{
  "schema": "ferrofinder.endpoint_parent_recovery.v4_variable_cell",
  "status": "complete",
  "input_atom_count": 27,
  "input_formula": "C3K12O12",
  "input_spacegroup": "R3",
  "input_pointgroup": "3",
  "input_is_polar_point_group": true,
  "input_energy_eV": -132.14481245265785,
  "input_cartesian_polarization_e_A2": [
    -9.684987824483395e-11,
    7.331993769908874e-10,
    -0.0015903628375531517
  ],
  "input_reduced_polarization": [
    2.0445773555734962e-08,
    5.302260408086206e-08,
    -0.07915731268270453
  ],
  "input_formal_targets": [
    {
      "orbit_id": 0,
      "representative_formal_class": [
        0.0,
        0.0,
        0.0
      ],
      "target_reduced_polarization": [
        0.0,
        0.0,
        0.0
      ]
    },
    {
      "orbit_id": 1,
      "representative_formal_class": [
        0.0,
        0.0,
        0.5
      ],
      "target_reduced_polarization": [
        0.0,
        0.0,
        -0.5
      ]
    },
    {
      "orbit_id": 2,
      "representative_formal_class": [
        0.0,
        0.5,
        0.0
      ],
      "target_reduced_polarization": [
        0.0,
        0.5,
        0.0
      ]
    },
    {
      "orbit_id": 3,
      "representative_formal_class": [
        0.0,
        0.5,
        0.5
      ],
      "target_reduced_polarization": [
        0.0,
        0.5,
        -0.5
      ]
    }
  ],
  "parent_candidates": [
    {
      "candidate_id": "inversion_parent_endpoint_00",
      "source": "same_species_inversion_center_projection_from_endpoint",
      "spacegroup": "P-1",
      "spacegroup_number": 2,
      "pointgroup": "-1",
      "has_inversion": true,
      "is_polar_point_group": false,
      "nonpolar_parent_hypothesis": true,
      "symmetry_tolerance_A": null,
      "target_reduced_polarization": [
        0.0,
        0.0,
        0.0
      ],
      "formal_class": [
        0.0,
        0.0,
        0.0
      ],
      "target_residual": 1.6729852722157583e-15,
      "parent_symmetrization_rmsd_A": 0.5712915490610011,
      "parent_cell_rmsd_A": 0.0,
      "energy_eV": -114.54799979102329,
      "reduced_polarization": [
        -1.18940375408339e-15,
        7.038850870693656e-16,
        -9.427323135569953e-16
      ],
      "cartesian_polarization_e_A2": [
        -2.4611079089659252e-17,
        9.733360257549324e-18,
        -1.8940592933609495e-17
      ],
      "ranking_score": 0.5712915490610044
    },
    {
      "candidate_id": "inversion_parent_endpoint_01",
      "source": "same_species_inversion_center_projection_from_endpoint",
      "spacegroup": "P-1",
      "spacegroup_number": 2,
      "pointgroup": "-1",
      "has_inversion": true,
      "is_polar_point_group": false,
      "nonpolar_parent_hypothesis": true,
      "symmetry_tolerance_A": null,
      "target_reduced_polarization": [
        0.0,
        0.0,
        0.0
      ],
      "formal_class": [
        0.0,
        0.0,
        0.0
      ],
      "target_residual": 1.0206786781926588e-15,
      "parent_symmetrization_rmsd_A": 0.5712915686225017,
      "parent_cell_rmsd_A": 0.0,
      "energy_eV": -114.5479994929104,
      "reduced_polarization": [
        2.649501848099903e-16,
        9.765612919701109e-16,
        1.3384471118401786e-16
      ],
      "cartesian_polarization_e_A2": [
        -3.5659758300931456e-18,
        1.3503941258221585e-17,
        2.689096527611225e-18
      ],
      "ranking_score": 0.5712915686225037
    },
    {
      "candidate_id": "inversion_parent_endpoint_02",
      "source": "same_species_inversion_center_projection_from_endpoint",
      "spacegroup": "P-1",
      "spacegroup_number": 2,
      "pointgroup": "-1",
      "has_inversion": true,
      "is_polar_point_group": false,
      "nonpolar_parent_hypothesis": true,
      "symmetry_tolerance_A": null,
      "target_reduced_polarization": [
        0.0,
        0.0,
        0.0
      ],
      "formal_class": [
        0.0,
        0.0,
        0.0
      ],
      "target_residual": 2.039396426949983e-15,
      "parent_symmetrization_rmsd_A": 0.5712915688540596,
      "parent_cell_rmsd_A": 0.0,
      "energy_eV": -114.54799970222844,
      "reduced_polarization": [
        -1.6563609749951893e-15,
        3.667389267463512e-16,
        1.1318607097952814e-15
      ],
      "cartesian_polarization_e_A2": [
        -2.9375456633144356e-17,
        5.0712852993537775e-18,
        2.2740403244364487e-17
      ],
      "ranking_score": 0.5712915688540637
    },
    {
      "candidate_id": "bec_projection_00",
      "source": "MACEField_BEC_backprojection",
      "spacegroup": "R3",
      "spacegroup_number": 146,
      "pointgroup": "3",
      "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": 5.134753377304506e-06,
      "parent_symmetrization_rmsd_A": 0.024095294869824473,
      "parent_cell_rmsd_A": 0.022810022930548193,
      "energy_eV": -132.0937822364537,
      "reduced_polarization": [
        -2.910587181723223e-11,
        -2.4145168350046658e-11,
        -5.134753377165245e-06
      ],
      "cartesian_polarization_e_A2": [
        -2.719845034340555e-13,
        -3.336997367700983e-13,
        -1.0349491128717044e-07
      ],
      "ranking_score": 0.5298080701092162
    },
    {
      "candidate_id": "inversion_parent_bec_00_00",
      "source": "same_species_inversion_center_projection_after_BEC",
      "spacegroup": "P-1",
      "spacegroup_number": 2,
      "pointgroup": "-1",
      "has_inversion": true,
      "is_polar_point_group": false,
      "nonpolar_parent_hypothesis": true,
      "symmetry_tolerance_A": null,
      "target_reduced_polarization": [
        0.0,
        0.0,
        0.0
      ],
      "formal_class": [
        0.0,
        0.0,
        0.0
      ],
      "target_residual": 1.894525441359003e-15,
      "parent_symmetrization_rmsd_A": 0.5713020959377076,
      "parent_cell_rmsd_A": 0.022810022930548193,
      "energy_eV": -114.62953803965748,
      "reduced_polarization": [
        -8.990240444860451e-16,
        -1.2406585183415797e-15,
        -1.1143378555263008e-15
      ],
      "cartesian_polarization_e_A2": [
        -4.445275279949374e-18,
        -1.7137706013489036e-17,
        -2.246033825658631e-17
      ],
      "ranking_score": 0.5770046016703485
    },
    {
      "candidate_id": "inversion_parent_bec_00_01",
      "source": "same_species_inversion_center_projection_after_BEC",
      "spacegroup": "P-1",
      "spacegroup_number": 2,
      "pointgroup": "-1",
      "has_inversion": true,
      "is_polar_point_group": false,
      "nonpolar_parent_hypothesis": true,
      "symmetry_tolerance_A": null,
      "target_reduced_polarization": [
        0.0,
        0.0,
        0.0
      ],
      "formal_class": [
        0.0,
        0.0,
        0.0
      ],
      "target_residual": 1.561724760277802e-15,
      "parent_symmetrization_rmsd_A": 0.5713021154900841,
      "parent_cell_rmsd_A": 0.022810022930548193,
      "energy_eV": -114.62953726398361,
      "reduced_polarization": [
        -8.702374153567383e-16,
        -1.2967633852817685e-15,
        8.705766511325541e-18
      ],
      "cartesian_polarization_e_A2": [
        -3.5386730846965414e-18,
        -1.791270466426968e-17,
        1.7547139262958055e-19
      ],
      "ranking_score": 0.5770046212227243
    },
    {
      "candidate_id": "bec_projection_01",
      "source": "MACEField_BEC_backprojection",
      "spacegroup": "R3",
      "spacegroup_number": 146,
      "pointgroup": "3",
      "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": 0.0007676530021824906,
      "parent_symmetrization_rmsd_A": 0.13758421235867876,
      "parent_cell_rmsd_A": 0.12941704586869313,
      "energy_eV": -128.59805220853394,
      "reduced_polarization": [
        1.1781883301803684e-09,
        -2.5001302724416133e-09,
        -0.5007676530021775
      ],
      "cartesian_polarization_e_A2": [
        2.1451167636222663e-10,
        -6.373404763897156e-11,
        -0.009877571825748896
      ],
      "ranking_score": 0.671473779830217
    },
    {
      "candidate_id": "bec_projection_02",
      "source": "MACEField_BEC_backprojection",
      "spacegroup": "P1",
      "spacegroup_number": 1,
      "pointgroup": "1",
      "has_inversion": false,
      "is_polar_point_group": true,
      "nonpolar_parent_hypothesis": false,
      "symmetry_tolerance_A": null,
      "target_reduced_polarization": [
        0.0,
        0.5,
        0.0
      ],
      "formal_class": [
        0.0,
        0.5,
        0.0
      ],
      "target_residual": 0.0007989976258780698,
      "parent_symmetrization_rmsd_A": 0.11611897426791669,
      "parent_cell_rmsd_A": 0.20991116763527864,
      "energy_eV": -129.49729484984772,
      "reduced_polarization": [
        -0.0003039253700269197,
        0.49926471980017967,
        7.341391806030265e-05
      ],
      "cartesian_polarization_e_A2": [
        -0.004100780274174344,
        0.006854900871566792,
        -0.0001591242216809637
      ],
      "ranking_score": 0.6701947614284924
    },
    {
      "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,
        -0.5
      ],
      "formal_class": [
        0.0,
        0.5,
        0.5
      ],
      "target_residual": 0.0002071523589006655,
      "parent_symmetrization_rmsd_A": 0.16283038303467923,
      "parent_cell_rmsd_A": 0.24063856849769258,
      "energy_eV": -128.10479977641393,
      "reduced_polarization": [
        0.00019169086719131643,
        0.4999217542712093,
        -0.4999933428865445
      ],
      "cartesian_polarization_e_A2": [
        -0.004174746541569374,
        0.007074841722184679,
        -0.010016789554267436
      ],
      "ranking_score": 0.7234043298769037
    }
  ],
  "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": [
              2.0445773555734962e-08,
              5.302260408086206e-08,
              -0.07915731268270453
            ],
            "branch_aligned_reduced_polarization": [
              2.0445773555734962e-08,
              5.302260408086206e-08,
              -0.07915731268270453
            ],
            "target_residual": 0.07915731268272493,
            "energy_eV": -132.14481245265785,
            "max_atomic_step_A": 0.02746194920826954,
            "max_log_strain_component": 0.0027134027100177488,
            "step_scale": 1.0,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 2.7944103688874016,
            "cell_principal_stretches": [
              1.0027170873190094,
              0.9983674841970478,
              0.9983674675647216
            ],
            "cell_volume_ratio": 0.9994458400360186,
            "cell_rmsd_from_input_A": 0.023218373271171367
          },
          {
            "iteration": 1,
            "reduced_polarization": [
              1.530627816503927e-09,
              1.8256292616123146e-09,
              0.00150506904698141
            ],
            "branch_aligned_reduced_polarization": [
              1.530627816503927e-09,
              1.8256292616123146e-09,
              0.00150506904698141
            ],
            "target_residual": 0.0015050690469832954,
            "energy_eV": -132.09150168829817,
            "max_atomic_step_A": 0.0005453078146508718,
            "max_log_strain_component": 4.76482338315386e-05,
            "step_scale": 1.0,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 2.7944103688874016,
            "cell_principal_stretches": [
              1.0026693107590097,
              0.9983961287398366,
              0.9983961123263199
            ],
            "cell_volume_ratio": 0.9994555686156888,
            "cell_rmsd_from_input_A": 0.022810022930548193
          },
          {
            "iteration": 2,
            "reduced_polarization": [
              -2.910587181723223e-11,
              -2.4145168350046658e-11,
              -5.134753377165245e-06
            ],
            "branch_aligned_reduced_polarization": [
              -2.910587181723223e-11,
              -2.4145168350046658e-11,
              -5.134753377165245e-06
            ],
            "target_residual": 5.134753377304506e-06,
            "energy_eV": -132.0937822364537
          }
        ],
        "iterations": 2
      },
      "parent": {
        "candidate_id": "bec_projection_00",
        "source": "MACEField_BEC_backprojection",
        "spacegroup": "R3",
        "spacegroup_number": 146,
        "pointgroup": "3",
        "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": 5.134753377304506e-06,
        "parent_symmetrization_rmsd_A": 0.024095294869824473,
        "parent_cell_rmsd_A": 0.022810022930548193,
        "energy_eV": -132.0937822364537,
        "reduced_polarization": [
          -2.910587181723223e-11,
          -2.4145168350046658e-11,
          -5.134753377165245e-06
        ],
        "cartesian_polarization_e_A2": [
          -2.719845034340555e-13,
          -3.336997367700983e-13,
          -1.0349491128717044e-07
        ],
        "ranking_score": 0.5298080701092162
      },
      "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": [
          -132.14481245265785,
          -132.14537959517992,
          -132.14386959360897,
          -132.1403296140852,
          -132.13480608497264,
          -132.12734475223152,
          -132.11799073174933,
          -132.10678855901676,
          -132.09378223645365
        ],
        "cartesian_polarizations_e_A2": [
          [
            -9.684986700966981e-11,
            7.331993784282777e-10,
            -0.0015903628375531543
          ],
          [
            -8.6379081605182e-11,
            6.404138464051703e-10,
            -0.0013957776626530357
          ],
          [
            -7.545973468831405e-11,
            5.479411769515213e-10,
            -0.001200071462876345
          ],
          [
            -6.408732493832921e-11,
            4.5578174836880763e-10,
            -0.0010032055301436831
          ],
          [
            -5.225743089659455e-11,
            3.639354781318835e-10,
            -0.0008051407776451299
          ],
          [
            -3.996556102863629e-11,
            2.7240188797226573e-10,
            -0.0006058378274761469
          ],
          [
            -2.720719483467932e-11,
            1.811800664007463e-10,
            -0.00040525709844297124
          ],
          [
            -1.3977583840492334e-11,
            9.026881929966121e-11,
            -0.00020335889455062338
          ],
          [
            -2.7202361304778517e-13,
            -3.3374601393165364e-13,
            -1.0349491127917186e-07
          ]
        ],
        "raw_reduced_polarization": [
          [
            2.0445774311346187e-08,
            5.302260418480947e-08,
            -0.07915731268270465
          ],
          [
            1.7790992665091304e-08,
            4.63399248864694e-08,
            -0.06944432933146392
          ],
          [
            1.5163102774308572e-08,
            3.9672168079582054e-08,
            -0.05968337501818134
          ],
          [
            1.2562315789664205e-08,
            3.3019319515046654e-08,
            -0.04987258786404808
          ],
          [
            9.98881668926879e-09,
            2.6381329278361068e-08,
            -0.040010090206756645
          ],
          [
            7.442775975059873e-09,
            1.9758116456802722e-08,
            -0.030093992988362368
          ],
          [
            4.924345708516259e-09,
            1.314956639557477e-08,
            -0.020122400141036736
          ],
          [
            2.4336774180947333e-09,
            6.55554157305458e-09,
            -0.010093412996174793
          ],
          [
            -2.910999886192327e-11,
            -2.4148518515760896e-11,
            -5.134753376768409e-06
          ]
        ],
        "unwrapped_reduced_polarization": [
          [
            2.0445774311346187e-08,
            5.302260418480947e-08,
            -0.07915731268270465
          ],
          [
            1.7790992665091304e-08,
            4.63399248864694e-08,
            -0.06944432933146392
          ],
          [
            1.5163102774308572e-08,
            3.9672168079582054e-08,
            -0.05968337501818134
          ],
          [
            1.2562315789664205e-08,
            3.3019319515046654e-08,
            -0.04987258786404808
          ],
          [
            9.98881668926879e-09,
            2.6381329278361068e-08,
            -0.040010090206756645
          ],
          [
            7.442775975059873e-09,
            1.9758116456802722e-08,
            -0.030093992988362368
          ],
          [
            4.924345708516259e-09,
            1.314956639557477e-08,
            -0.020122400141036736
          ],
          [
            2.4336774180947333e-09,
            6.55554157305458e-09,
            -0.010093412996174793
          ],
          [
            -2.910999886192326e-11,
            -2.4148518515760656e-11,
            -5.134753376767609e-06
          ]
        ],
        "berry_integer_shifts": [
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ]
        ],
        "folded_reduced_polarization": [
          [
            2.0445774295829722e-08,
            5.3022604196151235e-08,
            -0.07915731268270465
          ],
          [
            1.7790992679067585e-08,
            4.633992489733174e-08,
            -0.06944432933146394
          ],
          [
            1.5163102773385617e-08,
            3.9672168106186234e-08,
            -0.05968337501818133
          ],
          [
            1.25623157432031e-08,
            3.3019319500837696e-08,
            -0.04987258786404808
          ],
          [
            9.988816662698241e-09,
            2.638132923227232e-08,
            -0.040010090206756665
          ],
          [
            7.442775951105318e-09,
            1.9758116476253917e-08,
            -0.03009399298836235
          ],
          [
            4.924345708978706e-09,
            1.3149566435721738e-08,
            -0.020122400141036723
          ],
          [
            2.4336773707389625e-09,
            6.555541554043032e-09,
            -0.010093412996174778
          ],
          [
            -2.9109992194520373e-11,
            -2.414851651977301e-11,
            -5.134753376767609e-06
          ]
        ]
      },
      "reflected": {
        "reached": true,
        "construction": "reflect_displacements_about_reconstructed_parent",
        "energies_eV": [
          -132.09378223645368,
          -132.0816963436233,
          -132.06812413835067,
          -132.05309603523204,
          -132.03664217382885,
          -132.0187924417508,
          -131.99957649750013,
          -131.9790237923383,
          -131.957163590526
        ],
        "cartesian_polarizations_e_A2": [
          [
            -2.720152237377271e-13,
            -3.33712377763745e-13,
            -1.0349491127832375e-07
          ],
          [
            6.929182186135505e-11,
            -7.854905766423174e-11,
            0.00018944519117991703
          ],
          [
            1.382655487913479e-10,
            -1.5691790774298397e-10,
            0.00037957868952636064
          ],
          [
            2.0664717394001368e-10,
            -2.3543716984555517e-10,
            0.0005703049071063453
          ],
          [
            2.7443507172951523e-10,
            -3.141034954945343e-10,
            0.0007616321324239624
          ],
          [
            3.4162795292898343e-10,
            -3.929136571018826e-10,
            0.0009535689527947674
          ],
          [
            4.082247396903601e-10,
            -4.718649910171205e-10,
            0.001146124153405435
          ],
          [
            4.742249158128903e-10,
            -5.509544846797156e-10,
            0.0013393066041762016
          ],
          [
            5.39628212477625e-10,
            -6.301796359732959e-10,
            0.0015331251393260123
          ]
        ],
        "raw_reduced_polarization": [
          [
            -2.910825537745924e-11,
            -2.4146083475838186e-11,
            -5.13475337672633e-06
          ],
          [
            1.4608617868253654e-09,
            -5.705746238666185e-09,
            0.009402827247579222
          ],
          [
            2.9191877437601252e-09,
            -1.1391278624328871e-08,
            0.018847379367334185
          ],
          [
            4.345929920063621e-09,
            -1.708048708249341e-08,
            0.028328953883888557
          ],
          [
            5.7411817494415985e-09,
            -2.2773096600670843e-08,
            0.037848002695596
          ],
          [
            7.105054354338209e-09,
            -2.8468840537937198e-08,
            0.0474049932478682
          ],
          [
            8.437652734160095e-09,
            -3.416749264139028e-08,
            0.05700040354358509
          ],
          [
            9.739130754762825e-09,
            -3.9868800979088574e-08,
            0.06663471653460369
          ],
          [
            1.1009640375559726e-08,
            -4.557255009567354e-08,
            0.07630841413652448
          ]
        ],
        "unwrapped_reduced_polarization": [
          [
            -2.910825537745924e-11,
            -2.4146083475838186e-11,
            -5.13475337672633e-06
          ],
          [
            1.4608617868253654e-09,
            -5.705746238666185e-09,
            0.009402827247579222
          ],
          [
            2.9191877437601252e-09,
            -1.1391278624328871e-08,
            0.018847379367334185
          ],
          [
            4.345929920063621e-09,
            -1.708048708249341e-08,
            0.028328953883888557
          ],
          [
            5.7411817494415985e-09,
            -2.2773096600670843e-08,
            0.037848002695596
          ],
          [
            7.105054354338209e-09,
            -2.8468840537937198e-08,
            0.0474049932478682
          ],
          [
            8.437652734160095e-09,
            -3.416749264139028e-08,
            0.05700040354358509
          ],
          [
            9.739130754762825e-09,
            -3.9868800979088574e-08,
            0.06663471653460369
          ],
          [
            1.1009640375559726e-08,
            -4.557255009567354e-08,
            0.07630841413652448
          ]
        ],
        "gauge_integer_shift": [
          0,
          0,
          0
        ],
        "expected_opposite_endpoint_reduced_polarization": [
          -2.050398241211777e-08,
          -5.307087504623025e-08,
          0.07914701015442652
        ],
        "actual_opposite_endpoint_branch_residual": 0.002838596018086873
      },
      "pnp_branch": {
        "construction": "incoming_path_concatenated_with_parent_reflection",
        "reduced_polarization": [
          [
            2.0445774311346187e-08,
            5.302260418480947e-08,
            -0.07915731268270465
          ],
          [
            1.7790992665091304e-08,
            4.63399248864694e-08,
            -0.06944432933146392
          ],
          [
            1.5163102774308572e-08,
            3.9672168079582054e-08,
            -0.05968337501818134
          ],
          [
            1.2562315789664205e-08,
            3.3019319515046654e-08,
            -0.04987258786404808
          ],
          [
            9.98881668926879e-09,
            2.6381329278361068e-08,
            -0.040010090206756645
          ],
          [
            7.442775975059873e-09,
            1.9758116456802722e-08,
            -0.030093992988362368
          ],
          [
            4.924345708516259e-09,
            1.314956639557477e-08,
            -0.020122400141036736
          ],
          [
            2.4336774180947333e-09,
            6.55554157305458e-09,
            -0.010093412996174793
          ],
          [
            -2.910999886192327e-11,
            -2.4148518515760896e-11,
            -5.134753376768409e-06
          ],
          [
            1.4608617868253654e-09,
            -5.705746238666185e-09,
            0.009402827247579222
          ],
          [
            2.9191877437601252e-09,
            -1.1391278624328871e-08,
            0.018847379367334185
          ],
          [
            4.345929920063621e-09,
            -1.708048708249341e-08,
            0.028328953883888557
          ],
          [
            5.7411817494415985e-09,
            -2.2773096600670843e-08,
            0.037848002695596
          ],
          [
            7.105054354338209e-09,
            -2.8468840537937198e-08,
            0.0474049932478682
          ],
          [
            8.437652734160095e-09,
            -3.416749264139028e-08,
            0.05700040354358509
          ],
          [
            9.739130754762825e-09,
            -3.9868800979088574e-08,
            0.06663471653460369
          ],
          [
            1.1009640375559726e-08,
            -4.557255009567354e-08,
            0.07630841413652448
          ]
        ],
        "unwrapped_reduced_polarization": [
          [
            2.0445774311346187e-08,
            5.302260418480947e-08,
            -0.07915731268270465
          ],
          [
            1.7790992665091304e-08,
            4.63399248864694e-08,
            -0.06944432933146392
          ],
          [
            1.5163102774308572e-08,
            3.9672168079582054e-08,
            -0.05968337501818134
          ],
          [
            1.2562315789664205e-08,
            3.3019319515046654e-08,
            -0.04987258786404808
          ],
          [
            9.98881668926879e-09,
            2.6381329278361068e-08,
            -0.040010090206756645
          ],
          [
            7.442775975059873e-09,
            1.9758116456802722e-08,
            -0.030093992988362368
          ],
          [
            4.924345708516259e-09,
            1.314956639557477e-08,
            -0.020122400141036736
          ],
          [
            2.4336774180947333e-09,
            6.55554157305458e-09,
            -0.010093412996174793
          ],
          [
            -2.910999886192326e-11,
            -2.4148518515760656e-11,
            -5.134753376767609e-06
          ],
          [
            1.4608617868253654e-09,
            -5.705746238666185e-09,
            0.009402827247579222
          ],
          [
            2.9191877437601252e-09,
            -1.1391278624328871e-08,
            0.018847379367334185
          ],
          [
            4.345929920063621e-09,
            -1.708048708249341e-08,
            0.028328953883888557
          ],
          [
            5.7411817494415985e-09,
            -2.2773096600670843e-08,
            0.037848002695596
          ],
          [
            7.105054354338209e-09,
            -2.8468840537937198e-08,
            0.0474049932478682
          ],
          [
            8.437652734160095e-09,
            -3.416749264139028e-08,
            0.05700040354358509
          ],
          [
            9.739130754762825e-09,
            -3.9868800979088574e-08,
            0.06663471653460369
          ],
          [
            1.1009640375559726e-08,
            -4.557255009567354e-08,
            0.07630841413652448
          ]
        ],
        "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": [
          [
            2.0445774295829722e-08,
            5.3022604196151235e-08,
            -0.07915731268270465
          ],
          [
            1.7790992679067585e-08,
            4.633992489733174e-08,
            -0.06944432933146394
          ],
          [
            1.5163102773385617e-08,
            3.9672168106186234e-08,
            -0.05968337501818133
          ],
          [
            1.25623157432031e-08,
            3.3019319500837696e-08,
            -0.04987258786404808
          ],
          [
            9.988816662698241e-09,
            2.638132923227232e-08,
            -0.040010090206756665
          ],
          [
            7.442775951105318e-09,
            1.9758116476253917e-08,
            -0.03009399298836235
          ],
          [
            4.924345708978706e-09,
            1.3149566435721738e-08,
            -0.020122400141036723
          ],
          [
            2.4336773707389625e-09,
            6.555541554043032e-09,
            -0.010093412996174778
          ],
          [
            -2.9109992194520373e-11,
            -2.414851651977301e-11,
            -5.134753376767609e-06
          ],
          [
            1.4608617648903532e-09,
            -5.7057462643506085e-09,
            0.009402827247579237
          ],
          [
            2.9191877803924626e-09,
            -1.1391278642580716e-08,
            0.01884737936733416
          ],
          [
            4.345929949245431e-09,
            -1.708048708026766e-08,
            0.028328953883888564
          ],
          [
            5.741181752227931e-09,
            -2.277309657516824e-08,
            0.03784800269559596
          ],
          [
            7.105054322664728e-09,
            -2.8468840562734243e-08,
            0.04740499324786818
          ],
          [
            8.437652687653951e-09,
            -3.416749266849095e-08,
            0.05700040354358504
          ],
          [
            9.739130724106815e-09,
            -3.9868800982834074e-08,
            0.06663471653460373
          ],
          [
            1.1009640421555389e-08,
            -4.5572550122496835e-08,
            0.07630841413652445
          ]
        ]
      },
      "incoming_structure_ids": [
        "incoming_00_000",
        "incoming_00_001",
        "incoming_00_002",
        "incoming_00_003",
        "incoming_00_004",
        "incoming_00_005",
        "incoming_00_006",
        "incoming_00_007",
        "incoming_00_008"
      ],
      "reflected_structure_ids": [
        "reflected_00_001",
        "reflected_00_002",
        "reflected_00_003",
        "reflected_00_004",
        "reflected_00_005",
        "reflected_00_006",
        "reflected_00_007",
        "reflected_00_008"
      ]
    },
    {
      "orbit_id": 1,
      "formal_class": [
        0.0,
        0.0,
        0.5
      ],
      "formal_classes_in_orbit": [
        [
          0.0,
          0.0,
          0.5
        ]
      ],
      "target_reduced_polarization": [
        0.0,
        0.0,
        -0.5
      ],
      "bec_backprojection": {
        "converged_to_target": true,
        "history": [
          {
            "iteration": 0,
            "reduced_polarization": [
              2.0445773555734962e-08,
              5.302260408086206e-08,
              -0.07915731268270453
            ],
            "branch_aligned_reduced_polarization": [
              2.0445773555734962e-08,
              5.302260408086206e-08,
              -0.07915731268270454
            ],
            "target_residual": 0.4208426873172993,
            "energy_eV": -132.14481245265785,
            "max_atomic_step_A": 0.12,
            "max_log_strain_component": 0.011856708448952561,
            "step_scale": 0.821904093036192,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 2.7944103688874016,
            "cell_principal_stretches": [
              1.0071650256737004,
              1.0071649502359217,
              0.9882133053344623
            ],
            "cell_volume_ratio": 1.0024251101517028,
            "cell_rmsd_from_input_A": 0.10061978488198495
          },
          {
            "iteration": 1,
            "reduced_polarization": [
              2.21269203670938e-09,
              -4.280705546855388e-09,
              -0.4096819100854081
            ],
            "branch_aligned_reduced_polarization": [
              2.21269203670938e-09,
              -4.280705546855388e-09,
              -0.4096819100854081
            ],
            "target_residual": 0.09031808991459202,
            "energy_eV": -130.16632479436467,
            "max_atomic_step_A": 0.025294393644707175,
            "max_log_strain_component": 0.003422478353833789,
            "step_scale": 1.0,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 2.7944103688874016,
            "cell_principal_stretches": [
              1.009242765774751,
              1.0092426690810785,
              0.9848369477390811
            ],
            "cell_volume_ratio": 1.0031262194589943,
            "cell_rmsd_from_input_A": 0.12941704586869313
          },
          {
            "iteration": 2,
            "reduced_polarization": [
              1.1781883301803684e-09,
              -2.5001302724416133e-09,
              -0.5007676530021775
            ],
            "branch_aligned_reduced_polarization": [
              1.1781883301803684e-09,
              -2.5001302724416133e-09,
              -0.5007676530021775
            ],
            "target_residual": 0.0007676530021824906,
            "energy_eV": -128.59805220853394
          }
        ],
        "iterations": 2
      },
      "parent": {
        "candidate_id": "bec_projection_01",
        "source": "MACEField_BEC_backprojection",
        "spacegroup": "R3",
        "spacegroup_number": 146,
        "pointgroup": "3",
        "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": 0.0007676530021824906,
        "parent_symmetrization_rmsd_A": 0.13758421235867876,
        "parent_cell_rmsd_A": 0.12941704586869313,
        "energy_eV": -128.59805220853394,
        "reduced_polarization": [
          1.1781883301803684e-09,
          -2.5001302724416133e-09,
          -0.5007676530021775
        ],
        "cartesian_polarization_e_A2": [
          2.1451167636222663e-10,
          -6.373404763897156e-11,
          -0.009877571825748896
        ],
        "ranking_score": 0.671473779830217
      },
      "branch_status": "awaiting_branch_sampling"
    },
    {
      "orbit_id": 2,
      "formal_class": [
        0.0,
        0.5,
        0.0
      ],
      "formal_classes_in_orbit": [
        [
          0.0,
          0.5,
          0.0
        ],
        [
          0.5,
          0.0,
          0.0
        ],
        [
          0.5,
          0.5,
          0.0
        ]
      ],
      "target_reduced_polarization": [
        0.0,
        0.5,
        0.0
      ],
      "bec_backprojection": {
        "converged_to_target": true,
        "history": [
          {
            "iteration": 0,
            "reduced_polarization": [
              2.0445773555734962e-08,
              5.302260408086206e-08,
              -0.07915731268270453
            ],
            "branch_aligned_reduced_polarization": [
              2.0445773555734962e-08,
              5.302260408512893e-08,
              -0.07915731268270453
            ],
            "target_residual": 0.506227050964828,
            "energy_eV": -132.14481245265785,
            "max_atomic_step_A": 0.12,
            "max_log_strain_component": 0.017094964483589575,
            "step_scale": 0.9475435037547746,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 2.7944103688874016,
            "cell_principal_stretches": [
              1.025339952452222,
              0.9986903351599842,
              0.9760524840411197
            ],
            "cell_volume_ratio": 0.9994749138549566,
            "cell_rmsd_from_input_A": 0.20600255932147746
          },
          {
            "iteration": 1,
            "reduced_polarization": [
              -0.020177473962950755,
              0.4719775973715668,
              -0.007931229335404353
            ],
            "branch_aligned_reduced_polarization": [
              -0.020177473962950755,
              0.4719775973715668,
              -0.007931229335404353
            ],
            "target_residual": 0.035430070609107654,
            "energy_eV": -129.81153112428524,
            "max_atomic_step_A": 0.005712771278716953,
            "max_log_strain_component": 0.0009824504439514014,
            "step_scale": 1.0,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 2.7944103688874016,
            "cell_principal_stretches": [
              1.0255640294365789,
              0.9997081741638443,
              0.9747946562109372
            ],
            "cell_volume_ratio": 0.9994225930250596,
            "cell_rmsd_from_input_A": 0.20991116763527864
          },
          {
            "iteration": 2,
            "reduced_polarization": [
              -0.0003039253700269197,
              0.49926471980017967,
              7.341391806030265e-05
            ],
            "branch_aligned_reduced_polarization": [
              -0.0003039253700269197,
              0.49926471980017967,
              7.341391806030265e-05
            ],
            "target_residual": 0.0007989976258780698,
            "energy_eV": -129.49729484984772
          }
        ],
        "iterations": 2
      },
      "parent": {
        "candidate_id": "bec_projection_02",
        "source": "MACEField_BEC_backprojection",
        "spacegroup": "P1",
        "spacegroup_number": 1,
        "pointgroup": "1",
        "has_inversion": false,
        "is_polar_point_group": true,
        "nonpolar_parent_hypothesis": false,
        "symmetry_tolerance_A": null,
        "target_reduced_polarization": [
          0.0,
          0.5,
          0.0
        ],
        "formal_class": [
          0.0,
          0.5,
          0.0
        ],
        "target_residual": 0.0007989976258780698,
        "parent_symmetrization_rmsd_A": 0.11611897426791669,
        "parent_cell_rmsd_A": 0.20991116763527864,
        "energy_eV": -129.49729484984772,
        "reduced_polarization": [
          -0.0003039253700269197,
          0.49926471980017967,
          7.341391806030265e-05
        ],
        "cartesian_polarization_e_A2": [
          -0.004100780274174344,
          0.006854900871566792,
          -0.0001591242216809637
        ],
        "ranking_score": 0.6701947614284924
      },
      "branch_status": "awaiting_branch_sampling"
    },
    {
      "orbit_id": 3,
      "formal_class": [
        0.0,
        0.5,
        0.5
      ],
      "formal_classes_in_orbit": [
        [
          0.0,
          0.5,
          0.5
        ],
        [
          0.5,
          0.0,
          0.5
        ],
        [
          0.5,
          0.5,
          0.5
        ]
      ],
      "target_reduced_polarization": [
        0.0,
        0.5,
        -0.5
      ],
      "bec_backprojection": {
        "converged_to_target": true,
        "history": [
          {
            "iteration": 0,
            "reduced_polarization": [
              2.0445773555734962e-08,
              5.302260408086206e-08,
              -0.07915731268270453
            ],
            "branch_aligned_reduced_polarization": [
              2.0445773555734962e-08,
              5.302260408512893e-08,
              -0.07915731268270454
            ],
            "target_residual": 0.6535353964750816,
            "energy_eV": -132.14481245265785,
            "max_atomic_step_A": 0.12,
            "max_log_strain_component": 0.014229928696629434,
            "step_scale": 0.693053322665648,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 2.7944103688874016,
            "cell_principal_stretches": [
              1.0213619060880124,
              1.0001355179161386,
              0.9809537256809578
            ],
            "cell_volume_ratio": 1.0020445436339112,
            "cell_rmsd_from_input_A": 0.18960254446100439
          },
          {
            "iteration": 1,
            "reduced_polarization": [
              -0.0239800210859573,
              0.35210248416384876,
              -0.3647527376209547
            ],
            "branch_aligned_reduced_polarization": [
              -0.0239800210859573,
              0.35210248416384876,
              -0.3647527376209547
            ],
            "target_residual": 0.20184285615996886,
            "energy_eV": -130.20299946716875,
            "max_atomic_step_A": 0.055870264224991084,
            "max_log_strain_component": 0.005621842271311935,
            "step_scale": 1.0,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 2.7944103688874016,
            "cell_principal_stretches": [
              1.0262219611763792,
              1.0036697957643639,
              0.9737871909204111
            ],
            "cell_volume_ratio": 1.0029891077467217,
            "cell_rmsd_from_input_A": 0.24274936916077686
          },
          {
            "iteration": 2,
            "reduced_polarization": [
              -0.0031849484302592314,
              0.5034195949679645,
              -0.5053339316281432
            ],
            "branch_aligned_reduced_polarization": [
              -0.0031849484302592314,
              0.5034195949679645,
              -0.5053339316281432
            ],
            "target_residual": 0.0070914281257053935,
            "energy_eV": -128.02228078106845,
            "max_atomic_step_A": 0.0024183184409714465,
            "max_log_strain_component": 0.00015028140113572405,
            "step_scale": 1.0,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 2.7944103688874016,
            "cell_principal_stretches": [
              1.0259759399321444,
              1.0037183532089955,
              0.9739436758221166
            ],
            "cell_volume_ratio": 1.0029583158336077,
            "cell_rmsd_from_input_A": 0.24063856849769258
          },
          {
            "iteration": 3,
            "reduced_polarization": [
              0.00019169086719131643,
              0.4999217542712093,
              -0.4999933428865445
            ],
            "branch_aligned_reduced_polarization": [
              0.00019169086719131643,
              0.4999217542712093,
              -0.4999933428865445
            ],
            "target_residual": 0.0002071523589006655,
            "energy_eV": -128.10479977641393
          }
        ],
        "iterations": 3
      },
      "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,
          -0.5
        ],
        "formal_class": [
          0.0,
          0.5,
          0.5
        ],
        "target_residual": 0.0002071523589006655,
        "parent_symmetrization_rmsd_A": 0.16283038303467923,
        "parent_cell_rmsd_A": 0.24063856849769258,
        "energy_eV": -128.10479977641393,
        "reduced_polarization": [
          0.00019169086719131643,
          0.4999217542712093,
          -0.4999933428865445
        ],
        "cartesian_polarization_e_A2": [
          -0.004174746541569374,
          0.007074841722184679,
          -0.010016789554267436
        ],
        "ranking_score": 0.7234043298769037
      },
      "branch_status": "awaiting_branch_sampling"
    }
  ],
  "sampled_polarization_branches": [
    {
      "orbit_id": 0,
      "candidate_id": "bec_projection_00",
      "formal_class": [
        0.0,
        0.0,
        0.0
      ],
      "construction": "MACEField-BEC-parent plus variable-cell P-N-P path and symmetric log-strain continuation beyond both polar endpoints",
      "geometry_diagnostics": {
        "collision_aware": false,
        "permutations_tested": 1,
        "selected_order": [
          0,
          1,
          2,
          3,
          4,
          5,
          6,
          7,
          8,
          9,
          10,
          11,
          12,
          13,
          14,
          15,
          16,
          17,
          18,
          19,
          20,
          21,
          22,
          23,
          24,
          25,
          26
        ],
        "endpoint_rmsd_A": 0.024095294869824473,
        "minimum_distance_A_by_image": [
          1.4514638377039906,
          1.4494853130581218,
          1.4475141000371357,
          1.4455502455808074,
          1.4435938019505614,
          1.4416448205614925,
          1.439703351971361,
          1.4377694469224471,
          1.4358431563401677
        ],
        "minimum_distance_A": 1.4358431563401677,
        "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": [
          474.7901256832522,
          474.7578066537648,
          474.72548982423785,
          474.6931751945227,
          474.66086276446765,
          474.628552533925,
          474.59624450274424,
          474.5639386707756,
          474.53163503786857
        ],
        "cell_deformation_log_strain_norm": 0.0035013382440281953
      },
      "parent_reduced_polarization": [
        -2.910999886192327e-11,
        -2.4148518515760896e-11,
        -5.134753376768409e-06
      ],
      "incoming": {
        "reached": true,
        "construction": "variable_cell_linear_interpolation",
        "continuation_fractions": [
          0.0,
          0.125,
          0.25,
          0.375,
          0.5,
          0.625,
          0.75,
          0.875,
          1.0
        ],
        "energies_eV": [
          -132.14481245265785,
          -132.14537959517992,
          -132.14386959360897,
          -132.1403296140852,
          -132.13480608497264,
          -132.12734475223152,
          -132.11799073174933,
          -132.10678855901676,
          -132.09378223645365
        ],
        "cartesian_polarizations_e_A2": [
          [
            -9.684986700966981e-11,
            7.331993784282777e-10,
            -0.0015903628375531543
          ],
          [
            -8.6379081605182e-11,
            6.404138464051703e-10,
            -0.0013957776626530357
          ],
          [
            -7.545973468831405e-11,
            5.479411769515213e-10,
            -0.001200071462876345
          ],
          [
            -6.408732493832921e-11,
            4.5578174836880763e-10,
            -0.0010032055301436831
          ],
          [
            -5.225743089659455e-11,
            3.639354781318835e-10,
            -0.0008051407776451299
          ],
          [
            -3.996556102863629e-11,
            2.7240188797226573e-10,
            -0.0006058378274761469
          ],
          [
            -2.720719483467932e-11,
            1.811800664007463e-10,
            -0.00040525709844297124
          ],
          [
            -1.3977583840492334e-11,
            9.026881929966121e-11,
            -0.00020335889455062338
          ],
          [
            -2.7202361304778517e-13,
            -3.3374601393165364e-13,
            -1.0349491127917186e-07
          ]
        ],
        "raw_reduced_polarization": [
          [
            2.0445774311346187e-08,
            5.302260418480947e-08,
            -0.07915731268270465
          ],
          [
            1.7790992665091304e-08,
            4.63399248864694e-08,
            -0.06944432933146392
          ],
          [
            1.5163102774308572e-08,
            3.9672168079582054e-08,
            -0.05968337501818134
          ],
          [
            1.2562315789664205e-08,
            3.3019319515046654e-08,
            -0.04987258786404808
          ],
          [
            9.98881668926879e-09,
            2.6381329278361068e-08,
            -0.040010090206756645
          ],
          [
            7.442775975059873e-09,
            1.9758116456802722e-08,
            -0.030093992988362368
          ],
          [
            4.924345708516259e-09,
            1.314956639557477e-08,
            -0.020122400141036736
          ],
          [
            2.4336774180947333e-09,
            6.55554157305458e-09,
            -0.010093412996174793
          ],
          [
            -2.910999886192327e-11,
            -2.4148518515760896e-11,
            -5.134753376768409e-06
          ]
        ],
        "unwrapped_reduced_polarization": [
          [
            2.0445774311346187e-08,
            5.302260418480947e-08,
            -0.07915731268270465
          ],
          [
            1.7790992665091304e-08,
            4.63399248864694e-08,
            -0.06944432933146392
          ],
          [
            1.5163102774308572e-08,
            3.9672168079582054e-08,
            -0.05968337501818134
          ],
          [
            1.2562315789664205e-08,
            3.3019319515046654e-08,
            -0.04987258786404808
          ],
          [
            9.98881668926879e-09,
            2.6381329278361068e-08,
            -0.040010090206756645
          ],
          [
            7.442775975059873e-09,
            1.9758116456802722e-08,
            -0.030093992988362368
          ],
          [
            4.924345708516259e-09,
            1.314956639557477e-08,
            -0.020122400141036736
          ],
          [
            2.4336774180947333e-09,
            6.55554157305458e-09,
            -0.010093412996174793
          ],
          [
            -2.910999886192326e-11,
            -2.4148518515760656e-11,
            -5.134753376767609e-06
          ]
        ],
        "berry_integer_shifts": [
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ]
        ],
        "folded_reduced_polarization": [
          [
            2.0445774295829722e-08,
            5.3022604196151235e-08,
            -0.07915731268270465
          ],
          [
            1.7790992679067585e-08,
            4.633992489733174e-08,
            -0.06944432933146394
          ],
          [
            1.5163102773385617e-08,
            3.9672168106186234e-08,
            -0.05968337501818133
          ],
          [
            1.25623157432031e-08,
            3.3019319500837696e-08,
            -0.04987258786404808
          ],
          [
            9.988816662698241e-09,
            2.638132923227232e-08,
            -0.040010090206756665
          ],
          [
            7.442775951105318e-09,
            1.9758116476253917e-08,
            -0.03009399298836235
          ],
          [
            4.924345708978706e-09,
            1.3149566435721738e-08,
            -0.020122400141036723
          ],
          [
            2.4336773707389625e-09,
            6.555541554043032e-09,
            -0.010093412996174778
          ],
          [
            -2.9109992194520373e-11,
            -2.414851651977301e-11,
            -5.134753376767609e-06
          ]
        ]
      },
      "reflected": {
        "reached": true,
        "construction": "reflect_displacements_about_reconstructed_parent",
        "energies_eV": [
          -132.09378223645368,
          -132.0816963436233,
          -132.06812413835067,
          -132.05309603523204,
          -132.03664217382885,
          -132.0187924417508,
          -131.99957649750013,
          -131.9790237923383,
          -131.957163590526
        ],
        "cartesian_polarizations_e_A2": [
          [
            -2.720152237377271e-13,
            -3.33712377763745e-13,
            -1.0349491127832375e-07
          ],
          [
            6.929182186135505e-11,
            -7.854905766423174e-11,
            0.00018944519117991703
          ],
          [
            1.382655487913479e-10,
            -1.5691790774298397e-10,
            0.00037957868952636064
          ],
          [
            2.0664717394001368e-10,
            -2.3543716984555517e-10,
            0.0005703049071063453
          ],
          [
            2.7443507172951523e-10,
            -3.141034954945343e-10,
            0.0007616321324239624
          ],
          [
            3.4162795292898343e-10,
            -3.929136571018826e-10,
            0.0009535689527947674
          ],
          [
            4.082247396903601e-10,
            -4.718649910171205e-10,
            0.001146124153405435
          ],
          [
            4.742249158128903e-10,
            -5.509544846797156e-10,
            0.0013393066041762016
          ],
          [
            5.39628212477625e-10,
            -6.301796359732959e-10,
            0.0015331251393260123
          ]
        ],
        "raw_reduced_polarization": [
          [
            -2.910825537745924e-11,
            -2.4146083475838186e-11,
            -5.13475337672633e-06
          ],
          [
            1.4608617868253654e-09,
            -5.705746238666185e-09,
            0.009402827247579222
          ],
          [
            2.9191877437601252e-09,
            -1.1391278624328871e-08,
            0.018847379367334185
          ],
          [
            4.345929920063621e-09,
            -1.708048708249341e-08,
            0.028328953883888557
          ],
          [
            5.7411817494415985e-09,
            -2.2773096600670843e-08,
            0.037848002695596
          ],
          [
            7.105054354338209e-09,
            -2.8468840537937198e-08,
            0.0474049932478682
          ],
          [
            8.437652734160095e-09,
            -3.416749264139028e-08,
            0.05700040354358509
          ],
          [
            9.739130754762825e-09,
            -3.9868800979088574e-08,
            0.06663471653460369
          ],
          [
            1.1009640375559726e-08,
            -4.557255009567354e-08,
            0.07630841413652448
          ]
        ],
        "unwrapped_reduced_polarization": [
          [
            -2.910825537745924e-11,
            -2.4146083475838186e-11,
            -5.13475337672633e-06
          ],
          [
            1.4608617868253654e-09,
            -5.705746238666185e-09,
            0.009402827247579222
          ],
          [
            2.9191877437601252e-09,
            -1.1391278624328871e-08,
            0.018847379367334185
          ],
          [
            4.345929920063621e-09,
            -1.708048708249341e-08,
            0.028328953883888557
          ],
          [
            5.7411817494415985e-09,
            -2.2773096600670843e-08,
            0.037848002695596
          ],
          [
            7.105054354338209e-09,
            -2.8468840537937198e-08,
            0.0474049932478682
          ],
          [
            8.437652734160095e-09,
            -3.416749264139028e-08,
            0.05700040354358509
          ],
          [
            9.739130754762825e-09,
            -3.9868800979088574e-08,
            0.06663471653460369
          ],
          [
            1.1009640375559726e-08,
            -4.557255009567354e-08,
            0.07630841413652448
          ]
        ],
        "gauge_integer_shift": [
          0,
          0,
          0
        ],
        "expected_opposite_endpoint_reduced_polarization": [
          -2.050398241211777e-08,
          -5.307087504623025e-08,
          0.07914701015442652
        ],
        "actual_opposite_endpoint_branch_residual": 0.002838596018086873
      },
      "pnp_branch": {
        "construction": "incoming_path_concatenated_with_parent_reflection",
        "reduced_polarization": [
          [
            2.0445774311346187e-08,
            5.302260418480947e-08,
            -0.07915731268270465
          ],
          [
            1.7790992665091304e-08,
            4.63399248864694e-08,
            -0.06944432933146392
          ],
          [
            1.5163102774308572e-08,
            3.9672168079582054e-08,
            -0.05968337501818134
          ],
          [
            1.2562315789664205e-08,
            3.3019319515046654e-08,
            -0.04987258786404808
          ],
          [
            9.98881668926879e-09,
            2.6381329278361068e-08,
            -0.040010090206756645
          ],
          [
            7.442775975059873e-09,
            1.9758116456802722e-08,
            -0.030093992988362368
          ],
          [
            4.924345708516259e-09,
            1.314956639557477e-08,
            -0.020122400141036736
          ],
          [
            2.4336774180947333e-09,
            6.55554157305458e-09,
            -0.010093412996174793
          ],
          [
            -2.910999886192327e-11,
            -2.4148518515760896e-11,
            -5.134753376768409e-06
          ],
          [
            1.4608617868253654e-09,
            -5.705746238666185e-09,
            0.009402827247579222
          ],
          [
            2.9191877437601252e-09,
            -1.1391278624328871e-08,
            0.018847379367334185
          ],
          [
            4.345929920063621e-09,
            -1.708048708249341e-08,
            0.028328953883888557
          ],
          [
            5.7411817494415985e-09,
            -2.2773096600670843e-08,
            0.037848002695596
          ],
          [
            7.105054354338209e-09,
            -2.8468840537937198e-08,
            0.0474049932478682
          ],
          [
            8.437652734160095e-09,
            -3.416749264139028e-08,
            0.05700040354358509
          ],
          [
            9.739130754762825e-09,
            -3.9868800979088574e-08,
            0.06663471653460369
          ],
          [
            1.1009640375559726e-08,
            -4.557255009567354e-08,
            0.07630841413652448
          ]
        ],
        "unwrapped_reduced_polarization": [
          [
            2.0445774311346187e-08,
            5.302260418480947e-08,
            -0.07915731268270465
          ],
          [
            1.7790992665091304e-08,
            4.63399248864694e-08,
            -0.06944432933146392
          ],
          [
            1.5163102774308572e-08,
            3.9672168079582054e-08,
            -0.05968337501818134
          ],
          [
            1.2562315789664205e-08,
            3.3019319515046654e-08,
            -0.04987258786404808
          ],
          [
            9.98881668926879e-09,
            2.6381329278361068e-08,
            -0.040010090206756645
          ],
          [
            7.442775975059873e-09,
            1.9758116456802722e-08,
            -0.030093992988362368
          ],
          [
            4.924345708516259e-09,
            1.314956639557477e-08,
            -0.020122400141036736
          ],
          [
            2.4336774180947333e-09,
            6.55554157305458e-09,
            -0.010093412996174793
          ],
          [
            -2.910999886192326e-11,
            -2.4148518515760656e-11,
            -5.134753376767609e-06
          ],
          [
            1.4608617868253654e-09,
            -5.705746238666185e-09,
            0.009402827247579222
          ],
          [
            2.9191877437601252e-09,
            -1.1391278624328871e-08,
            0.018847379367334185
          ],
          [
            4.345929920063621e-09,
            -1.708048708249341e-08,
            0.028328953883888557
          ],
          [
            5.7411817494415985e-09,
            -2.2773096600670843e-08,
            0.037848002695596
          ],
          [
            7.105054354338209e-09,
            -2.8468840537937198e-08,
            0.0474049932478682
          ],
          [
            8.437652734160095e-09,
            -3.416749264139028e-08,
            0.05700040354358509
          ],
          [
            9.739130754762825e-09,
            -3.9868800979088574e-08,
            0.06663471653460369
          ],
          [
            1.1009640375559726e-08,
            -4.557255009567354e-08,
            0.07630841413652448
          ]
        ],
        "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": [
          [
            2.0445774295829722e-08,
            5.3022604196151235e-08,
            -0.07915731268270465
          ],
          [
            1.7790992679067585e-08,
            4.633992489733174e-08,
            -0.06944432933146394
          ],
          [
            1.5163102773385617e-08,
            3.9672168106186234e-08,
            -0.05968337501818133
          ],
          [
            1.25623157432031e-08,
            3.3019319500837696e-08,
            -0.04987258786404808
          ],
          [
            9.988816662698241e-09,
            2.638132923227232e-08,
            -0.040010090206756665
          ],
          [
            7.442775951105318e-09,
            1.9758116476253917e-08,
            -0.03009399298836235
          ],
          [
            4.924345708978706e-09,
            1.3149566435721738e-08,
            -0.020122400141036723
          ],
          [
            2.4336773707389625e-09,
            6.555541554043032e-09,
            -0.010093412996174778
          ],
          [
            -2.9109992194520373e-11,
            -2.414851651977301e-11,
            -5.134753376767609e-06
          ],
          [
            1.4608617648903532e-09,
            -5.7057462643506085e-09,
            0.009402827247579237
          ],
          [
            2.9191877803924626e-09,
            -1.1391278642580716e-08,
            0.01884737936733416
          ],
          [
            4.345929949245431e-09,
            -1.708048708026766e-08,
            0.028328953883888564
          ],
          [
            5.741181752227931e-09,
            -2.277309657516824e-08,
            0.03784800269559596
          ],
          [
            7.105054322664728e-09,
            -2.8468840562734243e-08,
            0.04740499324786818
          ],
          [
            8.437652687653951e-09,
            -3.416749266849095e-08,
            0.05700040354358504
          ],
          [
            9.739130724106815e-09,
            -3.9868800982834074e-08,
            0.06663471653460373
          ],
          [
            1.1009640421555389e-08,
            -4.5572550122496835e-08,
            0.07630841413652445
          ]
        ]
      },
      "incoming_structure_ids": [
        "incoming_00_000",
        "incoming_00_001",
        "incoming_00_002",
        "incoming_00_003",
        "incoming_00_004",
        "incoming_00_005",
        "incoming_00_006",
        "incoming_00_007",
        "incoming_00_008"
      ],
      "reflected_structure_ids": [
        "reflected_00_001",
        "reflected_00_002",
        "reflected_00_003",
        "reflected_00_004",
        "reflected_00_005",
        "reflected_00_006",
        "reflected_00_007",
        "reflected_00_008"
      ],
      "positive_extension_structure_ids": [
        "extension_plus_00_000",
        "extension_plus_00_001",
        "extension_plus_00_002",
        "extension_plus_00_003"
      ],
      "negative_extension_structure_ids": [
        "extension_minus_00_000",
        "extension_minus_00_001",
        "extension_minus_00_002",
        "extension_minus_00_003"
      ],
      "extension": {
        "enabled": true,
        "fraction_beyond_polar_endpoint": 0.35,
        "images_per_side": 4,
        "construction": "continue fractional atomic displacements and symmetric log strain beyond +P; reflect these structures about N for the -P side",
        "positive_path_coordinates": [
          1.35,
          1.2625,
          1.175,
          1.0875
        ],
        "negative_path_coordinates": [
          -1.0875,
          -1.175,
          -1.2625,
          -1.35
        ]
      },
      "branch_coordinates": [
        1.35,
        1.2625,
        1.175,
        1.0875,
        1.0,
        0.875,
        0.75,
        0.625,
        0.5,
        0.375,
        0.25,
        0.125,
        0.0,
        -0.125,
        -0.25,
        -0.375,
        -0.5,
        -0.625,
        -0.75,
        -0.875,
        -1.0,
        -1.0875,
        -1.175,
        -1.2625,
        -1.35
      ],
      "parent": {
        "candidate_id": "bec_projection_00",
        "source": "MACEField_BEC_backprojection",
        "spacegroup": "R3",
        "spacegroup_number": 146,
        "pointgroup": "3",
        "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": 5.134753377304506e-06,
        "parent_symmetrization_rmsd_A": 0.024095294869824473,
        "parent_cell_rmsd_A": 0.022810022930548193,
        "energy_eV": -132.0937822364537,
        "reduced_polarization": [
          -2.910587181723223e-11,
          -2.4145168350046658e-11,
          -5.134753377165245e-06
        ],
        "cartesian_polarization_e_A2": [
          -2.719845034340555e-13,
          -3.336997367700983e-13,
          -1.0349491128717044e-07
        ],
        "ranking_score": 0.5298080701092162
      }
    }
  ],
  "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": 45,
      "full_response": 10,
      "energy_polarization": 35
    },
    "model_evaluations_for_recovery_and_path_properties": {
      "total": 70,
      "full_response": 35,
      "energy_polarization": 35
    },
    "elapsed_seconds": 254.33582857000874
  }
}