{
  "schema": "ferrofinder.endpoint_parent_recovery.v4_variable_cell",
  "status": "complete",
  "input_atom_count": 48,
  "input_formula": "H20I4O24",
  "input_spacegroup": "Pc",
  "input_pointgroup": "m",
  "input_is_polar_point_group": true,
  "input_energy_eV": -212.48322237156225,
  "input_cartesian_polarization_e_A2": [
    -0.00024128480962607585,
    1.1134441068753272e-09,
    -0.00012578034569552218
  ],
  "input_reduced_polarization": [
    -0.027380215707629288,
    2.860359379708054e-08,
    -0.022486969738858675
  ],
  "input_formal_targets": [
    {
      "orbit_id": 0,
      "representative_formal_class": [
        0.0,
        0.0,
        0.0
      ],
      "target_reduced_polarization": [
        0.0,
        0.0,
        0.0
      ]
    },
    {
      "orbit_id": 1,
      "representative_formal_class": [
        0.5,
        0.0,
        0.0
      ],
      "target_reduced_polarization": [
        -0.5,
        0.0,
        0.0
      ]
    },
    {
      "orbit_id": 2,
      "representative_formal_class": [
        0.0,
        0.0,
        0.5
      ],
      "target_reduced_polarization": [
        0.0,
        0.0,
        -0.5
      ]
    },
    {
      "orbit_id": 3,
      "representative_formal_class": [
        0.0,
        0.5,
        0.0
      ],
      "target_reduced_polarization": [
        0.0,
        0.5,
        0.0
      ]
    },
    {
      "orbit_id": 4,
      "representative_formal_class": [
        0.5,
        0.0,
        0.5
      ],
      "target_reduced_polarization": [
        -0.5,
        0.0,
        -0.5
      ]
    },
    {
      "orbit_id": 5,
      "representative_formal_class": [
        0.5,
        0.5,
        0.0
      ],
      "target_reduced_polarization": [
        -0.5,
        0.5,
        0.0
      ]
    },
    {
      "orbit_id": 6,
      "representative_formal_class": [
        0.0,
        0.5,
        0.5
      ],
      "target_reduced_polarization": [
        0.0,
        0.5,
        -0.5
      ]
    },
    {
      "orbit_id": 7,
      "representative_formal_class": [
        0.5,
        0.5,
        0.5
      ],
      "target_reduced_polarization": [
        -0.5,
        0.5,
        -0.5
      ]
    }
  ],
  "parent_candidates": [
    {
      "candidate_id": "inversion_parent_endpoint_00",
      "source": "same_species_inversion_center_projection_from_endpoint",
      "spacegroup": "P2_1/c",
      "spacegroup_number": 14,
      "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": 9.251127424475032e-15,
      "parent_symmetrization_rmsd_A": 0.05283729570281214,
      "parent_cell_rmsd_A": 0.0,
      "energy_eV": -212.49249680605834,
      "reduced_polarization": [
        -9.003706746739882e-15,
        -1.624291323589321e-17,
        -2.1251728424658475e-15
      ],
      "cartesian_polarization_e_A2": [
        -7.869053654390756e-17,
        -6.322833469561601e-19,
        2.4860231596230842e-17
      ],
      "ranking_score": 0.05283729570283064
    },
    {
      "candidate_id": "symmetry_projection_00",
      "source": "spglib_refine_cell_from_polar_endpoint",
      "spacegroup": "P2_1/c",
      "spacegroup_number": 14,
      "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": 7.66351889048058e-15,
      "parent_symmetrization_rmsd_A": 1.6999698518091515,
      "parent_cell_rmsd_A": 1.4231150517256876e-16,
      "energy_eV": -212.16830124073743,
      "reduced_polarization": [
        4.837949292190338e-15,
        8.521992092058974e-16,
        5.8819660776628555e-15
      ],
      "cartesian_polarization_e_A2": [
        1.0432675224776644e-17,
        3.3173320601097636e-17,
        6.21649490666443e-17
      ],
      "ranking_score": 1.6999698518091668
    },
    {
      "candidate_id": "bec_projection_00",
      "source": "MACEField_BEC_backprojection",
      "spacegroup": "Pc",
      "spacegroup_number": 7,
      "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": 9.405747876199231e-06,
      "parent_symmetrization_rmsd_A": 0.0026188606611707416,
      "parent_cell_rmsd_A": 6.856222159444876e-05,
      "energy_eV": -212.47903889626352,
      "reduced_polarization": [
        8.664529336856593e-06,
        6.026128623376712e-11,
        3.6597847583903594e-06
      ],
      "cartesian_polarization_e_A2": [
        7.592454517516681e-08,
        2.3456339261735623e-12,
        -3.6296400286231717e-09
      ],
      "ranking_score": 0.5026548127123217
    },
    {
      "candidate_id": "inversion_parent_bec_00_00",
      "source": "same_species_inversion_center_projection_after_BEC",
      "spacegroup": "P2_1/c",
      "spacegroup_number": 14,
      "pointgroup": "2/m",
      "has_inversion": true,
      "is_polar_point_group": false,
      "nonpolar_parent_hypothesis": true,
      "symmetry_tolerance_A": null,
      "target_reduced_polarization": [
        0.0,
        0.0,
        0.0
      ],
      "formal_class": [
        0.0,
        0.0,
        0.0
      ],
      "target_residual": 3.862961588341842e-15,
      "parent_symmetrization_rmsd_A": 0.0528373661904957,
      "parent_cell_rmsd_A": 6.856222159444876e-05,
      "energy_eV": -212.49277561983297,
      "reduced_polarization": [
        3.437237435313865e-15,
        -1.1611852750583938e-15,
        -1.3264689228432934e-15
      ],
      "cartesian_polarization_e_A2": [
        2.9773819480494816e-17,
        -4.519958937060639e-17,
        -3.635509811083585e-17
      ],
      "ranking_score": 0.05285450674590204
    },
    {
      "candidate_id": "symmetry_parent_00_00",
      "source": "spglib_refine_cell_after_MACEField_BEC_backprojection",
      "spacegroup": "P2_1/c",
      "spacegroup_number": 14,
      "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": 1.2958054223935431e-15,
      "parent_symmetrization_rmsd_A": 1.6999895614265963,
      "parent_cell_rmsd_A": 6.856222124390504e-05,
      "energy_eV": -212.17789927889157,
      "reduced_polarization": [
        -6.247763345300062e-16,
        -6.882943714166379e-16,
        -9.027829654972083e-16
      ],
      "cartesian_polarization_e_A2": [
        -3.73609703905823e-19,
        -2.6792126651246426e-17,
        -9.541417053594865e-18
      ],
      "ranking_score": 1.7000067019819098
    },
    {
      "candidate_id": "bec_projection_01",
      "source": "MACEField_BEC_backprojection",
      "spacegroup": "Pc",
      "spacegroup_number": 7,
      "pointgroup": "m",
      "has_inversion": false,
      "is_polar_point_group": true,
      "nonpolar_parent_hypothesis": false,
      "symmetry_tolerance_A": null,
      "target_reduced_polarization": [
        -0.5,
        0.0,
        0.0
      ],
      "formal_class": [
        0.5,
        0.0,
        0.0
      ],
      "target_residual": 2.895641445607971e-05,
      "parent_symmetrization_rmsd_A": 0.04170454904929778,
      "parent_cell_rmsd_A": 0.005709441516078909,
      "energy_eV": -211.3703817594154,
      "reduced_polarization": [
        -0.4999711098165429,
        -6.328832043632553e-11,
        -1.957354838587655e-06
      ],
      "cartesian_polarization_e_A2": [
        -0.004356950487800362,
        2.8426291957278184e-11,
        0.0028630006510592873
      ],
      "ranking_score": 0.5431898222572297
    },
    {
      "candidate_id": "bec_projection_02",
      "source": "MACEField_BEC_backprojection",
      "spacegroup": "Pc",
      "spacegroup_number": 7,
      "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": 0.0003272277962106148,
      "parent_symmetrization_rmsd_A": 0.052573770856602635,
      "parent_cell_rmsd_A": 0.006712466996234711,
      "energy_eV": -210.93654812080837,
      "reduced_polarization": [
        -0.0002709024185641058,
        -3.822652064224539e-10,
        -0.4998164518857933
      ],
      "cartesian_polarization_e_A2": [
        -5.9843664907338704e-05,
        2.157392617445214e-11,
        -0.006281401749935568
      ],
      "ranking_score": 0.5549063431980825
    },
    {
      "candidate_id": "bec_projection_03",
      "source": "MACEField_BEC_backprojection",
      "spacegroup": "P1",
      "spacegroup_number": 1,
      "pointgroup": "1",
      "has_inversion": false,
      "is_polar_point_group": true,
      "nonpolar_parent_hypothesis": false,
      "symmetry_tolerance_A": null,
      "target_reduced_polarization": [
        0.0,
        0.5,
        0.0
      ],
      "formal_class": [
        0.0,
        0.5,
        0.0
      ],
      "target_residual": 0.02606719886337962,
      "parent_symmetrization_rmsd_A": 0.19694374961069538,
      "parent_cell_rmsd_A": 0.24893361342418652,
      "energy_eV": -182.38775082538444,
      "reduced_polarization": [
        0.01133290059570185,
        0.47656658156590925,
        0.0013925233081483394
      ],
      "cartesian_polarization_e_A2": [
        0.00020649826166420287,
        0.018672098045471413,
        -2.094381043067029e-06
      ],
      "ranking_score": 0.8113115506935014
    },
    {
      "candidate_id": "bec_projection_04",
      "source": "MACEField_BEC_backprojection",
      "spacegroup": "Pc",
      "spacegroup_number": 7,
      "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": 0.0003933336731375873,
      "parent_symmetrization_rmsd_A": 0.0543170573838361,
      "parent_cell_rmsd_A": 0.001482497966149178,
      "energy_eV": -210.36257018283283,
      "reduced_polarization": [
        -0.5000152953747526,
        5.789655659457446e-10,
        -0.4996069638312639
      ],
      "cartesian_polarization_e_A2": [
        -0.004416888410740725,
        -5.835954043353756e-11,
        -0.003412452347148752
      ],
      "ranking_score": 0.5554743492216485
    },
    {
      "candidate_id": "bec_projection_05",
      "source": "MACEField_BEC_backprojection",
      "spacegroup": "P1",
      "spacegroup_number": 1,
      "pointgroup": "1",
      "has_inversion": false,
      "is_polar_point_group": true,
      "nonpolar_parent_hypothesis": false,
      "symmetry_tolerance_A": null,
      "target_reduced_polarization": [
        -0.5,
        0.5,
        0.0
      ],
      "formal_class": [
        0.5,
        0.5,
        0.0
      ],
      "target_residual": 0.026368943321751288,
      "parent_symmetrization_rmsd_A": 0.2044720937910223,
      "parent_cell_rmsd_A": 0.3823644723955718,
      "energy_eV": -175.39268252564344,
      "reduced_polarization": [
        -0.506207154343779,
        0.48358877513228965,
        0.01968410793507499
      ],
      "cartesian_polarization_e_A2": [
        -0.004310199867942403,
        0.019031647067131313,
        0.0030099314224032213
      ],
      "ranking_score": 0.8528010985334178
    },
    {
      "candidate_id": "bec_projection_06",
      "source": "MACEField_BEC_backprojection",
      "spacegroup": "P1",
      "spacegroup_number": 1,
      "pointgroup": "1",
      "has_inversion": false,
      "is_polar_point_group": true,
      "nonpolar_parent_hypothesis": false,
      "symmetry_tolerance_A": null,
      "target_reduced_polarization": [
        0.0,
        0.5,
        -0.5
      ],
      "formal_class": [
        0.0,
        0.5,
        0.5
      ],
      "target_residual": 0.04184473532782909,
      "parent_symmetrization_rmsd_A": 0.2044216632564604,
      "parent_cell_rmsd_A": 0.3299296164277196,
      "energy_eV": -175.76069953115558,
      "reduced_polarization": [
        0.03618019715827117,
        0.47908459869092584,
        -0.5021263104959234
      ],
      "cartesian_polarization_e_A2": [
        0.0002829073893787418,
        0.018752542012951595,
        -0.006296232165686651
      ],
      "ranking_score": 0.8705935380190485
    },
    {
      "candidate_id": "bec_projection_07",
      "source": "MACEField_BEC_backprojection",
      "spacegroup": "P1",
      "spacegroup_number": 1,
      "pointgroup": "1",
      "has_inversion": false,
      "is_polar_point_group": true,
      "nonpolar_parent_hypothesis": false,
      "symmetry_tolerance_A": null,
      "target_reduced_polarization": [
        -0.5,
        0.5,
        -0.5
      ],
      "formal_class": [
        0.5,
        0.5,
        0.5
      ],
      "target_residual": 0.048941596051635124,
      "parent_symmetrization_rmsd_A": 0.20461172249322407,
      "parent_cell_rmsd_A": 0.39931644612749106,
      "energy_eV": -178.81474634121946,
      "reduced_polarization": [
        -0.46495686087314736,
        0.4820915458648058,
        -0.47090454511946717
      ],
      "cartesian_polarization_e_A2": [
        -0.004118697708781742,
        0.01888382953435796,
        -0.003187694223509429
      ],
      "ranking_score": 0.902324026128367
    }
  ],
  "formal_branches": [
    {
      "orbit_id": 0,
      "formal_class": [
        0.0,
        0.0,
        0.0
      ],
      "formal_classes_in_orbit": [
        [
          0.0,
          0.0,
          0.0
        ]
      ],
      "target_reduced_polarization": [
        0.0,
        0.0,
        0.0
      ],
      "bec_backprojection": {
        "converged_to_target": true,
        "history": [
          {
            "iteration": 0,
            "reduced_polarization": [
              -0.027380215707629288,
              2.860359379708054e-08,
              -0.022486969738858675
            ],
            "branch_aligned_reduced_polarization": [
              -0.027380215707629288,
              2.860359379708054e-08,
              -0.022486969738858675
            ],
            "target_residual": 0.03543077786661582,
            "energy_eV": -212.48322237156225,
            "max_atomic_step_A": 0.006804971671172413,
            "max_log_strain_component": 2.9932808293087075e-05,
            "step_scale": 1.0,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 0.1644037161115604,
            "cell_principal_stretches": [
              1.0000480615163787,
              0.9999986589376364,
              0.9999861322985083
            ],
            "cell_volume_ratio": 1.0000328520401656,
            "cell_rmsd_from_input_A": 6.856222159444876e-05
          },
          {
            "iteration": 1,
            "reduced_polarization": [
              8.664529336856593e-06,
              6.026128623376712e-11,
              3.6597847583903594e-06
            ],
            "branch_aligned_reduced_polarization": [
              8.664529336856593e-06,
              6.026128623376712e-11,
              3.6597847583903594e-06
            ],
            "target_residual": 9.405747876199231e-06,
            "energy_eV": -212.47903889626352
          }
        ],
        "iterations": 1
      },
      "parent": {
        "candidate_id": "inversion_parent_endpoint_00",
        "source": "same_species_inversion_center_projection_from_endpoint",
        "spacegroup": "P2_1/c",
        "spacegroup_number": 14,
        "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": 9.251127424475032e-15,
        "parent_symmetrization_rmsd_A": 0.05283729570281214,
        "parent_cell_rmsd_A": 0.0,
        "energy_eV": -212.49249680605834,
        "reduced_polarization": [
          -9.003706746739882e-15,
          -1.624291323589321e-17,
          -2.1251728424658475e-15
        ],
        "cartesian_polarization_e_A2": [
          -7.869053654390756e-17,
          -6.322833469561601e-19,
          2.4860231596230842e-17
        ],
        "ranking_score": 0.05283729570283064
      },
      "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": [
          -212.48322237156225,
          -212.48549451572956,
          -212.48741518207262,
          -212.4890054704771,
          -212.49028288890386,
          -212.49126110082017,
          -212.49195067992613,
          -212.4923606959207,
          -212.49249680605834
        ],
        "cartesian_polarizations_e_A2": [
          [
            -0.0002412848096261145,
            1.1134441165751286e-09,
            -0.0001257803456954852
          ],
          [
            -0.00021102032422522674,
            9.748138440765516e-10,
            -0.00011006801623945801
          ],
          [
            -0.00018077645723006818,
            8.360292072005855e-10,
            -9.436022731125169e-05
          ],
          [
            -0.0001505642787772697,
            6.970675700273758e-10,
            -7.864926583082283e-05
          ],
          [
            -0.00012038945914448449,
            5.579223303979144e-10,
            -6.293154193193859e-05
          ],
          [
            -9.025139123929724e-05,
            4.186092907220079e-10,
            -4.720663626918869e-05
          ],
          [
            -6.014547329099513e-05,
            2.7915708424560987e-10,
            -3.147525719404007e-05
          ],
          [
            -3.006533248125458e-05,
            1.3960494332411943e-10,
            -1.5738853488805313e-05
          ],
          [
            -5.155983292906142e-17,
            2.135393303583759e-17,
            1.632440641232268e-17
          ]
        ],
        "raw_reduced_polarization": [
          [
            -0.027380215707633743,
            2.86035940462616e-08,
            -0.02248696973885776
          ],
          [
            -0.02394582784601636,
            2.5042280121258375e-08,
            -0.019671505749877475
          ],
          [
            -0.02051378668190214,
            2.1477000684272722e-08,
            -0.01685747255025273
          ],
          [
            -0.017085363596815572,
            1.790717423448862e-08,
            -0.014044835812146094
          ],
          [
            -0.013661209403789556,
            1.4332631167097635e-08,
            -0.011233606483402136
          ],
          [
            -0.010241255327750371,
            1.0753777434862308e-08,
            -0.00842371985196606
          ],
          [
            -0.006824975677002897,
            7.171348605676251e-09,
            -0.005614992703528917
          ],
          [
            -0.003411641914384741,
            3.5863525310792126e-09,
            -0.0028072082966087222
          ],
          [
            -5.8994737250438785e-15,
            5.485674788303934e-16,
            -1.3896616996768471e-15
          ]
        ],
        "unwrapped_reduced_polarization": [
          [
            -0.027380215707633743,
            2.86035940462616e-08,
            -0.02248696973885776
          ],
          [
            -0.02394582784601636,
            2.5042280121258375e-08,
            -0.019671505749877475
          ],
          [
            -0.02051378668190214,
            2.1477000684272722e-08,
            -0.01685747255025273
          ],
          [
            -0.017085363596815572,
            1.790717423448862e-08,
            -0.014044835812146094
          ],
          [
            -0.013661209403789556,
            1.4332631167097635e-08,
            -0.011233606483402136
          ],
          [
            -0.010241255327750371,
            1.0753777434862308e-08,
            -0.00842371985196606
          ],
          [
            -0.006824975677002897,
            7.171348605676251e-09,
            -0.005614992703528917
          ],
          [
            -0.003411641914384741,
            3.5863525310792126e-09,
            -0.0028072082966087222
          ],
          [
            -5.899360860928127e-15,
            5.485674788643375e-16,
            -1.3895135042574225e-15
          ]
        ],
        "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": [
          [
            -0.027380215707633715,
            2.8603594048881575e-08,
            -0.022486969738857776
          ],
          [
            -0.023945827846016343,
            2.5042280138443118e-08,
            -0.01967150574987747
          ],
          [
            -0.020513786681902124,
            2.1477000733405305e-08,
            -0.016857472550252717
          ],
          [
            -0.01708536359681556,
            1.7907174187925534e-08,
            -0.014044835812146106
          ],
          [
            -0.013661209403789565,
            1.4332631192992551e-08,
            -0.011233606483402159
          ],
          [
            -0.010241255327750387,
            1.0753777424099553e-08,
            -0.00842371985196605
          ],
          [
            -0.006824975677002909,
            7.17134862604496e-09,
            -0.005614992703528943
          ],
          [
            -0.0034116419143847554,
            3.5863525482682235e-09,
            -0.002807208296608743
          ],
          [
            -5.88418203051333e-15,
            5.551115123125783e-16,
            -1.3877787807814457e-15
          ]
        ]
      },
      "reflected": {
        "reached": true,
        "construction": "reflect_displacements_about_reconstructed_parent",
        "energies_eV": [
          -212.49249680605837,
          -212.4923606959207,
          -212.49195067992613,
          -212.49126110082017,
          -212.49028288890386,
          -212.4890054704771,
          -212.48741518207265,
          -212.48549451572956,
          -212.48322237156222
        ],
        "cartesian_polarizations_e_A2": [
          [
            -4.538070022017168e-17,
            9.656691117148627e-18,
            1.4370076067185458e-19
          ],
          [
            3.0065332481284584e-05,
            -1.3960488870525656e-10,
            1.5738853488746844e-05
          ],
          [
            6.0145473291004784e-05,
            -2.791570709622708e-10,
            3.147525719406184e-05
          ],
          [
            9.025139123922266e-05,
            -4.1860928155749193e-10,
            4.7206636269141224e-05
          ],
          [
            0.00012038945914450355,
            -5.579223093331791e-10,
            6.293154193194162e-05
          ],
          [
            0.00015056427877727866,
            -6.970674513610839e-10,
            7.864926583081642e-05
          ],
          [
            0.00018077645722999286,
            -8.360291566376766e-10,
            9.436022731122713e-05
          ],
          [
            0.000211020324225281,
            -9.74813815742354e-10,
            0.00011006801623936495
          ],
          [
            0.00024128480962615212,
            -1.1134440067123046e-09,
            0.00012578034569546298
          ]
        ],
        "raw_reduced_polarization": [
          [
            -5.176445730403119e-15,
            2.48073583966369e-16,
            -2.3476876886663665e-15
          ],
          [
            0.003411641914388229,
            -3.586351127959148e-09,
            0.00280720829660566
          ],
          [
            0.006824975677003974,
            -7.1713482644366405e-09,
            0.00561499270353114
          ],
          [
            0.010241255327741918,
            -1.0753777199432357e-08,
            0.008423719851958427
          ],
          [
            0.013661209403791726,
            -1.4332630625959445e-08,
            0.011233606483403366
          ],
          [
            0.017085363596816602,
            -1.7907171186035277e-08,
            0.014044835812146054
          ],
          [
            0.02051378668189358,
            -2.147699938534725e-08,
            0.016857472550246878
          ],
          [
            0.023945827846022654,
            -2.504227939337282e-08,
            0.019671505749872937
          ],
          [
            0.02738021570763806,
            -2.860359122396314e-08,
            0.022486969738857956
          ]
        ],
        "unwrapped_reduced_polarization": [
          [
            -5.176445730403119e-15,
            2.48073583966369e-16,
            -2.3476876886663665e-15
          ],
          [
            0.003411641914388229,
            -3.586351127959148e-09,
            0.00280720829660566
          ],
          [
            0.006824975677003974,
            -7.1713482644366405e-09,
            0.00561499270353114
          ],
          [
            0.010241255327741918,
            -1.0753777199432357e-08,
            0.008423719851958427
          ],
          [
            0.013661209403791726,
            -1.4332630625959445e-08,
            0.011233606483403366
          ],
          [
            0.017085363596816602,
            -1.7907171186035277e-08,
            0.014044835812146054
          ],
          [
            0.02051378668189358,
            -2.147699938534725e-08,
            0.016857472550246878
          ],
          [
            0.023945827846022654,
            -2.504227939337282e-08,
            0.019671505749872937
          ],
          [
            0.02738021570763806,
            -2.860359122396314e-08,
            0.022486969738857956
          ]
        ],
        "gauge_integer_shift": [
          0,
          0,
          0
        ],
        "expected_opposite_endpoint_reduced_polarization": [
          0.027380215707621943,
          -2.860359294912664e-08,
          0.022486969738854983
        ],
        "actual_opposite_endpoint_branch_residual": 1.6478129484101214e-14
      },
      "pnp_branch": {
        "construction": "incoming_path_concatenated_with_parent_reflection",
        "reduced_polarization": [
          [
            -0.027380215707633743,
            2.86035940462616e-08,
            -0.02248696973885776
          ],
          [
            -0.02394582784601636,
            2.5042280121258375e-08,
            -0.019671505749877475
          ],
          [
            -0.02051378668190214,
            2.1477000684272722e-08,
            -0.01685747255025273
          ],
          [
            -0.017085363596815572,
            1.790717423448862e-08,
            -0.014044835812146094
          ],
          [
            -0.013661209403789556,
            1.4332631167097635e-08,
            -0.011233606483402136
          ],
          [
            -0.010241255327750371,
            1.0753777434862308e-08,
            -0.00842371985196606
          ],
          [
            -0.006824975677002897,
            7.171348605676251e-09,
            -0.005614992703528917
          ],
          [
            -0.003411641914384741,
            3.5863525310792126e-09,
            -0.0028072082966087222
          ],
          [
            -5.8994737250438785e-15,
            5.485674788303934e-16,
            -1.3896616996768471e-15
          ],
          [
            0.003411641914388229,
            -3.586351127959148e-09,
            0.00280720829660566
          ],
          [
            0.006824975677003974,
            -7.1713482644366405e-09,
            0.00561499270353114
          ],
          [
            0.010241255327741918,
            -1.0753777199432357e-08,
            0.008423719851958427
          ],
          [
            0.013661209403791726,
            -1.4332630625959445e-08,
            0.011233606483403366
          ],
          [
            0.017085363596816602,
            -1.7907171186035277e-08,
            0.014044835812146054
          ],
          [
            0.02051378668189358,
            -2.147699938534725e-08,
            0.016857472550246878
          ],
          [
            0.023945827846022654,
            -2.504227939337282e-08,
            0.019671505749872937
          ],
          [
            0.02738021570763806,
            -2.860359122396314e-08,
            0.022486969738857956
          ]
        ],
        "unwrapped_reduced_polarization": [
          [
            -0.027380215707633743,
            2.86035940462616e-08,
            -0.02248696973885776
          ],
          [
            -0.02394582784601636,
            2.5042280121258375e-08,
            -0.019671505749877475
          ],
          [
            -0.02051378668190214,
            2.1477000684272722e-08,
            -0.01685747255025273
          ],
          [
            -0.017085363596815572,
            1.790717423448862e-08,
            -0.014044835812146094
          ],
          [
            -0.013661209403789556,
            1.4332631167097635e-08,
            -0.011233606483402136
          ],
          [
            -0.010241255327750371,
            1.0753777434862308e-08,
            -0.00842371985196606
          ],
          [
            -0.006824975677002897,
            7.171348605676251e-09,
            -0.005614992703528917
          ],
          [
            -0.003411641914384741,
            3.5863525310792126e-09,
            -0.0028072082966087222
          ],
          [
            -5.899360860928127e-15,
            5.485674788643375e-16,
            -1.3895135042574225e-15
          ],
          [
            0.003411641914388229,
            -3.586351127959148e-09,
            0.00280720829660566
          ],
          [
            0.006824975677003974,
            -7.1713482644366405e-09,
            0.00561499270353114
          ],
          [
            0.010241255327741918,
            -1.0753777199432357e-08,
            0.008423719851958427
          ],
          [
            0.013661209403791726,
            -1.4332630625959445e-08,
            0.011233606483403366
          ],
          [
            0.017085363596816602,
            -1.7907171186035277e-08,
            0.014044835812146054
          ],
          [
            0.02051378668189358,
            -2.147699938534725e-08,
            0.016857472550246878
          ],
          [
            0.023945827846022654,
            -2.504227939337282e-08,
            0.019671505749872937
          ],
          [
            0.02738021570763806,
            -2.860359122396314e-08,
            0.022486969738857956
          ]
        ],
        "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": [
          [
            -0.027380215707633715,
            2.8603594048881575e-08,
            -0.022486969738857776
          ],
          [
            -0.023945827846016343,
            2.5042280138443118e-08,
            -0.01967150574987747
          ],
          [
            -0.020513786681902124,
            2.1477000733405305e-08,
            -0.016857472550252717
          ],
          [
            -0.01708536359681556,
            1.7907174187925534e-08,
            -0.014044835812146106
          ],
          [
            -0.013661209403789565,
            1.4332631192992551e-08,
            -0.011233606483402159
          ],
          [
            -0.010241255327750387,
            1.0753777424099553e-08,
            -0.00842371985196605
          ],
          [
            -0.006824975677002909,
            7.17134862604496e-09,
            -0.005614992703528943
          ],
          [
            -0.0034116419143847554,
            3.5863525482682235e-09,
            -0.002807208296608743
          ],
          [
            -5.88418203051333e-15,
            5.551115123125783e-16,
            -1.3877787807814457e-15
          ],
          [
            0.0034116419143882526,
            -3.5863511049782915e-09,
            0.0028072082966056344
          ],
          [
            0.006824975677004019,
            -7.171348237466901e-09,
            0.005614992703531163
          ],
          [
            0.010241255327741894,
            -1.0753777202054948e-08,
            0.008423719851958444
          ],
          [
            0.013661209403791674,
            -1.4332630637881039e-08,
            0.011233606483403324
          ],
          [
            0.01708536359681656,
            -1.7907171190323368e-08,
            0.014044835812146106
          ],
          [
            0.02051378668189363,
            -2.1476999401137675e-08,
            0.016857472550246833
          ],
          [
            0.023945827846022616,
            -2.5042279416798152e-08,
            0.019671505749872975
          ],
          [
            0.027380215707638045,
            -2.8603591217812863e-08,
            0.022486969738857998
          ]
        ]
      },
      "incoming_structure_ids": [
        "incoming_00_000",
        "incoming_00_001",
        "incoming_00_002",
        "incoming_00_003",
        "incoming_00_004",
        "incoming_00_005",
        "incoming_00_006",
        "incoming_00_007",
        "incoming_00_008"
      ],
      "reflected_structure_ids": [
        "reflected_00_001",
        "reflected_00_002",
        "reflected_00_003",
        "reflected_00_004",
        "reflected_00_005",
        "reflected_00_006",
        "reflected_00_007",
        "reflected_00_008"
      ]
    },
    {
      "orbit_id": 1,
      "formal_class": [
        0.5,
        0.0,
        0.0
      ],
      "formal_classes_in_orbit": [
        [
          0.5,
          0.0,
          0.0
        ]
      ],
      "target_reduced_polarization": [
        -0.5,
        0.0,
        0.0
      ],
      "bec_backprojection": {
        "converged_to_target": true,
        "history": [
          {
            "iteration": 0,
            "reduced_polarization": [
              -0.027380215707629288,
              2.860359379708054e-08,
              -0.022486969738858675
            ],
            "branch_aligned_reduced_polarization": [
              -0.027380215707629274,
              2.860359379708054e-08,
              -0.022486969738858675
            ],
            "target_residual": 0.47315444023342335,
            "energy_eV": -212.48322237156225,
            "max_atomic_step_A": 0.09583425282138817,
            "max_log_strain_component": 0.0007087403237334309,
            "step_scale": 1.0,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 0.1644037161115604,
            "cell_principal_stretches": [
              1.0002522154869509,
              0.9998338765774673,
              0.9992856188031723
            ],
            "cell_volume_ratio": 0.9993716074960709,
            "cell_rmsd_from_input_A": 0.005394734643259605
          },
          {
            "iteration": 1,
            "reduced_polarization": [
              -0.4763743187878924,
              -2.4797776844531325e-09,
              5.353067834318802e-05
            ],
            "branch_aligned_reduced_polarization": [
              -0.4763743187878924,
              -2.4797776844531325e-09,
              5.353067834318802e-05
            ],
            "target_residual": 0.023625741856493417,
            "energy_eV": -211.47630984555903,
            "max_atomic_step_A": 0.006108478528805224,
            "max_log_strain_component": 4.234261600985779e-05,
            "step_scale": 1.0,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 0.1644037161115604,
            "cell_principal_stretches": [
              1.0002669203290593,
              0.9998234903984371,
              0.9992432677772014
            ],
            "cell_volume_ratio": 0.999333563009639,
            "cell_rmsd_from_input_A": 0.005709441516078909
          },
          {
            "iteration": 2,
            "reduced_polarization": [
              -0.4999711098165429,
              -6.328832043632553e-11,
              -1.957354838587655e-06
            ],
            "branch_aligned_reduced_polarization": [
              -0.4999711098165429,
              -6.328832043632553e-11,
              -1.957354838587655e-06
            ],
            "target_residual": 2.895641445607971e-05,
            "energy_eV": -211.3703817594154
          }
        ],
        "iterations": 2
      },
      "parent": {
        "candidate_id": "bec_projection_01",
        "source": "MACEField_BEC_backprojection",
        "spacegroup": "Pc",
        "spacegroup_number": 7,
        "pointgroup": "m",
        "has_inversion": false,
        "is_polar_point_group": true,
        "nonpolar_parent_hypothesis": false,
        "symmetry_tolerance_A": null,
        "target_reduced_polarization": [
          -0.5,
          0.0,
          0.0
        ],
        "formal_class": [
          0.5,
          0.0,
          0.0
        ],
        "target_residual": 2.895641445607971e-05,
        "parent_symmetrization_rmsd_A": 0.04170454904929778,
        "parent_cell_rmsd_A": 0.005709441516078909,
        "energy_eV": -211.3703817594154,
        "reduced_polarization": [
          -0.4999711098165429,
          -6.328832043632553e-11,
          -1.957354838587655e-06
        ],
        "cartesian_polarization_e_A2": [
          -0.004356950487800362,
          2.8426291957278184e-11,
          0.0028630006510592873
        ],
        "ranking_score": 0.5431898222572297
      },
      "branch_status": "awaiting_branch_sampling"
    },
    {
      "orbit_id": 2,
      "formal_class": [
        0.0,
        0.0,
        0.5
      ],
      "formal_classes_in_orbit": [
        [
          0.0,
          0.0,
          0.5
        ]
      ],
      "target_reduced_polarization": [
        0.0,
        0.0,
        -0.5
      ],
      "bec_backprojection": {
        "converged_to_target": true,
        "history": [
          {
            "iteration": 0,
            "reduced_polarization": [
              -0.027380215707629288,
              2.860359379708054e-08,
              -0.022486969738858675
            ],
            "branch_aligned_reduced_polarization": [
              -0.027380215707629288,
              2.860359379708054e-08,
              -0.022486969738858664
            ],
            "target_residual": 0.4782973659569691,
            "energy_eV": -212.48322237156225,
            "max_atomic_step_A": 0.10845985198868686,
            "max_log_strain_component": 0.000668050137105707,
            "step_scale": 1.0,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 0.1644037161115604,
            "cell_principal_stretches": [
              1.0008832602845095,
              0.9997198242158764,
              0.9995052357631367
            ],
            "cell_volume_ratio": 1.000107774533175,
            "cell_rmsd_from_input_A": 0.006041925655594827
          },
          {
            "iteration": 1,
            "reduced_polarization": [
              -0.0195398809858345,
              -3.1406200344179627e-09,
              -0.4760195115093426
            ],
            "branch_aligned_reduced_polarization": [
              -0.0195398809858345,
              -3.1406200344179627e-09,
              -0.4760195115093426
            ],
            "target_residual": 0.03093332793591953,
            "energy_eV": -211.11783906438117,
            "max_atomic_step_A": 0.009364632746001479,
            "max_log_strain_component": 5.95143012802046e-05,
            "step_scale": 1.0,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 0.1644037161115604,
            "cell_principal_stretches": [
              1.0009709839479737,
              0.9996883885555666,
              0.9994873554968589
            ],
            "cell_volume_ratio": 1.0001460875621093,
            "cell_rmsd_from_input_A": 0.006712466996234711
          },
          {
            "iteration": 2,
            "reduced_polarization": [
              -0.0002709024185641058,
              -3.822652064224539e-10,
              -0.4998164518857933
            ],
            "branch_aligned_reduced_polarization": [
              -0.0002709024185641058,
              -3.822652064224539e-10,
              -0.4998164518857933
            ],
            "target_residual": 0.0003272277962106148,
            "energy_eV": -210.93654812080837
          }
        ],
        "iterations": 2
      },
      "parent": {
        "candidate_id": "bec_projection_02",
        "source": "MACEField_BEC_backprojection",
        "spacegroup": "Pc",
        "spacegroup_number": 7,
        "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": 0.0003272277962106148,
        "parent_symmetrization_rmsd_A": 0.052573770856602635,
        "parent_cell_rmsd_A": 0.006712466996234711,
        "energy_eV": -210.93654812080837,
        "reduced_polarization": [
          -0.0002709024185641058,
          -3.822652064224539e-10,
          -0.4998164518857933
        ],
        "cartesian_polarization_e_A2": [
          -5.9843664907338704e-05,
          2.157392617445214e-11,
          -0.006281401749935568
        ],
        "ranking_score": 0.5549063431980825
      },
      "branch_status": "awaiting_branch_sampling"
    },
    {
      "orbit_id": 3,
      "formal_class": [
        0.0,
        0.5,
        0.0
      ],
      "formal_classes_in_orbit": [
        [
          0.0,
          0.5,
          0.0
        ]
      ],
      "target_reduced_polarization": [
        0.0,
        0.5,
        0.0
      ],
      "bec_backprojection": {
        "converged_to_target": false,
        "history": [
          {
            "iteration": 0,
            "reduced_polarization": [
              -0.027380215707629288,
              2.860359379708054e-08,
              -0.022486969738858675
            ],
            "branch_aligned_reduced_polarization": [
              -0.027380215707629288,
              2.860359377132582e-08,
              -0.022486969738858675
            ],
            "target_residual": 0.5012537395537711,
            "energy_eV": -212.48322237156225,
            "max_atomic_step_A": 0.12000000000000001,
            "max_log_strain_component": 0.0018288128407669333,
            "step_scale": 0.28001375023265285,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 0.1644037161115604,
            "cell_principal_stretches": [
              1.0018322400074362,
              1.0000066372660272,
              0.9981736684841586
            ],
            "cell_volume_ratio": 1.0000091994969578,
            "cell_rmsd_from_input_A": 0.011427207806426715
          },
          {
            "iteration": 1,
            "reduced_polarization": [
              -0.025386292912996218,
              0.1347536032538733,
              -0.01653697833493583
            ],
            "branch_aligned_reduced_polarization": [
              -0.025386292912996218,
              0.1347536032538733,
              -0.01653697833493583
            ],
            "target_residual": 0.36650084018504453,
            "energy_eV": -210.91406976103593,
            "max_atomic_step_A": 0.12,
            "max_log_strain_component": 0.0017073186047199692,
            "step_scale": 0.3499949437503887,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 0.1644037161115604,
            "cell_principal_stretches": [
              1.0035443759652278,
              1.0000357596682452,
              0.9964702658816584
            ],
            "cell_volume_ratio": 1.0000378908865681,
            "cell_rmsd_from_input_A": 0.022095253518977218
          },
          {
            "iteration": 2,
            "reduced_polarization": [
              -0.021315901641036538,
              0.26145877843086585,
              -0.011867536071951285
            ],
            "branch_aligned_reduced_polarization": [
              -0.021315901641036538,
              0.26145877843086585,
              -0.011867536071951285
            ],
            "target_residual": 0.23978557184051788,
            "energy_eV": -206.65829002079215,
            "max_atomic_step_A": 0.12,
            "max_log_strain_component": 0.0019614602821646635,
            "step_scale": 0.5690200107955781,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 0.1644037161115604,
            "cell_principal_stretches": [
              1.0055156707326067,
              1.0000627258752832,
              0.9945175583071263
            ],
            "cell_volume_ratio": 1.0000657157593598,
            "cell_rmsd_from_input_A": 0.03435259543116607
          },
          {
            "iteration": 3,
            "reduced_polarization": [
              -0.019737469902461814,
              0.36931561328640833,
              -0.004460533910325113
            ],
            "branch_aligned_reduced_polarization": [
              -0.019737469902461814,
              0.36931561328640833,
              -0.004460533910325113
            ],
            "target_residual": 0.13224172190206585,
            "energy_eV": -197.78939911332284,
            "max_atomic_step_A": 0.12,
            "max_log_strain_component": 0.002699484030026714,
            "step_scale": 0.8994741352047956,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 0.1644037161115604,
            "cell_principal_stretches": [
              1.0082304936859037,
              1.0001425115672007,
              0.991831903986637
            ],
            "cell_volume_ratio": 1.0001376810887768,
            "cell_rmsd_from_input_A": 0.051222938937811414
          },
          {
            "iteration": 4,
            "reduced_polarization": [
              -0.03283268537105279,
              0.4349208689627829,
              -0.008799704990874983
            ],
            "branch_aligned_reduced_polarization": [
              -0.03283268537105279,
              0.4349208689627829,
              -0.008799704990874983
            ],
            "target_residual": 0.07342147732891408,
            "energy_eV": -187.8852820335863,
            "max_atomic_step_A": 0.06883431281588011,
            "max_log_strain_component": 0.012466305349622491,
            "step_scale": 1.0,
            "strain_jacobian_refreshed": true,
            "strain_jacobian_frobenius_norm": 4.214773316596727,
            "cell_principal_stretches": [
              0.999929286892192,
              0.9969310638805737,
              0.9843042585636836
            ],
            "cell_volume_ratio": 0.9812141020667353,
            "cell_rmsd_from_input_A": 0.24893361342418652
          },
          {
            "iteration": 5,
            "reduced_polarization": [
              0.01133290059570185,
              0.47656658156590925,
              0.0013925233081483394
            ],
            "branch_aligned_reduced_polarization": [
              0.01133290059570185,
              0.47656658156590925,
              0.0013925233081483394
            ],
            "target_residual": 0.02606719886337962,
            "energy_eV": -182.38775082538444
          }
        ],
        "iterations": 5
      },
      "parent": {
        "candidate_id": "bec_projection_03",
        "source": "MACEField_BEC_backprojection",
        "spacegroup": "P1",
        "spacegroup_number": 1,
        "pointgroup": "1",
        "has_inversion": false,
        "is_polar_point_group": true,
        "nonpolar_parent_hypothesis": false,
        "symmetry_tolerance_A": null,
        "target_reduced_polarization": [
          0.0,
          0.5,
          0.0
        ],
        "formal_class": [
          0.0,
          0.5,
          0.0
        ],
        "target_residual": 0.02606719886337962,
        "parent_symmetrization_rmsd_A": 0.19694374961069538,
        "parent_cell_rmsd_A": 0.24893361342418652,
        "energy_eV": -182.38775082538444,
        "reduced_polarization": [
          0.01133290059570185,
          0.47656658156590925,
          0.0013925233081483394
        ],
        "cartesian_polarization_e_A2": [
          0.00020649826166420287,
          0.018672098045471413,
          -2.094381043067029e-06
        ],
        "ranking_score": 0.8113115506935014
      },
      "branch_status": "awaiting_branch_sampling"
    },
    {
      "orbit_id": 4,
      "formal_class": [
        0.5,
        0.0,
        0.5
      ],
      "formal_classes_in_orbit": [
        [
          0.5,
          0.0,
          0.5
        ]
      ],
      "target_reduced_polarization": [
        -0.5,
        0.0,
        -0.5
      ],
      "bec_backprojection": {
        "converged_to_target": true,
        "history": [
          {
            "iteration": 0,
            "reduced_polarization": [
              -0.027380215707629288,
              2.860359379708054e-08,
              -0.022486969738858675
            ],
            "branch_aligned_reduced_polarization": [
              -0.027380215707629274,
              2.860359379708054e-08,
              -0.022486969738858664
            ],
            "target_residual": 0.6718542658744867,
            "energy_eV": -212.48322237156225,
            "max_atomic_step_A": 0.12,
            "max_log_strain_component": 0.0005887393701426945,
            "step_scale": 0.9178676119173607,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 0.1644037161115604,
            "cell_principal_stretches": [
              1.000355264465486,
              0.9999755021459446,
              0.9991614502290421
            ],
            "cell_volume_ratio": 0.9994919307802879,
            "cell_rmsd_from_input_A": 0.0012506781143542688
          },
          {
            "iteration": 1,
            "reduced_polarization": [
              -0.43503615102405524,
              1.7353391390328497e-08,
              -0.4330921342023097
            ],
            "branch_aligned_reduced_polarization": [
              -0.43503615102405524,
              1.7353391390328497e-08,
              -0.4330921342023097
            ],
            "target_residual": 0.09325751540423645,
            "energy_eV": -210.9093798114148,
            "max_atomic_step_A": 0.01752993028174908,
            "max_log_strain_component": 0.00010946393139048098,
            "step_scale": 1.0,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 0.1644037161115604,
            "cell_principal_stretches": [
              1.0004211932653373,
              0.9999710306257891,
              0.9990054469521978
            ],
            "cell_volume_ratio": 0.9993972685662872,
            "cell_rmsd_from_input_A": 0.001482497966149178
          },
          {
            "iteration": 2,
            "reduced_polarization": [
              -0.5000152953747526,
              5.789655659457446e-10,
              -0.4996069638312639
            ],
            "branch_aligned_reduced_polarization": [
              -0.5000152953747526,
              5.789655659457446e-10,
              -0.4996069638312639
            ],
            "target_residual": 0.0003933336731375873,
            "energy_eV": -210.36257018283283
          }
        ],
        "iterations": 2
      },
      "parent": {
        "candidate_id": "bec_projection_04",
        "source": "MACEField_BEC_backprojection",
        "spacegroup": "Pc",
        "spacegroup_number": 7,
        "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": 0.0003933336731375873,
        "parent_symmetrization_rmsd_A": 0.0543170573838361,
        "parent_cell_rmsd_A": 0.001482497966149178,
        "energy_eV": -210.36257018283283,
        "reduced_polarization": [
          -0.5000152953747526,
          5.789655659457446e-10,
          -0.4996069638312639
        ],
        "cartesian_polarization_e_A2": [
          -0.004416888410740725,
          -5.835954043353756e-11,
          -0.003412452347148752
        ],
        "ranking_score": 0.5554743492216485
      },
      "branch_status": "awaiting_branch_sampling"
    },
    {
      "orbit_id": 5,
      "formal_class": [
        0.5,
        0.5,
        0.0
      ],
      "formal_classes_in_orbit": [
        [
          0.5,
          0.5,
          0.0
        ]
      ],
      "target_reduced_polarization": [
        -0.5,
        0.5,
        0.0
      ],
      "bec_backprojection": {
        "converged_to_target": false,
        "history": [
          {
            "iteration": 0,
            "reduced_polarization": [
              -0.027380215707629288,
              2.860359379708054e-08,
              -0.022486969738858675
            ],
            "branch_aligned_reduced_polarization": [
              -0.027380215707629274,
              2.860359377132582e-08,
              -0.022486969738858675
            ],
            "target_residual": 0.6883858625139032,
            "energy_eV": -212.48322237156225,
            "max_atomic_step_A": 0.11999999999999998,
            "max_log_strain_component": 0.001736469669404606,
            "step_scale": 0.2658747028950138,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 0.1644037161115604,
            "cell_principal_stretches": [
              1.0017503182994305,
              0.9998110019556145,
              0.9982745922268702
            ],
            "cell_volume_ratio": 0.9998328883318511,
            "cell_rmsd_from_input_A": 0.01095212821339587
          },
          {
            "iteration": 1,
            "reduced_polarization": [
              -0.14648416976367282,
              0.12868855200336018,
              -0.014608978541161848
            ],
            "branch_aligned_reduced_polarization": [
              -0.14648416976367284,
              0.12868855200336016,
              -0.014608978541161848
            ],
            "target_residual": 0.512892830808793,
            "energy_eV": -210.9885113786938,
            "max_atomic_step_A": 0.12000000000000001,
            "max_log_strain_component": 0.0015887291390292285,
            "step_scale": 0.32018587061938303,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 0.1644037161115604,
            "cell_principal_stretches": [
              1.0033529808443389,
              0.9996234811030292,
              0.9966970438771552
            ],
            "cell_volume_ratio": 0.999662416410513,
            "cell_rmsd_from_input_A": 0.020994203062815662
          },
          {
            "iteration": 2,
            "reduced_polarization": [
              -0.252824997038031,
              0.2460303420163331,
              -0.01622649040215587
            ],
            "branch_aligned_reduced_polarization": [
              -0.252824997038031,
              0.24603034201633311,
              -0.01622649040215587
            ],
            "target_residual": 0.3547666391536292,
            "energy_eV": -206.9903049133399,
            "max_atomic_step_A": 0.12,
            "max_log_strain_component": 0.0018974018878353824,
            "step_scale": 0.4964195252221829,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 0.1644037161115604,
            "cell_principal_stretches": [
              1.0052868846046534,
              0.99930334890899,
              0.994829493755942
            ],
            "cell_volume_ratio": 0.999392329368177,
            "cell_rmsd_from_input_A": 0.03316480522910955
          },
          {
            "iteration": 3,
            "reduced_polarization": [
              -0.3627983416065288,
              0.3510040737348373,
              -0.010526182317290264
            ],
            "branch_aligned_reduced_polarization": [
              -0.3627983416065288,
              0.3510040737348373,
              -0.010526182317290264
            ],
            "target_residual": 0.20281736026215658,
            "energy_eV": -198.0363573770378,
            "max_atomic_step_A": 0.12,
            "max_log_strain_component": 0.0014326976361644886,
            "step_scale": 0.6221173715733995,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 0.1644037161115604,
            "cell_principal_stretches": [
              1.0067629244898626,
              0.9990149071368344,
              0.9934309518887816
            ],
            "cell_volume_ratio": 0.9991642103166073,
            "cell_rmsd_from_input_A": 0.042501451803768506
          },
          {
            "iteration": 4,
            "reduced_polarization": [
              -0.36641327729919615,
              0.4024547702298933,
              0.04086309578096376
            ],
            "branch_aligned_reduced_polarization": [
              -0.36641327729919615,
              0.4024547702298933,
              0.04086309578096376
            ],
            "target_residual": 0.17038273659513922,
            "energy_eV": -191.30314383895615,
            "max_atomic_step_A": 0.09271375733910978,
            "max_log_strain_component": 0.018583592462622322,
            "step_scale": 1.0,
            "strain_jacobian_refreshed": true,
            "strain_jacobian_frobenius_norm": 3.7107888637677258,
            "cell_principal_stretches": [
              1.0013448157719087,
              0.9952556669381061,
              0.9706112761204024
            ],
            "cell_volume_ratio": 0.9673054735589687,
            "cell_rmsd_from_input_A": 0.3823644723955718
          },
          {
            "iteration": 5,
            "reduced_polarization": [
              -0.506207154343779,
              0.48358877513228965,
              0.01968410793507499
            ],
            "branch_aligned_reduced_polarization": [
              -0.506207154343779,
              0.48358877513228965,
              0.01968410793507499
            ],
            "target_residual": 0.026368943321751288,
            "energy_eV": -175.39268252564344
          }
        ],
        "iterations": 5
      },
      "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,
          0.0
        ],
        "formal_class": [
          0.5,
          0.5,
          0.0
        ],
        "target_residual": 0.026368943321751288,
        "parent_symmetrization_rmsd_A": 0.2044720937910223,
        "parent_cell_rmsd_A": 0.3823644723955718,
        "energy_eV": -175.39268252564344,
        "reduced_polarization": [
          -0.506207154343779,
          0.48358877513228965,
          0.01968410793507499
        ],
        "cartesian_polarization_e_A2": [
          -0.004310199867942403,
          0.019031647067131313,
          0.0030099314224032213
        ],
        "ranking_score": 0.8528010985334178
      },
      "branch_status": "awaiting_branch_sampling"
    },
    {
      "orbit_id": 6,
      "formal_class": [
        0.0,
        0.5,
        0.5
      ],
      "formal_classes_in_orbit": [
        [
          0.0,
          0.5,
          0.5
        ]
      ],
      "target_reduced_polarization": [
        0.0,
        0.5,
        -0.5
      ],
      "bec_backprojection": {
        "converged_to_target": false,
        "history": [
          {
            "iteration": 0,
            "reduced_polarization": [
              -0.027380215707629288,
              2.860359379708054e-08,
              -0.022486969738858675
            ],
            "branch_aligned_reduced_polarization": [
              -0.027380215707629288,
              2.860359377132582e-08,
              -0.022486969738858664
            ],
            "target_residual": 0.6919308792630815,
            "energy_eV": -212.48322237156225,
            "max_atomic_step_A": 0.12000000000000001,
            "max_log_strain_component": 0.0017351294301630672,
            "step_scale": 0.2656694669378699,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 0.1644037161115604,
            "cell_principal_stretches": [
              1.0017095198310397,
              1.0001022168711513,
              0.998219945679604
            ],
            "cell_volume_ratio": 1.0000286318227694,
            "cell_rmsd_from_input_A": 0.01095229968996135
          },
          {
            "iteration": 1,
            "reduced_polarization": [
              -0.028630159791550917,
              0.12785538219723888,
              -0.14251928815836842
            ],
            "branch_aligned_reduced_polarization": [
              -0.028630159791550917,
              0.1278553821972389,
              -0.14251928815836845
            ],
            "target_residual": 0.5168208218987046,
            "energy_eV": -210.98588347461845,
            "max_atomic_step_A": 0.12000000000000001,
            "max_log_strain_component": 0.0016532250847764514,
            "step_scale": 0.33030708513948254,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 0.1644037161115604,
            "cell_principal_stretches": [
              1.0033379059145722,
              1.0002493365599718,
              0.9965180337906852
            ],
            "cell_volume_ratio": 1.0000936149722188,
            "cell_rmsd_from_input_A": 0.02144465383299756
          },
          {
            "iteration": 2,
            "reduced_polarization": [
              -0.045129239127376264,
              0.24948966362249633,
              -0.259438078298255
            ],
            "branch_aligned_reduced_polarization": [
              -0.045129239127376264,
              0.24948966362249636,
              -0.259438078298255
            ],
            "target_residual": 0.3502315163274465,
            "energy_eV": -206.88267688601445,
            "max_atomic_step_A": 0.12000000000000001,
            "max_log_strain_component": 0.0019154856296684337,
            "step_scale": 0.5166845649900232,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 0.1644037161115604,
            "cell_principal_stretches": [
              1.0052235868862134,
              1.0005387236318009,
              0.9945373107845487
            ],
            "cell_volume_ratio": 1.0002709422883496,
            "cell_rmsd_from_input_A": 0.03375767508232641
          },
          {
            "iteration": 3,
            "reduced_polarization": [
              -0.05173807490706882,
              0.3488571408606016,
              -0.38803486509267027
            ],
            "branch_aligned_reduced_polarization": [
              -0.05173807490706882,
              0.3488571408606016,
              -0.38803486509267027
            ],
            "target_residual": 0.19508250485048126,
            "energy_eV": -198.31588199451514,
            "max_atomic_step_A": 0.12,
            "max_log_strain_component": 0.0012935374604913694,
            "step_scale": 0.5732413970137209,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 0.1644037161115604,
            "cell_principal_stretches": [
              1.0064954819952698,
              1.0008237639958057,
              0.9931834297510997
            ],
            "cell_volume_ratio": 1.0004580978581883,
            "cell_rmsd_from_input_A": 0.04225815965047131
          },
          {
            "iteration": 4,
            "reduced_polarization": [
              -0.0981680605271527,
              0.3917618656948226,
              -0.4834063623416961
            ],
            "branch_aligned_reduced_polarization": [
              -0.0981680605271527,
              0.3917618656948226,
              -0.4834063623416961
            ],
            "target_residual": 0.14706396783802422,
            "energy_eV": -193.33189879602247,
            "max_atomic_step_A": 0.09504743415022643,
            "max_log_strain_component": 0.0192033966223997,
            "step_scale": 1.0,
            "strain_jacobian_refreshed": true,
            "strain_jacobian_frobenius_norm": 3.8045603834925528,
            "cell_principal_stretches": [
              1.0117394952422605,
              0.9912465026508049,
              0.9712430569818993
            ],
            "cell_volume_ratio": 0.974043380173858,
            "cell_rmsd_from_input_A": 0.3299296164277196
          },
          {
            "iteration": 5,
            "reduced_polarization": [
              0.03618019715827117,
              0.47908459869092584,
              -0.5021263104959234
            ],
            "branch_aligned_reduced_polarization": [
              0.03618019715827117,
              0.47908459869092584,
              -0.5021263104959234
            ],
            "target_residual": 0.04184473532782909,
            "energy_eV": -175.76069953115558
          }
        ],
        "iterations": 5
      },
      "parent": {
        "candidate_id": "bec_projection_06",
        "source": "MACEField_BEC_backprojection",
        "spacegroup": "P1",
        "spacegroup_number": 1,
        "pointgroup": "1",
        "has_inversion": false,
        "is_polar_point_group": true,
        "nonpolar_parent_hypothesis": false,
        "symmetry_tolerance_A": null,
        "target_reduced_polarization": [
          0.0,
          0.5,
          -0.5
        ],
        "formal_class": [
          0.0,
          0.5,
          0.5
        ],
        "target_residual": 0.04184473532782909,
        "parent_symmetrization_rmsd_A": 0.2044216632564604,
        "parent_cell_rmsd_A": 0.3299296164277196,
        "energy_eV": -175.76069953115558,
        "reduced_polarization": [
          0.03618019715827117,
          0.47908459869092584,
          -0.5021263104959234
        ],
        "cartesian_polarization_e_A2": [
          0.0002829073893787418,
          0.018752542012951595,
          -0.006296232165686651
        ],
        "ranking_score": 0.8705935380190485
      },
      "branch_status": "awaiting_branch_sampling"
    },
    {
      "orbit_id": 7,
      "formal_class": [
        0.5,
        0.5,
        0.5
      ],
      "formal_classes_in_orbit": [
        [
          0.5,
          0.5,
          0.5
        ]
      ],
      "target_reduced_polarization": [
        -0.5,
        0.5,
        -0.5
      ],
      "bec_backprojection": {
        "converged_to_target": false,
        "history": [
          {
            "iteration": 0,
            "reduced_polarization": [
              -0.027380215707629288,
              2.860359379708054e-08,
              -0.022486969738858675
            ],
            "branch_aligned_reduced_polarization": [
              -0.027380215707629274,
              2.860359377132582e-08,
              -0.022486969738858664
            ],
            "target_residual": 0.8374891796137738,
            "energy_eV": -212.48322237156225,
            "max_atomic_step_A": 0.12,
            "max_log_strain_component": 0.0016622393222176434,
            "step_scale": 0.25450893873318825,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 0.1644037161115604,
            "cell_principal_stretches": [
              1.0016450480449168,
              0.9999134600398399,
              0.9983033740223237
            ],
            "cell_volume_ratio": 0.9998590957809207,
            "cell_rmsd_from_input_A": 0.010391993192700394
          },
          {
            "iteration": 1,
            "reduced_polarization": [
              -0.14419366664171526,
              0.12295561436223924,
              -0.13569227616075033
            ],
            "branch_aligned_reduced_polarization": [
              -0.1441936666417153,
              0.12295561436223923,
              -0.1356922761607503
            ],
            "target_residual": 0.6336250730895663,
            "energy_eV": -211.07680834149187,
            "max_atomic_step_A": 0.12000000000000001,
            "max_log_strain_component": 0.0015632711537842423,
            "step_scale": 0.30839939180117465,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 0.1644037161115604,
            "cell_principal_stretches": [
              1.0031913970251476,
              0.9998444415014216,
              0.996701058373233
            ],
            "cell_volume_ratio": 0.9997263870345411,
            "cell_rmsd_from_input_A": 0.020169637945443852
          },
          {
            "iteration": 2,
            "reduced_polarization": [
              -0.26535734263837096,
              0.23829279420108634,
              -0.2515694158053095
            ],
            "branch_aligned_reduced_polarization": [
              -0.26535734263837096,
              0.23829279420108634,
              -0.2515694158053095
            ],
            "target_residual": 0.4304248986572652,
            "energy_eV": -207.26430079630728,
            "max_atomic_step_A": 0.12,
            "max_log_strain_component": 0.0019068331642369295,
            "step_scale": 0.5123899566766568,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 0.1644037161115604,
            "cell_principal_stretches": [
              1.0050836103502432,
              0.9997753805936811,
              0.9947611239184313
            ],
            "cell_volume_ratio": 0.9995935233155354,
            "cell_rmsd_from_input_A": 0.0320928033344828
          },
          {
            "iteration": 3,
            "reduced_polarization": [
              -0.3852945349598276,
              0.34820170753705887,
              -0.383961260599023
            ],
            "branch_aligned_reduced_polarization": [
              -0.3852945349598276,
              0.34820170753705887,
              -0.383961260599023
            ],
            "target_residual": 0.22285657797452307,
            "energy_eV": -198.6089111041649,
            "max_atomic_step_A": 0.11999999999999998,
            "max_log_strain_component": 0.0017705259888935768,
            "step_scale": 0.6547300335413688,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 0.1644037161115604,
            "cell_principal_stretches": [
              1.0068404454422337,
              0.9997848628909811,
              0.9929597621286013
            ],
            "cell_volume_ratio": 0.9995369654421732,
            "cell_rmsd_from_input_A": 0.043171408171212663
          },
          {
            "iteration": 4,
            "reduced_polarization": [
              -0.36039673228616353,
              0.40784560226405164,
              -0.4078494872162632
            ],
            "branch_aligned_reduced_polarization": [
              -0.36039673228616353,
              0.40784560226405164,
              -0.4078494872162632
            ],
            "target_residual": 0.19097963866538784,
            "energy_eV": -191.21550606543514,
            "max_atomic_step_A": 0.09086321969177182,
            "max_log_strain_component": 0.02,
            "step_scale": 0.9608886494616464,
            "strain_jacobian_refreshed": true,
            "strain_jacobian_frobenius_norm": 4.216267063233425,
            "cell_principal_stretches": [
              1.0021794361470493,
              0.9932845278569298,
              0.9763179939372895
            ],
            "cell_volume_ratio": 0.9718750910389783,
            "cell_rmsd_from_input_A": 0.39931644612749106
          },
          {
            "iteration": 5,
            "reduced_polarization": [
              -0.46495686087314736,
              0.4820915458648058,
              -0.47090454511946717
            ],
            "branch_aligned_reduced_polarization": [
              -0.46495686087314736,
              0.4820915458648058,
              -0.47090454511946717
            ],
            "target_residual": 0.048941596051635124,
            "energy_eV": -178.81474634121946
          }
        ],
        "iterations": 5
      },
      "parent": {
        "candidate_id": "bec_projection_07",
        "source": "MACEField_BEC_backprojection",
        "spacegroup": "P1",
        "spacegroup_number": 1,
        "pointgroup": "1",
        "has_inversion": false,
        "is_polar_point_group": true,
        "nonpolar_parent_hypothesis": false,
        "symmetry_tolerance_A": null,
        "target_reduced_polarization": [
          -0.5,
          0.5,
          -0.5
        ],
        "formal_class": [
          0.5,
          0.5,
          0.5
        ],
        "target_residual": 0.048941596051635124,
        "parent_symmetrization_rmsd_A": 0.20461172249322407,
        "parent_cell_rmsd_A": 0.39931644612749106,
        "energy_eV": -178.81474634121946,
        "reduced_polarization": [
          -0.46495686087314736,
          0.4820915458648058,
          -0.47090454511946717
        ],
        "cartesian_polarization_e_A2": [
          -0.004118697708781742,
          0.01888382953435796,
          -0.003187694223509429
        ],
        "ranking_score": 0.902324026128367
      },
      "branch_status": "awaiting_branch_sampling"
    }
  ],
  "sampled_polarization_branches": [
    {
      "orbit_id": 0,
      "candidate_id": "inversion_parent_endpoint_00",
      "formal_class": [
        0.0,
        0.0,
        0.0
      ],
      "construction": "MACEField-BEC-parent plus variable-cell P-N-P path and symmetric log-strain continuation beyond both polar endpoints",
      "geometry_diagnostics": {
        "collision_aware": false,
        "permutations_tested": 1,
        "selected_order": [
          0,
          1,
          2,
          3,
          4,
          5,
          6,
          7,
          8,
          9,
          10,
          11,
          12,
          13,
          14,
          15,
          16,
          17,
          18,
          19,
          20,
          21,
          22,
          23,
          24,
          25,
          26,
          27,
          28,
          29,
          30,
          31,
          32,
          33,
          34,
          35,
          36,
          37,
          38,
          39,
          40,
          41,
          42,
          43,
          44,
          45,
          46,
          47
        ],
        "endpoint_rmsd_A": 0.05283729570281214,
        "minimum_distance_A_by_image": [
          0.9931300054723953,
          0.9927022701573283,
          0.9923493636375665,
          0.9920713657689664,
          0.9918683395370468,
          0.9917403309857395,
          0.9916873691652444,
          0.9917094660990764,
          0.991806616770428
        ],
        "minimum_distance_A": 0.9916873691652444,
        "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": [
          482.87106285765776,
          482.87106285765776,
          482.87106285765776,
          482.87106285765776,
          482.87106285765776,
          482.87106285765776,
          482.87106285765776,
          482.87106285765776,
          482.87106285765776
        ],
        "cell_deformation_log_strain_norm": 0.0
      },
      "parent_reduced_polarization": [
        -5.8994737250438785e-15,
        5.485674788303934e-16,
        -1.3896616996768471e-15
      ],
      "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": [
          -212.48322237156225,
          -212.48549451572956,
          -212.48741518207262,
          -212.4890054704771,
          -212.49028288890386,
          -212.49126110082017,
          -212.49195067992613,
          -212.4923606959207,
          -212.49249680605834
        ],
        "cartesian_polarizations_e_A2": [
          [
            -0.0002412848096261145,
            1.1134441165751286e-09,
            -0.0001257803456954852
          ],
          [
            -0.00021102032422522674,
            9.748138440765516e-10,
            -0.00011006801623945801
          ],
          [
            -0.00018077645723006818,
            8.360292072005855e-10,
            -9.436022731125169e-05
          ],
          [
            -0.0001505642787772697,
            6.970675700273758e-10,
            -7.864926583082283e-05
          ],
          [
            -0.00012038945914448449,
            5.579223303979144e-10,
            -6.293154193193859e-05
          ],
          [
            -9.025139123929724e-05,
            4.186092907220079e-10,
            -4.720663626918869e-05
          ],
          [
            -6.014547329099513e-05,
            2.7915708424560987e-10,
            -3.147525719404007e-05
          ],
          [
            -3.006533248125458e-05,
            1.3960494332411943e-10,
            -1.5738853488805313e-05
          ],
          [
            -5.155983292906142e-17,
            2.135393303583759e-17,
            1.632440641232268e-17
          ]
        ],
        "raw_reduced_polarization": [
          [
            -0.027380215707633743,
            2.86035940462616e-08,
            -0.02248696973885776
          ],
          [
            -0.02394582784601636,
            2.5042280121258375e-08,
            -0.019671505749877475
          ],
          [
            -0.02051378668190214,
            2.1477000684272722e-08,
            -0.01685747255025273
          ],
          [
            -0.017085363596815572,
            1.790717423448862e-08,
            -0.014044835812146094
          ],
          [
            -0.013661209403789556,
            1.4332631167097635e-08,
            -0.011233606483402136
          ],
          [
            -0.010241255327750371,
            1.0753777434862308e-08,
            -0.00842371985196606
          ],
          [
            -0.006824975677002897,
            7.171348605676251e-09,
            -0.005614992703528917
          ],
          [
            -0.003411641914384741,
            3.5863525310792126e-09,
            -0.0028072082966087222
          ],
          [
            -5.8994737250438785e-15,
            5.485674788303934e-16,
            -1.3896616996768471e-15
          ]
        ],
        "unwrapped_reduced_polarization": [
          [
            -0.027380215707633743,
            2.86035940462616e-08,
            -0.02248696973885776
          ],
          [
            -0.02394582784601636,
            2.5042280121258375e-08,
            -0.019671505749877475
          ],
          [
            -0.02051378668190214,
            2.1477000684272722e-08,
            -0.01685747255025273
          ],
          [
            -0.017085363596815572,
            1.790717423448862e-08,
            -0.014044835812146094
          ],
          [
            -0.013661209403789556,
            1.4332631167097635e-08,
            -0.011233606483402136
          ],
          [
            -0.010241255327750371,
            1.0753777434862308e-08,
            -0.00842371985196606
          ],
          [
            -0.006824975677002897,
            7.171348605676251e-09,
            -0.005614992703528917
          ],
          [
            -0.003411641914384741,
            3.5863525310792126e-09,
            -0.0028072082966087222
          ],
          [
            -5.899360860928127e-15,
            5.485674788643375e-16,
            -1.3895135042574225e-15
          ]
        ],
        "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": [
          [
            -0.027380215707633715,
            2.8603594048881575e-08,
            -0.022486969738857776
          ],
          [
            -0.023945827846016343,
            2.5042280138443118e-08,
            -0.01967150574987747
          ],
          [
            -0.020513786681902124,
            2.1477000733405305e-08,
            -0.016857472550252717
          ],
          [
            -0.01708536359681556,
            1.7907174187925534e-08,
            -0.014044835812146106
          ],
          [
            -0.013661209403789565,
            1.4332631192992551e-08,
            -0.011233606483402159
          ],
          [
            -0.010241255327750387,
            1.0753777424099553e-08,
            -0.00842371985196605
          ],
          [
            -0.006824975677002909,
            7.17134862604496e-09,
            -0.005614992703528943
          ],
          [
            -0.0034116419143847554,
            3.5863525482682235e-09,
            -0.002807208296608743
          ],
          [
            -5.88418203051333e-15,
            5.551115123125783e-16,
            -1.3877787807814457e-15
          ]
        ]
      },
      "reflected": {
        "reached": true,
        "construction": "reflect_displacements_about_reconstructed_parent",
        "energies_eV": [
          -212.49249680605837,
          -212.4923606959207,
          -212.49195067992613,
          -212.49126110082017,
          -212.49028288890386,
          -212.4890054704771,
          -212.48741518207265,
          -212.48549451572956,
          -212.48322237156222
        ],
        "cartesian_polarizations_e_A2": [
          [
            -4.538070022017168e-17,
            9.656691117148627e-18,
            1.4370076067185458e-19
          ],
          [
            3.0065332481284584e-05,
            -1.3960488870525656e-10,
            1.5738853488746844e-05
          ],
          [
            6.0145473291004784e-05,
            -2.791570709622708e-10,
            3.147525719406184e-05
          ],
          [
            9.025139123922266e-05,
            -4.1860928155749193e-10,
            4.7206636269141224e-05
          ],
          [
            0.00012038945914450355,
            -5.579223093331791e-10,
            6.293154193194162e-05
          ],
          [
            0.00015056427877727866,
            -6.970674513610839e-10,
            7.864926583081642e-05
          ],
          [
            0.00018077645722999286,
            -8.360291566376766e-10,
            9.436022731122713e-05
          ],
          [
            0.000211020324225281,
            -9.74813815742354e-10,
            0.00011006801623936495
          ],
          [
            0.00024128480962615212,
            -1.1134440067123046e-09,
            0.00012578034569546298
          ]
        ],
        "raw_reduced_polarization": [
          [
            -5.176445730403119e-15,
            2.48073583966369e-16,
            -2.3476876886663665e-15
          ],
          [
            0.003411641914388229,
            -3.586351127959148e-09,
            0.00280720829660566
          ],
          [
            0.006824975677003974,
            -7.1713482644366405e-09,
            0.00561499270353114
          ],
          [
            0.010241255327741918,
            -1.0753777199432357e-08,
            0.008423719851958427
          ],
          [
            0.013661209403791726,
            -1.4332630625959445e-08,
            0.011233606483403366
          ],
          [
            0.017085363596816602,
            -1.7907171186035277e-08,
            0.014044835812146054
          ],
          [
            0.02051378668189358,
            -2.147699938534725e-08,
            0.016857472550246878
          ],
          [
            0.023945827846022654,
            -2.504227939337282e-08,
            0.019671505749872937
          ],
          [
            0.02738021570763806,
            -2.860359122396314e-08,
            0.022486969738857956
          ]
        ],
        "unwrapped_reduced_polarization": [
          [
            -5.176445730403119e-15,
            2.48073583966369e-16,
            -2.3476876886663665e-15
          ],
          [
            0.003411641914388229,
            -3.586351127959148e-09,
            0.00280720829660566
          ],
          [
            0.006824975677003974,
            -7.1713482644366405e-09,
            0.00561499270353114
          ],
          [
            0.010241255327741918,
            -1.0753777199432357e-08,
            0.008423719851958427
          ],
          [
            0.013661209403791726,
            -1.4332630625959445e-08,
            0.011233606483403366
          ],
          [
            0.017085363596816602,
            -1.7907171186035277e-08,
            0.014044835812146054
          ],
          [
            0.02051378668189358,
            -2.147699938534725e-08,
            0.016857472550246878
          ],
          [
            0.023945827846022654,
            -2.504227939337282e-08,
            0.019671505749872937
          ],
          [
            0.02738021570763806,
            -2.860359122396314e-08,
            0.022486969738857956
          ]
        ],
        "gauge_integer_shift": [
          0,
          0,
          0
        ],
        "expected_opposite_endpoint_reduced_polarization": [
          0.027380215707621943,
          -2.860359294912664e-08,
          0.022486969738854983
        ],
        "actual_opposite_endpoint_branch_residual": 1.6478129484101214e-14
      },
      "pnp_branch": {
        "construction": "incoming_path_concatenated_with_parent_reflection",
        "reduced_polarization": [
          [
            -0.027380215707633743,
            2.86035940462616e-08,
            -0.02248696973885776
          ],
          [
            -0.02394582784601636,
            2.5042280121258375e-08,
            -0.019671505749877475
          ],
          [
            -0.02051378668190214,
            2.1477000684272722e-08,
            -0.01685747255025273
          ],
          [
            -0.017085363596815572,
            1.790717423448862e-08,
            -0.014044835812146094
          ],
          [
            -0.013661209403789556,
            1.4332631167097635e-08,
            -0.011233606483402136
          ],
          [
            -0.010241255327750371,
            1.0753777434862308e-08,
            -0.00842371985196606
          ],
          [
            -0.006824975677002897,
            7.171348605676251e-09,
            -0.005614992703528917
          ],
          [
            -0.003411641914384741,
            3.5863525310792126e-09,
            -0.0028072082966087222
          ],
          [
            -5.8994737250438785e-15,
            5.485674788303934e-16,
            -1.3896616996768471e-15
          ],
          [
            0.003411641914388229,
            -3.586351127959148e-09,
            0.00280720829660566
          ],
          [
            0.006824975677003974,
            -7.1713482644366405e-09,
            0.00561499270353114
          ],
          [
            0.010241255327741918,
            -1.0753777199432357e-08,
            0.008423719851958427
          ],
          [
            0.013661209403791726,
            -1.4332630625959445e-08,
            0.011233606483403366
          ],
          [
            0.017085363596816602,
            -1.7907171186035277e-08,
            0.014044835812146054
          ],
          [
            0.02051378668189358,
            -2.147699938534725e-08,
            0.016857472550246878
          ],
          [
            0.023945827846022654,
            -2.504227939337282e-08,
            0.019671505749872937
          ],
          [
            0.02738021570763806,
            -2.860359122396314e-08,
            0.022486969738857956
          ]
        ],
        "unwrapped_reduced_polarization": [
          [
            -0.027380215707633743,
            2.86035940462616e-08,
            -0.02248696973885776
          ],
          [
            -0.02394582784601636,
            2.5042280121258375e-08,
            -0.019671505749877475
          ],
          [
            -0.02051378668190214,
            2.1477000684272722e-08,
            -0.01685747255025273
          ],
          [
            -0.017085363596815572,
            1.790717423448862e-08,
            -0.014044835812146094
          ],
          [
            -0.013661209403789556,
            1.4332631167097635e-08,
            -0.011233606483402136
          ],
          [
            -0.010241255327750371,
            1.0753777434862308e-08,
            -0.00842371985196606
          ],
          [
            -0.006824975677002897,
            7.171348605676251e-09,
            -0.005614992703528917
          ],
          [
            -0.003411641914384741,
            3.5863525310792126e-09,
            -0.0028072082966087222
          ],
          [
            -5.899360860928127e-15,
            5.485674788643375e-16,
            -1.3895135042574225e-15
          ],
          [
            0.003411641914388229,
            -3.586351127959148e-09,
            0.00280720829660566
          ],
          [
            0.006824975677003974,
            -7.1713482644366405e-09,
            0.00561499270353114
          ],
          [
            0.010241255327741918,
            -1.0753777199432357e-08,
            0.008423719851958427
          ],
          [
            0.013661209403791726,
            -1.4332630625959445e-08,
            0.011233606483403366
          ],
          [
            0.017085363596816602,
            -1.7907171186035277e-08,
            0.014044835812146054
          ],
          [
            0.02051378668189358,
            -2.147699938534725e-08,
            0.016857472550246878
          ],
          [
            0.023945827846022654,
            -2.504227939337282e-08,
            0.019671505749872937
          ],
          [
            0.02738021570763806,
            -2.860359122396314e-08,
            0.022486969738857956
          ]
        ],
        "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": [
          [
            -0.027380215707633715,
            2.8603594048881575e-08,
            -0.022486969738857776
          ],
          [
            -0.023945827846016343,
            2.5042280138443118e-08,
            -0.01967150574987747
          ],
          [
            -0.020513786681902124,
            2.1477000733405305e-08,
            -0.016857472550252717
          ],
          [
            -0.01708536359681556,
            1.7907174187925534e-08,
            -0.014044835812146106
          ],
          [
            -0.013661209403789565,
            1.4332631192992551e-08,
            -0.011233606483402159
          ],
          [
            -0.010241255327750387,
            1.0753777424099553e-08,
            -0.00842371985196605
          ],
          [
            -0.006824975677002909,
            7.17134862604496e-09,
            -0.005614992703528943
          ],
          [
            -0.0034116419143847554,
            3.5863525482682235e-09,
            -0.002807208296608743
          ],
          [
            -5.88418203051333e-15,
            5.551115123125783e-16,
            -1.3877787807814457e-15
          ],
          [
            0.0034116419143882526,
            -3.5863511049782915e-09,
            0.0028072082966056344
          ],
          [
            0.006824975677004019,
            -7.171348237466901e-09,
            0.005614992703531163
          ],
          [
            0.010241255327741894,
            -1.0753777202054948e-08,
            0.008423719851958444
          ],
          [
            0.013661209403791674,
            -1.4332630637881039e-08,
            0.011233606483403324
          ],
          [
            0.01708536359681656,
            -1.7907171190323368e-08,
            0.014044835812146106
          ],
          [
            0.02051378668189363,
            -2.1476999401137675e-08,
            0.016857472550246833
          ],
          [
            0.023945827846022616,
            -2.5042279416798152e-08,
            0.019671505749872975
          ],
          [
            0.027380215707638045,
            -2.8603591217812863e-08,
            0.022486969738857998
          ]
        ]
      },
      "incoming_structure_ids": [
        "incoming_00_000",
        "incoming_00_001",
        "incoming_00_002",
        "incoming_00_003",
        "incoming_00_004",
        "incoming_00_005",
        "incoming_00_006",
        "incoming_00_007",
        "incoming_00_008"
      ],
      "reflected_structure_ids": [
        "reflected_00_001",
        "reflected_00_002",
        "reflected_00_003",
        "reflected_00_004",
        "reflected_00_005",
        "reflected_00_006",
        "reflected_00_007",
        "reflected_00_008"
      ],
      "positive_extension_structure_ids": [
        "extension_plus_00_000",
        "extension_plus_00_001",
        "extension_plus_00_002",
        "extension_plus_00_003"
      ],
      "negative_extension_structure_ids": [
        "extension_minus_00_000",
        "extension_minus_00_001",
        "extension_minus_00_002",
        "extension_minus_00_003"
      ],
      "extension": {
        "enabled": true,
        "fraction_beyond_polar_endpoint": 0.35,
        "images_per_side": 4,
        "construction": "continue fractional atomic displacements and symmetric log strain beyond +P; reflect these structures about N for the -P side",
        "positive_path_coordinates": [
          1.35,
          1.2625,
          1.175,
          1.0875
        ],
        "negative_path_coordinates": [
          -1.0875,
          -1.175,
          -1.2625,
          -1.35
        ]
      },
      "branch_coordinates": [
        1.35,
        1.2625,
        1.175,
        1.0875,
        1.0,
        0.875,
        0.75,
        0.625,
        0.5,
        0.375,
        0.25,
        0.125,
        0.0,
        -0.125,
        -0.25,
        -0.375,
        -0.5,
        -0.625,
        -0.75,
        -0.875,
        -1.0,
        -1.0875,
        -1.175,
        -1.2625,
        -1.35
      ],
      "parent": {
        "candidate_id": "inversion_parent_endpoint_00",
        "source": "same_species_inversion_center_projection_from_endpoint",
        "spacegroup": "P2_1/c",
        "spacegroup_number": 14,
        "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": 9.251127424475032e-15,
        "parent_symmetrization_rmsd_A": 0.05283729570281214,
        "parent_cell_rmsd_A": 0.0,
        "energy_eV": -212.49249680605834,
        "reduced_polarization": [
          -9.003706746739882e-15,
          -1.624291323589321e-17,
          -2.1251728424658475e-15
        ],
        "cartesian_polarization_e_A2": [
          -7.869053654390756e-17,
          -6.322833469561601e-19,
          2.4860231596230842e-17
        ],
        "ranking_score": 0.05283729570283064
      }
    }
  ],
  "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": 110,
      "full_response": 28,
      "energy_polarization": 82
    },
    "model_evaluations_for_recovery_and_path_properties": {
      "total": 135,
      "full_response": 53,
      "energy_polarization": 82
    },
    "elapsed_seconds": 2349.10652775201
  }
}
