{
  "schema": "ferrofinder.endpoint_parent_recovery.v4_variable_cell",
  "status": "complete",
  "input_atom_count": 32,
  "input_formula": "Cl8O24",
  "input_spacegroup": "Cc",
  "input_pointgroup": "m",
  "input_is_polar_point_group": true,
  "input_energy_eV": -124.07574297484037,
  "input_cartesian_polarization_e_A2": [
    0.00018862629561173876,
    5.018350216848538e-12,
    5.127560331488276e-05
  ],
  "input_reduced_polarization": [
    0.018309904492892416,
    2.892278689127378e-10,
    0.002697605212032375
  ],
  "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": "C2/c",
      "spacegroup_number": 15,
      "pointgroup": "2/m",
      "has_inversion": true,
      "is_polar_point_group": false,
      "nonpolar_parent_hypothesis": true,
      "symmetry_tolerance_A": null,
      "target_reduced_polarization": [
        0.0,
        0.0,
        0.0
      ],
      "formal_class": [
        0.0,
        0.0,
        0.0
      ],
      "target_residual": 2.99390556771246e-15,
      "parent_symmetrization_rmsd_A": 0.5961435605502995,
      "parent_cell_rmsd_A": 0.0,
      "energy_eV": -107.63241249175407,
      "reduced_polarization": [
        -2.3740276362158284e-15,
        -4.119226746954232e-17,
        -1.823668425993024e-15
      ],
      "cartesian_polarization_e_A2": [
        -1.7153303393509053e-17,
        -7.147209747295439e-19,
        -3.466396727438288e-17
      ],
      "ranking_score": 0.5961435605503055
    },
    {
      "candidate_id": "inversion_parent_endpoint_01",
      "source": "same_species_inversion_center_projection_from_endpoint",
      "spacegroup": "C2/c",
      "spacegroup_number": 15,
      "pointgroup": "2/m",
      "has_inversion": true,
      "is_polar_point_group": false,
      "nonpolar_parent_hypothesis": true,
      "symmetry_tolerance_A": null,
      "target_reduced_polarization": [
        0.0,
        0.0,
        0.0
      ],
      "formal_class": [
        0.0,
        0.0,
        0.0
      ],
      "target_residual": 1.062130179839768e-14,
      "parent_symmetrization_rmsd_A": 0.7892897492548149,
      "parent_cell_rmsd_A": 0.0,
      "energy_eV": -37.98258138241543,
      "reduced_polarization": [
        1.0462376597463465e-14,
        1.8002546523725903e-15,
        3.313774465853439e-16
      ],
      "cartesian_polarization_e_A2": [
        1.1377821890408544e-16,
        3.123595371040229e-17,
        6.298763963985448e-18
      ],
      "ranking_score": 0.7892897492548361
    },
    {
      "candidate_id": "bec_projection_00",
      "source": "MACEField_BEC_backprojection",
      "spacegroup": "Cc",
      "spacegroup_number": 9,
      "pointgroup": "m",
      "has_inversion": false,
      "is_polar_point_group": true,
      "nonpolar_parent_hypothesis": false,
      "symmetry_tolerance_A": null,
      "target_reduced_polarization": [
        0.0,
        0.0,
        0.0
      ],
      "formal_class": [
        0.0,
        0.0,
        0.0
      ],
      "target_residual": 3.8136913024295175e-05,
      "parent_symmetrization_rmsd_A": 0.004393122951157375,
      "parent_cell_rmsd_A": 0.008386550980589635,
      "energy_eV": -124.06624829745603,
      "reduced_polarization": [
        -2.5087218134565358e-05,
        -2.5064109137269994e-12,
        -2.8723781458773562e-05
      ],
      "cartesian_polarization_e_A2": [
        -1.3403007893688468e-07,
        -4.3418987192714584e-14,
        -5.454985316169695e-07
      ],
      "ranking_score": 0.5065660345223534
    },
    {
      "candidate_id": "inversion_parent_bec_00_00",
      "source": "same_species_inversion_center_projection_after_BEC",
      "spacegroup": "C2/c",
      "spacegroup_number": 15,
      "pointgroup": "2/m",
      "has_inversion": true,
      "is_polar_point_group": false,
      "nonpolar_parent_hypothesis": true,
      "symmetry_tolerance_A": null,
      "target_reduced_polarization": [
        0.0,
        0.0,
        0.0
      ],
      "formal_class": [
        0.0,
        0.0,
        0.0
      ],
      "target_residual": 3.5286309243346725e-15,
      "parent_symmetrization_rmsd_A": 0.5961448363537111,
      "parent_cell_rmsd_A": 0.008386550980589635,
      "energy_eV": -107.7822013028624,
      "reduced_polarization": [
        3.467824774606415e-15,
        -3.234599362790529e-16,
        5.663931518117818e-16
      ],
      "cartesian_polarization_e_A2": [
        3.5431810886173737e-17,
        -5.605629781991666e-18,
        1.0735309865512341e-17
      ],
      "ranking_score": 0.5982414740988656
    },
    {
      "candidate_id": "bec_projection_01",
      "source": "MACEField_BEC_backprojection",
      "spacegroup": "Cc",
      "spacegroup_number": 9,
      "pointgroup": "m",
      "has_inversion": false,
      "is_polar_point_group": true,
      "nonpolar_parent_hypothesis": false,
      "symmetry_tolerance_A": null,
      "target_reduced_polarization": [
        0.5,
        0.0,
        0.0
      ],
      "formal_class": [
        0.5,
        0.0,
        0.0
      ],
      "target_residual": 0.0005196459234523793,
      "parent_symmetrization_rmsd_A": 0.1364239876715514,
      "parent_cell_rmsd_A": 0.23966394594856064,
      "energy_eV": -117.55744673006893,
      "reduced_polarization": [
        0.5002833969525824,
        -1.0572227535356803e-12,
        -0.000435566358925582
      ],
      "cartesian_polarization_e_A2": [
        0.005578338213926882,
        4.6113142218270303e-14,
        0.0001008782308797673
      ],
      "ranking_score": 0.6973792660055963
    },
    {
      "candidate_id": "bec_projection_02",
      "source": "MACEField_BEC_backprojection",
      "spacegroup": "Cc",
      "spacegroup_number": 9,
      "pointgroup": "m",
      "has_inversion": false,
      "is_polar_point_group": true,
      "nonpolar_parent_hypothesis": false,
      "symmetry_tolerance_A": null,
      "target_reduced_polarization": [
        0.0,
        0.0,
        0.5
      ],
      "formal_class": [
        0.0,
        0.0,
        0.5
      ],
      "target_residual": 0.006303152468048155,
      "parent_symmetrization_rmsd_A": 0.2354531337316841,
      "parent_cell_rmsd_A": 0.40912203032294464,
      "energy_eV": -106.29416689121211,
      "reduced_polarization": [
        0.006263805730325711,
        4.3376287445390585e-10,
        0.5007031847610693
      ],
      "cartesian_polarization_e_A2": [
        -0.0023697124223133613,
        1.0126808664484139e-11,
        0.008551167065790836
      ],
      "ranking_score": 0.8503399462485166
    },
    {
      "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": 0.007357197925943173,
      "parent_symmetrization_rmsd_A": 0.22097312354599094,
      "parent_cell_rmsd_A": 0.6366378916511516,
      "energy_eV": -104.18739984841709,
      "reduced_polarization": [
        -0.0037661032546971456,
        0.493680228836908,
        7.293862222930343e-05
      ],
      "cartesian_polarization_e_A2": [
        8.945948687399319e-05,
        0.00854873437528271,
        0.0005750992691612604
      ],
      "ranking_score": 0.8948469923106652
    },
    {
      "candidate_id": "bec_projection_04",
      "source": "MACEField_BEC_backprojection",
      "spacegroup": "Cc",
      "spacegroup_number": 9,
      "pointgroup": "m",
      "has_inversion": false,
      "is_polar_point_group": true,
      "nonpolar_parent_hypothesis": false,
      "symmetry_tolerance_A": null,
      "target_reduced_polarization": [
        0.5,
        0.0,
        0.5
      ],
      "formal_class": [
        0.5,
        0.0,
        0.5
      ],
      "target_residual": 0.00010359067399225807,
      "parent_symmetrization_rmsd_A": 0.22257687405171867,
      "parent_cell_rmsd_A": 0.4909163435589235,
      "energy_eV": -105.92990420804632,
      "reduced_polarization": [
        0.49995932785593555,
        -9.979078276506625e-12,
        0.49990472773522493
      ],
      "cartesian_polarization_e_A2": [
        0.003143122392120847,
        -5.76410845978752e-12,
        0.008679103709279047
      ],
      "ranking_score": 0.8455131412894341
    },
    {
      "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": 0.1164474181623368,
      "parent_symmetrization_rmsd_A": 0.21086929313997538,
      "parent_cell_rmsd_A": 0.6911215949669297,
      "energy_eV": -105.07088646369388,
      "reduced_polarization": [
        0.44482052244053927,
        0.39817744214475487,
        -0.01214055866730824
      ],
      "cartesian_polarization_e_A2": [
        0.00514319128587539,
        0.0073068725129276976,
        0.000320988871223934
      ],
      "ranking_score": 1.1165445282063815
    },
    {
      "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": 0.24162121197209185,
      "parent_symmetrization_rmsd_A": 0.21735474124771495,
      "parent_cell_rmsd_A": 0.5206521597279067,
      "energy_eV": -107.8130167312943,
      "reduced_polarization": [
        0.0015168650230566376,
        0.3235725605357949,
        0.3349186025032844
      ],
      "cartesian_polarization_e_A2": [
        -0.0015568668269841748,
        0.0056520768859267745,
        0.00608700741946022
      ],
      "ranking_score": 1.3307602051238754
    },
    {
      "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": 0.3592051425109473,
      "parent_symmetrization_rmsd_A": 0.18294311974486857,
      "parent_cell_rmsd_A": 0.6845401761677059,
      "energy_eV": -110.52531538672633,
      "reduced_polarization": [
        0.2785828370918355,
        0.2798870968401465,
        0.3223681215587971
      ],
      "cartesian_polarization_e_A2": [
        0.0015559786689020626,
        0.0052354212766085265,
        0.005922330015640618
      ],
      "ranking_score": 1.5724884488086897
    }
  ],
  "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": [
              0.018309904492892416,
              2.892278689127378e-10,
              0.002697605212032375
            ],
            "branch_aligned_reduced_polarization": [
              0.018309904492892416,
              2.892278689127378e-10,
              0.002697605212032375
            ],
            "target_residual": 0.018507557278550465,
            "energy_eV": -124.07574297484037,
            "max_atomic_step_A": 0.004817840283942903,
            "max_log_strain_component": 0.0007924404651616314,
            "step_scale": 1.0,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 2.9402979367496895,
            "cell_principal_stretches": [
              1.0012710256874942,
              0.9999247056398697,
              0.9999200218957977
            ],
            "cell_volume_ratio": 1.0011155618974252,
            "cell_rmsd_from_input_A": 0.008386550980589635
          },
          {
            "iteration": 1,
            "reduced_polarization": [
              -2.5087218134565358e-05,
              -2.5064109137269994e-12,
              -2.8723781458773562e-05
            ],
            "branch_aligned_reduced_polarization": [
              -2.5087218134565358e-05,
              -2.5064109137269994e-12,
              -2.8723781458773562e-05
            ],
            "target_residual": 3.8136913024295175e-05,
            "energy_eV": -124.06624829745603
          }
        ],
        "iterations": 1
      },
      "parent": {
        "candidate_id": "bec_projection_00",
        "source": "MACEField_BEC_backprojection",
        "spacegroup": "Cc",
        "spacegroup_number": 9,
        "pointgroup": "m",
        "has_inversion": false,
        "is_polar_point_group": true,
        "nonpolar_parent_hypothesis": false,
        "symmetry_tolerance_A": null,
        "target_reduced_polarization": [
          0.0,
          0.0,
          0.0
        ],
        "formal_class": [
          0.0,
          0.0,
          0.0
        ],
        "target_residual": 3.8136913024295175e-05,
        "parent_symmetrization_rmsd_A": 0.004393122951157375,
        "parent_cell_rmsd_A": 0.008386550980589635,
        "energy_eV": -124.06624829745603,
        "reduced_polarization": [
          -2.5087218134565358e-05,
          -2.5064109137269994e-12,
          -2.8723781458773562e-05
        ],
        "cartesian_polarization_e_A2": [
          -1.3403007893688468e-07,
          -4.3418987192714584e-14,
          -5.454985316169695e-07
        ],
        "ranking_score": 0.5065660345223534
      },
      "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": [
          -124.07574297484035,
          -124.07506555092806,
          -124.07424179758439,
          -124.07327211503775,
          -124.07215689676035,
          -124.07089652943299,
          -124.06949139291387,
          -124.06794186021062,
          -124.06624829745603
        ],
        "cartesian_polarizations_e_A2": [
          [
            0.00018862629561175367,
            5.018366311306043e-12,
            5.127560331490123e-05
          ],
          [
            0.00016504398679551013,
            4.389127133727057e-12,
            4.4832964112995006e-05
          ],
          [
            0.00014145717526049193,
            3.758754762833991e-12,
            3.837994623976801e-05
          ],
          [
            0.00011786629247330613,
            3.127595912743069e-12,
            3.191673843917634e-05
          ],
          [
            9.427177082657495e-05,
            2.495288655109443e-12,
            2.5443530088394434e-05
          ],
          [
            7.067404353040883e-05,
            1.862069570776201e-12,
            1.8960511208638427e-05
          ],
          [
            4.70735445078861e-05,
            1.2278479873558695e-12,
            1.2467872475316336e-05
          ],
          [
            2.3470708291371613e-05,
            5.926584753348959e-13,
            5.9658052260084015e-06
          ],
          [
            -1.3403007896240085e-07,
            -4.344082799554442e-14,
            -5.454985315978322e-07
          ]
        ],
        "raw_reduced_polarization": [
          [
            0.018309904492894203,
            2.892287965015756e-10,
            0.0026976052120333462
          ],
          [
            0.016021358477904632,
            2.530244979784308e-10,
            0.0023595707357457803
          ],
          [
            0.013731775110767439,
            2.1673730495537206e-10,
            0.002020729174457593
          ],
          [
            0.011441197511234314,
            1.8038716632082543e-10,
            0.0016810902080457329
          ],
          [
            0.009149668914608309,
            1.4395317690490568e-10,
            0.001340663560548448
          ],
          [
            0.00685723266222188,
            1.0744893959515908e-10,
            0.0009994590007710732
          ],
          [
            0.004563932192259354,
            7.086918792260817e-11,
            0.0006574863428540441
          ],
          [
            0.0022698110306011293,
            3.42158783813565e-11,
            0.0003147554467243419
          ],
          [
            -2.508721813642575e-05,
            -2.5076711868751057e-12,
            -2.8723781457766897e-05
          ]
        ],
        "unwrapped_reduced_polarization": [
          [
            0.018309904492894203,
            2.892287965015756e-10,
            0.0026976052120333462
          ],
          [
            0.016021358477904632,
            2.530244979784308e-10,
            0.0023595707357457803
          ],
          [
            0.013731775110767439,
            2.1673730495537206e-10,
            0.002020729174457593
          ],
          [
            0.011441197511234314,
            1.8038716632082543e-10,
            0.0016810902080457329
          ],
          [
            0.009149668914608309,
            1.4395317690490568e-10,
            0.001340663560548448
          ],
          [
            0.00685723266222188,
            1.0744893959515908e-10,
            0.0009994590007710732
          ],
          [
            0.004563932192259354,
            7.086918792260817e-11,
            0.0006574863428540441
          ],
          [
            0.0022698110306011293,
            3.42158783813565e-11,
            0.0003147554467243419
          ],
          [
            -2.5087218136425615e-05,
            -2.5076711868751053e-12,
            -2.8723781457766907e-05
          ]
        ],
        "berry_integer_shifts": [
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ]
        ],
        "folded_reduced_polarization": [
          [
            0.018309904492894158,
            2.892287520595005e-10,
            0.002697605212033327
          ],
          [
            0.016021358477904646,
            2.530244902487766e-10,
            0.002359570735745775
          ],
          [
            0.013731775110767397,
            2.167372947781132e-10,
            0.002020729174457614
          ],
          [
            0.011441197511234291,
            1.8038714966195357e-10,
            0.0016810902080457435
          ],
          [
            0.009149668914608333,
            1.4395318270743473e-10,
            0.0013406635605484052
          ],
          [
            0.006857232662221935,
            1.0744893863545713e-10,
            0.0009994590007710302
          ],
          [
            0.004563932192259368,
            7.0869199397805e-11,
            0.0006574863428540079
          ],
          [
            0.0022698110306010877,
            3.421585237362024e-11,
            0.0003147554467243241
          ],
          [
            -2.5087218136432554e-05,
            -2.507660745720841e-12,
            -2.8723781457740127e-05
          ]
        ]
      },
      "reflected": {
        "reached": true,
        "construction": "reflect_displacements_about_reconstructed_parent",
        "energies_eV": [
          -124.06624829745608,
          -124.06252794173245,
          -124.05874347425275,
          -124.05489489762073,
          -124.05098221182888,
          -124.04700541420848,
          -124.04296449941585,
          -124.03885945971255,
          -124.03469028512463
        ],
        "cartesian_polarizations_e_A2": [
          [
            -1.340300789355097e-07,
            -4.339529547439069e-14,
            -5.454985316087395e-07
          ],
          [
            -1.848876913526024e-05,
            -4.750288835449506e-13,
            -8.651942355726381e-06
          ],
          [
            -3.683246667386771e-05,
            -9.066861458345359e-13,
            -1.6758613302238013e-05
          ],
          [
            -5.5164910643134605e-05,
            -1.3384828770410902e-12,
            -2.4865372293841473e-05
          ],
          [
            -7.348589065625412e-05,
            -1.7703152425215152e-12,
            -3.297208127409065e-05
          ],
          [
            -9.179519804175072e-05,
            -2.2022689097589204e-12,
            -4.107860321540347e-05
          ],
          [
            -0.00011009262586289137,
            -2.634297381003379e-12,
            -4.918480212399839e-05
          ],
          [
            -0.00012837796898665369,
            -3.0664336937520972e-12,
            -5.7290542861393765e-05
          ],
          [
            -0.00014665102412740177,
            -3.4986506555858826e-12,
            -6.539569103834419e-05
          ]
        ],
        "raw_reduced_polarization": [
          [
            -2.5087218134245552e-05,
            -2.5050438377697007e-12,
            -2.8723781458340226e-05
          ],
          [
            -0.0018816786990115367,
            -2.7430338719267267e-11,
            -0.0004560134924213747
          ],
          [
            -0.0037369168536792036,
            -5.23429838430043e-11,
            -0.0008830823445702429
          ],
          [
            -0.005590779425286516,
            -7.724966463110079e-11,
            -0.0013099231998390224
          ],
          [
            -0.007443244341982807,
            -1.0214439706388875e-10,
            -0.0017365289801000111
          ],
          [
            -0.009294289721588371,
            -1.2703212752483991e-10,
            -0.0021628926675241146
          ],
          [
            -0.011143893873370855,
            -1.519101801582342e-10,
            -0.002589007304777861
          ],
          [
            -0.012992035299976647,
            -1.7678046550832287e-10,
            -0.003014865985568544
          ],
          [
            -0.014838692698789197,
            -2.0164142187364575e-10,
            -0.0034404618490035893
          ]
        ],
        "unwrapped_reduced_polarization": [
          [
            -2.5087218134245552e-05,
            -2.5050438377697007e-12,
            -2.8723781458340226e-05
          ],
          [
            -0.0018816786990115367,
            -2.7430338719267267e-11,
            -0.0004560134924213747
          ],
          [
            -0.0037369168536792036,
            -5.23429838430043e-11,
            -0.0008830823445702429
          ],
          [
            -0.005590779425286516,
            -7.724966463110079e-11,
            -0.0013099231998390224
          ],
          [
            -0.007443244341982807,
            -1.0214439706388875e-10,
            -0.0017365289801000111
          ],
          [
            -0.009294289721588371,
            -1.2703212752483991e-10,
            -0.0021628926675241146
          ],
          [
            -0.011143893873370855,
            -1.519101801582342e-10,
            -0.002589007304777861
          ],
          [
            -0.012992035299976647,
            -1.7678046550832287e-10,
            -0.003014865985568544
          ],
          [
            -0.014838692698789197,
            -2.0164142187364575e-10,
            -0.0034404618490035893
          ]
        ],
        "gauge_integer_shift": [
          0,
          0,
          0
        ],
        "expected_opposite_endpoint_reduced_polarization": [
          -0.018359984612296296,
          -2.9423613858095975e-10,
          -0.002755002476496823
        ],
        "actual_opposite_endpoint_branch_residual": 0.0035873878089060663
      },
      "pnp_branch": {
        "construction": "incoming_path_concatenated_with_parent_reflection",
        "reduced_polarization": [
          [
            0.018309904492894203,
            2.892287965015756e-10,
            0.0026976052120333462
          ],
          [
            0.016021358477904632,
            2.530244979784308e-10,
            0.0023595707357457803
          ],
          [
            0.013731775110767439,
            2.1673730495537206e-10,
            0.002020729174457593
          ],
          [
            0.011441197511234314,
            1.8038716632082543e-10,
            0.0016810902080457329
          ],
          [
            0.009149668914608309,
            1.4395317690490568e-10,
            0.001340663560548448
          ],
          [
            0.00685723266222188,
            1.0744893959515908e-10,
            0.0009994590007710732
          ],
          [
            0.004563932192259354,
            7.086918792260817e-11,
            0.0006574863428540441
          ],
          [
            0.0022698110306011293,
            3.42158783813565e-11,
            0.0003147554467243419
          ],
          [
            -2.508721813642575e-05,
            -2.5076711868751057e-12,
            -2.8723781457766897e-05
          ],
          [
            -0.0018816786990115367,
            -2.7430338719267267e-11,
            -0.0004560134924213747
          ],
          [
            -0.0037369168536792036,
            -5.23429838430043e-11,
            -0.0008830823445702429
          ],
          [
            -0.005590779425286516,
            -7.724966463110079e-11,
            -0.0013099231998390224
          ],
          [
            -0.007443244341982807,
            -1.0214439706388875e-10,
            -0.0017365289801000111
          ],
          [
            -0.009294289721588371,
            -1.2703212752483991e-10,
            -0.0021628926675241146
          ],
          [
            -0.011143893873370855,
            -1.519101801582342e-10,
            -0.002589007304777861
          ],
          [
            -0.012992035299976647,
            -1.7678046550832287e-10,
            -0.003014865985568544
          ],
          [
            -0.014838692698789197,
            -2.0164142187364575e-10,
            -0.0034404618490035893
          ]
        ],
        "unwrapped_reduced_polarization": [
          [
            0.018309904492894203,
            2.892287965015756e-10,
            0.0026976052120333462
          ],
          [
            0.016021358477904632,
            2.530244979784308e-10,
            0.0023595707357457803
          ],
          [
            0.013731775110767439,
            2.1673730495537206e-10,
            0.002020729174457593
          ],
          [
            0.011441197511234314,
            1.8038716632082543e-10,
            0.0016810902080457329
          ],
          [
            0.009149668914608309,
            1.4395317690490568e-10,
            0.001340663560548448
          ],
          [
            0.00685723266222188,
            1.0744893959515908e-10,
            0.0009994590007710732
          ],
          [
            0.004563932192259354,
            7.086918792260817e-11,
            0.0006574863428540441
          ],
          [
            0.0022698110306011293,
            3.42158783813565e-11,
            0.0003147554467243419
          ],
          [
            -2.5087218136425615e-05,
            -2.5076711868751053e-12,
            -2.8723781457766907e-05
          ],
          [
            -0.0018816786990115367,
            -2.7430338719267267e-11,
            -0.0004560134924213747
          ],
          [
            -0.0037369168536792036,
            -5.23429838430043e-11,
            -0.0008830823445702429
          ],
          [
            -0.005590779425286516,
            -7.724966463110079e-11,
            -0.0013099231998390224
          ],
          [
            -0.007443244341982807,
            -1.0214439706388875e-10,
            -0.0017365289801000111
          ],
          [
            -0.009294289721588371,
            -1.2703212752483991e-10,
            -0.0021628926675241146
          ],
          [
            -0.011143893873370855,
            -1.519101801582342e-10,
            -0.002589007304777861
          ],
          [
            -0.012992035299976647,
            -1.7678046550832287e-10,
            -0.003014865985568544
          ],
          [
            -0.014838692698789197,
            -2.0164142187364575e-10,
            -0.0034404618490035893
          ]
        ],
        "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": [
          [
            0.018309904492894158,
            2.892287520595005e-10,
            0.002697605212033327
          ],
          [
            0.016021358477904646,
            2.530244902487766e-10,
            0.002359570735745775
          ],
          [
            0.013731775110767397,
            2.167372947781132e-10,
            0.002020729174457614
          ],
          [
            0.011441197511234291,
            1.8038714966195357e-10,
            0.0016810902080457435
          ],
          [
            0.009149668914608333,
            1.4395318270743473e-10,
            0.0013406635605484052
          ],
          [
            0.006857232662221935,
            1.0744893863545713e-10,
            0.0009994590007710302
          ],
          [
            0.004563932192259368,
            7.0869199397805e-11,
            0.0006574863428540079
          ],
          [
            0.0022698110306010877,
            3.421585237362024e-11,
            0.0003147554467243241
          ],
          [
            -2.5087218136432554e-05,
            -2.507660745720841e-12,
            -2.8723781457740127e-05
          ],
          [
            -0.001881678699011513,
            -2.7430335780564974e-11,
            -0.0004560134924213588
          ],
          [
            -0.0037369168536792174,
            -5.234296329703625e-11,
            -0.0008830823445702407
          ],
          [
            -0.005590779425286518,
            -7.724965112032578e-11,
            -0.0013099231998390248
          ],
          [
            -0.007443244341982791,
            -1.0214440404610059e-10,
            -0.001736528980100016
          ],
          [
            -0.009294289721588356,
            -1.2703210705566903e-10,
            -0.002162892667524119
          ],
          [
            -0.011143893873370836,
            -1.5191020663607446e-10,
            -0.002589007304777846
          ],
          [
            -0.012992035299976668,
            -1.767804791441563e-10,
            -0.003014865985568549
          ],
          [
            -0.01483869269878918,
            -2.0164142577883126e-10,
            -0.0034404618490035954
          ]
        ]
      },
      "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": [
              0.018309904492892416,
              2.892278689127378e-10,
              0.002697605212032375
            ],
            "branch_aligned_reduced_polarization": [
              0.018309904492892437,
              2.892278689127378e-10,
              0.002697605212032375
            ],
            "target_residual": 0.48169764913639174,
            "energy_eV": -124.07574297484037,
            "max_atomic_step_A": 0.09106830769509873,
            "max_log_strain_component": 0.02,
            "step_scale": 0.6343644752120549,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 2.9402979367496895,
            "cell_principal_stretches": [
              1.0021717056286572,
              0.9978405395031414,
              0.9735517055001262
            ],
            "cell_volume_ratio": 0.9735590610914545,
            "cell_rmsd_from_input_A": 0.15133125404206188
          },
          {
            "iteration": 1,
            "reduced_polarization": [
              0.2970880198044554,
              -2.5203400538581826e-11,
              -0.015307182702736935
            ],
            "branch_aligned_reduced_polarization": [
              0.2970880198044554,
              -2.5203400538581826e-11,
              -0.015307182702736935
            ],
            "target_residual": 0.2034885292815594,
            "energy_eV": -121.23089864853688,
            "max_atomic_step_A": 0.047146581403092996,
            "max_log_strain_component": 0.007424751700727428,
            "step_scale": 1.0,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 2.9402979367496895,
            "cell_principal_stretches": [
              1.0026985291560382,
              0.9996046695037806,
              0.9608919422747269
            ],
            "cell_volume_ratio": 0.9631040422184362,
            "cell_rmsd_from_input_A": 0.23738988718500692
          },
          {
            "iteration": 2,
            "reduced_polarization": [
              0.4925436703769811,
              3.7298464811512644e-11,
              -0.012470232464875757
            ],
            "branch_aligned_reduced_polarization": [
              0.4925436703769811,
              3.7298464811512644e-11,
              -0.012470232464875757
            ],
            "target_residual": 0.014529402918742065,
            "energy_eV": -117.3129002802178,
            "max_atomic_step_A": 0.004033768289409539,
            "max_log_strain_component": 0.000641493962385188,
            "step_scale": 1.0,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 2.9402979367496895,
            "cell_principal_stretches": [
              1.0026190553688816,
              1.0001975457216938,
              0.9610579700604769
            ],
            "cell_volume_ratio": 0.9637653842222875,
            "cell_rmsd_from_input_A": 0.23966394594856064
          },
          {
            "iteration": 3,
            "reduced_polarization": [
              0.5002833969525824,
              -1.0572227535356803e-12,
              -0.000435566358925582
            ],
            "branch_aligned_reduced_polarization": [
              0.5002833969525824,
              -1.0572227535356803e-12,
              -0.000435566358925582
            ],
            "target_residual": 0.0005196459234523793,
            "energy_eV": -117.55744673006893
          }
        ],
        "iterations": 3
      },
      "parent": {
        "candidate_id": "bec_projection_01",
        "source": "MACEField_BEC_backprojection",
        "spacegroup": "Cc",
        "spacegroup_number": 9,
        "pointgroup": "m",
        "has_inversion": false,
        "is_polar_point_group": true,
        "nonpolar_parent_hypothesis": false,
        "symmetry_tolerance_A": null,
        "target_reduced_polarization": [
          0.5,
          0.0,
          0.0
        ],
        "formal_class": [
          0.5,
          0.0,
          0.0
        ],
        "target_residual": 0.0005196459234523793,
        "parent_symmetrization_rmsd_A": 0.1364239876715514,
        "parent_cell_rmsd_A": 0.23966394594856064,
        "energy_eV": -117.55744673006893,
        "reduced_polarization": [
          0.5002833969525824,
          -1.0572227535356803e-12,
          -0.000435566358925582
        ],
        "cartesian_polarization_e_A2": [
          0.005578338213926882,
          4.6113142218270303e-14,
          0.0001008782308797673
        ],
        "ranking_score": 0.6973792660055963
      },
      "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": false,
        "history": [
          {
            "iteration": 0,
            "reduced_polarization": [
              0.018309904492892416,
              2.892278689127378e-10,
              0.002697605212032375
            ],
            "branch_aligned_reduced_polarization": [
              0.018309904492892416,
              2.892278689127378e-10,
              0.0026976052120323835
            ],
            "target_residual": 0.49763935180448343,
            "energy_eV": -124.07574297484037,
            "max_atomic_step_A": 0.060384069299754636,
            "max_log_strain_component": 0.019999999999999997,
            "step_scale": 0.2729062871470403,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 2.9402979367496895,
            "cell_principal_stretches": [
              1.0210075793428979,
              1.0100109512887914,
              0.9934891191790451
            ],
            "cell_volume_ratio": 1.0245146284316993,
            "cell_rmsd_from_input_A": 0.10549406294032222
          },
          {
            "iteration": 1,
            "reduced_polarization": [
              -0.005687742459011278,
              2.311785058846126e-10,
              0.12379521843670586
            ],
            "branch_aligned_reduced_polarization": [
              -0.005687742459011278,
              2.311785058846126e-10,
              0.12379521843670588
            ],
            "target_residual": 0.37624777485769384,
            "energy_eV": -122.5246248704653,
            "max_atomic_step_A": 0.05640537934743694,
            "max_log_strain_component": 0.02,
            "step_scale": 0.32587435465474673,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 2.9402979367496895,
            "cell_principal_stretches": [
              1.0420765501900584,
              1.0212037289168339,
              0.9859892962320769
            ],
            "cell_volume_ratio": 1.049262653791656,
            "cell_rmsd_from_input_A": 0.21685906045425601
          },
          {
            "iteration": 2,
            "reduced_polarization": [
              -0.0284186067508362,
              3.293078871404087e-11,
              0.23255261157587795
            ],
            "branch_aligned_reduced_polarization": [
              -0.0284186067508362,
              3.293078871404087e-11,
              0.23255261157587792
            ],
            "target_residual": 0.26895301222433243,
            "energy_eV": -119.10472735902704,
            "max_atomic_step_A": 0.06559502252428012,
            "max_log_strain_component": 0.02,
            "step_scale": 0.4977176339709605,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 2.9402979367496895,
            "cell_principal_stretches": [
              1.0635867207602652,
              1.0325605005475884,
              0.9784897895428271
            ],
            "cell_volume_ratio": 1.0745947442694153,
            "cell_rmsd_from_input_A": 0.33169218787023164
          },
          {
            "iteration": 3,
            "reduced_polarization": [
              -0.017847847788592008,
              -2.5940763570882135e-10,
              0.3420759601233633
            ],
            "branch_aligned_reduced_polarization": [
              -0.017847847788592008,
              -2.5940763570882135e-10,
              0.3420759601233633
            ],
            "target_residual": 0.15892938067469556,
            "energy_eV": -114.08562483691516,
            "max_atomic_step_A": 0.05581449312282236,
            "max_log_strain_component": 0.02,
            "step_scale": 0.7339873927826686,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 2.9402979367496895,
            "cell_principal_stretches": [
              1.0861142436527584,
              1.0422940610229916,
              0.9727028117008546
            ],
            "cell_volume_ratio": 1.101148632115876,
            "cell_rmsd_from_input_A": 0.444346600640475
          },
          {
            "iteration": 4,
            "reduced_polarization": [
              0.02028083454065391,
              2.0242993709160777e-10,
              0.41574594509876894
            ],
            "branch_aligned_reduced_polarization": [
              0.02028083454065391,
              2.0242993709160777e-10,
              0.41574594509876894
            ],
            "target_residual": 0.08666059091054618,
            "energy_eV": -108.5031207984247,
            "max_atomic_step_A": 0.04005494475342735,
            "max_log_strain_component": 0.02,
            "step_scale": 0.9725587556826014,
            "strain_jacobian_refreshed": true,
            "strain_jacobian_frobenius_norm": 2.405220368245084,
            "cell_principal_stretches": [
              1.066289190059026,
              1.0427354708258518,
              0.9675652619841781
            ],
            "cell_volume_ratio": 1.0757947519426818,
            "cell_rmsd_from_input_A": 0.40912203032294464
          },
          {
            "iteration": 5,
            "reduced_polarization": [
              0.006263805730325711,
              4.3376287445390585e-10,
              0.5007031847610693
            ],
            "branch_aligned_reduced_polarization": [
              0.006263805730325711,
              4.3376287445390585e-10,
              0.5007031847610693
            ],
            "target_residual": 0.006303152468048155,
            "energy_eV": -106.29416689121211
          }
        ],
        "iterations": 5
      },
      "parent": {
        "candidate_id": "bec_projection_02",
        "source": "MACEField_BEC_backprojection",
        "spacegroup": "Cc",
        "spacegroup_number": 9,
        "pointgroup": "m",
        "has_inversion": false,
        "is_polar_point_group": true,
        "nonpolar_parent_hypothesis": false,
        "symmetry_tolerance_A": null,
        "target_reduced_polarization": [
          0.0,
          0.0,
          0.5
        ],
        "formal_class": [
          0.0,
          0.0,
          0.5
        ],
        "target_residual": 0.006303152468048155,
        "parent_symmetrization_rmsd_A": 0.2354531337316841,
        "parent_cell_rmsd_A": 0.40912203032294464,
        "energy_eV": -106.29416689121211,
        "reduced_polarization": [
          0.006263805730325711,
          4.3376287445390585e-10,
          0.5007031847610693
        ],
        "cartesian_polarization_e_A2": [
          -0.0023697124223133613,
          1.0126808664484139e-11,
          0.008551167065790836
        ],
        "ranking_score": 0.8503399462485166
      },
      "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": [
              0.018309904492892416,
              2.892278689127378e-10,
              0.002697605212032375
            ],
            "branch_aligned_reduced_polarization": [
              0.018309904492892416,
              2.892278638810808e-10,
              0.002697605212032375
            ],
            "target_residual": 0.5003424121411166,
            "energy_eV": -124.07574297484037,
            "max_atomic_step_A": 0.08254276665084553,
            "max_log_strain_component": 0.02,
            "step_scale": 0.3910559905905191,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 2.9402979367496895,
            "cell_principal_stretches": [
              1.0216286524577762,
              1.000458625219963,
              0.9788072034761253
            ],
            "cell_volume_ratio": 1.0004360991969747,
            "cell_rmsd_from_input_A": 0.1843080651543567
          },
          {
            "iteration": 1,
            "reduced_polarization": [
              0.0482345139463794,
              0.18572206118057186,
              -0.004444785933780637
            ],
            "branch_aligned_reduced_polarization": [
              0.0482345139463794,
              0.18572206118057188,
              -0.004444785933780637
            ],
            "target_residual": 0.3179889106340484,
            "energy_eV": -120.76152304819327,
            "max_atomic_step_A": 0.07963435426249933,
            "max_log_strain_component": 0.02,
            "step_scale": 0.5295021576884091,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 2.9402979367496895,
            "cell_principal_stretches": [
              1.0437152979903246,
              1.00603120935561,
              0.9580094164586709
            ],
            "cell_volume_ratio": 1.0059196239721389,
            "cell_rmsd_from_input_A": 0.3719864746401136
          },
          {
            "iteration": 2,
            "reduced_polarization": [
              0.04199968489570018,
              0.3227762326862196,
              0.0045151714206445644
            ],
            "branch_aligned_reduced_polarization": [
              0.04199968489570018,
              0.3227762326862196,
              0.0045151714206445644
            ],
            "target_residual": 0.18218842994324558,
            "energy_eV": -113.40977709063918,
            "max_atomic_step_A": 0.051829485876043614,
            "max_log_strain_component": 0.02,
            "step_scale": 0.6005621038011961,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 2.9402979367496895,
            "cell_principal_stretches": [
              1.066348010351364,
              1.0086858678049238,
              0.9377566450587217
            ],
            "cell_volume_ratio": 1.008660582725392,
            "cell_rmsd_from_input_A": 0.5594225275584898
          },
          {
            "iteration": 3,
            "reduced_polarization": [
              0.031124464543900648,
              0.38968377807030774,
              0.01303232500780918
            ],
            "branch_aligned_reduced_polarization": [
              0.031124464543900648,
              0.38968377807030774,
              0.01303232500780918
            ],
            "target_residual": 0.11536135665418822,
            "energy_eV": -105.79235938857843,
            "max_atomic_step_A": 0.04429904578688903,
            "max_log_strain_component": 0.02,
            "step_scale": 0.745648877375518,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 2.9402979367496895,
            "cell_principal_stretches": [
              1.0897005467591825,
              1.0099879993203515,
              0.9181499764440331
            ],
            "cell_volume_ratio": 1.0105016098690034,
            "cell_rmsd_from_input_A": 0.747233879788118
          },
          {
            "iteration": 4,
            "reduced_polarization": [
              0.028382698092222526,
              0.42324418853236867,
              0.009909022327374006
            ],
            "branch_aligned_reduced_polarization": [
              0.028382698092222526,
              0.42324418853236867,
              0.009909022327374006
            ],
            "target_residual": 0.08243312967814102,
            "energy_eV": -101.04523733489975,
            "max_atomic_step_A": 0.05331637972877752,
            "max_log_strain_component": 0.014666784381206647,
            "step_scale": 1.0,
            "strain_jacobian_refreshed": true,
            "strain_jacobian_frobenius_norm": 2.3901865768527797,
            "cell_principal_stretches": [
              1.065636640001019,
              1.0099077196228154,
              0.9274028511911272
            ],
            "cell_volume_ratio": 0.9980660045136136,
            "cell_rmsd_from_input_A": 0.6366378916511516
          },
          {
            "iteration": 5,
            "reduced_polarization": [
              -0.0037661032546971456,
              0.493680228836908,
              7.293862222930343e-05
            ],
            "branch_aligned_reduced_polarization": [
              -0.0037661032546971456,
              0.493680228836908,
              7.293862222930343e-05
            ],
            "target_residual": 0.007357197925943173,
            "energy_eV": -104.18739984841709
          }
        ],
        "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": 0.007357197925943173,
        "parent_symmetrization_rmsd_A": 0.22097312354599094,
        "parent_cell_rmsd_A": 0.6366378916511516,
        "energy_eV": -104.18739984841709,
        "reduced_polarization": [
          -0.0037661032546971456,
          0.493680228836908,
          7.293862222930343e-05
        ],
        "cartesian_polarization_e_A2": [
          8.945948687399319e-05,
          0.00854873437528271,
          0.0005750992691612604
        ],
        "ranking_score": 0.8948469923106652
      },
      "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": [
              0.018309904492892416,
              2.892278689127378e-10,
              0.002697605212032375
            ],
            "branch_aligned_reduced_polarization": [
              0.018309904492892437,
              2.892278689127378e-10,
              0.0026976052120323835
            ],
            "target_residual": 0.6923402487010949,
            "energy_eV": -124.07574297484037,
            "max_atomic_step_A": 0.08556784056528809,
            "max_log_strain_component": 0.02,
            "step_scale": 0.48821959332730697,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 2.9402979367496895,
            "cell_principal_stretches": [
              1.0202757829920024,
              1.0163250043019394,
              0.9859920740397122
            ],
            "cell_volume_ratio": 1.0224065258047867,
            "cell_rmsd_from_input_A": 0.15781624176719872
          },
          {
            "iteration": 1,
            "reduced_polarization": [
              0.2028018935561402,
              8.736895006335864e-11,
              0.2111793002964798
            ],
            "branch_aligned_reduced_polarization": [
              0.2028018935561402,
              8.736895006335864e-11,
              0.2111793002964798
            ],
            "target_residual": 0.41442021071739105,
            "energy_eV": -121.76663787249805,
            "max_atomic_step_A": 0.08180369568718404,
            "max_log_strain_component": 0.02,
            "step_scale": 0.7709696728661729,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 2.9402979367496895,
            "cell_principal_stretches": [
              1.041133054836972,
              1.034500902167479,
              0.970041038556588
            ],
            "cell_volume_ratio": 1.04478569267403,
            "cell_rmsd_from_input_A": 0.33601976103372505
          },
          {
            "iteration": 2,
            "reduced_polarization": [
              0.3491563810188807,
              9.272811395886713e-10,
              0.3999596827341185
            ],
            "branch_aligned_reduced_polarization": [
              0.3491563810188807,
              9.272811395886713e-10,
              0.3999596827341185
            ],
            "target_residual": 0.18100238248702508,
            "energy_eV": -115.17520019269958,
            "max_atomic_step_A": 0.06665561333111594,
            "max_log_strain_component": 0.011007731449624327,
            "step_scale": 1.0,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 2.9402979367496895,
            "cell_principal_stretches": [
              1.0478126882681358,
              1.0447060211345838,
              0.9585314348919741
            ],
            "cell_volume_ratio": 1.0492624015402203,
            "cell_rmsd_from_input_A": 0.4511646510356351
          },
          {
            "iteration": 3,
            "reduced_polarization": [
              0.4534173591686583,
              1.4944291435948542e-10,
              0.4651617591200523
            ],
            "branch_aligned_reduced_polarization": [
              0.4534173591686583,
              1.4944291435948542e-10,
              0.4651617591200523
            ],
            "target_residual": 0.0581691108272341,
            "energy_eV": -109.29253100410597,
            "max_atomic_step_A": 0.023358734395233026,
            "max_log_strain_component": 0.004608086041825765,
            "step_scale": 1.0,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 2.9402979367496895,
            "cell_principal_stretches": [
              1.0511839252008317,
              1.0491551559028571,
              0.9537177111209534
            ],
            "cell_volume_ratio": 1.0518123796084702,
            "cell_rmsd_from_input_A": 0.5004934698509067
          },
          {
            "iteration": 4,
            "reduced_polarization": [
              0.4823178122393146,
              5.429326545613325e-11,
              0.4863215086072549
            ],
            "branch_aligned_reduced_polarization": [
              0.4823178122393146,
              5.429326545613325e-11,
              0.4863215086072549
            ],
            "target_residual": 0.0223553324910531,
            "energy_eV": -106.66237324950289,
            "max_atomic_step_A": 0.01151150641477108,
            "max_log_strain_component": 0.001468414502989515,
            "step_scale": 1.0,
            "strain_jacobian_refreshed": true,
            "strain_jacobian_frobenius_norm": 2.3707961475209447,
            "cell_principal_stretches": [
              1.0506909172516075,
              1.048530919616445,
              0.9550201877745487
            ],
            "cell_volume_ratio": 1.0521284680881406,
            "cell_rmsd_from_input_A": 0.4909163435589235
          },
          {
            "iteration": 5,
            "reduced_polarization": [
              0.49995932785593555,
              -9.979078276506625e-12,
              0.49990472773522493
            ],
            "branch_aligned_reduced_polarization": [
              0.49995932785593555,
              -9.979078276506625e-12,
              0.49990472773522493
            ],
            "target_residual": 0.00010359067399225807,
            "energy_eV": -105.92990420804632
          }
        ],
        "iterations": 5
      },
      "parent": {
        "candidate_id": "bec_projection_04",
        "source": "MACEField_BEC_backprojection",
        "spacegroup": "Cc",
        "spacegroup_number": 9,
        "pointgroup": "m",
        "has_inversion": false,
        "is_polar_point_group": true,
        "nonpolar_parent_hypothesis": false,
        "symmetry_tolerance_A": null,
        "target_reduced_polarization": [
          0.5,
          0.0,
          0.5
        ],
        "formal_class": [
          0.5,
          0.0,
          0.5
        ],
        "target_residual": 0.00010359067399225807,
        "parent_symmetrization_rmsd_A": 0.22257687405171867,
        "parent_cell_rmsd_A": 0.4909163435589235,
        "energy_eV": -105.92990420804632,
        "reduced_polarization": [
          0.49995932785593555,
          -9.979078276506625e-12,
          0.49990472773522493
        ],
        "cartesian_polarization_e_A2": [
          0.003143122392120847,
          -5.76410845978752e-12,
          0.008679103709279047
        ],
        "ranking_score": 0.8455131412894341
      },
      "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": [
              0.018309904492892416,
              2.892278689127378e-10,
              0.002697605212032375
            ],
            "branch_aligned_reduced_polarization": [
              0.018309904492892437,
              2.892278638810808e-10,
              0.002697605212032375
            ],
            "target_residual": 0.6942856940008907,
            "energy_eV": -124.07574297484037,
            "max_atomic_step_A": 0.11162365972500485,
            "max_log_strain_component": 0.02,
            "step_scale": 0.3910559905313206,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 2.9402979367496895,
            "cell_principal_stretches": [
              1.0215825218984216,
              0.984364714935865,
              0.9781296258757813
            ],
            "cell_volume_ratio": 0.9836167256665153,
            "cell_rmsd_from_input_A": 0.20613489837166155
          },
          {
            "iteration": 1,
            "reduced_polarization": [
              0.21388051542970343,
              0.16706768508306227,
              -0.0159717301710893
            ],
            "branch_aligned_reduced_polarization": [
              0.21388051542970343,
              0.16706768508306225,
              -0.0159717301710893
            ],
            "target_residual": 0.4392759746803611,
            "energy_eV": -118.99301874406737,
            "max_atomic_step_A": 0.08662461421038838,
            "max_log_strain_component": 0.019999999999999997,
            "step_scale": 0.5184619844236674,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 2.9402979367496895,
            "cell_principal_stretches": [
              1.044094396652542,
              0.9748083283933764,
              0.9573246952624495
            ],
            "cell_volume_ratio": 0.9743573334183365,
            "cell_rmsd_from_input_A": 0.4005740515699176
          },
          {
            "iteration": 2,
            "reduced_polarization": [
              0.3276940315443881,
              0.2872082307546933,
              -0.018649104565802987
            ],
            "branch_aligned_reduced_polarization": [
              0.3276940315443881,
              0.2872082307546933,
              -0.018649104565802987
            ],
            "target_residual": 0.2744402902729124,
            "energy_eV": -107.25788025925924,
            "max_atomic_step_A": 0.052074215921835136,
            "max_log_strain_component": 0.02,
            "step_scale": 0.42205868726848106,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 2.9402979367496895,
            "cell_principal_stretches": [
              1.0677302806070457,
              0.9676725706813267,
              0.9369736227445356
            ],
            "cell_volume_ratio": 0.9680936138559613,
            "cell_rmsd_from_input_A": 0.5964752913249394
          },
          {
            "iteration": 3,
            "reduced_polarization": [
              0.38851379041730827,
              0.3238194620512397,
              -0.014856407358954524
            ],
            "branch_aligned_reduced_polarization": [
              0.38851379041730827,
              0.3238194620512397,
              -0.014856407358954524
            ],
            "target_residual": 0.2090202615026726,
            "energy_eV": -103.63603123891193,
            "max_atomic_step_A": 0.05552039570871586,
            "max_log_strain_component": 0.02,
            "step_scale": 0.46402253174433317,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 2.9402979367496895,
            "cell_principal_stretches": [
              1.0925231194225784,
              0.9628212313755455,
              0.9170450481672768
            ],
            "cell_volume_ratio": 0.9646437717392118,
            "cell_rmsd_from_input_A": 0.7943768504377282
          },
          {
            "iteration": 4,
            "reduced_polarization": [
              0.41762437394567453,
              0.34356322601338335,
              -0.017393425790238733
            ],
            "branch_aligned_reduced_polarization": [
              0.41762437394567453,
              0.34356322601338335,
              -0.017393425790238733
            ],
            "target_residual": 0.17765342463319525,
            "energy_eV": -102.07524899834618,
            "max_atomic_step_A": 0.030822706459950902,
            "max_log_strain_component": 0.02,
            "step_scale": 0.43042765007229256,
            "strain_jacobian_refreshed": true,
            "strain_jacobian_frobenius_norm": 2.0531834323831006,
            "cell_principal_stretches": [
              1.064464106587552,
              0.9711050899477536,
              0.9225118319529584
            ],
            "cell_volume_ratio": 0.9536064880627082,
            "cell_rmsd_from_input_A": 0.6911215949669297
          },
          {
            "iteration": 5,
            "reduced_polarization": [
              0.44482052244053927,
              0.39817744214475487,
              -0.01214055866730824
            ],
            "branch_aligned_reduced_polarization": [
              0.44482052244053927,
              0.39817744214475487,
              -0.01214055866730824
            ],
            "target_residual": 0.1164474181623368,
            "energy_eV": -105.07088646369388
          }
        ],
        "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": 0.1164474181623368,
        "parent_symmetrization_rmsd_A": 0.21086929313997538,
        "parent_cell_rmsd_A": 0.6911215949669297,
        "energy_eV": -105.07088646369388,
        "reduced_polarization": [
          0.44482052244053927,
          0.39817744214475487,
          -0.01214055866730824
        ],
        "cartesian_polarization_e_A2": [
          0.00514319128587539,
          0.0073068725129276976,
          0.000320988871223934
        ],
        "ranking_score": 1.1165445282063815
      },
      "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": [
              0.018309904492892416,
              2.892278689127378e-10,
              0.002697605212032375
            ],
            "branch_aligned_reduced_polarization": [
              0.018309904492892416,
              2.892278638810808e-10,
              0.0026976052120323835
            ],
            "target_residual": 0.7054395255265745,
            "energy_eV": -124.07574297484037,
            "max_atomic_step_A": 0.08407862398801504,
            "max_log_strain_component": 0.02,
            "step_scale": 0.2729062864595527,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 2.9402979367496895,
            "cell_principal_stretches": [
              1.0226853022965368,
              1.0170970018643029,
              0.9849490717562045
            ],
            "cell_volume_ratio": 1.0245146284550155,
            "cell_rmsd_from_input_A": 0.16678666538053577
          },
          {
            "iteration": 1,
            "reduced_polarization": [
              0.01627372180638291,
              0.14846926624225393,
              0.11607618194886217
            ],
            "branch_aligned_reduced_polarization": [
              0.01627372180638291,
              0.14846926624225393,
              0.11607618194886216
            ],
            "target_residual": 0.5208034071169794,
            "energy_eV": -121.50398121433481,
            "max_atomic_step_A": 0.06143105884566236,
            "max_log_strain_component": 0.02,
            "step_scale": 0.2705870890797323,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 2.9402979367496895,
            "cell_principal_stretches": [
              1.045385556234986,
              1.0337900396365634,
              0.9712363561272096
            ],
            "cell_volume_ratio": 1.049624041758191,
            "cell_rmsd_from_input_A": 0.32782170619051243
          },
          {
            "iteration": 2,
            "reduced_polarization": [
              0.002644061789384793,
              0.22381825471371983,
              0.20340022468634592
            ],
            "branch_aligned_reduced_polarization": [
              0.002644061789384793,
              0.22381825471371986,
              0.2034002246863459
            ],
            "target_residual": 0.4052835725861979,
            "energy_eV": -117.43409024745198,
            "max_atomic_step_A": 0.07075967286516131,
            "max_log_strain_component": 0.02,
            "step_scale": 0.31244030215286106,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 2.9402979367496895,
            "cell_principal_stretches": [
              1.0716527599032946,
              1.0541920097850195,
              0.9518913248073031
            ],
            "cell_volume_ratio": 1.0753780700860858,
            "cell_rmsd_from_input_A": 0.5403656339827047
          },
          {
            "iteration": 3,
            "reduced_polarization": [
              -7.3223216305739056e-06,
              0.2676473590389484,
              0.26431606850266026
            ],
            "branch_aligned_reduced_polarization": [
              -7.3223216305739056e-06,
              0.2676473590389484,
              0.26431606850266026
            ],
            "target_residual": 0.3309602172183758,
            "energy_eV": -112.80656160510681,
            "max_atomic_step_A": 0.05640901935191653,
            "max_log_strain_component": 0.02,
            "step_scale": 0.2934916200666843,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 2.9402979367496895,
            "cell_principal_stretches": [
              1.0985907215447694,
              1.0722627313167923,
              0.9321327039010963
            ],
            "cell_volume_ratio": 1.0980317135815452,
            "cell_rmsd_from_input_A": 0.7563428127125515
          },
          {
            "iteration": 4,
            "reduced_polarization": [
              0.006366732282483885,
              0.28308959859481114,
              0.29117667334808306
            ],
            "branch_aligned_reduced_polarization": [
              0.006366732282483885,
              0.28308959859481114,
              0.29117667334808306
            ],
            "target_residual": 0.3011608196158494,
            "energy_eV": -108.85776077790277,
            "max_atomic_step_A": 0.0694668470058599,
            "max_log_strain_component": 0.020000000000000004,
            "step_scale": 0.2521309875814671,
            "strain_jacobian_refreshed": true,
            "strain_jacobian_frobenius_norm": 1.6585552678122797,
            "cell_principal_stretches": [
              1.0804627132605484,
              1.0401286384526938,
              0.944219068839341
            ],
            "cell_volume_ratio": 1.0611324730246294,
            "cell_rmsd_from_input_A": 0.5206521597279067
          },
          {
            "iteration": 5,
            "reduced_polarization": [
              0.0015168650230566376,
              0.3235725605357949,
              0.3349186025032844
            ],
            "branch_aligned_reduced_polarization": [
              0.0015168650230566376,
              0.3235725605357949,
              0.3349186025032844
            ],
            "target_residual": 0.24162121197209185,
            "energy_eV": -107.8130167312943
          }
        ],
        "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": 0.24162121197209185,
        "parent_symmetrization_rmsd_A": 0.21735474124771495,
        "parent_cell_rmsd_A": 0.5206521597279067,
        "energy_eV": -107.8130167312943,
        "reduced_polarization": [
          0.0015168650230566376,
          0.3235725605357949,
          0.3349186025032844
        ],
        "cartesian_polarization_e_A2": [
          -0.0015568668269841748,
          0.0056520768859267745,
          0.00608700741946022
        ],
        "ranking_score": 1.3307602051238754
      },
      "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": [
              0.018309904492892416,
              2.892278689127378e-10,
              0.002697605212032375
            ],
            "branch_aligned_reduced_polarization": [
              0.018309904492892437,
              2.892278638810808e-10,
              0.0026976052120323835
            ],
            "target_residual": 0.8540111355727548,
            "energy_eV": -124.07574297484037,
            "max_atomic_step_A": 0.11741855167713947,
            "max_log_strain_component": 0.02,
            "step_scale": 0.39105599115069745,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 2.9402979367496895,
            "cell_principal_stretches": [
              1.028933225106411,
              1.0119983962513515,
              0.9775553180990003
            ],
            "cell_volume_ratio": 1.0179076028124145,
            "cell_rmsd_from_input_A": 0.2237078368211108
          },
          {
            "iteration": 1,
            "reduced_polarization": [
              0.19107171532492676,
              0.2044658748609931,
              0.15441116596753499
            ],
            "branch_aligned_reduced_polarization": [
              0.19107171532492673,
              0.2044658748609931,
              0.154411165967535
            ],
            "target_residual": 0.5497351602379822,
            "energy_eV": -120.35905024195252,
            "max_atomic_step_A": 0.10446204388038889,
            "max_log_strain_component": 0.02,
            "step_scale": 0.472772480649665,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 2.9402979367496895,
            "cell_principal_stretches": [
              1.0606678810796364,
              1.0273775547535358,
              0.9551014178335206
            ],
            "cell_volume_ratio": 1.0407801028957284,
            "cell_rmsd_from_input_A": 0.46113911916168165
          },
          {
            "iteration": 2,
            "reduced_polarization": [
              0.22028164757672303,
              0.2689369493036416,
              0.2587187606476894
            ],
            "branch_aligned_reduced_polarization": [
              0.22028164757672303,
              0.2689369493036416,
              0.2587187606476894
            ],
            "target_residual": 0.43571679625978094,
            "energy_eV": -114.16762022259425,
            "max_atomic_step_A": 0.05369771933039341,
            "max_log_strain_component": 0.019999999999999997,
            "step_scale": 0.2769713770637269,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 2.9402979367496895,
            "cell_principal_stretches": [
              1.0891768900061904,
              1.0349671644421847,
              0.934161348174489
            ],
            "cell_volume_ratio": 1.0530448861926567,
            "cell_rmsd_from_input_A": 0.6776803092600695
          },
          {
            "iteration": 3,
            "reduced_polarization": [
              0.2469014657728764,
              0.2758488486541717,
              0.2861063940397767
            ],
            "branch_aligned_reduced_polarization": [
              0.24690146577287642,
              0.2758488486541717,
              0.2861063940397767
            ],
            "target_residual": 0.40006634618303766,
            "energy_eV": -110.29216320720847,
            "max_atomic_step_A": 0.032708676383977536,
            "max_log_strain_component": 0.02,
            "step_scale": 0.1970954974086802,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 2.9402979367496895,
            "cell_principal_stretches": [
              1.1181648951479237,
              1.0406744726009634,
              0.913564016126201
            ],
            "cell_volume_ratio": 1.0630648048169424,
            "cell_rmsd_from_input_A": 0.8964685153942874
          },
          {
            "iteration": 4,
            "reduced_polarization": [
              0.26034071078580406,
              0.26058622820060473,
              0.2933206602589768
            ],
            "branch_aligned_reduced_polarization": [
              0.26034071078580406,
              0.26058622820060473,
              0.2933206602589768
            ],
            "target_residual": 0.39682726533046064,
            "energy_eV": -108.24614684826088,
            "max_atomic_step_A": 0.05266841251569972,
            "max_log_strain_component": 0.02,
            "step_scale": 0.2560039854645994,
            "strain_jacobian_refreshed": true,
            "strain_jacobian_frobenius_norm": 2.153173980340608,
            "cell_principal_stretches": [
              1.0745283198978024,
              1.0435928874818756,
              0.9230261803107144
            ],
            "cell_volume_ratio": 1.035053971233829,
            "cell_rmsd_from_input_A": 0.6845401761677059
          },
          {
            "iteration": 5,
            "reduced_polarization": [
              0.2785828370918355,
              0.2798870968401465,
              0.3223681215587971
            ],
            "branch_aligned_reduced_polarization": [
              0.2785828370918355,
              0.2798870968401465,
              0.3223681215587971
            ],
            "target_residual": 0.3592051425109473,
            "energy_eV": -110.52531538672633
          }
        ],
        "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": 0.3592051425109473,
        "parent_symmetrization_rmsd_A": 0.18294311974486857,
        "parent_cell_rmsd_A": 0.6845401761677059,
        "energy_eV": -110.52531538672633,
        "reduced_polarization": [
          0.2785828370918355,
          0.2798870968401465,
          0.3223681215587971
        ],
        "cartesian_polarization_e_A2": [
          0.0015559786689020626,
          0.0052354212766085265,
          0.005922330015640618
        ],
        "ranking_score": 1.5724884488086897
      },
      "branch_status": "awaiting_branch_sampling"
    }
  ],
  "sampled_polarization_branches": [
    {
      "orbit_id": 0,
      "candidate_id": "bec_projection_00",
      "formal_class": [
        0.0,
        0.0,
        0.0
      ],
      "construction": "MACEField-BEC-parent plus variable-cell P-N-P path and symmetric log-strain continuation beyond both polar endpoints",
      "geometry_diagnostics": {
        "collision_aware": false,
        "permutations_tested": 1,
        "selected_order": [
          0,
          1,
          2,
          3,
          4,
          5,
          6,
          7,
          8,
          9,
          10,
          11,
          12,
          13,
          14,
          15,
          16,
          17,
          18,
          19,
          20,
          21,
          22,
          23,
          24,
          25,
          26,
          27,
          28,
          29,
          30,
          31
        ],
        "endpoint_rmsd_A": 0.004393122951157375,
        "minimum_distance_A_by_image": [
          1.4379393377587832,
          1.438339495519359,
          1.4387401717418435,
          1.4391413663538073,
          1.4395098605553798,
          1.439841041815349,
          1.4401726508071466,
          1.4405046875401175,
          1.4408371520234176
        ],
        "minimum_distance_A": 1.4379393377587832,
        "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": [
          524.2609130825916,
          524.3339831149765,
          524.4070633316603,
          524.4801537340622,
          524.5532543236017,
          524.6263651016985,
          524.699486069773,
          524.7726172292453,
          524.8457585815357
        ],
        "cell_deformation_log_strain_norm": 0.0012749596127739854
      },
      "parent_reduced_polarization": [
        -2.508721813642575e-05,
        -2.5076711868751057e-12,
        -2.8723781457766897e-05
      ],
      "incoming": {
        "reached": true,
        "construction": "variable_cell_linear_interpolation",
        "continuation_fractions": [
          0.0,
          0.125,
          0.25,
          0.375,
          0.5,
          0.625,
          0.75,
          0.875,
          1.0
        ],
        "energies_eV": [
          -124.07574297484035,
          -124.07506555092806,
          -124.07424179758439,
          -124.07327211503775,
          -124.07215689676035,
          -124.07089652943299,
          -124.06949139291387,
          -124.06794186021062,
          -124.06624829745603
        ],
        "cartesian_polarizations_e_A2": [
          [
            0.00018862629561175367,
            5.018366311306043e-12,
            5.127560331490123e-05
          ],
          [
            0.00016504398679551013,
            4.389127133727057e-12,
            4.4832964112995006e-05
          ],
          [
            0.00014145717526049193,
            3.758754762833991e-12,
            3.837994623976801e-05
          ],
          [
            0.00011786629247330613,
            3.127595912743069e-12,
            3.191673843917634e-05
          ],
          [
            9.427177082657495e-05,
            2.495288655109443e-12,
            2.5443530088394434e-05
          ],
          [
            7.067404353040883e-05,
            1.862069570776201e-12,
            1.8960511208638427e-05
          ],
          [
            4.70735445078861e-05,
            1.2278479873558695e-12,
            1.2467872475316336e-05
          ],
          [
            2.3470708291371613e-05,
            5.926584753348959e-13,
            5.9658052260084015e-06
          ],
          [
            -1.3403007896240085e-07,
            -4.344082799554442e-14,
            -5.454985315978322e-07
          ]
        ],
        "raw_reduced_polarization": [
          [
            0.018309904492894203,
            2.892287965015756e-10,
            0.0026976052120333462
          ],
          [
            0.016021358477904632,
            2.530244979784308e-10,
            0.0023595707357457803
          ],
          [
            0.013731775110767439,
            2.1673730495537206e-10,
            0.002020729174457593
          ],
          [
            0.011441197511234314,
            1.8038716632082543e-10,
            0.0016810902080457329
          ],
          [
            0.009149668914608309,
            1.4395317690490568e-10,
            0.001340663560548448
          ],
          [
            0.00685723266222188,
            1.0744893959515908e-10,
            0.0009994590007710732
          ],
          [
            0.004563932192259354,
            7.086918792260817e-11,
            0.0006574863428540441
          ],
          [
            0.0022698110306011293,
            3.42158783813565e-11,
            0.0003147554467243419
          ],
          [
            -2.508721813642575e-05,
            -2.5076711868751057e-12,
            -2.8723781457766897e-05
          ]
        ],
        "unwrapped_reduced_polarization": [
          [
            0.018309904492894203,
            2.892287965015756e-10,
            0.0026976052120333462
          ],
          [
            0.016021358477904632,
            2.530244979784308e-10,
            0.0023595707357457803
          ],
          [
            0.013731775110767439,
            2.1673730495537206e-10,
            0.002020729174457593
          ],
          [
            0.011441197511234314,
            1.8038716632082543e-10,
            0.0016810902080457329
          ],
          [
            0.009149668914608309,
            1.4395317690490568e-10,
            0.001340663560548448
          ],
          [
            0.00685723266222188,
            1.0744893959515908e-10,
            0.0009994590007710732
          ],
          [
            0.004563932192259354,
            7.086918792260817e-11,
            0.0006574863428540441
          ],
          [
            0.0022698110306011293,
            3.42158783813565e-11,
            0.0003147554467243419
          ],
          [
            -2.5087218136425615e-05,
            -2.5076711868751053e-12,
            -2.8723781457766907e-05
          ]
        ],
        "berry_integer_shifts": [
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ]
        ],
        "folded_reduced_polarization": [
          [
            0.018309904492894158,
            2.892287520595005e-10,
            0.002697605212033327
          ],
          [
            0.016021358477904646,
            2.530244902487766e-10,
            0.002359570735745775
          ],
          [
            0.013731775110767397,
            2.167372947781132e-10,
            0.002020729174457614
          ],
          [
            0.011441197511234291,
            1.8038714966195357e-10,
            0.0016810902080457435
          ],
          [
            0.009149668914608333,
            1.4395318270743473e-10,
            0.0013406635605484052
          ],
          [
            0.006857232662221935,
            1.0744893863545713e-10,
            0.0009994590007710302
          ],
          [
            0.004563932192259368,
            7.0869199397805e-11,
            0.0006574863428540079
          ],
          [
            0.0022698110306010877,
            3.421585237362024e-11,
            0.0003147554467243241
          ],
          [
            -2.5087218136432554e-05,
            -2.507660745720841e-12,
            -2.8723781457740127e-05
          ]
        ]
      },
      "reflected": {
        "reached": true,
        "construction": "reflect_displacements_about_reconstructed_parent",
        "energies_eV": [
          -124.06624829745608,
          -124.06252794173245,
          -124.05874347425275,
          -124.05489489762073,
          -124.05098221182888,
          -124.04700541420848,
          -124.04296449941585,
          -124.03885945971255,
          -124.03469028512463
        ],
        "cartesian_polarizations_e_A2": [
          [
            -1.340300789355097e-07,
            -4.339529547439069e-14,
            -5.454985316087395e-07
          ],
          [
            -1.848876913526024e-05,
            -4.750288835449506e-13,
            -8.651942355726381e-06
          ],
          [
            -3.683246667386771e-05,
            -9.066861458345359e-13,
            -1.6758613302238013e-05
          ],
          [
            -5.5164910643134605e-05,
            -1.3384828770410902e-12,
            -2.4865372293841473e-05
          ],
          [
            -7.348589065625412e-05,
            -1.7703152425215152e-12,
            -3.297208127409065e-05
          ],
          [
            -9.179519804175072e-05,
            -2.2022689097589204e-12,
            -4.107860321540347e-05
          ],
          [
            -0.00011009262586289137,
            -2.634297381003379e-12,
            -4.918480212399839e-05
          ],
          [
            -0.00012837796898665369,
            -3.0664336937520972e-12,
            -5.7290542861393765e-05
          ],
          [
            -0.00014665102412740177,
            -3.4986506555858826e-12,
            -6.539569103834419e-05
          ]
        ],
        "raw_reduced_polarization": [
          [
            -2.5087218134245552e-05,
            -2.5050438377697007e-12,
            -2.8723781458340226e-05
          ],
          [
            -0.0018816786990115367,
            -2.7430338719267267e-11,
            -0.0004560134924213747
          ],
          [
            -0.0037369168536792036,
            -5.23429838430043e-11,
            -0.0008830823445702429
          ],
          [
            -0.005590779425286516,
            -7.724966463110079e-11,
            -0.0013099231998390224
          ],
          [
            -0.007443244341982807,
            -1.0214439706388875e-10,
            -0.0017365289801000111
          ],
          [
            -0.009294289721588371,
            -1.2703212752483991e-10,
            -0.0021628926675241146
          ],
          [
            -0.011143893873370855,
            -1.519101801582342e-10,
            -0.002589007304777861
          ],
          [
            -0.012992035299976647,
            -1.7678046550832287e-10,
            -0.003014865985568544
          ],
          [
            -0.014838692698789197,
            -2.0164142187364575e-10,
            -0.0034404618490035893
          ]
        ],
        "unwrapped_reduced_polarization": [
          [
            -2.5087218134245552e-05,
            -2.5050438377697007e-12,
            -2.8723781458340226e-05
          ],
          [
            -0.0018816786990115367,
            -2.7430338719267267e-11,
            -0.0004560134924213747
          ],
          [
            -0.0037369168536792036,
            -5.23429838430043e-11,
            -0.0008830823445702429
          ],
          [
            -0.005590779425286516,
            -7.724966463110079e-11,
            -0.0013099231998390224
          ],
          [
            -0.007443244341982807,
            -1.0214439706388875e-10,
            -0.0017365289801000111
          ],
          [
            -0.009294289721588371,
            -1.2703212752483991e-10,
            -0.0021628926675241146
          ],
          [
            -0.011143893873370855,
            -1.519101801582342e-10,
            -0.002589007304777861
          ],
          [
            -0.012992035299976647,
            -1.7678046550832287e-10,
            -0.003014865985568544
          ],
          [
            -0.014838692698789197,
            -2.0164142187364575e-10,
            -0.0034404618490035893
          ]
        ],
        "gauge_integer_shift": [
          0,
          0,
          0
        ],
        "expected_opposite_endpoint_reduced_polarization": [
          -0.018359984612296296,
          -2.9423613858095975e-10,
          -0.002755002476496823
        ],
        "actual_opposite_endpoint_branch_residual": 0.0035873878089060663
      },
      "pnp_branch": {
        "construction": "incoming_path_concatenated_with_parent_reflection",
        "reduced_polarization": [
          [
            0.018309904492894203,
            2.892287965015756e-10,
            0.0026976052120333462
          ],
          [
            0.016021358477904632,
            2.530244979784308e-10,
            0.0023595707357457803
          ],
          [
            0.013731775110767439,
            2.1673730495537206e-10,
            0.002020729174457593
          ],
          [
            0.011441197511234314,
            1.8038716632082543e-10,
            0.0016810902080457329
          ],
          [
            0.009149668914608309,
            1.4395317690490568e-10,
            0.001340663560548448
          ],
          [
            0.00685723266222188,
            1.0744893959515908e-10,
            0.0009994590007710732
          ],
          [
            0.004563932192259354,
            7.086918792260817e-11,
            0.0006574863428540441
          ],
          [
            0.0022698110306011293,
            3.42158783813565e-11,
            0.0003147554467243419
          ],
          [
            -2.508721813642575e-05,
            -2.5076711868751057e-12,
            -2.8723781457766897e-05
          ],
          [
            -0.0018816786990115367,
            -2.7430338719267267e-11,
            -0.0004560134924213747
          ],
          [
            -0.0037369168536792036,
            -5.23429838430043e-11,
            -0.0008830823445702429
          ],
          [
            -0.005590779425286516,
            -7.724966463110079e-11,
            -0.0013099231998390224
          ],
          [
            -0.007443244341982807,
            -1.0214439706388875e-10,
            -0.0017365289801000111
          ],
          [
            -0.009294289721588371,
            -1.2703212752483991e-10,
            -0.0021628926675241146
          ],
          [
            -0.011143893873370855,
            -1.519101801582342e-10,
            -0.002589007304777861
          ],
          [
            -0.012992035299976647,
            -1.7678046550832287e-10,
            -0.003014865985568544
          ],
          [
            -0.014838692698789197,
            -2.0164142187364575e-10,
            -0.0034404618490035893
          ]
        ],
        "unwrapped_reduced_polarization": [
          [
            0.018309904492894203,
            2.892287965015756e-10,
            0.0026976052120333462
          ],
          [
            0.016021358477904632,
            2.530244979784308e-10,
            0.0023595707357457803
          ],
          [
            0.013731775110767439,
            2.1673730495537206e-10,
            0.002020729174457593
          ],
          [
            0.011441197511234314,
            1.8038716632082543e-10,
            0.0016810902080457329
          ],
          [
            0.009149668914608309,
            1.4395317690490568e-10,
            0.001340663560548448
          ],
          [
            0.00685723266222188,
            1.0744893959515908e-10,
            0.0009994590007710732
          ],
          [
            0.004563932192259354,
            7.086918792260817e-11,
            0.0006574863428540441
          ],
          [
            0.0022698110306011293,
            3.42158783813565e-11,
            0.0003147554467243419
          ],
          [
            -2.5087218136425615e-05,
            -2.5076711868751053e-12,
            -2.8723781457766907e-05
          ],
          [
            -0.0018816786990115367,
            -2.7430338719267267e-11,
            -0.0004560134924213747
          ],
          [
            -0.0037369168536792036,
            -5.23429838430043e-11,
            -0.0008830823445702429
          ],
          [
            -0.005590779425286516,
            -7.724966463110079e-11,
            -0.0013099231998390224
          ],
          [
            -0.007443244341982807,
            -1.0214439706388875e-10,
            -0.0017365289801000111
          ],
          [
            -0.009294289721588371,
            -1.2703212752483991e-10,
            -0.0021628926675241146
          ],
          [
            -0.011143893873370855,
            -1.519101801582342e-10,
            -0.002589007304777861
          ],
          [
            -0.012992035299976647,
            -1.7678046550832287e-10,
            -0.003014865985568544
          ],
          [
            -0.014838692698789197,
            -2.0164142187364575e-10,
            -0.0034404618490035893
          ]
        ],
        "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": [
          [
            0.018309904492894158,
            2.892287520595005e-10,
            0.002697605212033327
          ],
          [
            0.016021358477904646,
            2.530244902487766e-10,
            0.002359570735745775
          ],
          [
            0.013731775110767397,
            2.167372947781132e-10,
            0.002020729174457614
          ],
          [
            0.011441197511234291,
            1.8038714966195357e-10,
            0.0016810902080457435
          ],
          [
            0.009149668914608333,
            1.4395318270743473e-10,
            0.0013406635605484052
          ],
          [
            0.006857232662221935,
            1.0744893863545713e-10,
            0.0009994590007710302
          ],
          [
            0.004563932192259368,
            7.0869199397805e-11,
            0.0006574863428540079
          ],
          [
            0.0022698110306010877,
            3.421585237362024e-11,
            0.0003147554467243241
          ],
          [
            -2.5087218136432554e-05,
            -2.507660745720841e-12,
            -2.8723781457740127e-05
          ],
          [
            -0.001881678699011513,
            -2.7430335780564974e-11,
            -0.0004560134924213588
          ],
          [
            -0.0037369168536792174,
            -5.234296329703625e-11,
            -0.0008830823445702407
          ],
          [
            -0.005590779425286518,
            -7.724965112032578e-11,
            -0.0013099231998390248
          ],
          [
            -0.007443244341982791,
            -1.0214440404610059e-10,
            -0.001736528980100016
          ],
          [
            -0.009294289721588356,
            -1.2703210705566903e-10,
            -0.002162892667524119
          ],
          [
            -0.011143893873370836,
            -1.5191020663607446e-10,
            -0.002589007304777846
          ],
          [
            -0.012992035299976668,
            -1.767804791441563e-10,
            -0.003014865985568549
          ],
          [
            -0.01483869269878918,
            -2.0164142577883126e-10,
            -0.0034404618490035954
          ]
        ]
      },
      "incoming_structure_ids": [
        "incoming_00_000",
        "incoming_00_001",
        "incoming_00_002",
        "incoming_00_003",
        "incoming_00_004",
        "incoming_00_005",
        "incoming_00_006",
        "incoming_00_007",
        "incoming_00_008"
      ],
      "reflected_structure_ids": [
        "reflected_00_001",
        "reflected_00_002",
        "reflected_00_003",
        "reflected_00_004",
        "reflected_00_005",
        "reflected_00_006",
        "reflected_00_007",
        "reflected_00_008"
      ],
      "positive_extension_structure_ids": [
        "extension_plus_00_000",
        "extension_plus_00_001",
        "extension_plus_00_002",
        "extension_plus_00_003"
      ],
      "negative_extension_structure_ids": [
        "extension_minus_00_000",
        "extension_minus_00_001",
        "extension_minus_00_002",
        "extension_minus_00_003"
      ],
      "extension": {
        "enabled": true,
        "fraction_beyond_polar_endpoint": 0.35,
        "images_per_side": 4,
        "construction": "continue fractional atomic displacements and symmetric log strain beyond +P; reflect these structures about N for the -P side",
        "positive_path_coordinates": [
          1.35,
          1.2625,
          1.175,
          1.0875
        ],
        "negative_path_coordinates": [
          -1.0875,
          -1.175,
          -1.2625,
          -1.35
        ]
      },
      "branch_coordinates": [
        1.35,
        1.2625,
        1.175,
        1.0875,
        1.0,
        0.875,
        0.75,
        0.625,
        0.5,
        0.375,
        0.25,
        0.125,
        0.0,
        -0.125,
        -0.25,
        -0.375,
        -0.5,
        -0.625,
        -0.75,
        -0.875,
        -1.0,
        -1.0875,
        -1.175,
        -1.2625,
        -1.35
      ],
      "parent": {
        "candidate_id": "bec_projection_00",
        "source": "MACEField_BEC_backprojection",
        "spacegroup": "Cc",
        "spacegroup_number": 9,
        "pointgroup": "m",
        "has_inversion": false,
        "is_polar_point_group": true,
        "nonpolar_parent_hypothesis": false,
        "symmetry_tolerance_A": null,
        "target_reduced_polarization": [
          0.0,
          0.0,
          0.0
        ],
        "formal_class": [
          0.0,
          0.0,
          0.0
        ],
        "target_residual": 3.8136913024295175e-05,
        "parent_symmetrization_rmsd_A": 0.004393122951157375,
        "parent_cell_rmsd_A": 0.008386550980589635,
        "energy_eV": -124.06624829745603,
        "reduced_polarization": [
          -2.5087218134565358e-05,
          -2.5064109137269994e-12,
          -2.8723781458773562e-05
        ],
        "cartesian_polarization_e_A2": [
          -1.3403007893688468e-07,
          -4.3418987192714584e-14,
          -5.454985316169695e-07
        ],
        "ranking_score": 0.5065660345223534
      }
    }
  ],
  "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": 140,
      "full_response": 35,
      "energy_polarization": 105
    },
    "model_evaluations_for_recovery_and_path_properties": {
      "total": 165,
      "full_response": 60,
      "energy_polarization": 105
    },
    "elapsed_seconds": 1284.5251154979924
  }
}
