{
  "schema": "ferrofinder.endpoint_parent_recovery.v4_variable_cell",
  "status": "complete",
  "input_atom_count": 28,
  "input_formula": "Li4Mn4O16P4",
  "input_spacegroup": "Cc",
  "input_pointgroup": "m",
  "input_is_polar_point_group": true,
  "input_energy_eV": -190.73209117166851,
  "input_cartesian_polarization_e_A2": [
    -0.005867211484924364,
    2.0612324291716113e-17,
    0.0035900102947713664
  ],
  "input_reduced_polarization": [
    -0.43638717601574406,
    8.57660595038902e-16,
    0.14023249549787517
  ],
  "input_formal_targets": [
    {
      "orbit_id": 0,
      "representative_formal_class": [
        0.5,
        0.0,
        0.0
      ],
      "target_reduced_polarization": [
        -0.5,
        0.0,
        0.0
      ]
    },
    {
      "orbit_id": 1,
      "representative_formal_class": [
        0.5,
        0.0,
        0.5
      ],
      "target_reduced_polarization": [
        -0.5,
        0.0,
        0.5
      ]
    },
    {
      "orbit_id": 2,
      "representative_formal_class": [
        0.0,
        0.0,
        0.0
      ],
      "target_reduced_polarization": [
        0.0,
        0.0,
        0.0
      ]
    },
    {
      "orbit_id": 3,
      "representative_formal_class": [
        0.5,
        0.5,
        0.0
      ],
      "target_reduced_polarization": [
        -0.5,
        0.5,
        0.0
      ]
    },
    {
      "orbit_id": 4,
      "representative_formal_class": [
        0.0,
        0.0,
        0.5
      ],
      "target_reduced_polarization": [
        0.0,
        0.0,
        0.5
      ]
    },
    {
      "orbit_id": 5,
      "representative_formal_class": [
        0.5,
        0.5,
        0.5
      ],
      "target_reduced_polarization": [
        -0.5,
        0.5,
        0.5
      ]
    },
    {
      "orbit_id": 6,
      "representative_formal_class": [
        0.0,
        0.5,
        0.0
      ],
      "target_reduced_polarization": [
        0.0,
        0.5,
        0.0
      ]
    },
    {
      "orbit_id": 7,
      "representative_formal_class": [
        0.0,
        0.5,
        0.5
      ],
      "target_reduced_polarization": [
        0.0,
        0.5,
        0.5
      ]
    }
  ],
  "parent_candidates": [
    {
      "candidate_id": "inversion_parent_endpoint_00",
      "source": "same_species_inversion_center_projection_from_endpoint",
      "spacegroup": "C2/c",
      "spacegroup_number": 15,
      "pointgroup": "2/m",
      "has_inversion": true,
      "is_polar_point_group": false,
      "nonpolar_parent_hypothesis": true,
      "symmetry_tolerance_A": null,
      "target_reduced_polarization": [
        0.0,
        0.0,
        0.0
      ],
      "formal_class": [
        0.0,
        0.0,
        0.0
      ],
      "target_residual": 1.3427253516275523e-15,
      "parent_symmetrization_rmsd_A": 0.6922644489704015,
      "parent_cell_rmsd_A": 0.0,
      "energy_eV": -144.08504130797883,
      "reduced_polarization": [
        -1.319028624822223e-15,
        3.656102003718232e-17,
        -2.484716253755543e-16
      ],
      "cartesian_polarization_e_A2": [
        -1.7752502804200226e-17,
        8.786781225598343e-19,
        -3.619180164747057e-18
      ],
      "ranking_score": 0.6922644489704042
    },
    {
      "candidate_id": "inversion_parent_endpoint_01",
      "source": "same_species_inversion_center_projection_from_endpoint",
      "spacegroup": "C2/c",
      "spacegroup_number": 15,
      "pointgroup": "2/m",
      "has_inversion": true,
      "is_polar_point_group": false,
      "nonpolar_parent_hypothesis": true,
      "symmetry_tolerance_A": null,
      "target_reduced_polarization": [
        0.0,
        0.0,
        0.0
      ],
      "formal_class": [
        0.0,
        0.0,
        0.0
      ],
      "target_residual": 9.77968228562888e-15,
      "parent_symmetrization_rmsd_A": 0.75365420496309,
      "parent_cell_rmsd_A": 0.0,
      "energy_eV": -158.30308507164492,
      "reduced_polarization": [
        2.8717615612405643e-15,
        -9.298686096123372e-15,
        9.641618271775515e-16
      ],
      "cartesian_polarization_e_A2": [
        3.8661837392632713e-17,
        -2.234771358377179e-16,
        1.6987777036156797e-17
      ],
      "ranking_score": 0.7536542049631095
    },
    {
      "candidate_id": "inversion_parent_endpoint_02",
      "source": "same_species_inversion_center_projection_from_endpoint",
      "spacegroup": "C2/c",
      "spacegroup_number": 15,
      "pointgroup": "2/m",
      "has_inversion": true,
      "is_polar_point_group": false,
      "nonpolar_parent_hypothesis": true,
      "symmetry_tolerance_A": null,
      "target_reduced_polarization": [
        0.0,
        0.0,
        0.0
      ],
      "formal_class": [
        0.0,
        0.0,
        0.0
      ],
      "target_residual": 1.0673458960813477e-15,
      "parent_symmetrization_rmsd_A": 1.2181933900841029,
      "parent_cell_rmsd_A": 0.0,
      "energy_eV": -133.00416098659974,
      "reduced_polarization": [
        3.2580898470997997e-16,
        -2.6811414693933705e-16,
        -9.804032698716069e-16
      ],
      "cartesian_polarization_e_A2": [
        4.356779024359179e-18,
        -6.4436395654387855e-18,
        -2.1527614002715942e-17
      ],
      "ranking_score": 1.218193390084105
    },
    {
      "candidate_id": "bec_projection_00",
      "source": "MACEField_BEC_backprojection",
      "spacegroup": "Cc",
      "spacegroup_number": 9,
      "pointgroup": "m",
      "has_inversion": false,
      "is_polar_point_group": true,
      "nonpolar_parent_hypothesis": false,
      "symmetry_tolerance_A": null,
      "target_reduced_polarization": [
        -0.5,
        0.0,
        0.0
      ],
      "formal_class": [
        0.5,
        0.0,
        0.0
      ],
      "target_residual": 0.0006625740239622227,
      "parent_symmetrization_rmsd_A": 0.01594361221665724,
      "parent_cell_rmsd_A": 0.05414380998509779,
      "energy_eV": -190.51014413195676,
      "reduced_polarization": [
        -0.49998779407835336,
        -1.137529567569367e-14,
        -0.0006624615858344152
      ],
      "cartesian_polarization_e_A2": [
        -0.006751121665980348,
        -2.8312293641090383e-16,
        0.0007113870763578789
      ],
      "ranking_score": 0.5308047127608562
    },
    {
      "candidate_id": "inversion_parent_bec_00_00",
      "source": "same_species_inversion_center_projection_after_BEC",
      "spacegroup": "C2/c",
      "spacegroup_number": 15,
      "pointgroup": "2/m",
      "has_inversion": true,
      "is_polar_point_group": false,
      "nonpolar_parent_hypothesis": true,
      "symmetry_tolerance_A": null,
      "target_reduced_polarization": [
        -0.5,
        0.0,
        0.0
      ],
      "formal_class": [
        0.5,
        0.0,
        0.0
      ],
      "target_residual": 0.49999999999999933,
      "parent_symmetrization_rmsd_A": 0.6922725549480654,
      "parent_cell_rmsd_A": 0.05414380998509779,
      "energy_eV": -142.84884027006865,
      "reduced_polarization": [
        7.118914347274523e-16,
        -6.706505234442005e-16,
        -3.8975054304801035e-16
      ],
      "cartesian_polarization_e_A2": [
        9.68971217610044e-18,
        -1.6142813531268328e-17,
        -9.422395968469275e-18
      ],
      "ranking_score": 1.7058085074443385
    },
    {
      "candidate_id": "inversion_parent_bec_00_01",
      "source": "same_species_inversion_center_projection_after_BEC",
      "spacegroup": "C2/c",
      "spacegroup_number": 15,
      "pointgroup": "2/m",
      "has_inversion": true,
      "is_polar_point_group": false,
      "nonpolar_parent_hypothesis": true,
      "symmetry_tolerance_A": null,
      "target_reduced_polarization": [
        -0.5,
        0.0,
        0.0
      ],
      "formal_class": [
        0.5,
        0.0,
        0.0
      ],
      "target_residual": 0.4999999999999958,
      "parent_symmetrization_rmsd_A": 0.7536628299559871,
      "parent_cell_rmsd_A": 0.05414380998509779,
      "energy_eV": -159.6442511526016,
      "reduced_polarization": [
        4.251661864658901e-15,
        -5.157912207579953e-15,
        -6.524433355198819e-15
      ],
      "cartesian_polarization_e_A2": [
        5.870114011370301e-17,
        -1.2415291134048185e-16,
        -1.4660609743397327e-16
      ],
      "ranking_score": 1.7671987824522533
    },
    {
      "candidate_id": "bec_projection_01",
      "source": "MACEField_BEC_backprojection",
      "spacegroup": "Cc",
      "spacegroup_number": 9,
      "pointgroup": "m",
      "has_inversion": false,
      "is_polar_point_group": true,
      "nonpolar_parent_hypothesis": false,
      "symmetry_tolerance_A": null,
      "target_reduced_polarization": [
        -0.5,
        0.0,
        0.5
      ],
      "formal_class": [
        0.5,
        0.0,
        0.5
      ],
      "target_residual": 0.00011946377763110501,
      "parent_symmetrization_rmsd_A": 0.04219702465797777,
      "parent_cell_rmsd_A": 0.1286368725879112,
      "energy_eV": -188.88133887003312,
      "reduced_polarization": [
        -0.49989733993384267,
        8.855140376461993e-16,
        0.49993890576964667
      ],
      "cartesian_polarization_e_A2": [
        -0.006429385364501132,
        1.5004259412640108e-16,
        0.011266276044565315
      ],
      "ranking_score": 0.5745951703602178
    },
    {
      "candidate_id": "bec_projection_02",
      "source": "MACEField_BEC_backprojection",
      "spacegroup": "Cc",
      "spacegroup_number": 9,
      "pointgroup": "m",
      "has_inversion": false,
      "is_polar_point_group": true,
      "nonpolar_parent_hypothesis": false,
      "symmetry_tolerance_A": null,
      "target_reduced_polarization": [
        0.0,
        0.0,
        0.0
      ],
      "formal_class": [
        0.0,
        0.0,
        0.0
      ],
      "target_residual": 3.269941962617376e-05,
      "parent_symmetrization_rmsd_A": 0.042799425112216204,
      "parent_cell_rmsd_A": 0.06375729597251814,
      "energy_eV": -189.39802880814932,
      "reduced_polarization": [
        1.957403852780841e-05,
        -1.9808615518498271e-16,
        -2.6193683582124707e-05
      ],
      "cartesian_polarization_e_A2": [
        2.626957053931146e-07,
        -4.743503627365882e-18,
        -5.889817325537594e-07
      ],
      "ranking_score": 0.5588041479445981
    },
    {
      "candidate_id": "bec_projection_03",
      "source": "MACEField_BEC_backprojection",
      "spacegroup": "P1",
      "spacegroup_number": 1,
      "pointgroup": "1",
      "has_inversion": false,
      "is_polar_point_group": true,
      "nonpolar_parent_hypothesis": false,
      "symmetry_tolerance_A": null,
      "target_reduced_polarization": [
        -0.5,
        0.5,
        0.0
      ],
      "formal_class": [
        0.5,
        0.5,
        0.0
      ],
      "target_residual": 8.166821025846399e-05,
      "parent_symmetrization_rmsd_A": 0.07201312076947293,
      "parent_cell_rmsd_A": 0.1663766064018102,
      "energy_eV": -185.24722439318336,
      "reduced_polarization": [
        -0.4999384873568646,
        0.4999602429179769,
        -3.6128461499556815e-05
      ],
      "cartesian_polarization_e_A2": [
        -0.006424412408668177,
        0.011857725569077908,
        0.0007770157866666958
      ],
      "ranking_score": 0.6137706087904424
    },
    {
      "candidate_id": "bec_projection_04",
      "source": "MACEField_BEC_backprojection",
      "spacegroup": "Cc",
      "spacegroup_number": 9,
      "pointgroup": "m",
      "has_inversion": false,
      "is_polar_point_group": true,
      "nonpolar_parent_hypothesis": false,
      "symmetry_tolerance_A": null,
      "target_reduced_polarization": [
        0.0,
        0.0,
        0.5
      ],
      "formal_class": [
        0.0,
        0.0,
        0.5
      ],
      "target_residual": 0.00017447715339236918,
      "parent_symmetrization_rmsd_A": 0.05050390052999775,
      "parent_cell_rmsd_A": 0.17062242946266515,
      "energy_eV": -188.3386844617406,
      "reduced_polarization": [
        0.0001369811710450325,
        -5.858126292911642e-15,
        0.49989193318809627
      ],
      "cartesian_polarization_e_A2": [
        0.00034423188728678025,
        -2.3091802277729037e-17,
        0.010744784632854743
      ],
      "ranking_score": 0.5935084622024488
    },
    {
      "candidate_id": "bec_projection_05",
      "source": "MACEField_BEC_backprojection",
      "spacegroup": "P1",
      "spacegroup_number": 1,
      "pointgroup": "1",
      "has_inversion": false,
      "is_polar_point_group": true,
      "nonpolar_parent_hypothesis": false,
      "symmetry_tolerance_A": null,
      "target_reduced_polarization": [
        -0.5,
        0.5,
        0.5
      ],
      "formal_class": [
        0.5,
        0.5,
        0.5
      ],
      "target_residual": 6.918028256134731e-05,
      "parent_symmetrization_rmsd_A": 0.08357927107383052,
      "parent_cell_rmsd_A": 0.2160065320775221,
      "energy_eV": -185.446561058873,
      "reduced_polarization": [
        -0.49995858007330884,
        0.49997265431073845,
        0.49995180752707136
      ],
      "cartesian_polarization_e_A2": [
        -0.006067111100093359,
        0.011864607880800791,
        0.0113108886852679
      ],
      "ranking_score": 0.6377192646583337
    },
    {
      "candidate_id": "bec_projection_06",
      "source": "MACEField_BEC_backprojection",
      "spacegroup": "P1",
      "spacegroup_number": 1,
      "pointgroup": "1",
      "has_inversion": false,
      "is_polar_point_group": true,
      "nonpolar_parent_hypothesis": false,
      "symmetry_tolerance_A": null,
      "target_reduced_polarization": [
        0.0,
        0.5,
        0.0
      ],
      "formal_class": [
        0.0,
        0.5,
        0.0
      ],
      "target_residual": 9.344626701995066e-05,
      "parent_symmetrization_rmsd_A": 0.08214024370582677,
      "parent_cell_rmsd_A": 0.17665133065680705,
      "energy_eV": -185.40740070255,
      "reduced_polarization": [
        3.2717162862078e-05,
        0.49993388111684134,
        -5.735926572116739e-05
      ],
      "cartesian_polarization_e_A2": [
        0.00033121401711381235,
        0.011978518881389415,
        5.3767876295786844e-05
      ],
      "ranking_score": 0.6264899689040684
    },
    {
      "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": [
        0.0,
        0.5,
        0.5
      ],
      "formal_class": [
        0.0,
        0.5,
        0.5
      ],
      "target_residual": 0.00026482152748938615,
      "parent_symmetrization_rmsd_A": 0.0899506686413186,
      "parent_cell_rmsd_A": 0.262014315074507,
      "energy_eV": -185.58350692347864,
      "reduced_polarization": [
        5.45095056144506e-05,
        0.49985100250362935,
        0.4997879648583495
      ],
      "cartesian_polarization_e_A2": [
        0.0007360743163561379,
        0.011988325728351845,
        0.01080766241268736
      ],
      "ranking_score": 0.6559838904649241
    }
  ],
  "formal_branches": [
    {
      "orbit_id": 0,
      "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": [
              -0.43638717601574406,
              8.57660595038902e-16,
              0.14023249549787517
            ],
            "branch_aligned_reduced_polarization": [
              -0.43638717601574406,
              8.57660595038902e-16,
              0.14023249549787517
            ],
            "target_residual": 0.15398618174632914,
            "energy_eV": -190.73209117166851,
            "max_atomic_step_A": 0.027007005250822683,
            "max_log_strain_component": 0.01044584720306053,
            "step_scale": 1.0,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 5.776926265610846,
            "cell_principal_stretches": [
              1.009796196596645,
              0.999455519554386,
              0.9887689425560787
            ],
            "cell_volume_ratio": 0.9979114782187095,
            "cell_rmsd_from_input_A": 0.05414380998509779
          },
          {
            "iteration": 1,
            "reduced_polarization": [
              -0.49998779407835336,
              -1.137529567569367e-14,
              -0.0006624615858344152
            ],
            "branch_aligned_reduced_polarization": [
              -0.49998779407835336,
              -1.137529567569367e-14,
              -0.0006624615858344152
            ],
            "target_residual": 0.0006625740239622227,
            "energy_eV": -190.51014413195676
          }
        ],
        "iterations": 1
      },
      "parent": {
        "candidate_id": "bec_projection_00",
        "source": "MACEField_BEC_backprojection",
        "spacegroup": "Cc",
        "spacegroup_number": 9,
        "pointgroup": "m",
        "has_inversion": false,
        "is_polar_point_group": true,
        "nonpolar_parent_hypothesis": false,
        "symmetry_tolerance_A": null,
        "target_reduced_polarization": [
          -0.5,
          0.0,
          0.0
        ],
        "formal_class": [
          0.5,
          0.0,
          0.0
        ],
        "target_residual": 0.0006625740239622227,
        "parent_symmetrization_rmsd_A": 0.01594361221665724,
        "parent_cell_rmsd_A": 0.05414380998509779,
        "energy_eV": -190.51014413195676,
        "reduced_polarization": [
          -0.49998779407835336,
          -1.137529567569367e-14,
          -0.0006624615858344152
        ],
        "cartesian_polarization_e_A2": [
          -0.006751121665980348,
          -2.8312293641090383e-16,
          0.0007113870763578789
        ],
        "ranking_score": 0.5308047127608562
      },
      "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": [
          -190.73209117166851,
          -190.72872715995584,
          -190.71833398006274,
          -190.70095003455626,
          -190.67660834319483,
          -190.6453366546366,
          -190.607157604876,
          -190.5620890070275,
          -190.51014413195682
        ],
        "cartesian_polarizations_e_A2": [
          [
            -0.005867211484924377,
            3.9458139441202563e-17,
            0.003590010294771337
          ],
          [
            -0.005982880283494407,
            -8.430190502036015e-17,
            0.0032299183855930436
          ],
          [
            -0.006097036885518659,
            -1.0808812494455779e-16,
            0.002869763876177813
          ],
          [
            -0.0062096988812816774,
            -1.0633016138823857e-16,
            0.0025096117369178715
          ],
          [
            -0.006320882360698102,
            -1.7253847483309219e-16,
            0.002149530963168866
          ],
          [
            -0.006430602409489559,
            -1.7086974188083925e-16,
            0.0017895933571438003
          ],
          [
            -0.0065388732533785115,
            -1.6603741998929415e-16,
            0.0014298730846978689
          ],
          [
            -0.006645708479127871,
            -1.336569123843537e-16,
            0.0010704458176177844
          ],
          [
            -0.00675112166598041,
            -2.906990523068286e-16,
            0.0007113870763579409
          ]
        ],
        "raw_reduced_polarization": [
          [
            -0.43638717601574495,
            1.6418183060447187e-15,
            0.14023249549787373
          ],
          [
            -0.4444930326298835,
            -3.4167747629658165e-15,
            0.12264406905642952
          ],
          [
            -0.4525518172188409,
            -4.327103301816314e-15,
            0.10504231222362569
          ],
          [
            -0.4605649600257942,
            -4.1867561786468354e-15,
            0.087430349029839
          ],
          [
            -0.4685337508790835,
            -6.884245906881245e-15,
            0.06981149492972506
          ],
          [
            -0.47645937475716293,
            -6.7710827561127844e-15,
            0.0521891984012987
          ],
          [
            -0.4843429215029708,
            -6.53845605339951e-15,
            0.03456702007367579
          ],
          [
            -0.49218540171574343,
            -5.173190214546274e-15,
            0.016948592137590302
          ],
          [
            -0.49998779407835797,
            -1.1690044159991903e-14,
            -0.0006624615858318438
          ]
        ],
        "unwrapped_reduced_polarization": [
          [
            -0.43638717601574495,
            1.6418183060447187e-15,
            0.14023249549787373
          ],
          [
            -0.4444930326298835,
            -3.4167747629658165e-15,
            0.12264406905642952
          ],
          [
            -0.4525518172188409,
            -4.327103301816314e-15,
            0.10504231222362569
          ],
          [
            -0.4605649600257942,
            -4.1867561786468354e-15,
            0.087430349029839
          ],
          [
            -0.4685337508790835,
            -6.884245906881245e-15,
            0.06981149492972506
          ],
          [
            -0.47645937475716293,
            -6.7710827561127844e-15,
            0.0521891984012987
          ],
          [
            -0.4843429215029708,
            -6.53845605339951e-15,
            0.03456702007367579
          ],
          [
            -0.49218540171574343,
            -5.173190214546274e-15,
            0.016948592137590302
          ],
          [
            -0.49998779407835797,
            -1.1690044159991903e-14,
            -0.0006624615858318444
          ]
        ],
        "berry_integer_shifts": [
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ]
        ],
        "folded_reduced_polarization": [
          [
            -0.43638717601574495,
            1.6653345369377348e-15,
            0.14023249549787375
          ],
          [
            -0.4444930326298835,
            -3.4416913763379853e-15,
            0.12264406905642955
          ],
          [
            -0.4525518172188409,
            -4.3298697960381105e-15,
            0.1050423122236257
          ],
          [
            -0.4605649600257942,
            -4.163336342344337e-15,
            0.08743034902983904
          ],
          [
            -0.4685337508790835,
            -6.8833827526759706e-15,
            0.06981149492972505
          ],
          [
            -0.47645937475716293,
            -6.772360450213455e-15,
            0.05218919840129865
          ],
          [
            -0.4843429215029708,
            -6.5503158452884236e-15,
            0.03456702007367585
          ],
          [
            -0.49218540171574343,
            -5.162537064506978e-15,
            0.016948592137590257
          ],
          [
            -0.49998779407835797,
            -1.1712852909795402e-14,
            -0.0006624615858318306
          ]
        ]
      },
      "reflected": {
        "reached": true,
        "construction": "reflect_displacements_about_reconstructed_parent",
        "energies_eV": [
          -190.5101441319568,
          -190.4726976220387,
          -190.43120939147764,
          -190.38562665902953,
          -190.33589507929634,
          -190.28195882049826,
          -190.22376108250742,
          -190.16124336130585,
          -190.0943451284405
        ],
        "cartesian_polarizations_e_A2": [
          [
            -0.006751121665980377,
            -2.5973420089685026e-16,
            0.0007113870763579134
          ],
          [
            -0.006785598322920131,
            -2.750346754978255e-16,
            0.0005704547391912588
          ],
          [
            -0.006820727623846931,
            -3.8966356968114716e-16,
            0.0004281471857043681
          ],
          [
            -0.006856557551397818,
            -3.517108568128667e-16,
            0.000284420689001315
          ],
          [
            -0.006893138421198187,
            -3.557420648860728e-16,
            0.0001392351264003299
          ],
          [
            -0.006930520957063461,
            -3.9397486572261723e-16,
            -7.443687228492153e-06
          ],
          [
            -0.006968753429070906,
            -4.283963809969002e-16,
            -0.00015564081312907863
          ],
          [
            -0.007007882521077522,
            -5.307504385143699e-16,
            -0.00030537307449165975
          ],
          [
            -0.0070479528239352825,
            -6.518510263798571e-16,
            -0.000456648806709034
          ]
        ],
        "raw_reduced_polarization": [
          [
            -0.4999877940783556,
            -1.0403614519567125e-14,
            -0.000662461585832953
          ],
          [
            -0.5028514181742868,
            -1.1105596697647847e-14,
            -0.006991147673000197
          ],
          [
            -0.5057393556591815,
            -1.5931700159098387e-14,
            -0.013381036576130233
          ],
          [
            -0.5086548314620267,
            -1.4412540285540453e-14,
            -0.01983428254261768
          ],
          [
            -0.5116012303530703,
            -1.4633818538513944e-14,
            -0.026352871601999252
          ],
          [
            -0.514581955640528,
            -1.6272851467148636e-14,
            -0.0329385035163935
          ],
          [
            -0.5176002192685975,
            -1.77493237595424e-14,
            -0.03959243050106066
          ],
          [
            -0.5206591104610658,
            -2.2047694199492305e-14,
            -0.046315503365690285
          ],
          [
            -0.5237615619414675,
            -2.7122945052167197e-14,
            -0.05310815833250716
          ]
        ],
        "unwrapped_reduced_polarization": [
          [
            -0.4999877940783556,
            -1.0403614519567125e-14,
            -0.000662461585832953
          ],
          [
            -0.5028514181742868,
            -1.1105596697647847e-14,
            -0.006991147673000197
          ],
          [
            -0.5057393556591815,
            -1.5931700159098387e-14,
            -0.013381036576130233
          ],
          [
            -0.5086548314620267,
            -1.4412540285540453e-14,
            -0.01983428254261768
          ],
          [
            -0.5116012303530703,
            -1.4633818538513944e-14,
            -0.026352871601999252
          ],
          [
            -0.514581955640528,
            -1.6272851467148636e-14,
            -0.0329385035163935
          ],
          [
            -0.5176002192685975,
            -1.77493237595424e-14,
            -0.03959243050106066
          ],
          [
            -0.5206591104610658,
            -2.2047694199492305e-14,
            -0.046315503365690285
          ],
          [
            -0.5237615619414675,
            -2.7122945052167197e-14,
            -0.05310815833250716
          ]
        ],
        "gauge_integer_shift": [
          0,
          0,
          0
        ],
        "expected_opposite_endpoint_reduced_polarization": [
          -0.5672333621771737,
          -2.5833279555169273e-14,
          -0.13523437645724445
        ],
        "actual_opposite_endpoint_branch_residual": 0.09292208090225418
      },
      "pnp_branch": {
        "construction": "incoming_path_concatenated_with_parent_reflection",
        "reduced_polarization": [
          [
            -0.43638717601574495,
            1.6418183060447187e-15,
            0.14023249549787373
          ],
          [
            -0.4444930326298835,
            -3.4167747629658165e-15,
            0.12264406905642952
          ],
          [
            -0.4525518172188409,
            -4.327103301816314e-15,
            0.10504231222362569
          ],
          [
            -0.4605649600257942,
            -4.1867561786468354e-15,
            0.087430349029839
          ],
          [
            -0.4685337508790835,
            -6.884245906881245e-15,
            0.06981149492972506
          ],
          [
            -0.47645937475716293,
            -6.7710827561127844e-15,
            0.0521891984012987
          ],
          [
            -0.4843429215029708,
            -6.53845605339951e-15,
            0.03456702007367579
          ],
          [
            -0.49218540171574343,
            -5.173190214546274e-15,
            0.016948592137590302
          ],
          [
            -0.49998779407835797,
            -1.1690044159991903e-14,
            -0.0006624615858318438
          ],
          [
            -0.5028514181742868,
            -1.1105596697647847e-14,
            -0.006991147673000197
          ],
          [
            -0.5057393556591815,
            -1.5931700159098387e-14,
            -0.013381036576130233
          ],
          [
            -0.5086548314620267,
            -1.4412540285540453e-14,
            -0.01983428254261768
          ],
          [
            -0.5116012303530703,
            -1.4633818538513944e-14,
            -0.026352871601999252
          ],
          [
            -0.514581955640528,
            -1.6272851467148636e-14,
            -0.0329385035163935
          ],
          [
            -0.5176002192685975,
            -1.77493237595424e-14,
            -0.03959243050106066
          ],
          [
            -0.5206591104610658,
            -2.2047694199492305e-14,
            -0.046315503365690285
          ],
          [
            -0.5237615619414675,
            -2.7122945052167197e-14,
            -0.05310815833250716
          ]
        ],
        "unwrapped_reduced_polarization": [
          [
            -0.43638717601574495,
            1.6418183060447187e-15,
            0.14023249549787373
          ],
          [
            -0.4444930326298835,
            -3.4167747629658165e-15,
            0.12264406905642952
          ],
          [
            -0.4525518172188409,
            -4.327103301816314e-15,
            0.10504231222362569
          ],
          [
            -0.4605649600257942,
            -4.1867561786468354e-15,
            0.087430349029839
          ],
          [
            -0.4685337508790835,
            -6.884245906881245e-15,
            0.06981149492972506
          ],
          [
            -0.47645937475716293,
            -6.7710827561127844e-15,
            0.0521891984012987
          ],
          [
            -0.4843429215029708,
            -6.53845605339951e-15,
            0.03456702007367579
          ],
          [
            -0.49218540171574343,
            -5.173190214546274e-15,
            0.016948592137590302
          ],
          [
            -0.49998779407835797,
            -1.1690044159991903e-14,
            -0.0006624615858318444
          ],
          [
            -0.5028514181742868,
            -1.1105596697647847e-14,
            -0.006991147673000197
          ],
          [
            -0.5057393556591815,
            -1.5931700159098387e-14,
            -0.013381036576130233
          ],
          [
            -0.5086548314620267,
            -1.4412540285540453e-14,
            -0.01983428254261768
          ],
          [
            -0.5116012303530703,
            -1.4633818538513944e-14,
            -0.026352871601999252
          ],
          [
            -0.514581955640528,
            -1.6272851467148636e-14,
            -0.0329385035163935
          ],
          [
            -0.5176002192685975,
            -1.77493237595424e-14,
            -0.03959243050106066
          ],
          [
            -0.5206591104610658,
            -2.2047694199492305e-14,
            -0.046315503365690285
          ],
          [
            -0.5237615619414675,
            -2.7122945052167197e-14,
            -0.05310815833250716
          ]
        ],
        "berry_integer_shifts": [
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ]
        ],
        "folded_reduced_polarization": [
          [
            -0.43638717601574495,
            1.6653345369377348e-15,
            0.14023249549787375
          ],
          [
            -0.4444930326298835,
            -3.4416913763379853e-15,
            0.12264406905642955
          ],
          [
            -0.4525518172188409,
            -4.3298697960381105e-15,
            0.1050423122236257
          ],
          [
            -0.4605649600257942,
            -4.163336342344337e-15,
            0.08743034902983904
          ],
          [
            -0.4685337508790835,
            -6.8833827526759706e-15,
            0.06981149492972505
          ],
          [
            -0.47645937475716293,
            -6.772360450213455e-15,
            0.05218919840129865
          ],
          [
            -0.4843429215029708,
            -6.5503158452884236e-15,
            0.03456702007367585
          ],
          [
            -0.49218540171574343,
            -5.162537064506978e-15,
            0.016948592137590257
          ],
          [
            -0.49998779407835797,
            -1.1712852909795402e-14,
            -0.0006624615858318306
          ],
          [
            0.4971485818257132,
            -1.1102230246251565e-14,
            -0.0069911476730001865
          ],
          [
            0.4942606443408185,
            -1.5931700403370996e-14,
            -0.013381036576130212
          ],
          [
            0.4913451685379733,
            -1.4432899320127035e-14,
            -0.019834282542617654
          ],
          [
            0.48839876964692974,
            -1.4654943925052066e-14,
            -0.026352871601999228
          ],
          [
            0.485418044359472,
            -1.6264767310758543e-14,
            -0.03293850351639349
          ],
          [
            0.48239978073140255,
            -1.7763568394002505e-14,
            -0.03959243050106065
          ],
          [
            0.47934088953893417,
            -2.2037927038809357e-14,
            -0.04631550336569029
          ],
          [
            0.4762384380585325,
            -2.7144952952085077e-14,
            -0.05310815833250715
          ]
        ]
      },
      "incoming_structure_ids": [
        "incoming_00_000",
        "incoming_00_001",
        "incoming_00_002",
        "incoming_00_003",
        "incoming_00_004",
        "incoming_00_005",
        "incoming_00_006",
        "incoming_00_007",
        "incoming_00_008"
      ],
      "reflected_structure_ids": [
        "reflected_00_001",
        "reflected_00_002",
        "reflected_00_003",
        "reflected_00_004",
        "reflected_00_005",
        "reflected_00_006",
        "reflected_00_007",
        "reflected_00_008"
      ]
    },
    {
      "orbit_id": 1,
      "formal_class": [
        0.5,
        0.0,
        0.5
      ],
      "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": [
              -0.43638717601574406,
              8.57660595038902e-16,
              0.14023249549787517
            ],
            "branch_aligned_reduced_polarization": [
              -0.43638717601574406,
              8.57660595038902e-16,
              0.1402324954978752
            ],
            "target_residual": 0.36534811984043153,
            "energy_eV": -190.73209117166851,
            "max_atomic_step_A": 0.05595731473608832,
            "max_log_strain_component": 0.02,
            "step_scale": 0.8247400649997555,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 5.776926265610846,
            "cell_principal_stretches": [
              1.0209627952321458,
              0.9987232377088696,
              0.980916567365771
            ],
            "cell_volume_ratio": 1.0002006694755088,
            "cell_rmsd_from_input_A": 0.10298688529879259
          },
          {
            "iteration": 1,
            "reduced_polarization": [
              -0.4872094725353364,
              1.956686175236717e-14,
              0.43198415524718975
            ],
            "branch_aligned_reduced_polarization": [
              -0.4872094725353364,
              1.956686175236717e-14,
              0.43198415524718975
            ],
            "target_residual": 0.069208039491541,
            "energy_eV": -189.57941668753156,
            "max_atomic_step_A": 0.013020403082384283,
            "max_log_strain_component": 0.004818699272665366,
            "step_scale": 1.0,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 5.776926265610846,
            "cell_principal_stretches": [
              1.0260772526813762,
              0.9984114089395443,
              0.9763721097442868
            ],
            "cell_volume_ratio": 1.000241708676548,
            "cell_rmsd_from_input_A": 0.1278561952250822
          },
          {
            "iteration": 2,
            "reduced_polarization": [
              -0.4972174358830143,
              4.418692754736044e-15,
              0.49759720844543204
            ],
            "branch_aligned_reduced_polarization": [
              -0.4972174358830143,
              4.418692754736044e-15,
              0.49759720844543204
            ],
            "target_residual": 0.0036764208572794624,
            "energy_eV": -188.91375041200968,
            "max_atomic_step_A": 0.0006303515226539175,
            "max_log_strain_component": 0.000148659307676558,
            "step_scale": 1.0,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 5.776926265610846,
            "cell_principal_stretches": [
              1.026223872390017,
              0.998368704950487,
              0.9762225911504646
            ],
            "cell_volume_ratio": 1.0001886590224294,
            "cell_rmsd_from_input_A": 0.1286368725879112
          },
          {
            "iteration": 3,
            "reduced_polarization": [
              -0.49989733993384267,
              8.855140376461993e-16,
              0.49993890576964667
            ],
            "branch_aligned_reduced_polarization": [
              -0.49989733993384267,
              8.855140376461993e-16,
              0.49993890576964667
            ],
            "target_residual": 0.00011946377763110501,
            "energy_eV": -188.88133887003312
          }
        ],
        "iterations": 3
      },
      "parent": {
        "candidate_id": "bec_projection_01",
        "source": "MACEField_BEC_backprojection",
        "spacegroup": "Cc",
        "spacegroup_number": 9,
        "pointgroup": "m",
        "has_inversion": false,
        "is_polar_point_group": true,
        "nonpolar_parent_hypothesis": false,
        "symmetry_tolerance_A": null,
        "target_reduced_polarization": [
          -0.5,
          0.0,
          0.5
        ],
        "formal_class": [
          0.5,
          0.0,
          0.5
        ],
        "target_residual": 0.00011946377763110501,
        "parent_symmetrization_rmsd_A": 0.04219702465797777,
        "parent_cell_rmsd_A": 0.1286368725879112,
        "energy_eV": -188.88133887003312,
        "reduced_polarization": [
          -0.49989733993384267,
          8.855140376461993e-16,
          0.49993890576964667
        ],
        "cartesian_polarization_e_A2": [
          -0.006429385364501132,
          1.5004259412640108e-16,
          0.011266276044565315
        ],
        "ranking_score": 0.5745951703602178
      },
      "branch_status": "awaiting_branch_sampling"
    },
    {
      "orbit_id": 2,
      "formal_class": [
        0.0,
        0.0,
        0.0
      ],
      "formal_classes_in_orbit": [
        [
          0.0,
          0.0,
          0.0
        ]
      ],
      "target_reduced_polarization": [
        0.0,
        0.0,
        0.0
      ],
      "bec_backprojection": {
        "converged_to_target": true,
        "history": [
          {
            "iteration": 0,
            "reduced_polarization": [
              -0.43638717601574406,
              8.57660595038902e-16,
              0.14023249549787517
            ],
            "branch_aligned_reduced_polarization": [
              -0.43638717601574406,
              8.57660595038902e-16,
              0.14023249549787517
            ],
            "target_residual": 0.4583654875582994,
            "energy_eV": -190.73209117166851,
            "max_atomic_step_A": 0.06961747597187265,
            "max_log_strain_component": 0.006076317086635495,
            "step_scale": 1.0,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 5.776926265610846,
            "cell_principal_stretches": [
              1.0082242565320727,
              1.0059681736397412,
              0.9950682750049462
            ],
            "cell_volume_ratio": 1.009239553737423,
            "cell_rmsd_from_input_A": 0.06266219747814661
          },
          {
            "iteration": 1,
            "reduced_polarization": [
              0.0021676921929867565,
              -9.63284108564749e-15,
              0.007920076091806061
            ],
            "branch_aligned_reduced_polarization": [
              0.0021676921929867565,
              -9.63284108564749e-15,
              0.007920076091806061
            ],
            "target_residual": 0.008211363756620071,
            "energy_eV": -189.40181423136443,
            "max_atomic_step_A": 0.001503392996978451,
            "max_log_strain_component": 0.0005966948357314061,
            "step_scale": 1.0,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 5.776926265610846,
            "cell_principal_stretches": [
              1.0086098595447306,
              1.0059632195600794,
              0.9946166402183835
            ],
            "cell_volume_ratio": 1.0091623332830357,
            "cell_rmsd_from_input_A": 0.06375729597251814
          },
          {
            "iteration": 2,
            "reduced_polarization": [
              1.957403852780841e-05,
              -1.9808615518498271e-16,
              -2.6193683582124707e-05
            ],
            "branch_aligned_reduced_polarization": [
              1.957403852780841e-05,
              -1.9808615518498271e-16,
              -2.6193683582124707e-05
            ],
            "target_residual": 3.269941962617376e-05,
            "energy_eV": -189.39802880814932
          }
        ],
        "iterations": 2
      },
      "parent": {
        "candidate_id": "bec_projection_02",
        "source": "MACEField_BEC_backprojection",
        "spacegroup": "Cc",
        "spacegroup_number": 9,
        "pointgroup": "m",
        "has_inversion": false,
        "is_polar_point_group": true,
        "nonpolar_parent_hypothesis": false,
        "symmetry_tolerance_A": null,
        "target_reduced_polarization": [
          0.0,
          0.0,
          0.0
        ],
        "formal_class": [
          0.0,
          0.0,
          0.0
        ],
        "target_residual": 3.269941962617376e-05,
        "parent_symmetrization_rmsd_A": 0.042799425112216204,
        "parent_cell_rmsd_A": 0.06375729597251814,
        "energy_eV": -189.39802880814932,
        "reduced_polarization": [
          1.957403852780841e-05,
          -1.9808615518498271e-16,
          -2.6193683582124707e-05
        ],
        "cartesian_polarization_e_A2": [
          2.626957053931146e-07,
          -4.743503627365882e-18,
          -5.889817325537594e-07
        ],
        "ranking_score": 0.5588041479445981
      },
      "branch_status": "awaiting_branch_sampling"
    },
    {
      "orbit_id": 3,
      "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": [
              -0.43638717601574406,
              8.57660595038902e-16,
              0.14023249549787517
            ],
            "branch_aligned_reduced_polarization": [
              -0.43638717601574406,
              8.326672684688674e-16,
              0.14023249549787517
            ],
            "target_residual": 0.5231746784476602,
            "energy_eV": -190.73209117166851,
            "max_atomic_step_A": 0.08477347626581033,
            "max_log_strain_component": 0.02,
            "step_scale": 0.7640523907026185,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 5.776926265610846,
            "cell_principal_stretches": [
              1.0207403277749394,
              1.0009065255114766,
              0.9772315058404035
            ],
            "cell_volume_ratio": 0.9984038664254934,
            "cell_rmsd_from_input_A": 0.12335875846330492
          },
          {
            "iteration": 1,
            "reduced_polarization": [
              -0.4918182537307296,
              0.37525500443573745,
              0.03073739307029492
            ],
            "branch_aligned_reduced_polarization": [
              -0.4918182537307296,
              0.37525500443573745,
              0.03073739307029492
            ],
            "target_residual": 0.1287363282958638,
            "energy_eV": -187.7968431171079,
            "max_atomic_step_A": 0.03019165386837574,
            "max_log_strain_component": 0.006966774920242214,
            "step_scale": 1.0,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 5.776926265610846,
            "cell_principal_stretches": [
              1.0280218386930093,
              1.0013760731215053,
              0.9696439522390484
            ],
            "cell_volume_ratio": 0.9981868492052821,
            "cell_rmsd_from_input_A": 0.16555069041415613
          },
          {
            "iteration": 2,
            "reduced_polarization": [
              -0.49891458962802937,
              0.4971641660169644,
              -0.0007236139671787786
            ],
            "branch_aligned_reduced_polarization": [
              -0.49891458962802937,
              0.4971641660169644,
              -0.0007236139671787786
            ],
            "target_residual": 0.003121487983064684,
            "energy_eV": -185.3054137763134,
            "max_atomic_step_A": 0.0007261233236326468,
            "max_log_strain_component": 0.00016016950531652215,
            "step_scale": 1.0,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 5.776926265610846,
            "cell_principal_stretches": [
              1.0281653036625518,
              1.0013597859845422,
              0.9695077746846139
            ],
            "cell_volume_ratio": 0.9981697096157159,
            "cell_rmsd_from_input_A": 0.1663766064018102
          },
          {
            "iteration": 3,
            "reduced_polarization": [
              -0.4999384873568646,
              0.4999602429179769,
              -3.6128461499556815e-05
            ],
            "branch_aligned_reduced_polarization": [
              -0.4999384873568646,
              0.4999602429179769,
              -3.6128461499556815e-05
            ],
            "target_residual": 8.166821025846399e-05,
            "energy_eV": -185.24722439318336
          }
        ],
        "iterations": 3
      },
      "parent": {
        "candidate_id": "bec_projection_03",
        "source": "MACEField_BEC_backprojection",
        "spacegroup": "P1",
        "spacegroup_number": 1,
        "pointgroup": "1",
        "has_inversion": false,
        "is_polar_point_group": true,
        "nonpolar_parent_hypothesis": false,
        "symmetry_tolerance_A": null,
        "target_reduced_polarization": [
          -0.5,
          0.5,
          0.0
        ],
        "formal_class": [
          0.5,
          0.5,
          0.0
        ],
        "target_residual": 8.166821025846399e-05,
        "parent_symmetrization_rmsd_A": 0.07201312076947293,
        "parent_cell_rmsd_A": 0.1663766064018102,
        "energy_eV": -185.24722439318336,
        "reduced_polarization": [
          -0.4999384873568646,
          0.4999602429179769,
          -3.6128461499556815e-05
        ],
        "cartesian_polarization_e_A2": [
          -0.006424412408668177,
          0.011857725569077908,
          0.0007770157866666958
        ],
        "ranking_score": 0.6137706087904424
      },
      "branch_status": "awaiting_branch_sampling"
    },
    {
      "orbit_id": 4,
      "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": [
              -0.43638717601574406,
              8.57660595038902e-16,
              0.14023249549787517
            ],
            "branch_aligned_reduced_polarization": [
              -0.43638717601574406,
              8.57660595038902e-16,
              0.1402324954978752
            ],
            "target_residual": 0.5655673476135997,
            "energy_eV": -190.73209117166851,
            "max_atomic_step_A": 0.05945229949663343,
            "max_log_strain_component": 0.02,
            "step_scale": 0.6695930320726784,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 5.776926265610846,
            "cell_principal_stretches": [
              1.0229107106375537,
              1.0033172944380326,
              0.9819225480348872
            ],
            "cell_volume_ratio": 1.0077510452667635,
            "cell_rmsd_from_input_A": 0.11070400637486058
          },
          {
            "iteration": 1,
            "reduced_polarization": [
              -0.14214242193212093,
              1.1972367762416552e-14,
              0.3762064729433728
            ],
            "branch_aligned_reduced_polarization": [
              -0.14214242193212093,
              1.1972367762416552e-14,
              0.3762064729433728
            ],
            "target_residual": 0.1884921893709365,
            "energy_eV": -189.7067222016828,
            "max_atomic_step_A": 0.03004820143153847,
            "max_log_strain_component": 0.010502779610801252,
            "step_scale": 1.0,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 5.776926265610846,
            "cell_principal_stretches": [
              1.035060799391046,
              1.0048827868897543,
              0.9725339578341679
            ],
            "cell_volume_ratio": 1.0115469442686078,
            "cell_rmsd_from_input_A": 0.1690946462957039
          },
          {
            "iteration": 2,
            "reduced_polarization": [
              0.001575093484245797,
              1.712649308463753e-14,
              0.4954455126982598
            ],
            "branch_aligned_reduced_polarization": [
              0.001575093484245797,
              1.712649308463753e-14,
              0.4954455126982598
            ],
            "target_residual": 0.004819156987049307,
            "energy_eV": -188.36632330969354,
            "max_atomic_step_A": 0.0009026872334313472,
            "max_log_strain_component": 0.00032379899572746856,
            "step_scale": 1.0,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 5.776926265610846,
            "cell_principal_stretches": [
              1.0353989927374536,
              1.0048534836168888,
              0.9722343019411602
            ],
            "cell_volume_ratio": 1.0115361782412053,
            "cell_rmsd_from_input_A": 0.17062242946266515
          },
          {
            "iteration": 3,
            "reduced_polarization": [
              0.0001369811710450325,
              -5.858126292911642e-15,
              0.49989193318809627
            ],
            "branch_aligned_reduced_polarization": [
              0.0001369811710450325,
              -5.858126292911642e-15,
              0.49989193318809627
            ],
            "target_residual": 0.00017447715339236918,
            "energy_eV": -188.3386844617406
          }
        ],
        "iterations": 3
      },
      "parent": {
        "candidate_id": "bec_projection_04",
        "source": "MACEField_BEC_backprojection",
        "spacegroup": "Cc",
        "spacegroup_number": 9,
        "pointgroup": "m",
        "has_inversion": false,
        "is_polar_point_group": true,
        "nonpolar_parent_hypothesis": false,
        "symmetry_tolerance_A": null,
        "target_reduced_polarization": [
          0.0,
          0.0,
          0.5
        ],
        "formal_class": [
          0.0,
          0.0,
          0.5
        ],
        "target_residual": 0.00017447715339236918,
        "parent_symmetrization_rmsd_A": 0.05050390052999775,
        "parent_cell_rmsd_A": 0.17062242946266515,
        "energy_eV": -188.3386844617406,
        "reduced_polarization": [
          0.0001369811710450325,
          -5.858126292911642e-15,
          0.49989193318809627
        ],
        "cartesian_polarization_e_A2": [
          0.00034423188728678025,
          -2.3091802277729037e-17,
          0.010744784632854743
        ],
        "ranking_score": 0.5935084622024488
      },
      "branch_status": "awaiting_branch_sampling"
    },
    {
      "orbit_id": 5,
      "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": [
              -0.43638717601574406,
              8.57660595038902e-16,
              0.14023249549787517
            ],
            "branch_aligned_reduced_polarization": [
              -0.43638717601574406,
              8.326672684688674e-16,
              0.1402324954978752
            ],
            "target_residual": 0.6192570134208716,
            "energy_eV": -190.73209117166851,
            "max_atomic_step_A": 0.09765426409842909,
            "max_log_strain_component": 0.02,
            "step_scale": 0.7640523907028154,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 5.776926265610846,
            "cell_principal_stretches": [
              1.0294911585177022,
              0.9967514435768613,
              0.9747006018997363
            ],
            "cell_volume_ratio": 1.000185902040048,
            "cell_rmsd_from_input_A": 0.15163028827009903
          },
          {
            "iteration": 1,
            "reduced_polarization": [
              -0.494347089923112,
              0.3747066614139574,
              0.4014077835936584
            ],
            "branch_aligned_reduced_polarization": [
              -0.494347089923112,
              0.3747066614139574,
              0.4014077835936584
            ],
            "target_residual": 0.15953307250313015,
            "energy_eV": -187.84539993399153,
            "max_atomic_step_A": 0.03553742516897583,
            "max_log_strain_component": 0.007897608819354272,
            "step_scale": 1.0,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 5.776926265610846,
            "cell_principal_stretches": [
              1.0413984769588962,
              0.9959030404383118,
              0.9650619366044032
            ],
            "cell_volume_ratio": 1.0008965291070935,
            "cell_rmsd_from_input_A": 0.2110583984750699
          },
          {
            "iteration": 2,
            "reduced_polarization": [
              -0.49782789889977747,
              0.49365791545715243,
              0.49030600458270773
            ],
            "branch_aligned_reduced_polarization": [
              -0.49782789889977747,
              0.49365791545715243,
              0.49030600458270773
            ],
            "target_residual": 0.011786161660553341,
            "energy_eV": -185.6404816278588,
            "max_atomic_step_A": 0.0025308696389331016,
            "max_log_strain_component": 0.0008063084066679946,
            "step_scale": 1.0,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 5.776926265610846,
            "cell_principal_stretches": [
              1.0423554795493255,
              0.9958280373704114,
              0.964287713673442
            ],
            "cell_volume_ratio": 1.0009372149827682,
            "cell_rmsd_from_input_A": 0.21569443168579114
          },
          {
            "iteration": 3,
            "reduced_polarization": [
              -0.4994290900040827,
              0.49957426805841926,
              0.49926192983858875
            ],
            "branch_aligned_reduced_polarization": [
              -0.4994290900040827,
              0.49957426805841926,
              0.49926192983858875
            ],
            "target_residual": 0.001025638080750727,
            "energy_eV": -185.46130628523346,
            "max_atomic_step_A": 0.0002008941924531841,
            "max_log_strain_component": 5.5562810465413776e-05,
            "step_scale": 1.0,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 5.776926265610846,
            "cell_principal_stretches": [
              1.0424182522703294,
              0.9958167613581139,
              0.9642338993556331
            ],
            "cell_volume_ratio": 1.0009302965062488,
            "cell_rmsd_from_input_A": 0.2160065320775221
          },
          {
            "iteration": 4,
            "reduced_polarization": [
              -0.49995858007330884,
              0.49997265431073845,
              0.49995180752707136
            ],
            "branch_aligned_reduced_polarization": [
              -0.49995858007330884,
              0.49997265431073845,
              0.49995180752707136
            ],
            "target_residual": 6.918028256134731e-05,
            "energy_eV": -185.446561058873
          }
        ],
        "iterations": 4
      },
      "parent": {
        "candidate_id": "bec_projection_05",
        "source": "MACEField_BEC_backprojection",
        "spacegroup": "P1",
        "spacegroup_number": 1,
        "pointgroup": "1",
        "has_inversion": false,
        "is_polar_point_group": true,
        "nonpolar_parent_hypothesis": false,
        "symmetry_tolerance_A": null,
        "target_reduced_polarization": [
          -0.5,
          0.5,
          0.5
        ],
        "formal_class": [
          0.5,
          0.5,
          0.5
        ],
        "target_residual": 6.918028256134731e-05,
        "parent_symmetrization_rmsd_A": 0.08357927107383052,
        "parent_cell_rmsd_A": 0.2160065320775221,
        "energy_eV": -185.446561058873,
        "reduced_polarization": [
          -0.49995858007330884,
          0.49997265431073845,
          0.49995180752707136
        ],
        "cartesian_polarization_e_A2": [
          -0.006067111100093359,
          0.011864607880800791,
          0.0113108886852679
        ],
        "ranking_score": 0.6377192646583337
      },
      "branch_status": "awaiting_branch_sampling"
    },
    {
      "orbit_id": 6,
      "formal_class": [
        0.0,
        0.5,
        0.0
      ],
      "formal_classes_in_orbit": [
        [
          0.0,
          0.5,
          0.0
        ]
      ],
      "target_reduced_polarization": [
        0.0,
        0.5,
        0.0
      ],
      "bec_backprojection": {
        "converged_to_target": true,
        "history": [
          {
            "iteration": 0,
            "reduced_polarization": [
              -0.43638717601574406,
              8.57660595038902e-16,
              0.14023249549787517
            ],
            "branch_aligned_reduced_polarization": [
              -0.43638717601574406,
              8.326672684688674e-16,
              0.14023249549787517
            ],
            "target_residual": 0.6783059193200047,
            "energy_eV": -190.73209117166851,
            "max_atomic_step_A": 0.09752505186481929,
            "max_log_strain_component": 0.02,
            "step_scale": 0.7640523907024316,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 5.776926265610846,
            "cell_principal_stretches": [
              1.0217057977567126,
              1.005661297193852,
              0.98010867148529
            ],
            "cell_volume_ratio": 1.0070518372260668,
            "cell_rmsd_from_input_A": 0.1270436288093049
          },
          {
            "iteration": 1,
            "reduced_polarization": [
              -0.11223124925490983,
              0.37165137768139345,
              0.034147275641836485
            ],
            "branch_aligned_reduced_polarization": [
              -0.11223124925490983,
              0.37165137768139345,
              0.034147275641836485
            ],
            "target_residual": 0.17388288758288312,
            "energy_eV": -187.85723501511308,
            "max_atomic_step_A": 0.033905681133247045,
            "max_log_strain_component": 0.007501751205384345,
            "step_scale": 1.0,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 5.776926265610846,
            "cell_principal_stretches": [
              1.0299630914603277,
              1.0077666088452453,
              0.972764057862283
            ],
            "cell_volume_ratio": 1.0096925277246505,
            "cell_rmsd_from_input_A": 0.17516689881763528
          },
          {
            "iteration": 2,
            "reduced_polarization": [
              -0.0017669526751677186,
              0.4958391097036442,
              -0.0006713265198309512
            ],
            "branch_aligned_reduced_polarization": [
              -0.0017669526751677186,
              0.4958391097036442,
              -0.0006713265198309512
            ],
            "target_residual": 0.004570099463996223,
            "energy_eV": -185.4805937574455,
            "max_atomic_step_A": 0.0009932216583217668,
            "max_log_strain_component": 0.00025774195091983015,
            "step_scale": 1.0,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 5.776926265610846,
            "cell_principal_stretches": [
              1.0302384143720262,
              1.0077861326342221,
              0.972542287457116
            ],
            "cell_volume_ratio": 1.0097517430348284,
            "cell_rmsd_from_input_A": 0.17665133065680705
          },
          {
            "iteration": 3,
            "reduced_polarization": [
              3.2717162862078e-05,
              0.49993388111684134,
              -5.735926572116739e-05
            ],
            "branch_aligned_reduced_polarization": [
              3.2717162862078e-05,
              0.49993388111684134,
              -5.735926572116739e-05
            ],
            "target_residual": 9.344626701995066e-05,
            "energy_eV": -185.40740070255
          }
        ],
        "iterations": 3
      },
      "parent": {
        "candidate_id": "bec_projection_06",
        "source": "MACEField_BEC_backprojection",
        "spacegroup": "P1",
        "spacegroup_number": 1,
        "pointgroup": "1",
        "has_inversion": false,
        "is_polar_point_group": true,
        "nonpolar_parent_hypothesis": false,
        "symmetry_tolerance_A": null,
        "target_reduced_polarization": [
          0.0,
          0.5,
          0.0
        ],
        "formal_class": [
          0.0,
          0.5,
          0.0
        ],
        "target_residual": 9.344626701995066e-05,
        "parent_symmetrization_rmsd_A": 0.08214024370582677,
        "parent_cell_rmsd_A": 0.17665133065680705,
        "energy_eV": -185.40740070255,
        "reduced_polarization": [
          3.2717162862078e-05,
          0.49993388111684134,
          -5.735926572116739e-05
        ],
        "cartesian_polarization_e_A2": [
          0.00033121401711381235,
          0.011978518881389415,
          5.3767876295786844e-05
        ],
        "ranking_score": 0.6264899689040684
      },
      "branch_status": "awaiting_branch_sampling"
    },
    {
      "orbit_id": 7,
      "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": [
              -0.43638717601574406,
              8.57660595038902e-16,
              0.14023249549787517
            ],
            "branch_aligned_reduced_polarization": [
              -0.43638717601574406,
              8.326672684688674e-16,
              0.1402324954978752
            ],
            "target_residual": 0.7548949759315409,
            "energy_eV": -190.73209117166851,
            "max_atomic_step_A": 0.09410315904607781,
            "max_log_strain_component": 0.02,
            "step_scale": 0.6695930320727692,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 5.776926265610846,
            "cell_principal_stretches": [
              1.0305307264398245,
              1.0017552739189797,
              0.9761817282659812
            ],
            "cell_volume_ratio": 1.0077510452667535,
            "cell_rmsd_from_input_A": 0.1521397186952089
          },
          {
            "iteration": 1,
            "reduced_polarization": [
              -0.152740779848219,
              0.3253855037201456,
              0.3674954515489675
            ],
            "branch_aligned_reduced_polarization": [
              -0.152740779848219,
              0.3253855037201456,
              0.3674954515489675
            ],
            "target_residual": 0.267165535763731,
            "energy_eV": -188.5635670271775,
            "max_atomic_step_A": 0.05194067661096215,
            "max_log_strain_component": 0.012662309738853772,
            "step_scale": 1.0,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 5.776926265610846,
            "cell_principal_stretches": [
              1.049838597003163,
              1.0027554449955525,
              0.9617078657814052
            ],
            "cell_volume_ratio": 1.012420038613957,
            "cell_rmsd_from_input_A": 0.24812205947555183
          },
          {
            "iteration": 2,
            "reduced_polarization": [
              -0.005649218506996335,
              0.4839203784221179,
              0.4813245644479366
            ],
            "branch_aligned_reduced_polarization": [
              -0.005649218506996335,
              0.4839203784221179,
              0.4813245644479366
            ],
            "target_residual": 0.025283191904642028,
            "energy_eV": -185.93756220719698,
            "max_atomic_step_A": 0.005417728372246233,
            "max_log_strain_component": 0.0019062850290011103,
            "step_scale": 1.0,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 5.776926265610846,
            "cell_principal_stretches": [
              1.0524299891308577,
              1.0027437111611817,
              0.9597223299661318
            ],
            "cell_volume_ratio": 1.0128118208561683,
            "cell_rmsd_from_input_A": 0.26074622090951954
          },
          {
            "iteration": 3,
            "reduced_polarization": [
              0.0003296761843524952,
              0.4984626563623186,
              0.4978700446626141
            ],
            "branch_aligned_reduced_polarization": [
              0.0003296761843524952,
              0.4984626563623186,
              0.4978700446626141
            ],
            "target_residual": 0.0026474179092291737,
            "energy_eV": -185.61464052963714,
            "max_atomic_step_A": 0.0005748822457579172,
            "max_log_strain_component": 0.00020381520941542143,
            "step_scale": 1.0,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 5.776926265610846,
            "cell_principal_stretches": [
              1.0526931538203774,
              1.0027307008525255,
              0.9595151216947209
            ],
            "cell_volume_ratio": 1.0128332122576675,
            "cell_rmsd_from_input_A": 0.262014315074507
          },
          {
            "iteration": 4,
            "reduced_polarization": [
              5.45095056144506e-05,
              0.49985100250362935,
              0.4997879648583495
            ],
            "branch_aligned_reduced_polarization": [
              5.45095056144506e-05,
              0.49985100250362935,
              0.4997879648583495
            ],
            "target_residual": 0.00026482152748938615,
            "energy_eV": -185.58350692347864
          }
        ],
        "iterations": 4
      },
      "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": [
          0.0,
          0.5,
          0.5
        ],
        "formal_class": [
          0.0,
          0.5,
          0.5
        ],
        "target_residual": 0.00026482152748938615,
        "parent_symmetrization_rmsd_A": 0.0899506686413186,
        "parent_cell_rmsd_A": 0.262014315074507,
        "energy_eV": -185.58350692347864,
        "reduced_polarization": [
          5.45095056144506e-05,
          0.49985100250362935,
          0.4997879648583495
        ],
        "cartesian_polarization_e_A2": [
          0.0007360743163561379,
          0.011988325728351845,
          0.01080766241268736
        ],
        "ranking_score": 0.6559838904649241
      },
      "branch_status": "awaiting_branch_sampling"
    }
  ],
  "sampled_polarization_branches": [
    {
      "orbit_id": 0,
      "candidate_id": "bec_projection_00",
      "formal_class": [
        0.5,
        0.0,
        0.0
      ],
      "construction": "MACEField-BEC-parent plus variable-cell P-N-P path and symmetric log-strain continuation beyond both polar endpoints",
      "geometry_diagnostics": {
        "collision_aware": false,
        "permutations_tested": 1,
        "selected_order": [
          0,
          1,
          2,
          3,
          4,
          5,
          6,
          7,
          8,
          9,
          10,
          11,
          12,
          13,
          14,
          15,
          16,
          17,
          18,
          19,
          20,
          21,
          22,
          23,
          24,
          25,
          26,
          27
        ],
        "endpoint_rmsd_A": 0.01594361221665724,
        "minimum_distance_A_by_image": [
          1.5512279072880302,
          1.5483480521624131,
          1.5454878560371665,
          1.5426473126333227,
          1.5379700541201677,
          1.533206419827118,
          1.5284617021747815,
          1.5237358886838608,
          1.5190289670043755
        ],
        "minimum_distance_A": 1.5190289670043755,
        "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": [
          379.05451249569086,
          378.9554640061015,
          378.8564413982864,
          378.75744466548235,
          378.65847380092794,
          378.55952879786423,
          378.4606096495333,
          378.3617163491788,
          378.26284889004717
        ],
        "cell_deformation_log_strain_norm": 0.014929782093347756
      },
      "parent_reduced_polarization": [
        -0.49998779407835797,
        -1.1690044159991903e-14,
        -0.0006624615858318438
      ],
      "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": [
          -190.73209117166851,
          -190.72872715995584,
          -190.71833398006274,
          -190.70095003455626,
          -190.67660834319483,
          -190.6453366546366,
          -190.607157604876,
          -190.5620890070275,
          -190.51014413195682
        ],
        "cartesian_polarizations_e_A2": [
          [
            -0.005867211484924377,
            3.9458139441202563e-17,
            0.003590010294771337
          ],
          [
            -0.005982880283494407,
            -8.430190502036015e-17,
            0.0032299183855930436
          ],
          [
            -0.006097036885518659,
            -1.0808812494455779e-16,
            0.002869763876177813
          ],
          [
            -0.0062096988812816774,
            -1.0633016138823857e-16,
            0.0025096117369178715
          ],
          [
            -0.006320882360698102,
            -1.7253847483309219e-16,
            0.002149530963168866
          ],
          [
            -0.006430602409489559,
            -1.7086974188083925e-16,
            0.0017895933571438003
          ],
          [
            -0.0065388732533785115,
            -1.6603741998929415e-16,
            0.0014298730846978689
          ],
          [
            -0.006645708479127871,
            -1.336569123843537e-16,
            0.0010704458176177844
          ],
          [
            -0.00675112166598041,
            -2.906990523068286e-16,
            0.0007113870763579409
          ]
        ],
        "raw_reduced_polarization": [
          [
            -0.43638717601574495,
            1.6418183060447187e-15,
            0.14023249549787373
          ],
          [
            -0.4444930326298835,
            -3.4167747629658165e-15,
            0.12264406905642952
          ],
          [
            -0.4525518172188409,
            -4.327103301816314e-15,
            0.10504231222362569
          ],
          [
            -0.4605649600257942,
            -4.1867561786468354e-15,
            0.087430349029839
          ],
          [
            -0.4685337508790835,
            -6.884245906881245e-15,
            0.06981149492972506
          ],
          [
            -0.47645937475716293,
            -6.7710827561127844e-15,
            0.0521891984012987
          ],
          [
            -0.4843429215029708,
            -6.53845605339951e-15,
            0.03456702007367579
          ],
          [
            -0.49218540171574343,
            -5.173190214546274e-15,
            0.016948592137590302
          ],
          [
            -0.49998779407835797,
            -1.1690044159991903e-14,
            -0.0006624615858318438
          ]
        ],
        "unwrapped_reduced_polarization": [
          [
            -0.43638717601574495,
            1.6418183060447187e-15,
            0.14023249549787373
          ],
          [
            -0.4444930326298835,
            -3.4167747629658165e-15,
            0.12264406905642952
          ],
          [
            -0.4525518172188409,
            -4.327103301816314e-15,
            0.10504231222362569
          ],
          [
            -0.4605649600257942,
            -4.1867561786468354e-15,
            0.087430349029839
          ],
          [
            -0.4685337508790835,
            -6.884245906881245e-15,
            0.06981149492972506
          ],
          [
            -0.47645937475716293,
            -6.7710827561127844e-15,
            0.0521891984012987
          ],
          [
            -0.4843429215029708,
            -6.53845605339951e-15,
            0.03456702007367579
          ],
          [
            -0.49218540171574343,
            -5.173190214546274e-15,
            0.016948592137590302
          ],
          [
            -0.49998779407835797,
            -1.1690044159991903e-14,
            -0.0006624615858318444
          ]
        ],
        "berry_integer_shifts": [
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ]
        ],
        "folded_reduced_polarization": [
          [
            -0.43638717601574495,
            1.6653345369377348e-15,
            0.14023249549787375
          ],
          [
            -0.4444930326298835,
            -3.4416913763379853e-15,
            0.12264406905642955
          ],
          [
            -0.4525518172188409,
            -4.3298697960381105e-15,
            0.1050423122236257
          ],
          [
            -0.4605649600257942,
            -4.163336342344337e-15,
            0.08743034902983904
          ],
          [
            -0.4685337508790835,
            -6.8833827526759706e-15,
            0.06981149492972505
          ],
          [
            -0.47645937475716293,
            -6.772360450213455e-15,
            0.05218919840129865
          ],
          [
            -0.4843429215029708,
            -6.5503158452884236e-15,
            0.03456702007367585
          ],
          [
            -0.49218540171574343,
            -5.162537064506978e-15,
            0.016948592137590257
          ],
          [
            -0.49998779407835797,
            -1.1712852909795402e-14,
            -0.0006624615858318306
          ]
        ]
      },
      "reflected": {
        "reached": true,
        "construction": "reflect_displacements_about_reconstructed_parent",
        "energies_eV": [
          -190.5101441319568,
          -190.4726976220387,
          -190.43120939147764,
          -190.38562665902953,
          -190.33589507929634,
          -190.28195882049826,
          -190.22376108250742,
          -190.16124336130585,
          -190.0943451284405
        ],
        "cartesian_polarizations_e_A2": [
          [
            -0.006751121665980377,
            -2.5973420089685026e-16,
            0.0007113870763579134
          ],
          [
            -0.006785598322920131,
            -2.750346754978255e-16,
            0.0005704547391912588
          ],
          [
            -0.006820727623846931,
            -3.8966356968114716e-16,
            0.0004281471857043681
          ],
          [
            -0.006856557551397818,
            -3.517108568128667e-16,
            0.000284420689001315
          ],
          [
            -0.006893138421198187,
            -3.557420648860728e-16,
            0.0001392351264003299
          ],
          [
            -0.006930520957063461,
            -3.9397486572261723e-16,
            -7.443687228492153e-06
          ],
          [
            -0.006968753429070906,
            -4.283963809969002e-16,
            -0.00015564081312907863
          ],
          [
            -0.007007882521077522,
            -5.307504385143699e-16,
            -0.00030537307449165975
          ],
          [
            -0.0070479528239352825,
            -6.518510263798571e-16,
            -0.000456648806709034
          ]
        ],
        "raw_reduced_polarization": [
          [
            -0.4999877940783556,
            -1.0403614519567125e-14,
            -0.000662461585832953
          ],
          [
            -0.5028514181742868,
            -1.1105596697647847e-14,
            -0.006991147673000197
          ],
          [
            -0.5057393556591815,
            -1.5931700159098387e-14,
            -0.013381036576130233
          ],
          [
            -0.5086548314620267,
            -1.4412540285540453e-14,
            -0.01983428254261768
          ],
          [
            -0.5116012303530703,
            -1.4633818538513944e-14,
            -0.026352871601999252
          ],
          [
            -0.514581955640528,
            -1.6272851467148636e-14,
            -0.0329385035163935
          ],
          [
            -0.5176002192685975,
            -1.77493237595424e-14,
            -0.03959243050106066
          ],
          [
            -0.5206591104610658,
            -2.2047694199492305e-14,
            -0.046315503365690285
          ],
          [
            -0.5237615619414675,
            -2.7122945052167197e-14,
            -0.05310815833250716
          ]
        ],
        "unwrapped_reduced_polarization": [
          [
            -0.4999877940783556,
            -1.0403614519567125e-14,
            -0.000662461585832953
          ],
          [
            -0.5028514181742868,
            -1.1105596697647847e-14,
            -0.006991147673000197
          ],
          [
            -0.5057393556591815,
            -1.5931700159098387e-14,
            -0.013381036576130233
          ],
          [
            -0.5086548314620267,
            -1.4412540285540453e-14,
            -0.01983428254261768
          ],
          [
            -0.5116012303530703,
            -1.4633818538513944e-14,
            -0.026352871601999252
          ],
          [
            -0.514581955640528,
            -1.6272851467148636e-14,
            -0.0329385035163935
          ],
          [
            -0.5176002192685975,
            -1.77493237595424e-14,
            -0.03959243050106066
          ],
          [
            -0.5206591104610658,
            -2.2047694199492305e-14,
            -0.046315503365690285
          ],
          [
            -0.5237615619414675,
            -2.7122945052167197e-14,
            -0.05310815833250716
          ]
        ],
        "gauge_integer_shift": [
          0,
          0,
          0
        ],
        "expected_opposite_endpoint_reduced_polarization": [
          -0.5672333621771737,
          -2.5833279555169273e-14,
          -0.13523437645724445
        ],
        "actual_opposite_endpoint_branch_residual": 0.09292208090225418
      },
      "pnp_branch": {
        "construction": "incoming_path_concatenated_with_parent_reflection",
        "reduced_polarization": [
          [
            -0.43638717601574495,
            1.6418183060447187e-15,
            0.14023249549787373
          ],
          [
            -0.4444930326298835,
            -3.4167747629658165e-15,
            0.12264406905642952
          ],
          [
            -0.4525518172188409,
            -4.327103301816314e-15,
            0.10504231222362569
          ],
          [
            -0.4605649600257942,
            -4.1867561786468354e-15,
            0.087430349029839
          ],
          [
            -0.4685337508790835,
            -6.884245906881245e-15,
            0.06981149492972506
          ],
          [
            -0.47645937475716293,
            -6.7710827561127844e-15,
            0.0521891984012987
          ],
          [
            -0.4843429215029708,
            -6.53845605339951e-15,
            0.03456702007367579
          ],
          [
            -0.49218540171574343,
            -5.173190214546274e-15,
            0.016948592137590302
          ],
          [
            -0.49998779407835797,
            -1.1690044159991903e-14,
            -0.0006624615858318438
          ],
          [
            -0.5028514181742868,
            -1.1105596697647847e-14,
            -0.006991147673000197
          ],
          [
            -0.5057393556591815,
            -1.5931700159098387e-14,
            -0.013381036576130233
          ],
          [
            -0.5086548314620267,
            -1.4412540285540453e-14,
            -0.01983428254261768
          ],
          [
            -0.5116012303530703,
            -1.4633818538513944e-14,
            -0.026352871601999252
          ],
          [
            -0.514581955640528,
            -1.6272851467148636e-14,
            -0.0329385035163935
          ],
          [
            -0.5176002192685975,
            -1.77493237595424e-14,
            -0.03959243050106066
          ],
          [
            -0.5206591104610658,
            -2.2047694199492305e-14,
            -0.046315503365690285
          ],
          [
            -0.5237615619414675,
            -2.7122945052167197e-14,
            -0.05310815833250716
          ]
        ],
        "unwrapped_reduced_polarization": [
          [
            -0.43638717601574495,
            1.6418183060447187e-15,
            0.14023249549787373
          ],
          [
            -0.4444930326298835,
            -3.4167747629658165e-15,
            0.12264406905642952
          ],
          [
            -0.4525518172188409,
            -4.327103301816314e-15,
            0.10504231222362569
          ],
          [
            -0.4605649600257942,
            -4.1867561786468354e-15,
            0.087430349029839
          ],
          [
            -0.4685337508790835,
            -6.884245906881245e-15,
            0.06981149492972506
          ],
          [
            -0.47645937475716293,
            -6.7710827561127844e-15,
            0.0521891984012987
          ],
          [
            -0.4843429215029708,
            -6.53845605339951e-15,
            0.03456702007367579
          ],
          [
            -0.49218540171574343,
            -5.173190214546274e-15,
            0.016948592137590302
          ],
          [
            -0.49998779407835797,
            -1.1690044159991903e-14,
            -0.0006624615858318444
          ],
          [
            -0.5028514181742868,
            -1.1105596697647847e-14,
            -0.006991147673000197
          ],
          [
            -0.5057393556591815,
            -1.5931700159098387e-14,
            -0.013381036576130233
          ],
          [
            -0.5086548314620267,
            -1.4412540285540453e-14,
            -0.01983428254261768
          ],
          [
            -0.5116012303530703,
            -1.4633818538513944e-14,
            -0.026352871601999252
          ],
          [
            -0.514581955640528,
            -1.6272851467148636e-14,
            -0.0329385035163935
          ],
          [
            -0.5176002192685975,
            -1.77493237595424e-14,
            -0.03959243050106066
          ],
          [
            -0.5206591104610658,
            -2.2047694199492305e-14,
            -0.046315503365690285
          ],
          [
            -0.5237615619414675,
            -2.7122945052167197e-14,
            -0.05310815833250716
          ]
        ],
        "berry_integer_shifts": [
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ]
        ],
        "folded_reduced_polarization": [
          [
            -0.43638717601574495,
            1.6653345369377348e-15,
            0.14023249549787375
          ],
          [
            -0.4444930326298835,
            -3.4416913763379853e-15,
            0.12264406905642955
          ],
          [
            -0.4525518172188409,
            -4.3298697960381105e-15,
            0.1050423122236257
          ],
          [
            -0.4605649600257942,
            -4.163336342344337e-15,
            0.08743034902983904
          ],
          [
            -0.4685337508790835,
            -6.8833827526759706e-15,
            0.06981149492972505
          ],
          [
            -0.47645937475716293,
            -6.772360450213455e-15,
            0.05218919840129865
          ],
          [
            -0.4843429215029708,
            -6.5503158452884236e-15,
            0.03456702007367585
          ],
          [
            -0.49218540171574343,
            -5.162537064506978e-15,
            0.016948592137590257
          ],
          [
            -0.49998779407835797,
            -1.1712852909795402e-14,
            -0.0006624615858318306
          ],
          [
            0.4971485818257132,
            -1.1102230246251565e-14,
            -0.0069911476730001865
          ],
          [
            0.4942606443408185,
            -1.5931700403370996e-14,
            -0.013381036576130212
          ],
          [
            0.4913451685379733,
            -1.4432899320127035e-14,
            -0.019834282542617654
          ],
          [
            0.48839876964692974,
            -1.4654943925052066e-14,
            -0.026352871601999228
          ],
          [
            0.485418044359472,
            -1.6264767310758543e-14,
            -0.03293850351639349
          ],
          [
            0.48239978073140255,
            -1.7763568394002505e-14,
            -0.03959243050106065
          ],
          [
            0.47934088953893417,
            -2.2037927038809357e-14,
            -0.04631550336569029
          ],
          [
            0.4762384380585325,
            -2.7144952952085077e-14,
            -0.05310815833250715
          ]
        ]
      },
      "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": "Cc",
        "spacegroup_number": 9,
        "pointgroup": "m",
        "has_inversion": false,
        "is_polar_point_group": true,
        "nonpolar_parent_hypothesis": false,
        "symmetry_tolerance_A": null,
        "target_reduced_polarization": [
          -0.5,
          0.0,
          0.0
        ],
        "formal_class": [
          0.5,
          0.0,
          0.0
        ],
        "target_residual": 0.0006625740239622227,
        "parent_symmetrization_rmsd_A": 0.01594361221665724,
        "parent_cell_rmsd_A": 0.05414380998509779,
        "energy_eV": -190.51014413195676,
        "reduced_polarization": [
          -0.49998779407835336,
          -1.137529567569367e-14,
          -0.0006624615858344152
        ],
        "cartesian_polarization_e_A2": [
          -0.006751121665980348,
          -2.8312293641090383e-16,
          0.0007113870763578789
        ],
        "ranking_score": 0.5308047127608562
      }
    }
  ],
  "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": 59,
      "full_response": 24,
      "energy_polarization": 35
    },
    "model_evaluations_for_recovery_and_path_properties": {
      "total": 84,
      "full_response": 49,
      "energy_polarization": 35
    },
    "elapsed_seconds": 416.75179974403
  }
}