727478e-16,
            0.041003183912082714
          ]
        ],
        "unwrapped_reduced_polarization": [
          [
            6.00167545172325e-16,
            -3.0920253944242795e-16,
            1.476829039863925e-16
          ],
          [
            0.02346233876508653,
            -3.4060592235454955e-16,
            0.017659903504222075
          ],
          [
            0.04154405837044581,
            -2.633052874939426e-16,
            0.03435871282138
          ],
          [
            0.05332975424867629,
            -5.676765372575827e-17,
            0.0496207498765414
          ],
          [
            0.059349979840383045,
            -2.7568546729583666e-16,
            0.05975767839444931
          ],
          [
            0.05516228377194184,
            -6.969135361651599e-16,
            0.05448210538476728
          ],
          [
            0.04377096793368591,
            -3.925422864015193e-17,
            0.03772597587697068
          ],
          [
            0.03980776309161491,
            -3.381902775151556e-16,
            0.029753140569014545
          ],
          [
            0.051301107735234185,
            -1.7030296117727478e-16,
            0.041003183912082714
          ]
        ],
        "gauge_integer_shift": [
          0,
          0,
          0
        ],
        "expected_opposite_endpoint_reduced_polarization": [
          0.05130110773523417,
          -9.698814030166783e-16,
          0.04100318391208366
        ],
        "actual_opposite_endpoint_branch_residual": 1.2369592895214559e-15
      },
      "pnp_branch": {
        "construction": "incoming_path_concatenated_with_parent_reflection",
        "reduced_polarization": [
          [
            -0.051301107735234615,
            -1.7996554053485066e-16,
            -0.041003183912083005
          ],
          [
            -0.039807763091616745,
            -4.3300433746136883e-16,
            -0.029753140569016772
          ],
          [
            -0.043770967933685435,
            -7.790454607045548e-17,
            -0.03772597587696975
          ],
          [
            -0.05516228377194187,
            -3.901266415621259e-16,
            -0.054482105384767186
          ],
          [
            -0.05934997984038365,
            -2.2193736961932084e-16,
            -0.05975767839444987
          ],
          [
            -0.05332975424867704,
            -7.379794984348574e-16,
            -0.04962074987654383
          ],
          [
            -0.04154405837044626,
            -5.31441864666673e-17,
            -0.03435871282138082
          ],
          [
            -0.02346233876508669,
            1.9325158715151747e-17,
            -0.01765990350422135
          ],
          [
            -2.2559104719628544e-16,
            -5.749234717757645e-16,
            3.29517428753504e-16
          ],
          [
            0.02346233876508653,
            -3.4060592235454955e-16,
            0.017659903504222075
          ],
          [
            0.04154405837044581,
            -2.633052874939426e-16,
            0.03435871282138
          ],
          [
            0.05332975424867629,
            -5.676765372575825e-17,
            0.0496207498765414
          ],
          [
            0.059349979840383045,
            -2.7568546729583666e-16,
            0.05975767839444931
          ],
          [
            0.05516228377194184,
            -6.969135361651599e-16,
            0.05448210538476728
          ],
          [
            0.04377096793368591,
            -3.925422864015198e-17,
            0.03772597587697068
          ],
          [
            0.03980776309161491,
            -3.381902775151556e-16,
            0.029753140569014545
          ],
          [
            0.051301107735234185,
            -1.7030296117727478e-16,
            0.041003183912082714
          ]
        ],
        "unwrapped_reduced_polarization": [
          [
            -0.051301107735234615,
            -1.7996554053485066e-16,
            -0.041003183912083005
          ],
          [
            -0.039807763091616745,
            -4.3300433746136883e-16,
            -0.029753140569016772
          ],
          [
            -0.043770967933685435,
            -7.790454607045547e-17,
            -0.03772597587696975
          ],
          [
            -0.05516228377194187,
            -3.901266415621259e-16,
            -0.054482105384767186
          ],
          [
            -0.05934997984038365,
            -2.2193736961932084e-16,
            -0.05975767839444987
          ],
          [
            -0.05332975424867704,
            -7.379794984348574e-16,
            -0.04962074987654383
          ],
          [
            -0.04154405837044626,
            -5.31441864666673e-17,
            -0.03435871282138082
          ],
          [
            -0.02346233876508669,
            1.9325158715151744e-17,
            -0.01765990350422135
          ],
          [
            -2.255140518769849e-16,
            -5.749234717757645e-16,
            3.2959746043559335e-16
          ],
          [
            0.02346233876508653,
            -3.4060592235454955e-16,
            0.017659903504222075
          ],
          [
            0.04154405837044581,
            -2.633052874939426e-16,
            0.03435871282138
          ],
          [
            0.05332975424867629,
            -5.676765372575827e-17,
            0.0496207498765414
          ],
          [
            0.059349979840383045,
            -2.7568546729583666e-16,
            0.05975767839444931
          ],
          [
            0.05516228377194184,
            -6.969135361651599e-16,
            0.05448210538476728
          ],
          [
            0.04377096793368591,
            -3.925422864015193e-17,
            0.03772597587697068
          ],
          [
            0.03980776309161491,
            -3.381902775151556e-16,
            0.029753140569014545
          ],
          [
            0.051301107735234185,
            -1.7030296117727478e-16,
            0.041003183912082714
          ]
        ],
        "berry_integer_shifts": [
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ]
        ],
        "folded_reduced_polarization": [
          [
            -0.05130110773523461,
            -1.6653345369377348e-16,
            -0.04100318391208302
          ],
          [
            -0.039807763091616766,
            -4.440892098500626e-16,
            -0.02975314056901679
          ],
          [
            -0.043770967933685456,
            -5.551115123125783e-17,
            -0.03772597587696974
          ],
          [
            -0.05516228377194188,
            -3.885780586188048e-16,
            -0.054482105384767165
          ],
          [
            -0.05934997984038365,
            -2.220446049250313e-16,
            -0.0597576783944499
          ],
          [
            -0.05332975424867703,
            -7.216449660063518e-16,
            -0.04962074987654386
          ],
          [
            -0.04154405837044628,
            -5.551115123125783e-17,
            -0.03435871282138081
          ],
          [
            -0.023462338765086688,
            0.0,
            -0.017659903504221364
          ],
          [
            -2.220446049250313e-16,
            -5.551115123125783e-16,
            3.3306690738754696e-16
          ],
          [
            0.02346233876508652,
            -3.3306690738754696e-16,
            0.017659903504222085
          ],
          [
            0.041544058370445835,
            -2.7755575615628914e-16,
            0.03435871282138003
          ],
          [
            0.05332975424867625,
            -5.551115123125783e-17,
            0.049620749876541415
          ],
          [
            0.05934997984038304,
            -2.7755575615628914e-16,
            0.05975767839444934
          ],
          [
            0.05516228377194188,
            -7.216449660063518e-16,
            0.054482105384767276
          ],
          [
            0.043770967933685956,
            -5.551115123125783e-17,
            0.037725975876970685
          ],
          [
            0.039807763091614934,
            -3.3306690738754696e-16,
            0.02975314056901457
          ],
          [
            0.05130110773523422,
            -1.6653345369377348e-16,
            0.041003183912082686
          ]
        ]
      },
      "incoming_structure_ids": [
        "incoming_00_000",
        "incoming_00_001",
        "incoming_00_002",
        "incoming_00_003",
        "incoming_00_004",
        "incoming_00_005",
        "incoming_00_006",
        "incoming_00_007",
        "incoming_00_008"
      ],
      "reflected_structure_ids": [
        "reflected_00_001",
        "reflected_00_002",
        "reflected_00_003",
        "reflected_00_004",
        "reflected_00_005",
        "reflected_00_006",
        "reflected_00_007",
        "reflected_00_008"
      ],
      "positive_extension_structure_ids": [
        "extension_plus_00_000",
        "extension_plus_00_001",
        "extension_plus_00_002",
        "extension_plus_00_003"
      ],
      "negative_extension_structure_ids": [
        "extension_minus_00_000",
        "extension_minus_00_001",
        "extension_minus_00_002",
        "extension_minus_00_003"
      ],
      "extension": {
        "enabled": true,
        "fraction_beyond_polar_endpoint": 0.35,
        "images_per_side": 4,
        "construction": "continue fractional atomic displacements and symmetric log strain beyond +P; reflect these structures about N for the -P side",
        "positive_path_coordinates": [
          1.35,
          1.2625,
          1.175,
          1.0875
        ],
        "negative_path_coordinates": [
          -1.0875,
          -1.175,
          -1.2625,
          -1.35
        ]
      },
      "branch_coordinates": [
        1.35,
        1.2625,
        1.175,
        1.0875,
        1.0,
        0.875,
        0.75,
        0.625,
        0.5,
        0.375,
        0.25,
        0.125,
        0.0,
        -0.125,
        -0.25,
        -0.375,
        -0.5,
        -0.625,
        -0.75,
        -0.875,
        -1.0,
        -1.0875,
        -1.175,
        -1.2625,
        -1.35
      ],
      "parent": {
        "candidate_id": "inversion_parent_endpoint_00",
        "source": "same_species_inversion_center_projection_from_endpoint",
        "spacegroup": "C2/m",
        "spacegroup_number": 12,
        "pointgroup": "2/m",
        "has_inversion": true,
        "is_polar_point_group": false,
        "nonpolar_parent_hypothesis": true,
        "symmetry_tolerance_A": null,
        "target_reduced_polarization": [
          0.0,
          0.0,
          0.0
        ],
        "formal_class": [
          0.0,
          0.0,
          0.0
        ],
        "target_residual": 3.1637788234913204e-16,
        "parent_symmetrization_rmsd_A": 0.3641878565555496,
        "parent_cell_rmsd_A": 0.0,
        "energy_eV": -36.2918145715905,
        "reduced_polarization": [
          -6.59372601811935e-17,
          2.608896426545486e-16,
          -1.6638460420093191e-16
        ],
        "cartesian_polarization_e_A2": [
          -8.081437726684733e-19,
          9.609884961973672e-18,
          -3.923836198001369e-18
        ],
        "ranking_score": 0.3641878565555502
      }
    }
  ],
  "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": 141,
      "full_response": 37,
      "energy_polarization": 104
    },
    "model_evaluations_for_recovery_and_path_properties": {
      "total": 166,
      "full_response": 62,
      "energy_polarization": 104
    },
    "elapsed_seconds": 195.89034337899648
  }
}