{
  "schema": "ferrofinder.endpoint_parent_recovery.v4_variable_cell",
  "status": "complete",
  "input_atom_count": 78,
  "input_formula": "O46Rb12Si20",
  "input_spacegroup": "Amm2",
  "input_pointgroup": "mm2",
  "input_is_polar_point_group": true,
  "input_energy_eV": -529.6479508691879,
  "input_cartesian_polarization_e_A2": [
    -1.5834675323741861e-18,
    1.5450808739199045e-17,
    -0.00034465373492842904
  ],
  "input_reduced_polarization": [
    -2.50914172949723e-16,
    1.2089112971791434e-15,
    -0.04746602989823206
  ],
  "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": "P2/c",
      "spacegroup_number": 13,
      "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": 0.001041104640150574,
      "parent_symmetrization_rmsd_A": 0.8224487465823755,
      "parent_cell_rmsd_A": 0.0,
      "energy_eV": "Infinity",
      "reduced_polarization": [
        -4.940801796878139e-05,
        -1.0478527379522925e-07,
        -0.001039931588386226
      ],
      "cartesian_polarization_e_A2": [
        -3.1180379877625433e-07,
        -1.339235746967114e-09,
        -7.551006620436066e-06
      ],
      "ranking_score": 0.8245309558626767
    },
    {
      "candidate_id": "inversion_parent_endpoint_01",
      "source": "same_species_inversion_center_projection_from_endpoint",
      "spacegroup": "P2/c",
      "spacegroup_number": 13,
      "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": 0.0010411046401490006,
      "parent_symmetrization_rmsd_A": 0.8224487465823755,
      "parent_cell_rmsd_A": 0.0,
      "energy_eV": "Infinity",
      "reduced_polarization": [
        4.940801797414224e-05,
        -1.0478527336437276e-07,
        -0.0010399315883843963
      ],
      "cartesian_polarization_e_A2": [
        3.1180379881008557e-07,
        -1.3392357414604393e-09,
        -7.5510066204227805e-06
      ],
      "ranking_score": 0.8245309558626736
    },
    {
      "candidate_id": "inversion_parent_endpoint_02",
      "source": "same_species_inversion_center_projection_from_endpoint",
      "spacegroup": "P2/c",
      "spacegroup_number": 13,
      "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": 0.0010411046401481352,
      "parent_symmetrization_rmsd_A": 0.8224487465823755,
      "parent_cell_rmsd_A": 0.0,
      "energy_eV": "Infinity",
      "reduced_polarization": [
        -4.9408017970706614e-05,
        1.0478527699653036e-07,
        -0.0010399315883836927
      ],
      "cartesian_polarization_e_A2": [
        -3.11803798788404e-07,
        1.3392357878821847e-09,
        -7.551006620417672e-06
      ],
      "ranking_score": 0.8245309558626718
    },
    {
      "candidate_id": "bec_projection_00",
      "source": "MACEField_BEC_backprojection",
      "spacegroup": "Amm2",
      "spacegroup_number": 38,
      "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": 8.421830975318233e-05,
      "parent_symmetrization_rmsd_A": 0.002244091552626341,
      "parent_cell_rmsd_A": 0.009442999532165045,
      "energy_eV": -529.6367861960671,
      "reduced_polarization": [
        -6.763800754755188e-16,
        -7.351808879398566e-16,
        -8.421830975318233e-05
      ],
      "cartesian_polarization_e_A2": [
        -4.267575054384137e-18,
        -9.391054823641054e-18,
        -6.120416955041238e-07
      ],
      "ranking_score": 0.5047732780551739
    },
    {
      "candidate_id": "inversion_parent_bec_00_00",
      "source": "same_species_inversion_center_projection_after_BEC",
      "spacegroup": "P2/c",
      "spacegroup_number": 13,
      "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": 6.643673280290622e-05,
      "parent_symmetrization_rmsd_A": 0.8224487632311319,
      "parent_cell_rmsd_A": 0.009442999532165045,
      "energy_eV": "Infinity",
      "reduced_polarization": [
        -2.185407461615571e-06,
        1.2235563721712787e-05,
        -6.526372989772631e-05
      ],
      "cartesian_polarization_e_A2": [
        -1.3787113051538159e-08,
        1.562944568652721e-07,
        -4.7429263325981477e-07
      ],
      "ranking_score": 0.824942386579779
    },
    {
      "candidate_id": "inversion_parent_bec_00_01",
      "source": "same_species_inversion_center_projection_after_BEC",
      "spacegroup": "P2/c",
      "spacegroup_number": 13,
      "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": 6.605741031784377e-05,
      "parent_symmetrization_rmsd_A": 0.8224487632311321,
      "parent_cell_rmsd_A": 0.009442999532165045,
      "energy_eV": "Infinity",
      "reduced_polarization": [
        3.956766939258059e-06,
        1.2213068616356454e-05,
        -6.479788891823973e-05
      ],
      "cartesian_polarization_e_A2": [
        2.496211533468863e-08,
        1.56007109232277e-07,
        -4.7090721619604497e-07
      ],
      "ranking_score": 0.8249416279348091
    },
    {
      "candidate_id": "bec_projection_01",
      "source": "MACEField_BEC_backprojection",
      "spacegroup": "Amm2",
      "spacegroup_number": 38,
      "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": 1.9588097835643303e-05,
      "parent_symmetrization_rmsd_A": 0.021229564918797777,
      "parent_cell_rmsd_A": 0.08881240890595225,
      "energy_eV": -528.5384474926335,
      "reduced_polarization": [
        1.455894999120829e-15,
        -5.101096519253317e-16,
        -0.49998041190216436
      ],
      "cartesian_polarization_e_A2": [
        3.6692391581382445e-17,
        -8.097136629440844e-18,
        -0.003601145339465241
      ],
      "ranking_score": 0.5434718433409571
    },
    {
      "candidate_id": "bec_projection_02",
      "source": "MACEField_BEC_backprojection",
      "spacegroup": "Pm",
      "spacegroup_number": 6,
      "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": 2.679547554568526e-05,
      "parent_symmetrization_rmsd_A": 0.04206576000582252,
      "parent_cell_rmsd_A": 0.24143677670120445,
      "energy_eV": -525.5773044524904,
      "reduced_polarization": [
        -8.94500202597224e-16,
        0.4999777730684114,
        -1.4965327322688127e-05
      ],
      "cartesian_polarization_e_A2": [
        -7.447549666744818e-17,
        0.0063893992364483536,
        -0.0001246420267219036
      ],
      "ranking_score": 0.602478545132215
    },
    {
      "candidate_id": "bec_projection_03",
      "source": "MACEField_BEC_backprojection",
      "spacegroup": "Cm",
      "spacegroup_number": 8,
      "pointgroup": "m",
      "has_inversion": false,
      "is_polar_point_group": true,
      "nonpolar_parent_hypothesis": false,
      "symmetry_tolerance_A": null,
      "target_reduced_polarization": [
        -0.5,
        0.0,
        0.0
      ],
      "formal_class": [
        0.5,
        0.0,
        0.0
      ],
      "target_residual": 2.778159256529765e-06,
      "parent_symmetrization_rmsd_A": 0.021068066764285392,
      "parent_cell_rmsd_A": 0.03783587798656662,
      "energy_eV": -528.754038123081,
      "reduced_polarization": [
        -0.49999751107833446,
        4.27296378212134e-15,
        1.2342762241191527e-06
      ],
      "cartesian_polarization_e_A2": [
        -0.003154455589659513,
        3.5224791969579556e-17,
        -1.8956888782651628e-05
      ],
      "ranking_score": 0.5305325925794401
    },
    {
      "candidate_id": "bec_projection_04",
      "source": "MACEField_BEC_backprojection",
      "spacegroup": "Pm",
      "spacegroup_number": 6,
      "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": 7.521490419435985e-05,
      "parent_symmetrization_rmsd_A": 0.04753098865467037,
      "parent_cell_rmsd_A": 0.26529351237881427,
      "energy_eV": -524.6205666403853,
      "reduced_polarization": [
        4.946642069438757e-15,
        0.49992871685689877,
        -0.4999760000974465
      ],
      "cartesian_polarization_e_A2": [
        -3.1996901641265745e-17,
        0.006497699499576819,
        -0.003727678594032507
      ],
      "ranking_score": 0.6140047965577626
    },
    {
      "candidate_id": "bec_projection_05",
      "source": "MACEField_BEC_backprojection",
      "spacegroup": "Cm",
      "spacegroup_number": 8,
      "pointgroup": "m",
      "has_inversion": false,
      "is_polar_point_group": true,
      "nonpolar_parent_hypothesis": false,
      "symmetry_tolerance_A": null,
      "target_reduced_polarization": [
        -0.5,
        0.0,
        -0.5
      ],
      "formal_class": [
        0.5,
        0.0,
        0.5
      ],
      "target_residual": 4.502433822864771e-06,
      "parent_symmetrization_rmsd_A": 0.030009858955836258,
      "parent_cell_rmsd_A": 0.09685684541943487,
      "energy_eV": -527.724824171429,
      "reduced_polarization": [
        -0.500004407082842,
        1.5334512671838704e-15,
        -0.4999990782998573
      ],
      "cartesian_polarization_e_A2": [
        -0.003187533074111259,
        -1.1575840791619555e-18,
        -0.0036204521737066802
      ],
      "ranking_score": 0.5542330751783408
    },
    {
      "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": 4.200293768871647e-05,
      "parent_symmetrization_rmsd_A": 0.04705539606928644,
      "parent_cell_rmsd_A": 0.24448281013345305,
      "energy_eV": -524.6648800553507,
      "reduced_polarization": [
        -0.4999750687822829,
        0.4999737159243395,
        -2.1256258473638876e-05
      ],
      "cartesian_polarization_e_A2": [
        -0.003155168233314945,
        0.006389752668471103,
        -0.00014384205309154988
      ],
      "ranking_score": 0.6082601044780271
    },
    {
      "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": 8.611925788052366e-05,
      "parent_symmetrization_rmsd_A": 0.05211866400263141,
      "parent_cell_rmsd_A": 0.2684338673401139,
      "energy_eV": -523.7766677825898,
      "reduced_polarization": [
        -0.4999718384653182,
        0.4999187040990425,
        -0.4999962011804777
      ],
      "cartesian_polarization_e_A2": [
        -0.0031883716809611097,
        0.006498118297076072,
        -0.0037472068485388094
      ],
      "ranking_score": 0.6193993693534209
    }
  ],
  "formal_branches": [
    {
      "orbit_id": 0,
      "formal_class": [
        0.0,
        0.0,
        0.0
      ],
      "formal_classes_in_orbit": [
        [
          0.0,
          0.0,
          0.0
        ]
      ],
      "target_reduced_polarization": [
        0.0,
        0.0,
        0.0
      ],
      "bec_backprojection": {
        "converged_to_target": true,
        "history": [
          {
            "iteration": 0,
            "reduced_polarization": [
              -2.50914172949723e-16,
              1.2089112971791434e-15,
              -0.04746602989823206
            ],
            "branch_aligned_reduced_polarization": [
              -2.50914172949723e-16,
              1.2089112971791434e-15,
              -0.04746602989823206
            ],
            "target_residual": 0.04746602989823206,
            "energy_eV": -529.6479508691879,
            "max_atomic_step_A": 0.00329456039019493,
            "max_log_strain_component": 0.000868823449043133,
            "step_scale": 1.0,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 4.588505992450732,
            "cell_principal_stretches": [
              1.0008692009854658,
              0.9996773742345719,
              0.9994607172864184
            ],
            "cell_volume_ratio": 1.0000067174724845,
            "cell_rmsd_from_input_A": 0.009442999532165045
          },
          {
            "iteration": 1,
            "reduced_polarization": [
              -6.763800754755188e-16,
              -7.351808879398566e-16,
              -8.421830975318233e-05
            ],
            "branch_aligned_reduced_polarization": [
              -6.763800754755188e-16,
              -7.351808879398566e-16,
              -8.421830975318233e-05
            ],
            "target_residual": 8.421830975318233e-05,
            "energy_eV": -529.6367861960671
          }
        ],
        "iterations": 1
      },
      "parent": {
        "candidate_id": "bec_projection_00",
        "source": "MACEField_BEC_backprojection",
        "spacegroup": "Amm2",
        "spacegroup_number": 38,
        "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": 8.421830975318233e-05,
        "parent_symmetrization_rmsd_A": 0.002244091552626341,
        "parent_cell_rmsd_A": 0.009442999532165045,
        "energy_eV": -529.6367861960671,
        "reduced_polarization": [
          -6.763800754755188e-16,
          -7.351808879398566e-16,
          -8.421830975318233e-05
        ],
        "cartesian_polarization_e_A2": [
          -4.267575054384137e-18,
          -9.391054823641054e-18,
          -6.120416955041238e-07
        ],
        "ranking_score": 0.5047732780551739
      },
      "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": [
          -529.6479508691878,
          -529.6478141361001,
          -529.6473159272821,
          -529.6464571505056,
          -529.6452387088672,
          -529.6436615008993,
          -529.6417264205811,
          -529.6394343573413,
          -529.6367861960671
        ],
        "cartesian_polarizations_e_A2": [
          [
            1.005110599648366e-17,
            1.0881091479152084e-17,
            -0.0003446537349284646
          ],
          [
            2.1723269093715215e-17,
            -3.1071350775449196e-18,
            -0.0003016428517254664
          ],
          [
            2.702887811621544e-17,
            -3.021781579100587e-17,
            -0.00025863355427548936
          ],
          [
            1.8538044543346106e-17,
            -1.1654848460063594e-17,
            -0.00021562585976297953
          ],
          [
            2.904597273220845e-17,
            -1.0501316143352312e-18,
            -0.00017261978547158303
          ],
          [
            2.9842930642229737e-17,
            -2.456332884167886e-17,
            -0.0001296153488395679
          ],
          [
            2.3121486264597598e-17,
            -3.8419009652620056e-17,
            -8.661256746438694e-05
          ],
          [
            9.504358348950554e-19,
            -2.3438426491893943e-17,
            -4.361145910693588e-05
          ],
          [
            3.1579824428142965e-17,
            -5.800609869473033e-17,
            -6.120416954916662e-07
          ]
        ],
        "raw_reduced_polarization": [
          [
            1.5926849757104706e-15,
            8.513647820527338e-16,
            -0.04746602989823696
          ],
          [
            3.44713070008208e-15,
            -2.4186724399951915e-16,
            -0.041538054921301734
          ],
          [
            4.291455547187032e-15,
            -2.362482970256096e-15,
            -0.03561157530436869
          ],
          [
            2.9480593554070725e-15,
            -9.093910825830654e-16,
            -0.029686593136363675
          ],
          [
            4.614212962239557e-15,
            -7.930421174258008e-17,
            -0.02376311051889366
          ],
          [
            4.740045635355603e-15,
            -1.919848476330388e-15,
            -0.017841129573868356
          ],
          [
            3.672884747495209e-15,
            -3.005064436536647e-15,
            -0.011920652444116836
          ],
          [
            1.5545296699825436e-16,
            -1.8334850923516116e-15,
            -0.006001681293962183
          ],
          [
            5.005822864021741e-15,
            -4.5410258235112376e-15,
            -8.421830975146814e-05
          ]
        ],
        "unwrapped_reduced_polarization": [
          [
            1.5926849757104706e-15,
            8.513647820527338e-16,
            -0.04746602989823696
          ],
          [
            3.44713070008208e-15,
            -2.418672439995191e-16,
            -0.041538054921301734
          ],
          [
            4.291455547187032e-15,
            -2.362482970256096e-15,
            -0.03561157530436869
          ],
          [
            2.9480593554070725e-15,
            -9.093910825830654e-16,
            -0.029686593136363675
          ],
          [
            4.614212962239557e-15,
            -7.930421174258009e-17,
            -0.02376311051889366
          ],
          [
            4.740045635355603e-15,
            -1.919848476330388e-15,
            -0.017841129573868356
          ],
          [
            3.672884747495209e-15,
            -3.005064436536647e-15,
            -0.011920652444116836
          ],
          [
            1.5545296699825454e-16,
            -1.8334850923516116e-15,
            -0.006001681293962183
          ],
          [
            5.005822864021741e-15,
            -4.5410258235112376e-15,
            -8.421830975146802e-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": [
          [
            1.5543122344752192e-15,
            8.881784197001252e-16,
            -0.04746602989823695
          ],
          [
            3.4416913763379853e-15,
            -2.220446049250313e-16,
            -0.04153805492130175
          ],
          [
            4.3298697960381105e-15,
            -2.3869795029440866e-15,
            -0.0356115753043687
          ],
          [
            2.9976021664879227e-15,
            -8.881784197001252e-16,
            -0.02968659313636368
          ],
          [
            4.6629367034256575e-15,
            -5.551115123125783e-17,
            -0.023763110518893682
          ],
          [
            4.773959005888173e-15,
            -1.942890293094024e-15,
            -0.017841129573868353
          ],
          [
            3.6637359812630166e-15,
            -2.9976021664879227e-15,
            -0.01192065244411683
          ],
          [
            1.1102230246251565e-16,
            -1.8318679906315083e-15,
            -0.006001681293962169
          ],
          [
            4.9960036108132044e-15,
            -4.551914400963142e-15,
            -8.421830975147149e-05
          ]
        ]
      },
      "reflected": {
        "reached": true,
        "construction": "reflect_displacements_about_reconstructed_parent",
        "energies_eV": [
          -529.6367861960671,
          -529.6349903395135,
          -529.632979318261,
          -529.6307533470235,
          -529.6283126391081,
          -529.6256574064194,
          -529.6227878594638,
          -529.6197042073561,
          -529.6164066578219
        ],
        "cartesian_polarizations_e_A2": [
          [
            8.66952898092045e-18,
            -4.591390685307714e-17,
            -6.120416954577661e-07
          ],
          [
            2.7472153293703377e-17,
            -2.3815816340175016e-17,
            3.575294325987086e-05
          ],
          [
            2.5603170755086413e-17,
            -2.5909180935198447e-17,
            7.21026427602837e-05
          ],
          [
            3.9539554250509347e-17,
            -1.0091700812175685e-16,
            0.00010843702979461489
          ],
          [
            5.388444206428044e-17,
            -1.0450109639037044e-16,
            0.0001447560774416137
          ],
          [
            9.109646068905306e-18,
            -6.983730586667716e-17,
            0.00018105975886946896
          ],
          [
            -6.265358089659369e-18,
            -1.5880158222706257e-17,
            0.00021734804733545708
          ],
          [
            4.144905500940247e-17,
            -8.394729371530275e-17,
            0.0002536209161860233
          ],
          [
            4.218863387052766e-17,
            -9.937607001193527e-17,
            0.00028987833885618793
          ]
        ],
        "raw_reduced_polarization": [
          [
            1.3742917065548778e-15,
            -3.594384549206403e-15,
            -8.42183097468034e-05
          ],
          [
            4.350517015267619e-15,
            -1.8653468517692e-15,
            0.004920215355342977
          ],
          [
            4.051237926189329e-15,
            -2.029838368435732e-15,
            0.009923623901358997
          ],
          [
            6.258141607485456e-15,
            -7.900967774437537e-15,
            0.014926003104506997
          ],
          [
            8.53074980921822e-15,
            -8.181087374769123e-15,
            0.019927348751646264
          ],
          [
            1.4351306639294798e-15,
            -5.4676391335706124e-15,
            0.024927656640230465
          ],
          [
            -9.997248609609504e-16,
            -1.2444896114331967e-15,
            0.0299269225782652
          ],
          [
            6.564240439591408e-15,
            -6.569761234836081e-15,
            0.0349251423843255
          ],
          [
            6.685155179424687e-15,
            -7.775441126386102e-15,
            0.03992231188748016
          ]
        ],
        "unwrapped_reduced_polarization": [
          [
            1.3742917065548778e-15,
            -3.594384549206403e-15,
            -8.42183097468034e-05
          ],
          [
            4.350517015267619e-15,
            -1.8653468517692e-15,
            0.004920215355342977
          ],
          [
            4.051237926189329e-15,
            -2.029838368435732e-15,
            0.009923623901358997
          ],
          [
            6.258141607485456e-15,
            -7.900967774437537e-15,
            0.014926003104506997
          ],
          [
            8.53074980921822e-15,
            -8.181087374769123e-15,
            0.019927348751646264
          ],
          [
            1.4351306639294795e-15,
            -5.4676391335706124e-15,
            0.024927656640230465
          ],
          [
            -9.997248609609504e-16,
            -1.2444896114331969e-15,
            0.0299269225782652
          ],
          [
            6.564240439591407e-15,
            -6.569761234836081e-15,
            0.0349251423843255
          ],
          [
            6.685155179424687e-15,
            -7.775441126386102e-15,
            0.03992231188748016
          ]
        ],
        "gauge_integer_shift": [
          0,
          0,
          0
        ],
        "expected_opposite_endpoint_reduced_polarization": [
          8.415509529426359e-15,
          -9.928459606149693e-15,
          0.04729744800590258
        ],
        "actual_opposite_endpoint_branch_residual": 0.007375136118422422
      },
      "pnp_branch": {
        "construction": "incoming_path_concatenated_with_parent_reflection",
        "reduced_polarization": [
          [
            1.5926849757104706e-15,
            8.513647820527338e-16,
            -0.04746602989823696
          ],
          [
            3.44713070008208e-15,
            -2.4186724399951915e-16,
            -0.041538054921301734
          ],
          [
            4.291455547187032e-15,
            -2.362482970256096e-15,
            -0.03561157530436869
          ],
          [
            2.9480593554070725e-15,
            -9.093910825830654e-16,
            -0.029686593136363675
          ],
          [
            4.614212962239557e-15,
            -7.930421174258008e-17,
            -0.02376311051889366
          ],
          [
            4.740045635355603e-15,
            -1.919848476330388e-15,
            -0.017841129573868356
          ],
          [
            3.672884747495209e-15,
            -3.005064436536647e-15,
            -0.011920652444116836
          ],
          [
            1.5545296699825436e-16,
            -1.8334850923516116e-15,
            -0.006001681293962183
          ],
          [
            5.005822864021741e-15,
            -4.5410258235112376e-15,
            -8.421830975146814e-05
          ],
          [
            4.350517015267619e-15,
            -1.8653468517692e-15,
            0.004920215355342977
          ],
          [
            4.051237926189329e-15,
            -2.029838368435732e-15,
            0.009923623901358997
          ],
          [
            6.258141607485456e-15,
            -7.900967774437537e-15,
            0.014926003104506997
          ],
          [
            8.53074980921822e-15,
            -8.181087374769123e-15,
            0.019927348751646264
          ],
          [
            1.4351306639294798e-15,
            -5.4676391335706124e-15,
            0.024927656640230465
          ],
          [
            -9.997248609609504e-16,
            -1.2444896114331967e-15,
            0.0299269225782652
          ],
          [
            6.564240439591408e-15,
            -6.569761234836081e-15,
            0.0349251423843255
          ],
          [
            6.685155179424687e-15,
            -7.775441126386102e-15,
            0.03992231188748016
          ]
        ],
        "unwrapped_reduced_polarization": [
          [
            1.5926849757104706e-15,
            8.513647820527338e-16,
            -0.04746602989823696
          ],
          [
            3.44713070008208e-15,
            -2.418672439995191e-16,
            -0.041538054921301734
          ],
          [
            4.291455547187032e-15,
            -2.362482970256096e-15,
            -0.03561157530436869
          ],
          [
            2.9480593554070725e-15,
            -9.093910825830654e-16,
            -0.029686593136363675
          ],
          [
            4.614212962239557e-15,
            -7.930421174258009e-17,
            -0.02376311051889366
          ],
          [
            4.740045635355603e-15,
            -1.919848476330388e-15,
            -0.017841129573868356
          ],
          [
            3.672884747495209e-15,
            -3.005064436536647e-15,
            -0.011920652444116836
          ],
          [
            1.5545296699825454e-16,
            -1.8334850923516116e-15,
            -0.006001681293962183
          ],
          [
            5.005822864021741e-15,
            -4.5410258235112376e-15,
            -8.421830975146802e-05
          ],
          [
            4.350517015267619e-15,
            -1.8653468517692e-15,
            0.004920215355342977
          ],
          [
            4.051237926189329e-15,
            -2.029838368435732e-15,
            0.009923623901358997
          ],
          [
            6.258141607485456e-15,
            -7.900967774437537e-15,
            0.014926003104506997
          ],
          [
            8.53074980921822e-15,
            -8.181087374769123e-15,
            0.019927348751646264
          ],
          [
            1.4351306639294795e-15,
            -5.4676391335706124e-15,
            0.024927656640230465
          ],
          [
            -9.997248609609504e-16,
            -1.2444896114331969e-15,
            0.0299269225782652
          ],
          [
            6.564240439591407e-15,
            -6.569761234836081e-15,
            0.0349251423843255
          ],
          [
            6.685155179424687e-15,
            -7.775441126386102e-15,
            0.03992231188748016
          ]
        ],
        "berry_integer_shifts": [
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ]
        ],
        "folded_reduced_polarization": [
          [
            1.5543122344752192e-15,
            8.881784197001252e-16,
            -0.04746602989823695
          ],
          [
            3.4416913763379853e-15,
            -2.220446049250313e-16,
            -0.04153805492130175
          ],
          [
            4.3298697960381105e-15,
            -2.3869795029440866e-15,
            -0.0356115753043687
          ],
          [
            2.9976021664879227e-15,
            -8.881784197001252e-16,
            -0.02968659313636368
          ],
          [
            4.6629367034256575e-15,
            -5.551115123125783e-17,
            -0.023763110518893682
          ],
          [
            4.773959005888173e-15,
            -1.942890293094024e-15,
            -0.017841129573868353
          ],
          [
            3.6637359812630166e-15,
            -2.9976021664879227e-15,
            -0.01192065244411683
          ],
          [
            1.1102230246251565e-16,
            -1.8318679906315083e-15,
            -0.006001681293962169
          ],
          [
            4.9960036108132044e-15,
            -4.551914400963142e-15,
            -8.421830975147149e-05
          ],
          [
            4.3298697960381105e-15,
            -1.887379141862766e-15,
            0.004920215355342927
          ],
          [
            3.9968028886505635e-15,
            -2.0539125955565396e-15,
            0.009923623901359035
          ],
          [
            6.217248937900877e-15,
            -7.882583474838611e-15,
            0.01492600310450698
          ],
          [
            8.548717289613705e-15,
            -8.1601392309949e-15,
            0.019927348751646257
          ],
          [
            1.4432899320127035e-15,
            -5.440092820663267e-15,
            0.024927656640230444
          ],
          [
            -9.992007221626409e-16,
            -1.2212453270876722e-15,
            0.029926922578265236
          ],
          [
            6.5503158452884236e-15,
            -6.5503158452884236e-15,
            0.034925142384325536
          ],
          [
            6.661338147750939e-15,
            -7.771561172376096e-15,
            0.03992231188748019
          ]
        ]
      },
      "incoming_structure_ids": [
        "incoming_00_000",
        "incoming_00_001",
        "incoming_00_002",
        "incoming_00_003",
        "incoming_00_004",
        "incoming_00_005",
        "incoming_00_006",
        "incoming_00_007",
        "incoming_00_008"
      ],
      "reflected_structure_ids": [
        "reflected_00_001",
        "reflected_00_002",
        "reflected_00_003",
        "reflected_00_004",
        "reflected_00_005",
        "reflected_00_006",
        "reflected_00_007",
        "reflected_00_008"
      ]
    },
    {
      "orbit_id": 1,
      "formal_class": [
        0.0,
        0.0,
        0.5
      ],
      "formal_classes_in_orbit": [
        [
          0.0,
          0.0,
          0.5
        ]
      ],
      "target_reduced_polarization": [
        0.0,
        0.0,
        -0.5
      ],
      "bec_backprojection": {
        "converged_to_target": true,
        "history": [
          {
            "iteration": 0,
            "reduced_polarization": [
              -2.50914172949723e-16,
              1.2089112971791434e-15,
              -0.04746602989823206
            ],
            "branch_aligned_reduced_polarization": [
              -2.50914172949723e-16,
              1.2089112971791434e-15,
              -0.047466029898232065
            ],
            "target_residual": 0.45253397010176794,
            "energy_eV": -529.6479508691879,
            "max_atomic_step_A": 0.031409841866097854,
            "max_log_strain_component": 0.008283231725003492,
            "step_scale": 1.0,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 4.588505992450732,
            "cell_principal_stretches": [
              1.0051560739323682,
              1.0030810985285579,
              0.9917509797133108
            ],
            "cell_volume_ratio": 0.9999359588963045,
            "cell_rmsd_from_input_A": 0.09026030165485482
          },
          {
            "iteration": 1,
            "reduced_polarization": [
              -8.562445654208144e-15,
              3.2428572247888126e-15,
              -0.5075821238993489
            ],
            "branch_aligned_reduced_polarization": [
              -8.562445654208144e-15,
              3.2428572247888126e-15,
              -0.5075821238993489
            ],
            "target_residual": 0.007582123899348869,
            "energy_eV": -528.4999654402056,
            "max_atomic_step_A": 0.0005133863347371641,
            "max_log_strain_component": 0.00013256476230972934,
            "step_scale": 1.0,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 4.588505992450732,
            "cell_principal_stretches": [
              1.0050733472091844,
              1.0030317139861231,
              0.9918824596608186
            ],
            "cell_volume_ratio": 0.9999369837772297,
            "cell_rmsd_from_input_A": 0.08881240890595225
          },
          {
            "iteration": 2,
            "reduced_polarization": [
              1.455894999120829e-15,
              -5.101096519253317e-16,
              -0.49998041190216436
            ],
            "branch_aligned_reduced_polarization": [
              1.455894999120829e-15,
              -5.101096519253317e-16,
              -0.49998041190216436
            ],
            "target_residual": 1.9588097835643303e-05,
            "energy_eV": -528.5384474926335
          }
        ],
        "iterations": 2
      },
      "parent": {
        "candidate_id": "bec_projection_01",
        "source": "MACEField_BEC_backprojection",
        "spacegroup": "Amm2",
        "spacegroup_number": 38,
        "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": 1.9588097835643303e-05,
        "parent_symmetrization_rmsd_A": 0.021229564918797777,
        "parent_cell_rmsd_A": 0.08881240890595225,
        "energy_eV": -528.5384474926335,
        "reduced_polarization": [
          1.455894999120829e-15,
          -5.101096519253317e-16,
          -0.49998041190216436
        ],
        "cartesian_polarization_e_A2": [
          3.6692391581382445e-17,
          -8.097136629440844e-18,
          -0.003601145339465241
        ],
        "ranking_score": 0.5434718433409571
      },
      "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": [
              -2.50914172949723e-16,
              1.2089112971791434e-15,
              -0.04746602989823206
            ],
            "branch_aligned_reduced_polarization": [
              -2.50914172949723e-16,
              1.2212453270876722e-15,
              -0.04746602989823206
            ],
            "target_residual": 0.5022479706223796,
            "energy_eV": -529.6479508691879,
            "max_atomic_step_A": 0.06426449016144113,
            "max_log_strain_component": 0.019457152280449686,
            "step_scale": 1.0,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 4.588505992450732,
            "cell_principal_stretches": [
              1.01982861267349,
              0.9996773742345689,
              0.9808799607067638
            ],
            "cell_volume_ratio": 1.0000067174724692,
            "cell_rmsd_from_input_A": 0.24109749593905125
          },
          {
            "iteration": 1,
            "reduced_polarization": [
              2.923418773073192e-14,
              0.4998374863089342,
              0.02106522948377046
            ],
            "branch_aligned_reduced_polarization": [
              2.923418773073192e-14,
              0.4998374863089342,
              0.02106522948377046
            ],
            "target_residual": 0.021065856353438283,
            "energy_eV": -525.558426191325,
            "max_atomic_step_A": 0.001518712603061932,
            "max_log_strain_component": 0.00039215210909741735,
            "step_scale": 1.0,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 4.588505992450732,
            "cell_principal_stretches": [
              1.0197790153606692,
              0.9998229816943289,
              0.9807818367534323
            ],
            "cell_volume_ratio": 1.000003685468833,
            "cell_rmsd_from_input_A": 0.24143677670120445
          },
          {
            "iteration": 2,
            "reduced_polarization": [
              -8.94500202597224e-16,
              0.4999777730684114,
              -1.4965327322688127e-05
            ],
            "branch_aligned_reduced_polarization": [
              -8.94500202597224e-16,
              0.4999777730684114,
              -1.4965327322688127e-05
            ],
            "target_residual": 2.679547554568526e-05,
            "energy_eV": -525.5773044524904
          }
        ],
        "iterations": 2
      },
      "parent": {
        "candidate_id": "bec_projection_02",
        "source": "MACEField_BEC_backprojection",
        "spacegroup": "Pm",
        "spacegroup_number": 6,
        "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": 2.679547554568526e-05,
        "parent_symmetrization_rmsd_A": 0.04206576000582252,
        "parent_cell_rmsd_A": 0.24143677670120445,
        "energy_eV": -525.5773044524904,
        "reduced_polarization": [
          -8.94500202597224e-16,
          0.4999777730684114,
          -1.4965327322688127e-05
        ],
        "cartesian_polarization_e_A2": [
          -7.447549666744818e-17,
          0.0063893992364483536,
          -0.0001246420267219036
        ],
        "ranking_score": 0.602478545132215
      },
      "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": [
              -2.50914172949723e-16,
              1.2089112971791434e-15,
              -0.04746602989823206
            ],
            "branch_aligned_reduced_polarization": [
              -2.7755575615628914e-16,
              1.2089112971791434e-15,
              -0.04746602989823206
            ],
            "target_residual": 0.5022479706223805,
            "energy_eV": -529.6479508691879,
            "max_atomic_step_A": 0.030734889658002584,
            "max_log_strain_component": 0.006018379700295842,
            "step_scale": 1.0,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 4.588505992450732,
            "cell_principal_stretches": [
              1.0063408857135774,
              0.999460717286417,
              0.9942419204044781
            ],
            "cell_volume_ratio": 1.0000067174724891,
            "cell_rmsd_from_input_A": 0.03801687742078849
          },
          {
            "iteration": 1,
            "reduced_polarization": [
              -0.5008235090909112,
              -4.1139385082363825e-15,
              0.002591812280643952
            ],
            "branch_aligned_reduced_polarization": [
              -0.5008235090909112,
              -4.1139385082363825e-15,
              0.002591812280643952
            ],
            "target_residual": 0.002719495931401669,
            "energy_eV": -528.7494231068833,
            "max_atomic_step_A": 0.00018829302963340984,
            "max_log_strain_component": 4.7510244857384223e-05,
            "step_scale": 1.0,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 4.588505992450732,
            "cell_principal_stretches": [
              1.0063135998806132,
              0.9994901995957882,
              0.9942391854067921
            ],
            "cell_volume_ratio": 1.0000063501368972,
            "cell_rmsd_from_input_A": 0.03783587798656662
          },
          {
            "iteration": 2,
            "reduced_polarization": [
              -0.49999751107833446,
              4.27296378212134e-15,
              1.2342762241191527e-06
            ],
            "branch_aligned_reduced_polarization": [
              -0.49999751107833446,
              4.27296378212134e-15,
              1.2342762241191527e-06
            ],
            "target_residual": 2.778159256529765e-06,
            "energy_eV": -528.754038123081
          }
        ],
        "iterations": 2
      },
      "parent": {
        "candidate_id": "bec_projection_03",
        "source": "MACEField_BEC_backprojection",
        "spacegroup": "Cm",
        "spacegroup_number": 8,
        "pointgroup": "m",
        "has_inversion": false,
        "is_polar_point_group": true,
        "nonpolar_parent_hypothesis": false,
        "symmetry_tolerance_A": null,
        "target_reduced_polarization": [
          -0.5,
          0.0,
          0.0
        ],
        "formal_class": [
          0.5,
          0.0,
          0.0
        ],
        "target_residual": 2.778159256529765e-06,
        "parent_symmetrization_rmsd_A": 0.021068066764285392,
        "parent_cell_rmsd_A": 0.03783587798656662,
        "energy_eV": -528.754038123081,
        "reduced_polarization": [
          -0.49999751107833446,
          4.27296378212134e-15,
          1.2342762241191527e-06
        ],
        "cartesian_polarization_e_A2": [
          -0.003154455589659513,
          3.5224791969579556e-17,
          -1.8956888782651628e-05
        ],
        "ranking_score": 0.5305325925794401
      },
      "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": [
              -2.50914172949723e-16,
              1.2089112971791434e-15,
              -0.04746602989823206
            ],
            "branch_aligned_reduced_polarization": [
              -2.50914172949723e-16,
              1.2212453270876722e-15,
              -0.047466029898232065
            ],
            "target_residual": 0.6743789691976364,
            "energy_eV": -529.6479508691879,
            "max_atomic_step_A": 0.06942072306323738,
            "max_log_strain_component": 0.019457152280449405,
            "step_scale": 1.0,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 4.588505992450732,
            "cell_principal_stretches": [
              1.0191943364444829,
              1.0030810985285548,
              0.9780907187581296
            ],
            "cell_volume_ratio": 0.9999359588962893,
            "cell_rmsd_from_input_A": 0.25815887865078396
          },
          {
            "iteration": 1,
            "reduced_polarization": [
              2.245591897722986e-14,
              0.4879455464782583,
              -0.4845257487144736
            ],
            "branch_aligned_reduced_polarization": [
              2.245591897722986e-14,
              0.4879455464782583,
              -0.4845257487144736
            ],
            "target_residual": 0.019615358843402438,
            "energy_eV": -524.8864491433878,
            "max_atomic_step_A": 0.001950763534555198,
            "max_log_strain_component": 0.0005109812583439987,
            "step_scale": 1.0,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 4.588505992450732,
            "cell_principal_stretches": [
              1.0197097028887414,
              1.0031927251256094,
              0.9774853438987083
            ],
            "cell_volume_ratio": 0.9999336424913571,
            "cell_rmsd_from_input_A": 0.26529351237881427
          },
          {
            "iteration": 2,
            "reduced_polarization": [
              4.946642069438757e-15,
              0.49992871685689877,
              -0.4999760000974465
            ],
            "branch_aligned_reduced_polarization": [
              4.946642069438757e-15,
              0.49992871685689877,
              -0.4999760000974465
            ],
            "target_residual": 7.521490419435985e-05,
            "energy_eV": -524.6205666403853
          }
        ],
        "iterations": 2
      },
      "parent": {
        "candidate_id": "bec_projection_04",
        "source": "MACEField_BEC_backprojection",
        "spacegroup": "Pm",
        "spacegroup_number": 6,
        "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": 7.521490419435985e-05,
        "parent_symmetrization_rmsd_A": 0.04753098865467037,
        "parent_cell_rmsd_A": 0.26529351237881427,
        "energy_eV": -524.6205666403853,
        "reduced_polarization": [
          4.946642069438757e-15,
          0.49992871685689877,
          -0.4999760000974465
        ],
        "cartesian_polarization_e_A2": [
          -3.1996901641265745e-17,
          0.006497699499576819,
          -0.003727678594032507
        ],
        "ranking_score": 0.6140047965577626
      },
      "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": [
              -2.50914172949723e-16,
              1.2089112971791434e-15,
              -0.04746602989823206
            ],
            "branch_aligned_reduced_polarization": [
              -2.7755575615628914e-16,
              1.2089112971791434e-15,
              -0.047466029898232065
            ],
            "target_residual": 0.6743789691976371,
            "energy_eV": -529.6479508691879,
            "max_atomic_step_A": 0.044247107939242025,
            "max_log_strain_component": 0.00828323172500161,
            "step_scale": 1.0,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 4.588505992450732,
            "cell_principal_stretches": [
              1.0056880044347984,
              1.0051560739323668,
              0.9891802008284802
            ],
            "cell_volume_ratio": 0.9999359588963095,
            "cell_rmsd_from_input_A": 0.09733923285976716
          },
          {
            "iteration": 1,
            "reduced_polarization": [
              -0.49046217669663295,
              6.094067238650041e-15,
              -0.5044616670322576
            ],
            "branch_aligned_reduced_polarization": [
              -0.49046217669663295,
              6.094067238650041e-15,
              -0.5044616670322576
            ],
            "target_residual": 0.010529793258796008,
            "energy_eV": -527.733846384879,
            "max_atomic_step_A": 0.000673044305958203,
            "max_log_strain_component": 0.00011645290203092842,
            "step_scale": 1.0,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 4.588505992450732,
            "cell_principal_stretches": [
              1.0057623292337665,
              1.0051097171034047,
              0.9891532883010626
            ],
            "cell_volume_ratio": 0.9999365331890849,
            "cell_rmsd_from_input_A": 0.09685684541943487
          },
          {
            "iteration": 2,
            "reduced_polarization": [
              -0.500004407082842,
              1.5334512671838704e-15,
              -0.4999990782998573
            ],
            "branch_aligned_reduced_polarization": [
              -0.500004407082842,
              1.5334512671838704e-15,
              -0.4999990782998573
            ],
            "target_residual": 4.502433822864771e-06,
            "energy_eV": -527.724824171429
          }
        ],
        "iterations": 2
      },
      "parent": {
        "candidate_id": "bec_projection_05",
        "source": "MACEField_BEC_backprojection",
        "spacegroup": "Cm",
        "spacegroup_number": 8,
        "pointgroup": "m",
        "has_inversion": false,
        "is_polar_point_group": true,
        "nonpolar_parent_hypothesis": false,
        "symmetry_tolerance_A": null,
        "target_reduced_polarization": [
          -0.5,
          0.0,
          -0.5
        ],
        "formal_class": [
          0.5,
          0.0,
          0.5
        ],
        "target_residual": 4.502433822864771e-06,
        "parent_symmetrization_rmsd_A": 0.030009858955836258,
        "parent_cell_rmsd_A": 0.09685684541943487,
        "energy_eV": -527.724824171429,
        "reduced_polarization": [
          -0.500004407082842,
          1.5334512671838704e-15,
          -0.4999990782998573
        ],
        "cartesian_polarization_e_A2": [
          -0.003187533074111259,
          -1.1575840791619555e-18,
          -0.0036204521737066802
        ],
        "ranking_score": 0.5542330751783408
      },
      "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": [
              -2.50914172949723e-16,
              1.2089112971791434e-15,
              -0.04746602989823206
            ],
            "branch_aligned_reduced_polarization": [
              -2.7755575615628914e-16,
              1.2212453270876722e-15,
              -0.04746602989823206
            ],
            "target_residual": 0.7086981190847753,
            "energy_eV": -529.6479508691879,
            "max_atomic_step_A": 0.07083463206634048,
            "max_log_strain_component": 0.019457152280451452,
            "step_scale": 1.0,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 4.588505992450732,
            "cell_principal_stretches": [
              1.0207654338661,
              0.9996584645793913,
              0.979998282353318
            ],
            "cell_volume_ratio": 1.0000067174724743,
            "cell_rmsd_from_input_A": 0.24390545668802321
          },
          {
            "iteration": 1,
            "reduced_polarization": [
              -0.49932221618917316,
              0.49945189128106643,
              0.023837485113254328
            ],
            "branch_aligned_reduced_polarization": [
              -0.49932221618917316,
              0.49945189128106643,
              0.023837485113254328
            ],
            "target_residual": 0.02385341716791562,
            "energy_eV": -524.6479156991377,
            "max_atomic_step_A": 0.0017529961488629785,
            "max_log_strain_component": 0.00044597041788063647,
            "step_scale": 1.0,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 4.588505992450732,
            "cell_principal_stretches": [
              1.0207222794713975,
              0.9998337590440388,
              0.9798645122359222
            ],
            "cell_volume_ratio": 1.0000032693623766,
            "cell_rmsd_from_input_A": 0.24448281013345305
          },
          {
            "iteration": 2,
            "reduced_polarization": [
              -0.4999750687822829,
              0.4999737159243395,
              -2.1256258473638876e-05
            ],
            "branch_aligned_reduced_polarization": [
              -0.4999750687822829,
              0.4999737159243395,
              -2.1256258473638876e-05
            ],
            "target_residual": 4.200293768871647e-05,
            "energy_eV": -524.6648800553507
          }
        ],
        "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": 4.200293768871647e-05,
        "parent_symmetrization_rmsd_A": 0.04705539606928644,
        "parent_cell_rmsd_A": 0.24448281013345305,
        "energy_eV": -524.6648800553507,
        "reduced_polarization": [
          -0.4999750687822829,
          0.4999737159243395,
          -2.1256258473638876e-05
        ],
        "cartesian_polarization_e_A2": [
          -0.003155168233314945,
          0.006389752668471103,
          -0.00014384205309154988
        ],
        "ranking_score": 0.6082601044780271
      },
      "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": [
              -2.50914172949723e-16,
              1.2089112971791434e-15,
              -0.04746602989823206
            ],
            "branch_aligned_reduced_polarization": [
              -2.7755575615628914e-16,
              1.2212453270876722e-15,
              -0.047466029898232065
            ],
            "target_residual": 0.8395159284349918,
            "energy_eV": -529.6479508691879,
            "max_atomic_step_A": 0.07630293271178341,
            "max_log_strain_component": 0.01945715228045117,
            "step_scale": 1.0,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 4.588505992450732,
            "cell_principal_stretches": [
              1.0199662035293218,
              1.0032530570057128,
              0.9771830224982561
            ],
            "cell_volume_ratio": 0.9999359588962944,
            "cell_rmsd_from_input_A": 0.2607292353580957
          },
          {
            "iteration": 1,
            "reduced_polarization": [
              -0.48878390857344683,
              0.48758546447389617,
              -0.48122864772478346
            ],
            "branch_aligned_reduced_polarization": [
              -0.48878390857344683,
              0.48758546447389617,
              -0.48122864772478346
            ],
            "target_residual": 0.0251452791883083,
            "energy_eV": -524.1007665910155,
            "max_atomic_step_A": 0.002280386043682717,
            "max_log_strain_component": 0.0005335029050433318,
            "step_scale": 1.0,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 4.588505992450732,
            "cell_principal_stretches": [
              1.0205227337491705,
              1.0033953547037853,
              0.9765088699574852
            ],
            "cell_volume_ratio": 0.9999331405367966,
            "cell_rmsd_from_input_A": 0.2684338673401139
          },
          {
            "iteration": 2,
            "reduced_polarization": [
              -0.4999718384653182,
              0.4999187040990425,
              -0.4999962011804777
            ],
            "branch_aligned_reduced_polarization": [
              -0.4999718384653182,
              0.4999187040990425,
              -0.4999962011804777
            ],
            "target_residual": 8.611925788052366e-05,
            "energy_eV": -523.7766677825898
          }
        ],
        "iterations": 2
      },
      "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": 8.611925788052366e-05,
        "parent_symmetrization_rmsd_A": 0.05211866400263141,
        "parent_cell_rmsd_A": 0.2684338673401139,
        "energy_eV": -523.7766677825898,
        "reduced_polarization": [
          -0.4999718384653182,
          0.4999187040990425,
          -0.4999962011804777
        ],
        "cartesian_polarization_e_A2": [
          -0.0031883716809611097,
          0.006498118297076072,
          -0.0037472068485388094
        ],
        "ranking_score": 0.6193993693534209
      },
      "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,
          40,
          41,
          42,
          43,
          44,
          45,
          46,
          47,
          48,
          49,
          50,
          51,
          52,
          53,
          54,
          55,
          56,
          57,
          58,
          59,
          60,
          61,
          62,
          63,
          64,
          65,
          66,
          67,
          68,
          69,
          70,
          71,
          72,
          73,
          74,
          75,
          76,
          77
        ],
        "endpoint_rmsd_A": 0.002244091552626341,
        "minimum_distance_A_by_image": [
          1.5837836917995338,
          1.583550115363466,
          1.5832851289491299,
          1.5830202221065524,
          1.58275539498055,
          1.5824906477160854,
          1.5822259804582446,
          1.5819613933522574,
          1.5816968865434842
        ],
        "minimum_distance_A": 1.5816968865434842,
        "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": [
          1306.7111127207347,
          1306.712209942003,
          1306.7133071641927,
          1306.7144043873034,
          1306.7155016113345,
          1306.7165988362892,
          1306.717696062164,
          1306.7187932889601,
          1306.71989051668
        ],
        "cell_deformation_log_strain_norm": 0.0010723609100574663
      },
      "parent_reduced_polarization": [
        5.005822864021741e-15,
        -4.5410258235112376e-15,
        -8.421830975146814e-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": [
          -529.6479508691878,
          -529.6478141361001,
          -529.6473159272821,
          -529.6464571505056,
          -529.6452387088672,
          -529.6436615008993,
          -529.6417264205811,
          -529.6394343573413,
          -529.6367861960671
        ],
        "cartesian_polarizations_e_A2": [
          [
            1.005110599648366e-17,
            1.0881091479152084e-17,
            -0.0003446537349284646
          ],
          [
            2.1723269093715215e-17,
            -3.1071350775449196e-18,
            -0.0003016428517254664
          ],
          [
            2.702887811621544e-17,
            -3.021781579100587e-17,
            -0.00025863355427548936
          ],
          [
            1.8538044543346106e-17,
            -1.1654848460063594e-17,
            -0.00021562585976297953
          ],
          [
            2.904597273220845e-17,
            -1.0501316143352312e-18,
            -0.00017261978547158303
          ],
          [
            2.9842930642229737e-17,
            -2.456332884167886e-17,
            -0.0001296153488395679
          ],
          [
            2.3121486264597598e-17,
            -3.8419009652620056e-17,
            -8.661256746438694e-05
          ],
          [
            9.504358348950554e-19,
            -2.3438426491893943e-17,
            -4.361145910693588e-05
          ],
          [
            3.1579824428142965e-17,
            -5.800609869473033e-17,
            -6.120416954916662e-07
          ]
        ],
        "raw_reduced_polarization": [
          [
            1.5926849757104706e-15,
            8.513647820527338e-16,
            -0.04746602989823696
          ],
          [
            3.44713070008208e-15,
            -2.4186724399951915e-16,
            -0.041538054921301734
          ],
          [
            4.291455547187032e-15,
            -2.362482970256096e-15,
            -0.03561157530436869
          ],
          [
            2.9480593554070725e-15,
            -9.093910825830654e-16,
            -0.029686593136363675
          ],
          [
            4.614212962239557e-15,
            -7.930421174258008e-17,
            -0.02376311051889366
          ],
          [
            4.740045635355603e-15,
            -1.919848476330388e-15,
            -0.017841129573868356
          ],
          [
            3.672884747495209e-15,
            -3.005064436536647e-15,
            -0.011920652444116836
          ],
          [
            1.5545296699825436e-16,
            -1.8334850923516116e-15,
            -0.006001681293962183
          ],
          [
            5.005822864021741e-15,
            -4.5410258235112376e-15,
            -8.421830975146814e-05
          ]
        ],
        "unwrapped_reduced_polarization": [
          [
            1.5926849757104706e-15,
            8.513647820527338e-16,
            -0.04746602989823696
          ],
          [
            3.44713070008208e-15,
            -2.418672439995191e-16,
            -0.041538054921301734
          ],
          [
            4.291455547187032e-15,
            -2.362482970256096e-15,
            -0.03561157530436869
          ],
          [
            2.9480593554070725e-15,
            -9.093910825830654e-16,
            -0.029686593136363675
          ],
          [
            4.614212962239557e-15,
            -7.930421174258009e-17,
            -0.02376311051889366
          ],
          [
            4.740045635355603e-15,
            -1.919848476330388e-15,
            -0.017841129573868356
          ],
          [
            3.672884747495209e-15,
            -3.005064436536647e-15,
            -0.011920652444116836
          ],
          [
            1.5545296699825454e-16,
            -1.8334850923516116e-15,
            -0.006001681293962183
          ],
          [
            5.005822864021741e-15,
            -4.5410258235112376e-15,
            -8.421830975146802e-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": [
          [
            1.5543122344752192e-15,
            8.881784197001252e-16,
            -0.04746602989823695
          ],
          [
            3.4416913763379853e-15,
            -2.220446049250313e-16,
            -0.04153805492130175
          ],
          [
            4.3298697960381105e-15,
            -2.3869795029440866e-15,
            -0.0356115753043687
          ],
          [
            2.9976021664879227e-15,
            -8.881784197001252e-16,
            -0.02968659313636368
          ],
          [
            4.6629367034256575e-15,
            -5.551115123125783e-17,
            -0.023763110518893682
          ],
          [
            4.773959005888173e-15,
            -1.942890293094024e-15,
            -0.017841129573868353
          ],
          [
            3.6637359812630166e-15,
            -2.9976021664879227e-15,
            -0.01192065244411683
          ],
          [
            1.1102230246251565e-16,
            -1.8318679906315083e-15,
            -0.006001681293962169
          ],
          [
            4.9960036108132044e-15,
            -4.551914400963142e-15,
            -8.421830975147149e-05
          ]
        ]
      },
      "reflected": {
        "reached": true,
        "construction": "reflect_displacements_about_reconstructed_parent",
        "energies_eV": [
          -529.6367861960671,
          -529.6349903395135,
          -529.632979318261,
          -529.6307533470235,
          -529.6283126391081,
          -529.6256574064194,
          -529.6227878594638,
          -529.6197042073561,
          -529.6164066578219
        ],
        "cartesian_polarizations_e_A2": [
          [
            8.66952898092045e-18,
            -4.591390685307714e-17,
            -6.120416954577661e-07
          ],
          [
            2.7472153293703377e-17,
            -2.3815816340175016e-17,
            3.575294325987086e-05
          ],
          [
            2.5603170755086413e-17,
            -2.5909180935198447e-17,
            7.21026427602837e-05
          ],
          [
            3.9539554250509347e-17,
            -1.0091700812175685e-16,
            0.00010843702979461489
          ],
          [
            5.388444206428044e-17,
            -1.0450109639037044e-16,
            0.0001447560774416137
          ],
          [
            9.109646068905306e-18,
            -6.983730586667716e-17,
            0.00018105975886946896
          ],
          [
            -6.265358089659369e-18,
            -1.5880158222706257e-17,
            0.00021734804733545708
          ],
          [
            4.144905500940247e-17,
            -8.394729371530275e-17,
            0.0002536209161860233
          ],
          [
            4.218863387052766e-17,
            -9.937607001193527e-17,
            0.00028987833885618793
          ]
        ],
        "raw_reduced_polarization": [
          [
            1.3742917065548778e-15,
            -3.594384549206403e-15,
            -8.42183097468034e-05
          ],
          [
            4.350517015267619e-15,
            -1.8653468517692e-15,
            0.004920215355342977
          ],
          [
            4.051237926189329e-15,
            -2.029838368435732e-15,
            0.009923623901358997
          ],
          [
            6.258141607485456e-15,
            -7.900967774437537e-15,
            0.014926003104506997
          ],
          [
            8.53074980921822e-15,
            -8.181087374769123e-15,
            0.019927348751646264
          ],
          [
            1.4351306639294798e-15,
            -5.4676391335706124e-15,
            0.024927656640230465
          ],
          [
            -9.997248609609504e-16,
            -1.2444896114331967e-15,
            0.0299269225782652
          ],
          [
            6.564240439591408e-15,
            -6.569761234836081e-15,
            0.0349251423843255
          ],
          [
            6.685155179424687e-15,
            -7.775441126386102e-15,
            0.03992231188748016
          ]
        ],
        "unwrapped_reduced_polarization": [
          [
            1.3742917065548778e-15,
            -3.594384549206403e-15,
            -8.42183097468034e-05
          ],
          [
            4.350517015267619e-15,
            -1.8653468517692e-15,
            0.004920215355342977
          ],
          [
            4.051237926189329e-15,
            -2.029838368435732e-15,
            0.009923623901358997
          ],
          [
            6.258141607485456e-15,
            -7.900967774437537e-15,
            0.014926003104506997
          ],
          [
            8.53074980921822e-15,
            -8.181087374769123e-15,
            0.019927348751646264
          ],
          [
            1.4351306639294795e-15,
            -5.4676391335706124e-15,
            0.024927656640230465
          ],
          [
            -9.997248609609504e-16,
            -1.2444896114331969e-15,
            0.0299269225782652
          ],
          [
            6.564240439591407e-15,
            -6.569761234836081e-15,
            0.0349251423843255
          ],
          [
            6.685155179424687e-15,
            -7.775441126386102e-15,
            0.03992231188748016
          ]
        ],
        "gauge_integer_shift": [
          0,
          0,
          0
        ],
        "expected_opposite_endpoint_reduced_polarization": [
          8.415509529426359e-15,
          -9.928459606149693e-15,
          0.04729744800590258
        ],
        "actual_opposite_endpoint_branch_residual": 0.007375136118422422
      },
      "pnp_branch": {
        "construction": "incoming_path_concatenated_with_parent_reflection",
        "reduced_polarization": [
          [
            1.5926849757104706e-15,
            8.513647820527338e-16,
            -0.04746602989823696
          ],
          [
            3.44713070008208e-15,
            -2.4186724399951915e-16,
            -0.041538054921301734
          ],
          [
            4.291455547187032e-15,
            -2.362482970256096e-15,
            -0.03561157530436869
          ],
          [
            2.9480593554070725e-15,
            -9.093910825830654e-16,
            -0.029686593136363675
          ],
          [
            4.614212962239557e-15,
            -7.930421174258008e-17,
            -0.02376311051889366
          ],
          [
            4.740045635355603e-15,
            -1.919848476330388e-15,
            -0.017841129573868356
          ],
          [
            3.672884747495209e-15,
            -3.005064436536647e-15,
            -0.011920652444116836
          ],
          [
            1.5545296699825436e-16,
            -1.8334850923516116e-15,
            -0.006001681293962183
          ],
          [
            5.005822864021741e-15,
            -4.5410258235112376e-15,
            -8.421830975146814e-05
          ],
          [
            4.350517015267619e-15,
            -1.8653468517692e-15,
            0.004920215355342977
          ],
          [
            4.051237926189329e-15,
            -2.029838368435732e-15,
            0.009923623901358997
          ],
          [
            6.258141607485456e-15,
            -7.900967774437537e-15,
            0.014926003104506997
          ],
          [
            8.53074980921822e-15,
            -8.181087374769123e-15,
            0.019927348751646264
          ],
          [
            1.4351306639294798e-15,
            -5.4676391335706124e-15,
            0.024927656640230465
          ],
          [
            -9.997248609609504e-16,
            -1.2444896114331967e-15,
            0.0299269225782652
          ],
          [
            6.564240439591408e-15,
            -6.569761234836081e-15,
            0.0349251423843255
          ],
          [
            6.685155179424687e-15,
            -7.775441126386102e-15,
            0.03992231188748016
          ]
        ],
        "unwrapped_reduced_polarization": [
          [
            1.5926849757104706e-15,
            8.513647820527338e-16,
            -0.04746602989823696
          ],
          [
            3.44713070008208e-15,
            -2.418672439995191e-16,
            -0.041538054921301734
          ],
          [
            4.291455547187032e-15,
            -2.362482970256096e-15,
            -0.03561157530436869
          ],
          [
            2.9480593554070725e-15,
            -9.093910825830654e-16,
            -0.029686593136363675
          ],
          [
            4.614212962239557e-15,
            -7.930421174258009e-17,
            -0.02376311051889366
          ],
          [
            4.740045635355603e-15,
            -1.919848476330388e-15,
            -0.017841129573868356
          ],
          [
            3.672884747495209e-15,
            -3.005064436536647e-15,
            -0.011920652444116836
          ],
          [
            1.5545296699825454e-16,
            -1.8334850923516116e-15,
            -0.006001681293962183
          ],
          [
            5.005822864021741e-15,
            -4.5410258235112376e-15,
            -8.421830975146802e-05
          ],
          [
            4.350517015267619e-15,
            -1.8653468517692e-15,
            0.004920215355342977
          ],
          [
            4.051237926189329e-15,
            -2.029838368435732e-15,
            0.009923623901358997
          ],
          [
            6.258141607485456e-15,
            -7.900967774437537e-15,
            0.014926003104506997
          ],
          [
            8.53074980921822e-15,
            -8.181087374769123e-15,
            0.019927348751646264
          ],
          [
            1.4351306639294795e-15,
            -5.4676391335706124e-15,
            0.024927656640230465
          ],
          [
            -9.997248609609504e-16,
            -1.2444896114331969e-15,
            0.0299269225782652
          ],
          [
            6.564240439591407e-15,
            -6.569761234836081e-15,
            0.0349251423843255
          ],
          [
            6.685155179424687e-15,
            -7.775441126386102e-15,
            0.03992231188748016
          ]
        ],
        "berry_integer_shifts": [
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ]
        ],
        "folded_reduced_polarization": [
          [
            1.5543122344752192e-15,
            8.881784197001252e-16,
            -0.04746602989823695
          ],
          [
            3.4416913763379853e-15,
            -2.220446049250313e-16,
            -0.04153805492130175
          ],
          [
            4.3298697960381105e-15,
            -2.3869795029440866e-15,
            -0.0356115753043687
          ],
          [
            2.9976021664879227e-15,
            -8.881784197001252e-16,
            -0.02968659313636368
          ],
          [
            4.6629367034256575e-15,
            -5.551115123125783e-17,
            -0.023763110518893682
          ],
          [
            4.773959005888173e-15,
            -1.942890293094024e-15,
            -0.017841129573868353
          ],
          [
            3.6637359812630166e-15,
            -2.9976021664879227e-15,
            -0.01192065244411683
          ],
          [
            1.1102230246251565e-16,
            -1.8318679906315083e-15,
            -0.006001681293962169
          ],
          [
            4.9960036108132044e-15,
            -4.551914400963142e-15,
            -8.421830975147149e-05
          ],
          [
            4.3298697960381105e-15,
            -1.887379141862766e-15,
            0.004920215355342927
          ],
          [
            3.9968028886505635e-15,
            -2.0539125955565396e-15,
            0.009923623901359035
          ],
          [
            6.217248937900877e-15,
            -7.882583474838611e-15,
            0.01492600310450698
          ],
          [
            8.548717289613705e-15,
            -8.1601392309949e-15,
            0.019927348751646257
          ],
          [
            1.4432899320127035e-15,
            -5.440092820663267e-15,
            0.024927656640230444
          ],
          [
            -9.992007221626409e-16,
            -1.2212453270876722e-15,
            0.029926922578265236
          ],
          [
            6.5503158452884236e-15,
            -6.5503158452884236e-15,
            0.034925142384325536
          ],
          [
            6.661338147750939e-15,
            -7.771561172376096e-15,
            0.03992231188748019
          ]
        ]
      },
      "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": "Amm2",
        "spacegroup_number": 38,
        "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": 8.421830975318233e-05,
        "parent_symmetrization_rmsd_A": 0.002244091552626341,
        "parent_cell_rmsd_A": 0.009442999532165045,
        "energy_eV": -529.6367861960671,
        "reduced_polarization": [
          -6.763800754755188e-16,
          -7.351808879398566e-16,
          -8.421830975318233e-05
        ],
        "cartesian_polarization_e_A2": [
          -4.267575054384137e-18,
          -9.391054823641054e-18,
          -6.120416955041238e-07
        ],
        "ranking_score": 0.5047732780551739
      }
    }
  ],
  "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": 51,
      "full_response": 16,
      "energy_polarization": 35
    },
    "model_evaluations_for_recovery_and_path_properties": {
      "total": 76,
      "full_response": 41,
      "energy_polarization": 35
    },
    "elapsed_seconds": 1631.166530033981
  }
}