{
  "schema": "ferrofinder.endpoint_parent_recovery.v4_variable_cell",
  "status": "complete",
  "input_atom_count": 40,
  "input_formula": "Bi4Ca8O24V4",
  "input_spacegroup": "Cmc2_1",
  "input_pointgroup": "mm2",
  "input_is_polar_point_group": true,
  "input_energy_eV": -264.87898292551245,
  "input_cartesian_polarization_e_A2": [
    -9.077526348299424e-18,
    4.38373130150724e-17,
    -0.000577099605279783
  ],
  "input_reduced_polarization": [
    -6.146603563560365e-16,
    2.2168149316747226e-15,
    -0.06285135839679987
  ],
  "input_formal_targets": [
    {
      "orbit_id": 0,
      "representative_formal_class": [
        0.0,
        0.0,
        0.0
      ],
      "target_reduced_polarization": [
        0.0,
        0.0,
        0.0
      ]
    },
    {
      "orbit_id": 1,
      "representative_formal_class": [
        0.0,
        0.0,
        0.5
      ],
      "target_reduced_polarization": [
        0.0,
        0.0,
        -0.5
      ]
    },
    {
      "orbit_id": 2,
      "representative_formal_class": [
        0.0,
        0.5,
        0.0
      ],
      "target_reduced_polarization": [
        0.0,
        0.5,
        0.0
      ]
    },
    {
      "orbit_id": 3,
      "representative_formal_class": [
        0.5,
        0.0,
        0.0
      ],
      "target_reduced_polarization": [
        -0.5,
        0.0,
        0.0
      ]
    },
    {
      "orbit_id": 4,
      "representative_formal_class": [
        0.0,
        0.5,
        0.5
      ],
      "target_reduced_polarization": [
        0.0,
        0.5,
        -0.5
      ]
    },
    {
      "orbit_id": 5,
      "representative_formal_class": [
        0.5,
        0.0,
        0.5
      ],
      "target_reduced_polarization": [
        -0.5,
        0.0,
        -0.5
      ]
    },
    {
      "orbit_id": 6,
      "representative_formal_class": [
        0.5,
        0.5,
        0.0
      ],
      "target_reduced_polarization": [
        -0.5,
        0.5,
        0.0
      ]
    },
    {
      "orbit_id": 7,
      "representative_formal_class": [
        0.5,
        0.5,
        0.5
      ],
      "target_reduced_polarization": [
        -0.5,
        0.5,
        -0.5
      ]
    }
  ],
  "parent_candidates": [
    {
      "candidate_id": "inversion_parent_endpoint_00",
      "source": "same_species_inversion_center_projection_from_endpoint",
      "spacegroup": "Pbcm",
      "spacegroup_number": 57,
      "pointgroup": "mmm",
      "has_inversion": true,
      "is_polar_point_group": false,
      "nonpolar_parent_hypothesis": true,
      "symmetry_tolerance_A": null,
      "target_reduced_polarization": [
        0.0,
        0.0,
        0.0
      ],
      "formal_class": [
        0.0,
        0.0,
        0.0
      ],
      "target_residual": 4.5436924885855265e-15,
      "parent_symmetrization_rmsd_A": 0.5464743771165491,
      "parent_cell_rmsd_A": 0.0,
      "energy_eV": -240.4505901143723,
      "reduced_polarization": [
        -1.563410743347385e-15,
        8.642015700463409e-16,
        4.177803720227166e-15
      ],
      "cartesian_polarization_e_A2": [
        -2.308901504578204e-17,
        1.708950719924025e-17,
        3.8360489564252046e-17
      ],
      "ranking_score": 0.5464743771165582
    },
    {
      "candidate_id": "inversion_parent_endpoint_01",
      "source": "same_species_inversion_center_projection_from_endpoint",
      "spacegroup": "P2_1/m",
      "spacegroup_number": 11,
      "pointgroup": "2/m",
      "has_inversion": true,
      "is_polar_point_group": false,
      "nonpolar_parent_hypothesis": true,
      "symmetry_tolerance_A": null,
      "target_reduced_polarization": [
        0.0,
        0.0,
        0.0
      ],
      "formal_class": [
        0.0,
        0.0,
        0.0
      ],
      "target_residual": 9.283093959971425e-16,
      "parent_symmetrization_rmsd_A": 0.5464743771165492,
      "parent_cell_rmsd_A": 0.0,
      "energy_eV": -240.44987239038406,
      "reduced_polarization": [
        -1.7849965179950456e-16,
        -1.8387267447794486e-17,
        9.108008110447851e-16
      ],
      "cartesian_polarization_e_A2": [
        -2.636147387116847e-18,
        -3.6360653615404787e-19,
        8.362950331543101e-18
      ],
      "ranking_score": 0.5464743771165511
    },
    {
      "candidate_id": "inversion_parent_endpoint_02",
      "source": "same_species_inversion_center_projection_from_endpoint",
      "spacegroup": "C2/c",
      "spacegroup_number": 15,
      "pointgroup": "2/m",
      "has_inversion": true,
      "is_polar_point_group": false,
      "nonpolar_parent_hypothesis": true,
      "symmetry_tolerance_A": null,
      "target_reduced_polarization": [
        0.0,
        0.0,
        0.0
      ],
      "formal_class": [
        0.0,
        0.0,
        0.0
      ],
      "target_residual": 2.4712871596870456e-15,
      "parent_symmetrization_rmsd_A": 0.5515636432986661,
      "parent_cell_rmsd_A": 0.0,
      "energy_eV": -227.86413401001926,
      "reduced_polarization": [
        -1.8157723200294433e-15,
        1.6594508871634522e-15,
        2.3760021157690048e-16
      ],
      "cartesian_polarization_e_A2": [
        -2.681598204136103e-17,
        3.281548988790282e-17,
        2.1816392169242872e-18
      ],
      "ranking_score": 0.5515636432986711
    },
    {
      "candidate_id": "bec_projection_00",
      "source": "MACEField_BEC_backprojection",
      "spacegroup": "Cmc2_1",
      "spacegroup_number": 36,
      "pointgroup": "mm2",
      "has_inversion": false,
      "is_polar_point_group": true,
      "nonpolar_parent_hypothesis": false,
      "symmetry_tolerance_A": null,
      "target_reduced_polarization": [
        0.0,
        0.0,
        0.0
      ],
      "formal_class": [
        0.0,
        0.0,
        0.0
      ],
      "target_residual": 3.1552629530160584e-05,
      "parent_symmetrization_rmsd_A": 0.0033843440932180766,
      "parent_cell_rmsd_A": 0.0033917333233062425,
      "energy_eV": -264.8712938441722,
      "reduced_polarization": [
        6.390590801724028e-16,
        -2.7874469603007214e-15,
        -3.1552629530160584e-05
      ],
      "cartesian_polarization_e_A2": [
        9.434421585352544e-18,
        -5.5107256393856383e-17,
        -2.8988094129512436e-07
      ],
      "ranking_score": 0.5042953826831049
    },
    {
      "candidate_id": "inversion_parent_bec_00_00",
      "source": "same_species_inversion_center_projection_after_BEC",
      "spacegroup": "C2/c",
      "spacegroup_number": 15,
      "pointgroup": "2/m",
      "has_inversion": true,
      "is_polar_point_group": false,
      "nonpolar_parent_hypothesis": true,
      "symmetry_tolerance_A": null,
      "target_reduced_polarization": [
        0.0,
        0.0,
        0.0
      ],
      "formal_class": [
        0.0,
        0.0,
        0.0
      ],
      "target_residual": 3.1806146838497424e-15,
      "parent_symmetrization_rmsd_A": 0.5515638946600491,
      "parent_cell_rmsd_A": 0.0033917333233062425,
      "energy_eV": -228.02554893099318,
      "reduced_polarization": [
        -1.4069404798527998e-15,
        2.8092879890706543e-15,
        4.947011701376181e-16
      ],
      "cartesian_polarization_e_A2": [
        -2.077032261607618e-17,
        5.553902458828248e-17,
        4.544928362379908e-18
      ],
      "ranking_score": 0.552411827990882
    },
    {
      "candidate_id": "inversion_parent_bec_00_01",
      "source": "same_species_inversion_center_projection_after_BEC",
      "spacegroup": "Pbcm",
      "spacegroup_number": 57,
      "pointgroup": "mmm",
      "has_inversion": true,
      "is_polar_point_group": false,
      "nonpolar_parent_hypothesis": true,
      "symmetry_tolerance_A": null,
      "target_reduced_polarization": [
        0.0,
        0.0,
        0.0
      ],
      "formal_class": [
        0.0,
        0.0,
        0.0
      ],
      "target_residual": 1.041531128738306e-15,
      "parent_symmetrization_rmsd_A": 0.5515638946600491,
      "parent_cell_rmsd_A": 0.0033917333233062425,
      "energy_eV": -233.35097223246862,
      "reduced_polarization": [
        6.095715864570114e-16,
        2.344904868127715e-16,
        -8.113099190256958e-16
      ],
      "cartesian_polarization_e_A2": [
        8.998958157512218e-18,
        4.635826929627506e-18,
        -7.453682514303049e-18
      ],
      "ranking_score": 0.5524118279908777
    },
    {
      "candidate_id": "bec_projection_01",
      "source": "MACEField_BEC_backprojection",
      "spacegroup": "Cmc2_1",
      "spacegroup_number": 36,
      "pointgroup": "mm2",
      "has_inversion": false,
      "is_polar_point_group": true,
      "nonpolar_parent_hypothesis": false,
      "symmetry_tolerance_A": null,
      "target_reduced_polarization": [
        0.0,
        0.0,
        -0.5
      ],
      "formal_class": [
        0.0,
        0.0,
        0.5
      ],
      "target_residual": 0.0007442020907184599,
      "parent_symmetrization_rmsd_A": 0.02364677068660285,
      "parent_cell_rmsd_A": 0.02361565845712995,
      "energy_eV": -264.7039548491334,
      "reduced_polarization": [
        1.2519372861171857e-14,
        -6.2241286432162505e-15,
        -0.5007442020907185
      ],
      "cartesian_polarization_e_A2": [
        1.698438631771669e-16,
        -1.2399619663248097e-16,
        -0.004579595908301039
      ],
      "ranking_score": 0.5310390894823223
    },
    {
      "candidate_id": "bec_projection_02",
      "source": "MACEField_BEC_backprojection",
      "spacegroup": "Cm",
      "spacegroup_number": 8,
      "pointgroup": "m",
      "has_inversion": false,
      "is_polar_point_group": true,
      "nonpolar_parent_hypothesis": false,
      "symmetry_tolerance_A": null,
      "target_reduced_polarization": [
        0.0,
        0.5,
        0.0
      ],
      "formal_class": [
        0.0,
        0.5,
        0.0
      ],
      "target_residual": 0.0004788747538788348,
      "parent_symmetrization_rmsd_A": 0.09126137283793748,
      "parent_cell_rmsd_A": 0.14458706573036947,
      "energy_eV": -261.81221687552136,
      "reduced_polarization": [
        3.548178498155727e-15,
        0.4997579300781867,
        0.00041318661988962765
      ],
      "cartesian_polarization_e_A2": [
        -1.0110389938768028e-16,
        0.009884252625428407,
        -0.00020380116082491907
      ],
      "ranking_score": 0.6283658887782875
    },
    {
      "candidate_id": "bec_projection_03",
      "source": "MACEField_BEC_backprojection",
      "spacegroup": "Cc",
      "spacegroup_number": 9,
      "pointgroup": "m",
      "has_inversion": false,
      "is_polar_point_group": true,
      "nonpolar_parent_hypothesis": false,
      "symmetry_tolerance_A": null,
      "target_reduced_polarization": [
        -0.5,
        0.0,
        0.0
      ],
      "formal_class": [
        0.5,
        0.0,
        0.0
      ],
      "target_residual": 1.1233592651383837e-05,
      "parent_symmetrization_rmsd_A": 0.06397566853227664,
      "parent_cell_rmsd_A": 0.07353249838658965,
      "energy_eV": -263.58400213133166,
      "reduced_polarization": [
        -0.4999912971085546,
        2.830335016624937e-15,
        -7.103047539401595e-06
      ],
      "cartesian_polarization_e_A2": [
        -0.007383064827441009,
        6.553870133538436e-17,
        -0.00010572288286350254
      ],
      "ranking_score": 0.5823812603142269
    },
    {
      "candidate_id": "bec_projection_04",
      "source": "MACEField_BEC_backprojection",
      "spacegroup": "Cm",
      "spacegroup_number": 8,
      "pointgroup": "m",
      "has_inversion": false,
      "is_polar_point_group": true,
      "nonpolar_parent_hypothesis": false,
      "symmetry_tolerance_A": null,
      "target_reduced_polarization": [
        0.0,
        0.5,
        -0.5
      ],
      "formal_class": [
        0.0,
        0.5,
        0.5
      ],
      "target_residual": 1.380966516614524e-05,
      "parent_symmetrization_rmsd_A": 0.09496702214997342,
      "parent_cell_rmsd_A": 0.1490641896917923,
      "energy_eV": -261.9053069183156,
      "reduced_polarization": [
        1.0382856707607567e-15,
        0.49999321221239856,
        -0.49998797366259085
      ],
      "cartesian_polarization_e_A2": [
        -2.0483904102921846e-16,
        0.010007567135617042,
        -0.004781346507603552
      ],
      "ranking_score": 0.6322606889032538
    },
    {
      "candidate_id": "bec_projection_05",
      "source": "MACEField_BEC_backprojection",
      "spacegroup": "Cc",
      "spacegroup_number": 9,
      "pointgroup": "m",
      "has_inversion": false,
      "is_polar_point_group": true,
      "nonpolar_parent_hypothesis": false,
      "symmetry_tolerance_A": null,
      "target_reduced_polarization": [
        -0.5,
        0.0,
        -0.5
      ],
      "formal_class": [
        0.5,
        0.0,
        0.5
      ],
      "target_residual": 0.0002758845356221563,
      "parent_symmetrization_rmsd_A": 0.06914566652827771,
      "parent_cell_rmsd_A": 0.07924541370472495,
      "energy_eV": -263.4896228150784,
      "reduced_polarization": [
        -0.49987052904581813,
        1.2780724560643158e-15,
        -0.49975638237128917
      ],
      "cartesian_polarization_e_A2": [
        -0.007470875112896072,
        3.5619601428994904e-17,
        -0.0046777758542269135
      ],
      "ranking_score": 0.5895087890257033
    },
    {
      "candidate_id": "bec_projection_06",
      "source": "MACEField_BEC_backprojection",
      "spacegroup": "P1",
      "spacegroup_number": 1,
      "pointgroup": "1",
      "has_inversion": false,
      "is_polar_point_group": true,
      "nonpolar_parent_hypothesis": false,
      "symmetry_tolerance_A": null,
      "target_reduced_polarization": [
        -0.5,
        0.5,
        0.0
      ],
      "formal_class": [
        0.5,
        0.5,
        0.0
      ],
      "target_residual": 0.0009171020738574753,
      "parent_symmetrization_rmsd_A": 0.11120863764920648,
      "parent_cell_rmsd_A": 0.1623559578947082,
      "energy_eV": -260.4254998842241,
      "reduced_polarization": [
        -0.49997116956649673,
        0.49964219528928566,
        0.0008439317561084693
      ],
      "cartesian_polarization_e_A2": [
        -0.007386586797569154,
        0.009884205943378875,
        -0.0003051997227443402
      ],
      "ranking_score": 0.6536318312705984
    },
    {
      "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": 3.779943838065062e-05,
      "parent_symmetrization_rmsd_A": 0.11529609763446352,
      "parent_cell_rmsd_A": 0.1680052919809488,
      "energy_eV": -260.5684836961411,
      "reduced_polarization": [
        -0.49999327225944556,
        0.49998626527644857,
        -0.4999654327840593
      ],
      "cartesian_polarization_e_A2": [
        -0.007477351864598008,
        0.010010611684569662,
        -0.004888985122673626
      ],
      "ranking_score": 0.657373019506462
    }
  ],
  "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": [
              -6.146603563560365e-16,
              2.2168149316747226e-15,
              -0.06285135839679987
            ],
            "branch_aligned_reduced_polarization": [
              -6.146603563560365e-16,
              2.2168149316747226e-15,
              -0.06285135839679987
            ],
            "target_residual": 0.06285135839679987,
            "energy_eV": -264.87898292551245,
            "max_atomic_step_A": 0.004214921720166877,
            "max_log_strain_component": 0.0006047694646704781,
            "step_scale": 1.0,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 4.757113643124521,
            "cell_principal_stretches": [
              1.0006049523745941,
              0.9997747164325946,
              0.9996543372745288
            ],
            "cell_volume_ratio": 1.0000337386056422,
            "cell_rmsd_from_input_A": 0.0033917333233062425
          },
          {
            "iteration": 1,
            "reduced_polarization": [
              6.390590801724028e-16,
              -2.7874469603007214e-15,
              -3.1552629530160584e-05
            ],
            "branch_aligned_reduced_polarization": [
              6.390590801724028e-16,
              -2.7874469603007214e-15,
              -3.1552629530160584e-05
            ],
            "target_residual": 3.1552629530160584e-05,
            "energy_eV": -264.8712938441722
          }
        ],
        "iterations": 1
      },
      "parent": {
        "candidate_id": "bec_projection_00",
        "source": "MACEField_BEC_backprojection",
        "spacegroup": "Cmc2_1",
        "spacegroup_number": 36,
        "pointgroup": "mm2",
        "has_inversion": false,
        "is_polar_point_group": true,
        "nonpolar_parent_hypothesis": false,
        "symmetry_tolerance_A": null,
        "target_reduced_polarization": [
          0.0,
          0.0,
          0.0
        ],
        "formal_class": [
          0.0,
          0.0,
          0.0
        ],
        "target_residual": 3.1552629530160584e-05,
        "parent_symmetrization_rmsd_A": 0.0033843440932180766,
        "parent_cell_rmsd_A": 0.0033917333233062425,
        "energy_eV": -264.8712938441722,
        "reduced_polarization": [
          6.390590801724028e-16,
          -2.7874469603007214e-15,
          -3.1552629530160584e-05
        ],
        "cartesian_polarization_e_A2": [
          9.434421585352544e-18,
          -5.5107256393856383e-17,
          -2.8988094129512436e-07
        ],
        "ranking_score": 0.5042953826831049
      },
      "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": [
          -264.87898292551245,
          -264.8784444504346,
          -264.87778449969284,
          -264.87700343403026,
          -264.87610161184716,
          -264.87507938920606,
          -264.8739371198351,
          -264.8726751551329,
          -264.8712938441723
        ],
        "cartesian_polarizations_e_A2": [
          [
            -3.908464643322472e-17,
            2.204364625433915e-17,
            -0.0005770996052797927
          ],
          [
            4.070956218176675e-17,
            6.415355767022546e-17,
            -0.0005050359327014456
          ],
          [
            -1.815394895564945e-17,
            1.1226257115388798e-17,
            -0.0004329611031765768
          ],
          [
            -5.46768160394049e-17,
            -5.6517375914437e-17,
            -0.00036087533179317
          ],
          [
            -1.1589510120144676e-17,
            4.742712750376593e-17,
            -0.0002887788337218982
          ],
          [
            -2.7888865589907063e-17,
            2.5656445202863033e-17,
            -0.00021667182421715507
          ],
          [
            -4.871781086687417e-17,
            2.779247135081778e-17,
            -0.00014455451861919967
          ],
          [
            -5.548759833800211e-17,
            -2.0520438095873976e-17,
            -7.242713235539482e-05
          ],
          [
            -3.345826231989606e-17,
            -1.2725799414663742e-17,
            -2.8988094133330177e-07
          ]
        ],
        "raw_reduced_polarization": [
          [
            -2.646512032344163e-15,
            1.1147280890225406e-15,
            -0.06285135839680092
          ],
          [
            2.7545046302146897e-15,
            3.242816179846192e-15,
            -0.054999047783315665
          ],
          [
            -1.2330745501934647e-15,
            5.652035841236161e-16,
            -0.047146642869883154
          ],
          [
            -3.707461700729306e-15,
            -2.8614820625093986e-15,
            -0.039294167216694105
          ],
          [
            -7.898530317017184e-16,
            2.395277547985444e-15,
            -0.03144164438622955
          ],
          [
            -1.8935115469671233e-15,
            1.2944625665070573e-15,
            -0.02358909794337192
          ],
          [
            -3.3034526881445e-15,
            1.4031750835757402e-15,
            -0.015736551455636006
          ],
          [
            -3.7606148265924925e-15,
            -1.039420248378414e-15,
            -0.007884028493301644
          ],
          [
            -2.2664062990276374e-15,
            -6.436981470369035e-16,
            -3.1552629534316074e-05
          ]
        ],
        "unwrapped_reduced_polarization": [
          [
            -2.646512032344163e-15,
            1.1147280890225406e-15,
            -0.06285135839680092
          ],
          [
            2.7545046302146897e-15,
            3.242816179846192e-15,
            -0.054999047783315665
          ],
          [
            -1.2330745501934647e-15,
            5.652035841236161e-16,
            -0.047146642869883154
          ],
          [
            -3.707461700729306e-15,
            -2.8614820625093986e-15,
            -0.039294167216694105
          ],
          [
            -7.898530317017184e-16,
            2.3952775479854435e-15,
            -0.03144164438622955
          ],
          [
            -1.8935115469671233e-15,
            1.2944625665070573e-15,
            -0.02358909794337192
          ],
          [
            -3.3034526881445e-15,
            1.4031750835757402e-15,
            -0.015736551455636006
          ],
          [
            -3.7606148265924925e-15,
            -1.0394202483784142e-15,
            -0.007884028493301644
          ],
          [
            -2.2664062990276374e-15,
            -6.436981470369035e-16,
            -3.1552629534315965e-05
          ]
        ],
        "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": [
          [
            -2.6645352591003757e-15,
            1.1102230246251565e-15,
            -0.0628513583968009
          ],
          [
            2.7755575615628914e-15,
            3.219646771412954e-15,
            -0.05499904778331566
          ],
          [
            -1.2212453270876722e-15,
            5.551115123125783e-16,
            -0.047146642869883126
          ],
          [
            -3.7192471324942744e-15,
            -2.886579864025407e-15,
            -0.0392941672166941
          ],
          [
            -7.771561172376096e-16,
            2.4424906541753444e-15,
            -0.03144164438622954
          ],
          [
            -1.887379141862766e-15,
            1.3322676295501878e-15,
            -0.02358909794337194
          ],
          [
            -3.3306690738754696e-15,
            1.4432899320127035e-15,
            -0.015736551455636016
          ],
          [
            -3.774758283725532e-15,
            -1.0547118733938987e-15,
            -0.007884028493301665
          ],
          [
            -2.275957200481571e-15,
            -6.661338147750939e-16,
            -3.155262953430382e-05
          ]
        ]
      },
      "reflected": {
        "reached": true,
        "construction": "reflect_displacements_about_reconstructed_parent",
        "energies_eV": [
          -264.8712938441722,
          -264.8705268426911,
          -264.8696752805794,
          -264.86873933285,
          -264.8677191734919,
          -264.86661497547516,
          -264.8654269107552,
          -264.8641551502782,
          -264.8627998639847
        ],
        "cartesian_polarizations_e_A2": [
          [
            5.962267995559273e-20,
            -1.0794204860652281e-17,
            -2.89880941300851e-07
          ],
          [
            -1.4787659714138142e-17,
            9.337594699440328e-17,
            6.536529379382145e-05
          ],
          [
            -3.7219727515963085e-17,
            -4.544966696781322e-19,
            0.00013100552014508912
          ],
          [
            -8.868807525089152e-17,
            2.199773158225989e-17,
            0.00019663065407364412
          ],
          [
            -5.754962248588348e-17,
            4.990415524593674e-17,
            0.000262240551615786
          ],
          [
            -1.2412211140351716e-16,
            3.62465679869429e-17,
            0.00032783506888255294
          ],
          [
            -8.240326162874004e-17,
            -6.153988718314346e-17,
            0.0003934140620585617
          ],
          [
            -1.1035525691196487e-16,
            2.597503238294995e-17,
            0.00045897738740239733
          ],
          [
            -1.6041140123757891e-16,
            3.381540786232645e-17,
            0.0005245249012456144
          ]
        ],
        "raw_reduced_polarization": [
          [
            4.028786503597091e-18,
            -5.459937775315824e-16,
            -3.155262953078391e-05
          ],
          [
            -9.99677946758974e-16,
            4.724350669836735e-15,
            0.007115314689179953
          ],
          [
            -2.5175820637932816e-15,
            -2.068677338923766e-17,
            0.014261574999024187
          ],
          [
            -6.002485265575e-15,
            1.1154646831924056e-15,
            0.02140721237923298
          ],
          [
            -3.8930613008469644e-15,
            2.527007841559134e-15,
            0.028552210912703664
          ],
          [
            -8.401576044735079e-15,
            1.8360150843214896e-15,
            0.03569655468595616
          ],
          [
            -5.576872349174031e-15,
            -3.109916611138558e-15,
            0.04284022778900872
          ],
          [
            -7.470797235245136e-15,
            1.314921248734034e-15,
            0.049983214315422866
          ],
          [
            -1.0861827910500395e-14,
            1.7100158726448872e-15,
            0.057125498362195944
          ]
        ],
        "unwrapped_reduced_polarization": [
          [
            4.028786503597091e-18,
            -5.459937775315824e-16,
            -3.155262953078391e-05
          ],
          [
            -9.99677946758974e-16,
            4.724350669836735e-15,
            0.007115314689179953
          ],
          [
            -2.5175820637932816e-15,
            -2.068677338923728e-17,
            0.014261574999024187
          ],
          [
            -6.002485265575e-15,
            1.1154646831924056e-15,
            0.02140721237923298
          ],
          [
            -3.8930613008469644e-15,
            2.527007841559134e-15,
            0.028552210912703664
          ],
          [
            -8.401576044735079e-15,
            1.8360150843214896e-15,
            0.03569655468595616
          ],
          [
            -5.576872349174031e-15,
            -3.1099166111385583e-15,
            0.04284022778900872
          ],
          [
            -7.470797235245136e-15,
            1.3149212487340343e-15,
            0.049983214315422866
          ],
          [
            -1.0861827910500395e-14,
            1.7100158726448872e-15,
            0.057125498362195944
          ]
        ],
        "gauge_integer_shift": [
          0,
          0,
          0
        ],
        "expected_opposite_endpoint_reduced_polarization": [
          -1.8845610048503312e-15,
          -2.4017933865796448e-15,
          0.06278821709235555
        ],
        "actual_opposite_endpoint_branch_residual": 0.0056627187301596035
      },
      "pnp_branch": {
        "construction": "incoming_path_concatenated_with_parent_reflection",
        "reduced_polarization": [
          [
            -2.646512032344163e-15,
            1.1147280890225406e-15,
            -0.06285135839680092
          ],
          [
            2.7545046302146897e-15,
            3.242816179846192e-15,
            -0.054999047783315665
          ],
          [
            -1.2330745501934647e-15,
            5.652035841236161e-16,
            -0.047146642869883154
          ],
          [
            -3.707461700729306e-15,
            -2.8614820625093986e-15,
            -0.039294167216694105
          ],
          [
            -7.898530317017184e-16,
            2.395277547985444e-15,
            -0.03144164438622955
          ],
          [
            -1.8935115469671233e-15,
            1.2944625665070573e-15,
            -0.02358909794337192
          ],
          [
            -3.3034526881445e-15,
            1.4031750835757402e-15,
            -0.015736551455636006
          ],
          [
            -3.7606148265924925e-15,
            -1.039420248378414e-15,
            -0.007884028493301644
          ],
          [
            -2.2664062990276374e-15,
            -6.436981470369035e-16,
            -3.1552629534316074e-05
          ],
          [
            -9.99677946758974e-16,
            4.724350669836735e-15,
            0.007115314689179953
          ],
          [
            -2.5175820637932816e-15,
            -2.068677338923766e-17,
            0.014261574999024187
          ],
          [
            -6.002485265575e-15,
            1.1154646831924056e-15,
            0.02140721237923298
          ],
          [
            -3.8930613008469644e-15,
            2.527007841559134e-15,
            0.028552210912703664
          ],
          [
            -8.401576044735079e-15,
            1.8360150843214896e-15,
            0.03569655468595616
          ],
          [
            -5.576872349174031e-15,
            -3.109916611138558e-15,
            0.04284022778900872
          ],
          [
            -7.470797235245136e-15,
            1.314921248734034e-15,
            0.049983214315422866
          ],
          [
            -1.0861827910500395e-14,
            1.7100158726448872e-15,
            0.057125498362195944
          ]
        ],
        "unwrapped_reduced_polarization": [
          [
            -2.646512032344163e-15,
            1.1147280890225406e-15,
            -0.06285135839680092
          ],
          [
            2.7545046302146897e-15,
            3.242816179846192e-15,
            -0.054999047783315665
          ],
          [
            -1.2330745501934647e-15,
            5.652035841236161e-16,
            -0.047146642869883154
          ],
          [
            -3.707461700729306e-15,
            -2.8614820625093986e-15,
            -0.039294167216694105
          ],
          [
            -7.898530317017184e-16,
            2.3952775479854435e-15,
            -0.03144164438622955
          ],
          [
            -1.8935115469671233e-15,
            1.2944625665070573e-15,
            -0.02358909794337192
          ],
          [
            -3.3034526881445e-15,
            1.4031750835757402e-15,
            -0.015736551455636006
          ],
          [
            -3.7606148265924925e-15,
            -1.0394202483784142e-15,
            -0.007884028493301644
          ],
          [
            -2.2664062990276374e-15,
            -6.436981470369035e-16,
            -3.1552629534315965e-05
          ],
          [
            -9.99677946758974e-16,
            4.724350669836735e-15,
            0.007115314689179953
          ],
          [
            -2.5175820637932816e-15,
            -2.068677338923728e-17,
            0.014261574999024187
          ],
          [
            -6.002485265575e-15,
            1.1154646831924056e-15,
            0.02140721237923298
          ],
          [
            -3.8930613008469644e-15,
            2.527007841559134e-15,
            0.028552210912703664
          ],
          [
            -8.401576044735079e-15,
            1.8360150843214896e-15,
            0.03569655468595616
          ],
          [
            -5.576872349174031e-15,
            -3.1099166111385583e-15,
            0.04284022778900872
          ],
          [
            -7.470797235245136e-15,
            1.3149212487340343e-15,
            0.049983214315422866
          ],
          [
            -1.0861827910500395e-14,
            1.7100158726448872e-15,
            0.057125498362195944
          ]
        ],
        "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": [
          [
            -2.6645352591003757e-15,
            1.1102230246251565e-15,
            -0.0628513583968009
          ],
          [
            2.7755575615628914e-15,
            3.219646771412954e-15,
            -0.05499904778331566
          ],
          [
            -1.2212453270876722e-15,
            5.551115123125783e-16,
            -0.047146642869883126
          ],
          [
            -3.7192471324942744e-15,
            -2.886579864025407e-15,
            -0.0392941672166941
          ],
          [
            -7.771561172376096e-16,
            2.4424906541753444e-15,
            -0.03144164438622954
          ],
          [
            -1.887379141862766e-15,
            1.3322676295501878e-15,
            -0.02358909794337194
          ],
          [
            -3.3306690738754696e-15,
            1.4432899320127035e-15,
            -0.015736551455636016
          ],
          [
            -3.774758283725532e-15,
            -1.0547118733938987e-15,
            -0.007884028493301665
          ],
          [
            -2.275957200481571e-15,
            -6.661338147750939e-16,
            -3.155262953430382e-05
          ],
          [
            -9.992007221626409e-16,
            4.773959005888173e-15,
            0.007115314689179919
          ],
          [
            -2.4980018054066022e-15,
            0.0,
            0.01426157499902414
          ],
          [
            -5.995204332975845e-15,
            1.1102230246251565e-15,
            0.02140721237923293
          ],
          [
            -3.885780586188048e-15,
            2.55351295663786e-15,
            0.028552210912703657
          ],
          [
            -8.382183835919932e-15,
            1.887379141862766e-15,
            0.03569655468595612
          ],
          [
            -5.551115123125783e-15,
            -3.1086244689504383e-15,
            0.042840227789008756
          ],
          [
            -7.494005416219807e-15,
            1.3322676295501878e-15,
            0.04998321431542285
          ],
          [
            -1.0880185641326534e-14,
            1.6653345369377348e-15,
            0.05712549836219594
          ]
        ]
      },
      "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": [
              -6.146603563560365e-16,
              2.2168149316747226e-15,
              -0.06285135839679987
            ],
            "branch_aligned_reduced_polarization": [
              -6.146603563560365e-16,
              2.2168149316747226e-15,
              -0.0628513583967999
            ],
            "target_residual": 0.4371486416032001,
            "energy_eV": -264.87898292551245,
            "max_atomic_step_A": 0.029315950385705385,
            "max_log_strain_component": 0.004206339476304061,
            "step_scale": 1.0,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 4.757113643124521,
            "cell_principal_stretches": [
              1.0024074891645816,
              1.001568314784529,
              0.9958024947786251
            ],
            "cell_volume_ratio": 0.9997653701222263,
            "cell_rmsd_from_input_A": 0.02361565845712995
          },
          {
            "iteration": 1,
            "reduced_polarization": [
              1.2519372861171857e-14,
              -6.2241286432162505e-15,
              -0.5007442020907185
            ],
            "branch_aligned_reduced_polarization": [
              1.2519372861171857e-14,
              -6.2241286432162505e-15,
              -0.5007442020907185
            ],
            "target_residual": 0.0007442020907184599,
            "energy_eV": -264.7039548491334
          }
        ],
        "iterations": 1
      },
      "parent": {
        "candidate_id": "bec_projection_01",
        "source": "MACEField_BEC_backprojection",
        "spacegroup": "Cmc2_1",
        "spacegroup_number": 36,
        "pointgroup": "mm2",
        "has_inversion": false,
        "is_polar_point_group": true,
        "nonpolar_parent_hypothesis": false,
        "symmetry_tolerance_A": null,
        "target_reduced_polarization": [
          0.0,
          0.0,
          -0.5
        ],
        "formal_class": [
          0.0,
          0.0,
          0.5
        ],
        "target_residual": 0.0007442020907184599,
        "parent_symmetrization_rmsd_A": 0.02364677068660285,
        "parent_cell_rmsd_A": 0.02361565845712995,
        "energy_eV": -264.7039548491334,
        "reduced_polarization": [
          1.2519372861171857e-14,
          -6.2241286432162505e-15,
          -0.5007442020907185
        ],
        "cartesian_polarization_e_A2": [
          1.698438631771669e-16,
          -1.2399619663248097e-16,
          -0.004579595908301039
        ],
        "ranking_score": 0.5310390894823223
      },
      "branch_status": "awaiting_branch_sampling"
    },
    {
      "orbit_id": 2,
      "formal_class": [
        0.0,
        0.5,
        0.0
      ],
      "formal_classes_in_orbit": [
        [
          0.0,
          0.5,
          0.0
        ]
      ],
      "target_reduced_polarization": [
        0.0,
        0.5,
        0.0
      ],
      "bec_backprojection": {
        "converged_to_target": true,
        "history": [
          {
            "iteration": 0,
            "reduced_polarization": [
              -6.146603563560365e-16,
              2.2168149316747226e-15,
              -0.06285135839679987
            ],
            "branch_aligned_reduced_polarization": [
              -6.146603563560365e-16,
              2.220446049250313e-15,
              -0.06285135839679987
            ],
            "target_residual": 0.5039348105185042,
            "energy_eV": -264.87898292551245,
            "max_atomic_step_A": 0.09286246610627773,
            "max_log_strain_component": 0.02,
            "step_scale": 0.9613128511433965,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 4.757113643124521,
            "cell_principal_stretches": [
              1.0203914920736898,
              0.9996677077577609,
              0.9803735669914666
            ],
            "cell_volume_ratio": 1.0000324333340245,
            "cell_rmsd_from_input_A": 0.13765083986955903
          },
          {
            "iteration": 1,
            "reduced_polarization": [
              8.546150076653513e-15,
              0.47698191777404736,
              0.04199285937591345
            ],
            "branch_aligned_reduced_polarization": [
              8.546150076653513e-15,
              0.47698191777404736,
              0.04199285937591345
            ],
            "target_residual": 0.04788770560306642,
            "energy_eV": -262.0625371907747,
            "max_atomic_step_A": 0.005131344834347872,
            "max_log_strain_component": 0.0010105983758877963,
            "step_scale": 1.0,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 4.757113643124521,
            "cell_principal_stretches": [
              1.0212721730722167,
              0.9999301916542096,
              0.9792459372881273
            ],
            "cell_volume_ratio": 1.0000068126514363,
            "cell_rmsd_from_input_A": 0.14458706573036947
          },
          {
            "iteration": 2,
            "reduced_polarization": [
              3.548178498155727e-15,
              0.4997579300781867,
              0.00041318661988962765
            ],
            "branch_aligned_reduced_polarization": [
              3.548178498155727e-15,
              0.4997579300781867,
              0.00041318661988962765
            ],
            "target_residual": 0.0004788747538788348,
            "energy_eV": -261.81221687552136
          }
        ],
        "iterations": 2
      },
      "parent": {
        "candidate_id": "bec_projection_02",
        "source": "MACEField_BEC_backprojection",
        "spacegroup": "Cm",
        "spacegroup_number": 8,
        "pointgroup": "m",
        "has_inversion": false,
        "is_polar_point_group": true,
        "nonpolar_parent_hypothesis": false,
        "symmetry_tolerance_A": null,
        "target_reduced_polarization": [
          0.0,
          0.5,
          0.0
        ],
        "formal_class": [
          0.0,
          0.5,
          0.0
        ],
        "target_residual": 0.0004788747538788348,
        "parent_symmetrization_rmsd_A": 0.09126137283793748,
        "parent_cell_rmsd_A": 0.14458706573036947,
        "energy_eV": -261.81221687552136,
        "reduced_polarization": [
          3.548178498155727e-15,
          0.4997579300781867,
          0.00041318661988962765
        ],
        "cartesian_polarization_e_A2": [
          -1.0110389938768028e-16,
          0.009884252625428407,
          -0.00020380116082491907
        ],
        "ranking_score": 0.6283658887782875
      },
      "branch_status": "awaiting_branch_sampling"
    },
    {
      "orbit_id": 3,
      "formal_class": [
        0.5,
        0.0,
        0.0
      ],
      "formal_classes_in_orbit": [
        [
          0.5,
          0.0,
          0.0
        ]
      ],
      "target_reduced_polarization": [
        -0.5,
        0.0,
        0.0
      ],
      "bec_backprojection": {
        "converged_to_target": true,
        "history": [
          {
            "iteration": 0,
            "reduced_polarization": [
              -6.146603563560365e-16,
              2.2168149316747226e-15,
              -0.06285135839679987
            ],
            "branch_aligned_reduced_polarization": [
              -6.106226635438361e-16,
              2.2168149316747226e-15,
              -0.06285135839679987
            ],
            "target_residual": 0.5039348105185059,
            "energy_eV": -264.87898292551245,
            "max_atomic_step_A": 0.06356126920726163,
            "max_log_strain_component": 0.014303932244803379,
            "step_scale": 1.0,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 4.757113643124521,
            "cell_principal_stretches": [
              1.0145461286015682,
              0.9997747164325943,
              0.9859177935244413
            ],
            "cell_volume_ratio": 1.0000337386056288,
            "cell_rmsd_from_input_A": 0.07354665482270493
          },
          {
            "iteration": 1,
            "reduced_polarization": [
              -0.5005354749243985,
              -1.1729732941025059e-14,
              0.023398011958716113
            ],
            "branch_aligned_reduced_polarization": [
              -0.5005354749243985,
              -1.1729732941025059e-14,
              0.023398011958716113
            ],
            "target_residual": 0.023404138459146108,
            "energy_eV": -263.5722063944935,
            "max_atomic_step_A": 0.0015789888692859676,
            "max_log_strain_component": 0.0002282039641779482,
            "step_scale": 1.0,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 4.757113643124521,
            "cell_principal_stretches": [
              1.0144979198753965,
              0.9998597190657724,
              0.9858682718819214
            ],
            "cell_volume_ratio": 1.0000210075322629,
            "cell_rmsd_from_input_A": 0.07353249838658965
          },
          {
            "iteration": 2,
            "reduced_polarization": [
              -0.4999912971085546,
              2.830335016624937e-15,
              -7.103047539401595e-06
            ],
            "branch_aligned_reduced_polarization": [
              -0.4999912971085546,
              2.830335016624937e-15,
              -7.103047539401595e-06
            ],
            "target_residual": 1.1233592651383837e-05,
            "energy_eV": -263.58400213133166
          }
        ],
        "iterations": 2
      },
      "parent": {
        "candidate_id": "bec_projection_03",
        "source": "MACEField_BEC_backprojection",
        "spacegroup": "Cc",
        "spacegroup_number": 9,
        "pointgroup": "m",
        "has_inversion": false,
        "is_polar_point_group": true,
        "nonpolar_parent_hypothesis": false,
        "symmetry_tolerance_A": null,
        "target_reduced_polarization": [
          -0.5,
          0.0,
          0.0
        ],
        "formal_class": [
          0.5,
          0.0,
          0.0
        ],
        "target_residual": 1.1233592651383837e-05,
        "parent_symmetrization_rmsd_A": 0.06397566853227664,
        "parent_cell_rmsd_A": 0.07353249838658965,
        "energy_eV": -263.58400213133166,
        "reduced_polarization": [
          -0.4999912971085546,
          2.830335016624937e-15,
          -7.103047539401595e-06
        ],
        "cartesian_polarization_e_A2": [
          -0.007383064827441009,
          6.553870133538436e-17,
          -0.00010572288286350254
        ],
        "ranking_score": 0.5823812603142269
      },
      "branch_status": "awaiting_branch_sampling"
    },
    {
      "orbit_id": 4,
      "formal_class": [
        0.0,
        0.5,
        0.5
      ],
      "formal_classes_in_orbit": [
        [
          0.0,
          0.5,
          0.5
        ]
      ],
      "target_reduced_polarization": [
        0.0,
        0.5,
        -0.5
      ],
      "bec_backprojection": {
        "converged_to_target": true,
        "history": [
          {
            "iteration": 0,
            "reduced_polarization": [
              -6.146603563560365e-16,
              2.2168149316747226e-15,
              -0.06285135839679987
            ],
            "branch_aligned_reduced_polarization": [
              -6.146603563560365e-16,
              2.220446049250313e-15,
              -0.0628513583967999
            ],
            "target_residual": 0.6641527948111947,
            "energy_eV": -264.87898292551245,
            "max_atomic_step_A": 0.09798789396666632,
            "max_log_strain_component": 0.02,
            "step_scale": 0.9613128511433996,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 4.757113643124521,
            "cell_principal_stretches": [
              1.0191032037605159,
              1.0023142425846105,
              0.9787684545863146
            ],
            "cell_volume_ratio": 0.9997744462594691,
            "cell_rmsd_from_input_A": 0.1395549504220237
          },
          {
            "iteration": 1,
            "reduced_polarization": [
              2.3728413870456795e-14,
              0.4722943195277754,
              -0.43147645889900654
            ],
            "branch_aligned_reduced_polarization": [
              2.3728413870456795e-14,
              0.4722943195277754,
              -0.43147645889900654
            ],
            "target_residual": 0.07391265396025601,
            "energy_eV": -262.2471506225636,
            "max_atomic_step_A": 0.0068227506170593505,
            "max_log_strain_component": 0.0012680118249188382,
            "step_scale": 1.0,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 4.757113643124521,
            "cell_principal_stretches": [
              1.0202197267369486,
              1.002741463041959,
              0.9772401049191289
            ],
            "cell_volume_ratio": 0.9997328704431401,
            "cell_rmsd_from_input_A": 0.14890374412817195
          },
          {
            "iteration": 2,
            "reduced_polarization": [
              1.9254879420864346e-15,
              0.4995169350970845,
              -0.49906055820404827
            ],
            "branch_aligned_reduced_polarization": [
              1.9254879420864346e-15,
              0.4995169350970845,
              -0.49906055820404827
            ],
            "target_residual": 0.001056362905638862,
            "energy_eV": -261.9113023395188,
            "max_atomic_step_A": 0.00011008541324329784,
            "max_log_strain_component": 2.2024600912142807e-05,
            "step_scale": 1.0,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 4.757113643124521,
            "cell_principal_stretches": [
              1.020239664785242,
              1.0027475651072908,
              0.9772144801413044
            ],
            "cell_volume_ratio": 0.9997322767492434,
            "cell_rmsd_from_input_A": 0.1490641896917923
          },
          {
            "iteration": 3,
            "reduced_polarization": [
              1.0382856707607567e-15,
              0.49999321221239856,
              -0.49998797366259085
            ],
            "branch_aligned_reduced_polarization": [
              1.0382856707607567e-15,
              0.49999321221239856,
              -0.49998797366259085
            ],
            "target_residual": 1.380966516614524e-05,
            "energy_eV": -261.9053069183156
          }
        ],
        "iterations": 3
      },
      "parent": {
        "candidate_id": "bec_projection_04",
        "source": "MACEField_BEC_backprojection",
        "spacegroup": "Cm",
        "spacegroup_number": 8,
        "pointgroup": "m",
        "has_inversion": false,
        "is_polar_point_group": true,
        "nonpolar_parent_hypothesis": false,
        "symmetry_tolerance_A": null,
        "target_reduced_polarization": [
          0.0,
          0.5,
          -0.5
        ],
        "formal_class": [
          0.0,
          0.5,
          0.5
        ],
        "target_residual": 1.380966516614524e-05,
        "parent_symmetrization_rmsd_A": 0.09496702214997342,
        "parent_cell_rmsd_A": 0.1490641896917923,
        "energy_eV": -261.9053069183156,
        "reduced_polarization": [
          1.0382856707607567e-15,
          0.49999321221239856,
          -0.49998797366259085
        ],
        "cartesian_polarization_e_A2": [
          -2.0483904102921846e-16,
          0.010007567135617042,
          -0.004781346507603552
        ],
        "ranking_score": 0.6322606889032538
      },
      "branch_status": "awaiting_branch_sampling"
    },
    {
      "orbit_id": 5,
      "formal_class": [
        0.5,
        0.0,
        0.5
      ],
      "formal_classes_in_orbit": [
        [
          0.5,
          0.0,
          0.5
        ]
      ],
      "target_reduced_polarization": [
        -0.5,
        0.0,
        -0.5
      ],
      "bec_backprojection": {
        "converged_to_target": true,
        "history": [
          {
            "iteration": 0,
            "reduced_polarization": [
              -6.146603563560365e-16,
              2.2168149316747226e-15,
              -0.06285135839679987
            ],
            "branch_aligned_reduced_polarization": [
              -6.106226635438361e-16,
              2.2168149316747226e-15,
              -0.0628513583967999
            ],
            "target_residual": 0.6641527948111959,
            "energy_eV": -264.87898292551245,
            "max_atomic_step_A": 0.0681831073955692,
            "max_log_strain_component": 0.014303932244807267,
            "step_scale": 1.0,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 4.757113643124521,
            "cell_principal_stretches": [
              1.0138754024019085,
              1.0015683147845293,
              0.9845390036389895
            ],
            "cell_volume_ratio": 0.9997653701222131,
            "cell_rmsd_from_input_A": 0.07721199008642168
          },
          {
            "iteration": 1,
            "reduced_polarization": [
              -0.48996018376084555,
              -1.521553562912354e-14,
              -0.4742486001992249
            ],
            "branch_aligned_reduced_polarization": [
              -0.48996018376084555,
              -1.521553562912354e-14,
              -0.4742486001992249
            ],
            "target_residual": 0.027639328895893083,
            "energy_eV": -263.5570749997464,
            "max_atomic_step_A": 0.0020019788765572068,
            "max_log_strain_component": 0.00032027042962458704,
            "step_scale": 1.0,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 4.757113643124521,
            "cell_principal_stretches": [
              1.0141823597969435,
              1.0016676554669104,
              0.9841287900916068
            ],
            "cell_volume_ratio": 0.9997505223514206,
            "cell_rmsd_from_input_A": 0.07924541370472495
          },
          {
            "iteration": 2,
            "reduced_polarization": [
              -0.49987052904581813,
              1.2780724560643158e-15,
              -0.49975638237128917
            ],
            "branch_aligned_reduced_polarization": [
              -0.49987052904581813,
              1.2780724560643158e-15,
              -0.49975638237128917
            ],
            "target_residual": 0.0002758845356221563,
            "energy_eV": -263.4896228150784
          }
        ],
        "iterations": 2
      },
      "parent": {
        "candidate_id": "bec_projection_05",
        "source": "MACEField_BEC_backprojection",
        "spacegroup": "Cc",
        "spacegroup_number": 9,
        "pointgroup": "m",
        "has_inversion": false,
        "is_polar_point_group": true,
        "nonpolar_parent_hypothesis": false,
        "symmetry_tolerance_A": null,
        "target_reduced_polarization": [
          -0.5,
          0.0,
          -0.5
        ],
        "formal_class": [
          0.5,
          0.0,
          0.5
        ],
        "target_residual": 0.0002758845356221563,
        "parent_symmetrization_rmsd_A": 0.06914566652827771,
        "parent_cell_rmsd_A": 0.07924541370472495,
        "energy_eV": -263.4896228150784,
        "reduced_polarization": [
          -0.49987052904581813,
          1.2780724560643158e-15,
          -0.49975638237128917
        ],
        "cartesian_polarization_e_A2": [
          -0.007470875112896072,
          3.5619601428994904e-17,
          -0.0046777758542269135
        ],
        "ranking_score": 0.5895087890257033
      },
      "branch_status": "awaiting_branch_sampling"
    },
    {
      "orbit_id": 6,
      "formal_class": [
        0.5,
        0.5,
        0.0
      ],
      "formal_classes_in_orbit": [
        [
          0.5,
          0.5,
          0.0
        ]
      ],
      "target_reduced_polarization": [
        -0.5,
        0.5,
        0.0
      ],
      "bec_backprojection": {
        "converged_to_target": true,
        "history": [
          {
            "iteration": 0,
            "reduced_polarization": [
              -6.146603563560365e-16,
              2.2168149316747226e-15,
              -0.06285135839679987
            ],
            "branch_aligned_reduced_polarization": [
              -6.106226635438361e-16,
              2.220446049250313e-15,
              -0.06285135839679987
            ],
            "target_residual": 0.7098945648843356,
            "energy_eV": -264.87898292551245,
            "max_atomic_step_A": 0.11110826727094959,
            "max_log_strain_component": 0.02,
            "step_scale": 0.9613128511434715,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 4.757113643124521,
            "cell_principal_stretches": [
              1.0247394511342014,
              0.9997048546386559,
              0.9761775779199776
            ],
            "cell_volume_ratio": 1.0000324333340112,
            "cell_rmsd_from_input_A": 0.15476780792023667
          },
          {
            "iteration": 1,
            "reduced_polarization": [
              -0.4854315863773345,
              0.4765662876893062,
              0.06648993877500928
            ],
            "branch_aligned_reduced_polarization": [
              -0.4854315863773345,
              0.4765662876893062,
              0.06648993877500928
            ],
            "target_residual": 0.0719881205925388,
            "energy_eV": -260.73190756928767,
            "max_atomic_step_A": 0.006391319502861406,
            "max_log_strain_component": 0.001055986166741383,
            "step_scale": 1.0,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 4.757113643124521,
            "cell_principal_stretches": [
              1.0256917987235317,
              1.0000811762629223,
              0.9748639309762253
            ],
            "cell_volume_ratio": 0.999991107825794,
            "cell_rmsd_from_input_A": 0.1623559578947082
          },
          {
            "iteration": 2,
            "reduced_polarization": [
              -0.49997116956649673,
              0.49964219528928566,
              0.0008439317561084693
            ],
            "branch_aligned_reduced_polarization": [
              -0.49997116956649673,
              0.49964219528928566,
              0.0008439317561084693
            ],
            "target_residual": 0.0009171020738574753,
            "energy_eV": -260.4254998842241
          }
        ],
        "iterations": 2
      },
      "parent": {
        "candidate_id": "bec_projection_06",
        "source": "MACEField_BEC_backprojection",
        "spacegroup": "P1",
        "spacegroup_number": 1,
        "pointgroup": "1",
        "has_inversion": false,
        "is_polar_point_group": true,
        "nonpolar_parent_hypothesis": false,
        "symmetry_tolerance_A": null,
        "target_reduced_polarization": [
          -0.5,
          0.5,
          0.0
        ],
        "formal_class": [
          0.5,
          0.5,
          0.0
        ],
        "target_residual": 0.0009171020738574753,
        "parent_symmetrization_rmsd_A": 0.11120863764920648,
        "parent_cell_rmsd_A": 0.1623559578947082,
        "energy_eV": -260.4254998842241,
        "reduced_polarization": [
          -0.49997116956649673,
          0.49964219528928566,
          0.0008439317561084693
        ],
        "cartesian_polarization_e_A2": [
          -0.007386586797569154,
          0.009884205943378875,
          -0.0003051997227443402
        ],
        "ranking_score": 0.6536318312705984
      },
      "branch_status": "awaiting_branch_sampling"
    },
    {
      "orbit_id": 7,
      "formal_class": [
        0.5,
        0.5,
        0.5
      ],
      "formal_classes_in_orbit": [
        [
          0.5,
          0.5,
          0.5
        ]
      ],
      "target_reduced_polarization": [
        -0.5,
        0.5,
        -0.5
      ],
      "bec_backprojection": {
        "converged_to_target": true,
        "history": [
          {
            "iteration": 0,
            "reduced_polarization": [
              -6.146603563560365e-16,
              2.2168149316747226e-15,
              -0.06285135839679987
            ],
            "branch_aligned_reduced_polarization": [
              -6.106226635438361e-16,
              2.220446049250313e-15,
              -0.0628513583967999
            ],
            "target_residual": 0.8313236041732006,
            "energy_eV": -264.87898292551245,
            "max_atomic_step_A": 0.11542632632391649,
            "max_log_strain_component": 0.02,
            "step_scale": 0.9613128511434746,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 4.757113643124521,
            "cell_principal_stretches": [
              1.0235821832080552,
              1.002053791130185,
              0.9747388565379571
            ],
            "cell_volume_ratio": 0.9997744462594562,
            "cell_rmsd_from_input_A": 0.15648173282581643
          },
          {
            "iteration": 1,
            "reduced_polarization": [
              -0.4745703903605632,
              0.4710212175917823,
              -0.4045837831605786
            ],
            "branch_aligned_reduced_polarization": [
              -0.4745703903605632,
              0.4710212175917823,
              -0.4045837831605786
            ],
            "target_residual": 0.10291107477926976,
            "energy_eV": -261.0632434805435,
            "max_atomic_step_A": 0.008783678933929211,
            "max_log_strain_component": 0.0013698365835512225,
            "step_scale": 1.0,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 4.757113643124521,
            "cell_principal_stretches": [
              1.025008503097636,
              1.0026036798943603,
              0.9727901736478745
            ],
            "cell_volume_ratio": 0.9997143763278066,
            "cell_rmsd_from_input_A": 0.16773810757194815
          },
          {
            "iteration": 2,
            "reduced_polarization": [
              -0.49957062262321056,
              0.499268116447336,
              -0.49803549106305106
            ],
            "branch_aligned_reduced_polarization": [
              -0.49957062262321056,
              0.499268116447336,
              -0.49803549106305106
            ],
            "target_residual": 0.0021399331367383725,
            "energy_eV": -260.5800327883401,
            "max_atomic_step_A": 0.00019426292574962377,
            "max_log_strain_component": 3.4640180704649276e-05,
            "step_scale": 1.0,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 4.757113643124521,
            "cell_principal_stretches": [
              1.0250417882008842,
              1.0026155788562292,
              0.9727457987886685
            ],
            "cell_volume_ratio": 0.9997131000540677,
            "cell_rmsd_from_input_A": 0.1680052919809488
          },
          {
            "iteration": 3,
            "reduced_polarization": [
              -0.49999327225944556,
              0.49998626527644857,
              -0.4999654327840593
            ],
            "branch_aligned_reduced_polarization": [
              -0.49999327225944556,
              0.49998626527644857,
              -0.4999654327840593
            ],
            "target_residual": 3.779943838065062e-05,
            "energy_eV": -260.5684836961411
          }
        ],
        "iterations": 3
      },
      "parent": {
        "candidate_id": "bec_projection_07",
        "source": "MACEField_BEC_backprojection",
        "spacegroup": "P1",
        "spacegroup_number": 1,
        "pointgroup": "1",
        "has_inversion": false,
        "is_polar_point_group": true,
        "nonpolar_parent_hypothesis": false,
        "symmetry_tolerance_A": null,
        "target_reduced_polarization": [
          -0.5,
          0.5,
          -0.5
        ],
        "formal_class": [
          0.5,
          0.5,
          0.5
        ],
        "target_residual": 3.779943838065062e-05,
        "parent_symmetrization_rmsd_A": 0.11529609763446352,
        "parent_cell_rmsd_A": 0.1680052919809488,
        "energy_eV": -260.5684836961411,
        "reduced_polarization": [
          -0.49999327225944556,
          0.49998626527644857,
          -0.4999654327840593
        ],
        "cartesian_polarization_e_A2": [
          -0.007477351864598008,
          0.010010611684569662,
          -0.004888985122673626
        ],
        "ranking_score": 0.657373019506462
      },
      "branch_status": "awaiting_branch_sampling"
    }
  ],
  "sampled_polarization_branches": [
    {
      "orbit_id": 0,
      "candidate_id": "bec_projection_00",
      "formal_class": [
        0.0,
        0.0,
        0.0
      ],
      "construction": "MACEField-BEC-parent plus variable-cell P-N-P path and symmetric log-strain continuation beyond both polar endpoints",
      "geometry_diagnostics": {
        "collision_aware": false,
        "permutations_tested": 1,
        "selected_order": [
          0,
          1,
          2,
          3,
          4,
          5,
          6,
          7,
          8,
          9,
          10,
          11,
          12,
          13,
          14,
          15,
          16,
          17,
          18,
          19,
          20,
          21,
          22,
          23,
          24,
          25,
          26,
          27,
          28,
          29,
          30,
          31,
          32,
          33,
          34,
          35,
          36,
          37,
          38,
          39
        ],
        "endpoint_rmsd_A": 0.0033843440932180766,
        "minimum_distance_A_by_image": [
          1.7439499024810166,
          1.743619710551888,
          1.743289608618561,
          1.7429595968041354,
          1.7426296752318118,
          1.742299844024899,
          1.741970103306803,
          1.741640453201041,
          1.7413108938312285
        ],
        "minimum_distance_A": 1.7413108938312285,
        "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": [
          610.6727543284824,
          610.6753296963733,
          610.6779050751242,
          610.6804804647377,
          610.6830558652107,
          610.6856312765453,
          610.6882066987423,
          610.6907821317994,
          610.6933575757167
        ],
        "cell_deformation_log_strain_norm": 0.0007321436067070611
      },
      "parent_reduced_polarization": [
        -2.2664062990276374e-15,
        -6.436981470369035e-16,
        -3.1552629534316074e-05
      ],
      "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": [
          -264.87898292551245,
          -264.8784444504346,
          -264.87778449969284,
          -264.87700343403026,
          -264.87610161184716,
          -264.87507938920606,
          -264.8739371198351,
          -264.8726751551329,
          -264.8712938441723
        ],
        "cartesian_polarizations_e_A2": [
          [
            -3.908464643322472e-17,
            2.204364625433915e-17,
            -0.0005770996052797927
          ],
          [
            4.070956218176675e-17,
            6.415355767022546e-17,
            -0.0005050359327014456
          ],
          [
            -1.815394895564945e-17,
            1.1226257115388798e-17,
            -0.0004329611031765768
          ],
          [
            -5.46768160394049e-17,
            -5.6517375914437e-17,
            -0.00036087533179317
          ],
          [
            -1.1589510120144676e-17,
            4.742712750376593e-17,
            -0.0002887788337218982
          ],
          [
            -2.7888865589907063e-17,
            2.5656445202863033e-17,
            -0.00021667182421715507
          ],
          [
            -4.871781086687417e-17,
            2.779247135081778e-17,
            -0.00014455451861919967
          ],
          [
            -5.548759833800211e-17,
            -2.0520438095873976e-17,
            -7.242713235539482e-05
          ],
          [
            -3.345826231989606e-17,
            -1.2725799414663742e-17,
            -2.8988094133330177e-07
          ]
        ],
        "raw_reduced_polarization": [
          [
            -2.646512032344163e-15,
            1.1147280890225406e-15,
            -0.06285135839680092
          ],
          [
            2.7545046302146897e-15,
            3.242816179846192e-15,
            -0.054999047783315665
          ],
          [
            -1.2330745501934647e-15,
            5.652035841236161e-16,
            -0.047146642869883154
          ],
          [
            -3.707461700729306e-15,
            -2.8614820625093986e-15,
            -0.039294167216694105
          ],
          [
            -7.898530317017184e-16,
            2.395277547985444e-15,
            -0.03144164438622955
          ],
          [
            -1.8935115469671233e-15,
            1.2944625665070573e-15,
            -0.02358909794337192
          ],
          [
            -3.3034526881445e-15,
            1.4031750835757402e-15,
            -0.015736551455636006
          ],
          [
            -3.7606148265924925e-15,
            -1.039420248378414e-15,
            -0.007884028493301644
          ],
          [
            -2.2664062990276374e-15,
            -6.436981470369035e-16,
            -3.1552629534316074e-05
          ]
        ],
        "unwrapped_reduced_polarization": [
          [
            -2.646512032344163e-15,
            1.1147280890225406e-15,
            -0.06285135839680092
          ],
          [
            2.7545046302146897e-15,
            3.242816179846192e-15,
            -0.054999047783315665
          ],
          [
            -1.2330745501934647e-15,
            5.652035841236161e-16,
            -0.047146642869883154
          ],
          [
            -3.707461700729306e-15,
            -2.8614820625093986e-15,
            -0.039294167216694105
          ],
          [
            -7.898530317017184e-16,
            2.3952775479854435e-15,
            -0.03144164438622955
          ],
          [
            -1.8935115469671233e-15,
            1.2944625665070573e-15,
            -0.02358909794337192
          ],
          [
            -3.3034526881445e-15,
            1.4031750835757402e-15,
            -0.015736551455636006
          ],
          [
            -3.7606148265924925e-15,
            -1.0394202483784142e-15,
            -0.007884028493301644
          ],
          [
            -2.2664062990276374e-15,
            -6.436981470369035e-16,
            -3.1552629534315965e-05
          ]
        ],
        "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": [
          [
            -2.6645352591003757e-15,
            1.1102230246251565e-15,
            -0.0628513583968009
          ],
          [
            2.7755575615628914e-15,
            3.219646771412954e-15,
            -0.05499904778331566
          ],
          [
            -1.2212453270876722e-15,
            5.551115123125783e-16,
            -0.047146642869883126
          ],
          [
            -3.7192471324942744e-15,
            -2.886579864025407e-15,
            -0.0392941672166941
          ],
          [
            -7.771561172376096e-16,
            2.4424906541753444e-15,
            -0.03144164438622954
          ],
          [
            -1.887379141862766e-15,
            1.3322676295501878e-15,
            -0.02358909794337194
          ],
          [
            -3.3306690738754696e-15,
            1.4432899320127035e-15,
            -0.015736551455636016
          ],
          [
            -3.774758283725532e-15,
            -1.0547118733938987e-15,
            -0.007884028493301665
          ],
          [
            -2.275957200481571e-15,
            -6.661338147750939e-16,
            -3.155262953430382e-05
          ]
        ]
      },
      "reflected": {
        "reached": true,
        "construction": "reflect_displacements_about_reconstructed_parent",
        "energies_eV": [
          -264.8712938441722,
          -264.8705268426911,
          -264.8696752805794,
          -264.86873933285,
          -264.8677191734919,
          -264.86661497547516,
          -264.8654269107552,
          -264.8641551502782,
          -264.8627998639847
        ],
        "cartesian_polarizations_e_A2": [
          [
            5.962267995559273e-20,
            -1.0794204860652281e-17,
            -2.89880941300851e-07
          ],
          [
            -1.4787659714138142e-17,
            9.337594699440328e-17,
            6.536529379382145e-05
          ],
          [
            -3.7219727515963085e-17,
            -4.544966696781322e-19,
            0.00013100552014508912
          ],
          [
            -8.868807525089152e-17,
            2.199773158225989e-17,
            0.00019663065407364412
          ],
          [
            -5.754962248588348e-17,
            4.990415524593674e-17,
            0.000262240551615786
          ],
          [
            -1.2412211140351716e-16,
            3.62465679869429e-17,
            0.00032783506888255294
          ],
          [
            -8.240326162874004e-17,
            -6.153988718314346e-17,
            0.0003934140620585617
          ],
          [
            -1.1035525691196487e-16,
            2.597503238294995e-17,
            0.00045897738740239733
          ],
          [
            -1.6041140123757891e-16,
            3.381540786232645e-17,
            0.0005245249012456144
          ]
        ],
        "raw_reduced_polarization": [
          [
            4.028786503597091e-18,
            -5.459937775315824e-16,
            -3.155262953078391e-05
          ],
          [
            -9.99677946758974e-16,
            4.724350669836735e-15,
            0.007115314689179953
          ],
          [
            -2.5175820637932816e-15,
            -2.068677338923766e-17,
            0.014261574999024187
          ],
          [
            -6.002485265575e-15,
            1.1154646831924056e-15,
            0.02140721237923298
          ],
          [
            -3.8930613008469644e-15,
            2.527007841559134e-15,
            0.028552210912703664
          ],
          [
            -8.401576044735079e-15,
            1.8360150843214896e-15,
            0.03569655468595616
          ],
          [
            -5.576872349174031e-15,
            -3.109916611138558e-15,
            0.04284022778900872
          ],
          [
            -7.470797235245136e-15,
            1.314921248734034e-15,
            0.049983214315422866
          ],
          [
            -1.0861827910500395e-14,
            1.7100158726448872e-15,
            0.057125498362195944
          ]
        ],
        "unwrapped_reduced_polarization": [
          [
            4.028786503597091e-18,
            -5.459937775315824e-16,
            -3.155262953078391e-05
          ],
          [
            -9.99677946758974e-16,
            4.724350669836735e-15,
            0.007115314689179953
          ],
          [
            -2.5175820637932816e-15,
            -2.068677338923728e-17,
            0.014261574999024187
          ],
          [
            -6.002485265575e-15,
            1.1154646831924056e-15,
            0.02140721237923298
          ],
          [
            -3.8930613008469644e-15,
            2.527007841559134e-15,
            0.028552210912703664
          ],
          [
            -8.401576044735079e-15,
            1.8360150843214896e-15,
            0.03569655468595616
          ],
          [
            -5.576872349174031e-15,
            -3.1099166111385583e-15,
            0.04284022778900872
          ],
          [
            -7.470797235245136e-15,
            1.3149212487340343e-15,
            0.049983214315422866
          ],
          [
            -1.0861827910500395e-14,
            1.7100158726448872e-15,
            0.057125498362195944
          ]
        ],
        "gauge_integer_shift": [
          0,
          0,
          0
        ],
        "expected_opposite_endpoint_reduced_polarization": [
          -1.8845610048503312e-15,
          -2.4017933865796448e-15,
          0.06278821709235555
        ],
        "actual_opposite_endpoint_branch_residual": 0.0056627187301596035
      },
      "pnp_branch": {
        "construction": "incoming_path_concatenated_with_parent_reflection",
        "reduced_polarization": [
          [
            -2.646512032344163e-15,
            1.1147280890225406e-15,
            -0.06285135839680092
          ],
          [
            2.7545046302146897e-15,
            3.242816179846192e-15,
            -0.054999047783315665
          ],
          [
            -1.2330745501934647e-15,
            5.652035841236161e-16,
            -0.047146642869883154
          ],
          [
            -3.707461700729306e-15,
            -2.8614820625093986e-15,
            -0.039294167216694105
          ],
          [
            -7.898530317017184e-16,
            2.395277547985444e-15,
            -0.03144164438622955
          ],
          [
            -1.8935115469671233e-15,
            1.2944625665070573e-15,
            -0.02358909794337192
          ],
          [
            -3.3034526881445e-15,
            1.4031750835757402e-15,
            -0.015736551455636006
          ],
          [
            -3.7606148265924925e-15,
            -1.039420248378414e-15,
            -0.007884028493301644
          ],
          [
            -2.2664062990276374e-15,
            -6.436981470369035e-16,
            -3.1552629534316074e-05
          ],
          [
            -9.99677946758974e-16,
            4.724350669836735e-15,
            0.007115314689179953
          ],
          [
            -2.5175820637932816e-15,
            -2.068677338923766e-17,
            0.014261574999024187
          ],
          [
            -6.002485265575e-15,
            1.1154646831924056e-15,
            0.02140721237923298
          ],
          [
            -3.8930613008469644e-15,
            2.527007841559134e-15,
            0.028552210912703664
          ],
          [
            -8.401576044735079e-15,
            1.8360150843214896e-15,
            0.03569655468595616
          ],
          [
            -5.576872349174031e-15,
            -3.109916611138558e-15,
            0.04284022778900872
          ],
          [
            -7.470797235245136e-15,
            1.314921248734034e-15,
            0.049983214315422866
          ],
          [
            -1.0861827910500395e-14,
            1.7100158726448872e-15,
            0.057125498362195944
          ]
        ],
        "unwrapped_reduced_polarization": [
          [
            -2.646512032344163e-15,
            1.1147280890225406e-15,
            -0.06285135839680092
          ],
          [
            2.7545046302146897e-15,
            3.242816179846192e-15,
            -0.054999047783315665
          ],
          [
            -1.2330745501934647e-15,
            5.652035841236161e-16,
            -0.047146642869883154
          ],
          [
            -3.707461700729306e-15,
            -2.8614820625093986e-15,
            -0.039294167216694105
          ],
          [
            -7.898530317017184e-16,
            2.3952775479854435e-15,
            -0.03144164438622955
          ],
          [
            -1.8935115469671233e-15,
            1.2944625665070573e-15,
            -0.02358909794337192
          ],
          [
            -3.3034526881445e-15,
            1.4031750835757402e-15,
            -0.015736551455636006
          ],
          [
            -3.7606148265924925e-15,
            -1.0394202483784142e-15,
            -0.007884028493301644
          ],
          [
            -2.2664062990276374e-15,
            -6.436981470369035e-16,
            -3.1552629534315965e-05
          ],
          [
            -9.99677946758974e-16,
            4.724350669836735e-15,
            0.007115314689179953
          ],
          [
            -2.5175820637932816e-15,
            -2.068677338923728e-17,
            0.014261574999024187
          ],
          [
            -6.002485265575e-15,
            1.1154646831924056e-15,
            0.02140721237923298
          ],
          [
            -3.8930613008469644e-15,
            2.527007841559134e-15,
            0.028552210912703664
          ],
          [
            -8.401576044735079e-15,
            1.8360150843214896e-15,
            0.03569655468595616
          ],
          [
            -5.576872349174031e-15,
            -3.1099166111385583e-15,
            0.04284022778900872
          ],
          [
            -7.470797235245136e-15,
            1.3149212487340343e-15,
            0.049983214315422866
          ],
          [
            -1.0861827910500395e-14,
            1.7100158726448872e-15,
            0.057125498362195944
          ]
        ],
        "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": [
          [
            -2.6645352591003757e-15,
            1.1102230246251565e-15,
            -0.0628513583968009
          ],
          [
            2.7755575615628914e-15,
            3.219646771412954e-15,
            -0.05499904778331566
          ],
          [
            -1.2212453270876722e-15,
            5.551115123125783e-16,
            -0.047146642869883126
          ],
          [
            -3.7192471324942744e-15,
            -2.886579864025407e-15,
            -0.0392941672166941
          ],
          [
            -7.771561172376096e-16,
            2.4424906541753444e-15,
            -0.03144164438622954
          ],
          [
            -1.887379141862766e-15,
            1.3322676295501878e-15,
            -0.02358909794337194
          ],
          [
            -3.3306690738754696e-15,
            1.4432899320127035e-15,
            -0.015736551455636016
          ],
          [
            -3.774758283725532e-15,
            -1.0547118733938987e-15,
            -0.007884028493301665
          ],
          [
            -2.275957200481571e-15,
            -6.661338147750939e-16,
            -3.155262953430382e-05
          ],
          [
            -9.992007221626409e-16,
            4.773959005888173e-15,
            0.007115314689179919
          ],
          [
            -2.4980018054066022e-15,
            0.0,
            0.01426157499902414
          ],
          [
            -5.995204332975845e-15,
            1.1102230246251565e-15,
            0.02140721237923293
          ],
          [
            -3.885780586188048e-15,
            2.55351295663786e-15,
            0.028552210912703657
          ],
          [
            -8.382183835919932e-15,
            1.887379141862766e-15,
            0.03569655468595612
          ],
          [
            -5.551115123125783e-15,
            -3.1086244689504383e-15,
            0.042840227789008756
          ],
          [
            -7.494005416219807e-15,
            1.3322676295501878e-15,
            0.04998321431542285
          ],
          [
            -1.0880185641326534e-14,
            1.6653345369377348e-15,
            0.05712549836219594
          ]
        ]
      },
      "incoming_structure_ids": [
        "incoming_00_000",
        "incoming_00_001",
        "incoming_00_002",
        "incoming_00_003",
        "incoming_00_004",
        "incoming_00_005",
        "incoming_00_006",
        "incoming_00_007",
        "incoming_00_008"
      ],
      "reflected_structure_ids": [
        "reflected_00_001",
        "reflected_00_002",
        "reflected_00_003",
        "reflected_00_004",
        "reflected_00_005",
        "reflected_00_006",
        "reflected_00_007",
        "reflected_00_008"
      ],
      "positive_extension_structure_ids": [
        "extension_plus_00_000",
        "extension_plus_00_001",
        "extension_plus_00_002",
        "extension_plus_00_003"
      ],
      "negative_extension_structure_ids": [
        "extension_minus_00_000",
        "extension_minus_00_001",
        "extension_minus_00_002",
        "extension_minus_00_003"
      ],
      "extension": {
        "enabled": true,
        "fraction_beyond_polar_endpoint": 0.35,
        "images_per_side": 4,
        "construction": "continue fractional atomic displacements and symmetric log strain beyond +P; reflect these structures about N for the -P side",
        "positive_path_coordinates": [
          1.35,
          1.2625,
          1.175,
          1.0875
        ],
        "negative_path_coordinates": [
          -1.0875,
          -1.175,
          -1.2625,
          -1.35
        ]
      },
      "branch_coordinates": [
        1.35,
        1.2625,
        1.175,
        1.0875,
        1.0,
        0.875,
        0.75,
        0.625,
        0.5,
        0.375,
        0.25,
        0.125,
        0.0,
        -0.125,
        -0.25,
        -0.375,
        -0.5,
        -0.625,
        -0.75,
        -0.875,
        -1.0,
        -1.0875,
        -1.175,
        -1.2625,
        -1.35
      ],
      "parent": {
        "candidate_id": "bec_projection_00",
        "source": "MACEField_BEC_backprojection",
        "spacegroup": "Cmc2_1",
        "spacegroup_number": 36,
        "pointgroup": "mm2",
        "has_inversion": false,
        "is_polar_point_group": true,
        "nonpolar_parent_hypothesis": false,
        "symmetry_tolerance_A": null,
        "target_reduced_polarization": [
          0.0,
          0.0,
          0.0
        ],
        "formal_class": [
          0.0,
          0.0,
          0.0
        ],
        "target_residual": 3.1552629530160584e-05,
        "parent_symmetrization_rmsd_A": 0.0033843440932180766,
        "parent_cell_rmsd_A": 0.0033917333233062425,
        "energy_eV": -264.8712938441722,
        "reduced_polarization": [
          6.390590801724028e-16,
          -2.7874469603007214e-15,
          -3.1552629530160584e-05
        ],
        "cartesian_polarization_e_A2": [
          9.434421585352544e-18,
          -5.5107256393856383e-17,
          -2.8988094129512436e-07
        ],
        "ranking_score": 0.5042953826831049
      }
    }
  ],
  "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": 52,
      "full_response": 17,
      "energy_polarization": 35
    },
    "model_evaluations_for_recovery_and_path_properties": {
      "total": 77,
      "full_response": 42,
      "energy_polarization": 35
    },
    "elapsed_seconds": 757.2537171220174
  }
}