{
  "schema": "ferrofinder.endpoint_parent_recovery.v4_variable_cell",
  "status": "complete",
  "input_atom_count": 24,
  "input_formula": "Al4O14Si2Sr4",
  "input_spacegroup": "P2_1",
  "input_pointgroup": "2",
  "input_is_polar_point_group": true,
  "input_energy_eV": -168.93082887422793,
  "input_cartesian_polarization_e_A2": [
    1.814819202011202e-09,
    0.0006533306975140327,
    -6.672744949009308e-08
  ],
  "input_reduced_polarization": [
    1.1310417829330154e-07,
    0.027610792422356867,
    -2.814474404178354e-06
  ],
  "input_formal_targets": [
    {
      "orbit_id": 0,
      "representative_formal_class": [
        0.0,
        0.0,
        0.0
      ],
      "target_reduced_polarization": [
        0.0,
        0.0,
        0.0
      ]
    },
    {
      "orbit_id": 1,
      "representative_formal_class": [
        0.0,
        0.5,
        0.0
      ],
      "target_reduced_polarization": [
        0.0,
        0.5,
        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": [
        0.5,
        0.0,
        0.0
      ],
      "target_reduced_polarization": [
        0.5,
        0.0,
        0.0
      ]
    },
    {
      "orbit_id": 4,
      "representative_formal_class": [
        0.0,
        0.5,
        0.5
      ],
      "target_reduced_polarization": [
        0.0,
        0.5,
        -0.5
      ]
    },
    {
      "orbit_id": 5,
      "representative_formal_class": [
        0.5,
        0.5,
        0.0
      ],
      "target_reduced_polarization": [
        0.5,
        0.5,
        0.0
      ]
    },
    {
      "orbit_id": 6,
      "representative_formal_class": [
        0.5,
        0.0,
        0.5
      ],
      "target_reduced_polarization": [
        0.5,
        0.0,
        -0.5
      ]
    },
    {
      "orbit_id": 7,
      "representative_formal_class": [
        0.5,
        0.5,
        0.5
      ],
      "target_reduced_polarization": [
        0.5,
        0.5,
        -0.5
      ]
    }
  ],
  "parent_candidates": [
    {
      "candidate_id": "inversion_parent_endpoint_00",
      "source": "same_species_inversion_center_projection_from_endpoint",
      "spacegroup": "P2_1/m",
      "spacegroup_number": 11,
      "pointgroup": "2/m",
      "has_inversion": true,
      "is_polar_point_group": false,
      "nonpolar_parent_hypothesis": true,
      "symmetry_tolerance_A": null,
      "target_reduced_polarization": [
        0.0,
        0.0,
        0.0
      ],
      "formal_class": [
        0.0,
        0.0,
        0.0
      ],
      "target_residual": 3.141425420828893e-15,
      "parent_symmetrization_rmsd_A": 0.4831736928107981,
      "parent_cell_rmsd_A": 0.0,
      "energy_eV": -162.37622735832988,
      "reduced_polarization": [
        2.2067989841903842e-16,
        2.1139197194696598e-15,
        -2.3132655439229333e-15
      ],
      "cartesian_polarization_e_A2": [
        3.527641711616589e-18,
        5.0019884387363447e-17,
        -5.4844453198839076e-17
      ],
      "ranking_score": 0.48317369281080436
    },
    {
      "candidate_id": "inversion_parent_endpoint_01",
      "source": "same_species_inversion_center_projection_from_endpoint",
      "spacegroup": "P2_1/m",
      "spacegroup_number": 11,
      "pointgroup": "2/m",
      "has_inversion": true,
      "is_polar_point_group": false,
      "nonpolar_parent_hypothesis": true,
      "symmetry_tolerance_A": null,
      "target_reduced_polarization": [
        0.0,
        0.0,
        0.0
      ],
      "formal_class": [
        0.0,
        0.0,
        0.0
      ],
      "target_residual": 3.4440198143562784e-15,
      "parent_symmetrization_rmsd_A": 0.515358798912036,
      "parent_cell_rmsd_A": 0.0,
      "energy_eV": -129.99805800594373,
      "reduced_polarization": [
        -2.624782889220417e-15,
        1.71884781172393e-16,
        -2.223115581371264e-15
      ],
      "cartesian_polarization_e_A2": [
        -4.183368053305319e-17,
        4.067163385157949e-18,
        -5.270711733827138e-17
      ],
      "ranking_score": 0.5153587989120428
    },
    {
      "candidate_id": "bec_projection_00",
      "source": "MACEField_BEC_backprojection",
      "spacegroup": "P2_1",
      "spacegroup_number": 4,
      "pointgroup": "2",
      "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": 1.6050786214330847e-06,
      "parent_symmetrization_rmsd_A": 0.005196265633929463,
      "parent_cell_rmsd_A": 0.00036649227311306266,
      "energy_eV": -168.92561522274005,
      "reduced_polarization": [
        4.164840600875961e-10,
        1.6050781571112385e-06,
        -1.1476440867734987e-09
      ],
      "cartesian_polarization_e_A2": [
        6.642901021942437e-12,
        3.797630673362562e-08,
        -2.7208162630933483e-11
      ],
      "ranking_score": 0.5052910988594506
    },
    {
      "candidate_id": "inversion_parent_bec_00_00",
      "source": "same_species_inversion_center_projection_after_BEC",
      "spacegroup": "P2_1/m",
      "spacegroup_number": 11,
      "pointgroup": "2/m",
      "has_inversion": true,
      "is_polar_point_group": false,
      "nonpolar_parent_hypothesis": true,
      "symmetry_tolerance_A": null,
      "target_reduced_polarization": [
        0.0,
        0.0,
        0.0
      ],
      "formal_class": [
        0.0,
        0.0,
        0.0
      ],
      "target_residual": 3.4273115153948815e-15,
      "parent_symmetrization_rmsd_A": 0.483173871108925,
      "parent_cell_rmsd_A": 0.00036649227311306266,
      "energy_eV": -162.38774226837884,
      "reduced_polarization": [
        -2.0232786279005318e-15,
        -1.423958267253665e-15,
        -2.3717400090564815e-15
      ],
      "cartesian_polarization_e_A2": [
        -3.22437575112491e-17,
        -3.3690991801087984e-17,
        -5.622946129696593e-17
      ],
      "ranking_score": 0.4832654941772101
    },
    {
      "candidate_id": "inversion_parent_bec_00_01",
      "source": "same_species_inversion_center_projection_after_BEC",
      "spacegroup": "P2_1/m",
      "spacegroup_number": 11,
      "pointgroup": "2/m",
      "has_inversion": true,
      "is_polar_point_group": false,
      "nonpolar_parent_hypothesis": true,
      "symmetry_tolerance_A": null,
      "target_reduced_polarization": [
        0.0,
        0.0,
        0.0
      ],
      "formal_class": [
        0.0,
        0.0,
        0.0
      ],
      "target_residual": 2.7658085176990286e-15,
      "parent_symmetrization_rmsd_A": 0.5153589413422184,
      "parent_cell_rmsd_A": 0.00036649227311306266,
      "energy_eV": -130.01302864902283,
      "reduced_polarization": [
        2.2984011167554236e-15,
        -6.989343997658239e-16,
        -1.3705983247829786e-15
      ],
      "cartesian_polarization_e_A2": [
        3.664251979721101e-17,
        -1.65368563297719e-17,
        -3.2492744055737506e-17
      ],
      "ranking_score": 0.5154505644105022
    },
    {
      "candidate_id": "bec_projection_01",
      "source": "MACEField_BEC_backprojection",
      "spacegroup": "P2_1",
      "spacegroup_number": 4,
      "pointgroup": "2",
      "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": 0.0009395030395946692,
      "parent_symmetrization_rmsd_A": 0.08891505979238344,
      "parent_cell_rmsd_A": 0.006262280316534061,
      "energy_eV": -167.68398907544352,
      "reduced_polarization": [
        3.601105368786957e-08,
        0.4990604969614338,
        2.5212645270614402e-08
      ],
      "cartesian_polarization_e_A2": [
        5.408703379162758e-10,
        0.011826372819032161,
        6.627543387846081e-10
      ],
      "ranking_score": 0.5923596359507063
    },
    {
      "candidate_id": "bec_projection_02",
      "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,
        0.0,
        -0.5
      ],
      "formal_class": [
        0.0,
        0.0,
        0.5
      ],
      "target_residual": 3.0601556236552106e-07,
      "parent_symmetrization_rmsd_A": 0.09420322074386638,
      "parent_cell_rmsd_A": 0.011771544691336044,
      "energy_eV": -167.450134546524,
      "reduced_polarization": [
        1.1376470880649154e-07,
        1.5079108098447817e-07,
        -0.4999997592404408
      ],
      "cartesian_polarization_e_A2": [
        1.7498635857787101e-06,
        -1.6322233825510976e-05,
        -0.011853858557587983
      ],
      "ranking_score": 0.5971467189478251
    },
    {
      "candidate_id": "bec_projection_03",
      "source": "MACEField_BEC_backprojection",
      "spacegroup": "P1",
      "spacegroup_number": 1,
      "pointgroup": "1",
      "has_inversion": false,
      "is_polar_point_group": true,
      "nonpolar_parent_hypothesis": false,
      "symmetry_tolerance_A": null,
      "target_reduced_polarization": [
        0.5,
        0.0,
        0.0
      ],
      "formal_class": [
        0.5,
        0.0,
        0.0
      ],
      "target_residual": 6.269046670687185e-07,
      "parent_symmetrization_rmsd_A": 0.06777111184665542,
      "parent_cell_rmsd_A": 0.006743956759454403,
      "energy_eV": -168.15054282063537,
      "reduced_polarization": [
        0.49999997542490504,
        6.263224299902168e-07,
        1.1213384477774574e-08
      ],
      "cartesian_polarization_e_A2": [
        0.007970260209765411,
        -7.145959569582467e-06,
        2.2499762491085386e-07
      ],
      "ranking_score": 0.5694583548458532
    },
    {
      "candidate_id": "bec_projection_04",
      "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": 0.0002545378780732874,
      "parent_symmetrization_rmsd_A": 0.1296672888085847,
      "parent_cell_rmsd_A": 0.013333010260866744,
      "energy_eV": -165.77011765140858,
      "reduced_polarization": [
        0.00020585439050056382,
        0.49987395808942675,
        -0.4999192105324641
      ],
      "cartesian_polarization_e_A2": [
        1.7541567253646057e-05,
        0.011829391501537504,
        -0.01184425145084193
      ],
      "ranking_score": 0.6335096171299479
    },
    {
      "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": 4.098744116585444e-06,
      "parent_symmetrization_rmsd_A": 0.11219110820376091,
      "parent_cell_rmsd_A": 0.009237262858984394,
      "energy_eV": -166.86406719108052,
      "reduced_polarization": [
        0.5000037227769447,
        0.5000015427792717,
        7.48643621529156e-07
      ],
      "cartesian_polarization_e_A2": [
        0.00796859489842979,
        0.011841552678536958,
        -1.0361673190108705e-05
      ],
      "ranking_score": 0.6145086214067402
    },
    {
      "candidate_id": "bec_projection_06",
      "source": "MACEField_BEC_backprojection",
      "spacegroup": "P1",
      "spacegroup_number": 1,
      "pointgroup": "1",
      "has_inversion": false,
      "is_polar_point_group": true,
      "nonpolar_parent_hypothesis": false,
      "symmetry_tolerance_A": null,
      "target_reduced_polarization": [
        0.5,
        0.0,
        -0.5
      ],
      "formal_class": [
        0.5,
        0.0,
        0.5
      ],
      "target_residual": 1.820108686859215e-06,
      "parent_symmetrization_rmsd_A": 0.11690001641107371,
      "parent_cell_rmsd_A": 0.007152447752607323,
      "energy_eV": -166.63498119199258,
      "reduced_polarization": [
        0.49999852707245307,
        8.310935530116824e-07,
        -0.49999932727154095
      ],
      "cartesian_polarization_e_A2": [
        0.007971907801662874,
        -1.2675343089829138e-05,
        -0.011853555121512217
      ],
      "ranking_score": 0.6186917685665992
    },
    {
      "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": 0.0005773028801663222,
      "parent_symmetrization_rmsd_A": 0.14618073451456756,
      "parent_cell_rmsd_A": 0.009433719882538064,
      "energy_eV": -164.79852629554756,
      "reduced_polarization": [
        0.500565458334183,
        0.49989541985467345,
        -0.49994902470250385
      ],
      "cartesian_polarization_e_A2": [
        0.007991728191020545,
        0.01183356669265908,
        -0.01185534486108565
      ],
      "ranking_score": 0.6496937702455348
    }
  ],
  "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": [
              1.1310417829330154e-07,
              0.027610792422356867,
              -2.814474404178354e-06
            ],
            "branch_aligned_reduced_polarization": [
              1.1310417829330154e-07,
              0.027610792422356867,
              -2.814474404178354e-06
            ],
            "target_residual": 0.027610792566033632,
            "energy_eV": -168.93082887422793,
            "max_atomic_step_A": 0.005427023058672898,
            "max_log_strain_component": 5.429110855314467e-05,
            "step_scale": 1.0,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 0.3670433138065003,
            "cell_principal_stretches": [
              1.0000733677621025,
              1.0000133312308381,
              1.0000075160530755
            ],
            "cell_volume_ratio": 1.0000942166757398,
            "cell_rmsd_from_input_A": 0.00036649227311306266
          },
          {
            "iteration": 1,
            "reduced_polarization": [
              4.164840600875961e-10,
              1.6050781571112385e-06,
              -1.1476440867734987e-09
            ],
            "branch_aligned_reduced_polarization": [
              4.164840600875961e-10,
              1.6050781571112385e-06,
              -1.1476440867734987e-09
            ],
            "target_residual": 1.6050786214330847e-06,
            "energy_eV": -168.92561522274005
          }
        ],
        "iterations": 1
      },
      "parent": {
        "candidate_id": "inversion_parent_endpoint_00",
        "source": "same_species_inversion_center_projection_from_endpoint",
        "spacegroup": "P2_1/m",
        "spacegroup_number": 11,
        "pointgroup": "2/m",
        "has_inversion": true,
        "is_polar_point_group": false,
        "nonpolar_parent_hypothesis": true,
        "symmetry_tolerance_A": null,
        "target_reduced_polarization": [
          0.0,
          0.0,
          0.0
        ],
        "formal_class": [
          0.0,
          0.0,
          0.0
        ],
        "target_residual": 3.141425420828893e-15,
        "parent_symmetrization_rmsd_A": 0.4831736928107981,
        "parent_cell_rmsd_A": 0.0,
        "energy_eV": -162.37622735832988,
        "reduced_polarization": [
          2.2067989841903842e-16,
          2.1139197194696598e-15,
          -2.3132655439229333e-15
        ],
        "cartesian_polarization_e_A2": [
          3.527641711616589e-18,
          5.0019884387363447e-17,
          -5.4844453198839076e-17
        ],
        "ranking_score": 0.48317369281080436
      },
      "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": [
          -168.93082887422796,
          -168.56184981965447,
          -167.69454608535105,
          -166.55001249669078,
          -165.3075731277825,
          -164.13269822550902,
          -163.18063613342935,
          -162.57743735839404,
          -162.37622735832988
        ],
        "cartesian_polarizations_e_A2": [
          [
            1.8148191648879607e-09,
            0.0006533306975140298,
            -6.672744949463752e-08
          ],
          [
            2.986161508910642e-09,
            0.0014285332197285323,
            -5.7255635461204714e-08
          ],
          [
            4.292404590700929e-09,
            0.0022258271270576635,
            -4.706855042978449e-08
          ],
          [
            5.827729000199205e-09,
            0.00301227577918306,
            -3.550147853986896e-08
          ],
          [
            7.80844527801707e-09,
            0.0036391356055229702,
            -2.2526276635963588e-08
          ],
          [
            9.226788946491755e-09,
            0.0038340469055031016,
            -9.5303827950327e-09
          ],
          [
            8.868118949887625e-09,
            0.0032966117692049142,
            4.776047940227528e-10
          ],
          [
            5.550655718223897e-09,
            0.0019212441696999018,
            3.5959745337182253e-09
          ],
          [
            3.9634092171692256e-17,
            1.4229884139653387e-17,
            -3.11470012302147e-17
          ]
        ],
        "raw_reduced_polarization": [
          [
            1.1310417596453431e-07,
            0.027610792422356745,
            -2.814474404370032e-06
          ],
          [
            1.8668651839238606e-07,
            0.06037208162489325,
            -2.4149659807460806e-06
          ],
          [
            2.6873901053447193e-07,
            0.09406698783187066,
            -1.985288384895853e-06
          ],
          [
            3.651768942119698e-07,
            0.12730355633737897,
            -1.4974047925476753e-06
          ],
          [
            4.895695012401657e-07,
            0.153795647722101,
            -9.501281631148398e-07
          ],
          [
            5.786850667866362e-07,
            0.16203290867585796,
            -4.019787755056286e-07
          ],
          [
            5.562966557936849e-07,
            0.13932004665165834,
            2.0144730217651805e-08
          ],
          [
            3.4822883176430063e-07,
            0.08119482853644418,
            1.5167338719771918e-07
          ],
          [
            2.4858763892847465e-15,
            6.013774933110639e-16,
            -1.3137387746607351e-15
          ]
        ],
        "unwrapped_reduced_polarization": [
          [
            1.1310417596453431e-07,
            0.027610792422356745,
            -2.814474404370032e-06
          ],
          [
            1.8668651839238606e-07,
            0.06037208162489324,
            -2.4149659807460806e-06
          ],
          [
            2.6873901053447193e-07,
            0.09406698783187066,
            -1.985288384895853e-06
          ],
          [
            3.651768942119698e-07,
            0.12730355633737897,
            -1.4974047925476753e-06
          ],
          [
            4.895695012401657e-07,
            0.153795647722101,
            -9.501281631148398e-07
          ],
          [
            5.786850667866362e-07,
            0.16203290867585796,
            -4.019787755056286e-07
          ],
          [
            5.562966557936849e-07,
            0.13932004665165834,
            2.0144730217651812e-08
          ],
          [
            3.4822883176430063e-07,
            0.08119482853644418,
            1.5167338719771918e-07
          ],
          [
            2.4858763699479793e-15,
            5.967448757360216e-16,
            -1.313738783829e-15
          ]
        ],
        "berry_integer_shifts": [
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ]
        ],
        "folded_reduced_polarization": [
          [
            1.1310417591392508e-07,
            0.027610792422356756,
            -2.8144744043667735e-06
          ],
          [
            1.866865183552946e-07,
            0.06037208162489327,
            -2.4149659807459756e-06
          ],
          [
            2.6873901048940496e-07,
            0.09406698783187062,
            -1.9852883849091896e-06
          ],
          [
            3.65176894168151e-07,
            0.127303556337379,
            -1.4974047925497835e-06
          ],
          [
            4.895695012718804e-07,
            0.15379564772210097,
            -9.501281630908132e-07
          ],
          [
            5.78685066754403e-07,
            0.16203290867585796,
            -4.0197877548830974e-07
          ],
          [
            5.562966557404181e-07,
            0.1393200466516583,
            2.0144730217275253e-08
          ],
          [
            3.4822883177021424e-07,
            0.08119482853644422,
            1.5167338718313772e-07
          ],
          [
            2.4424906541753444e-15,
            5.551115123125783e-16,
            -1.3322676295501878e-15
          ]
        ]
      },
      "reflected": {
        "reached": true,
        "construction": "reflect_displacements_about_reconstructed_parent",
        "energies_eV": [
          -162.37622735832988,
          -162.57743735839404,
          -163.18063613342935,
          -164.132698225509,
          -165.3075731277825,
          -166.55001249669075,
          -167.69454608535102,
          -168.5618498196545,
          -168.93082887422798
        ],
        "cartesian_polarizations_e_A2": [
          [
            -4.76024122732262e-17,
            -1.0416918466067807e-17,
            -3.820228465344788e-17
          ],
          [
            -5.550655669978209e-09,
            -0.0019212441696999356,
            -3.595974481166739e-09
          ],
          [
            -8.868118951402436e-09,
            -0.0032966117692048826,
            -4.776049330222116e-10
          ],
          [
            -9.226789041281563e-09,
            -0.0038340469055031753,
            9.530382773119821e-09
          ],
          [
            -7.808445243840448e-09,
            -0.0036391356055229564,
            2.252627676024033e-08
          ],
          [
            -5.827729017277141e-09,
            -0.003012275779183027,
            3.550147844898031e-08
          ],
          [
            -4.29240462657912e-09,
            -0.002225827127057734,
            4.706855040277728e-08
          ],
          [
            -2.98616154259962e-09,
            -0.0014285332197284445,
            5.7255635378076874e-08
          ],
          [
            -1.8148192797542002e-09,
            -0.0006533306975139606,
            6.672744951728704e-08
          ]
        ],
        "raw_reduced_polarization": [
          [
            -2.9864912256391634e-15,
            -4.4023551096194537e-16,
            -1.6113211753167311e-15
          ],
          [
            -3.4822882873729837e-07,
            -0.0811948285364456,
            -1.516733849811679e-07
          ],
          [
            -5.562966558902459e-07,
            -0.13932004665165698,
            -2.0144736080462718e-08
          ],
          [
            -5.786850727329821e-07,
            -0.16203290867586106,
            4.0197877458137266e-07
          ],
          [
            -4.895694990949133e-07,
            -0.15379564772210041,
            9.501281683566664e-07
          ],
          [
            -3.651768952842632e-07,
            -0.12730355633737758,
            1.4974047887141138e-06
          ],
          [
            -2.6873901278538655e-07,
            -0.09406698783187364,
            1.9852883837567254e-06
          ],
          [
            -1.866865205065936e-07,
            -0.06037208162488953,
            2.4149659772398597e-06
          ],
          [
            -1.131041831697687e-07,
            -0.02761079242235382,
            2.814474405325359e-06
          ]
        ],
        "unwrapped_reduced_polarization": [
          [
            -2.9864912256391634e-15,
            -4.4023551096194537e-16,
            -1.6113211753167311e-15
          ],
          [
            -3.4822882873729837e-07,
            -0.0811948285364456,
            -1.516733849811679e-07
          ],
          [
            -5.562966558902459e-07,
            -0.13932004665165698,
            -2.0144736080462725e-08
          ],
          [
            -5.786850727329821e-07,
            -0.16203290867586106,
            4.0197877458137266e-07
          ],
          [
            -4.895694990949133e-07,
            -0.15379564772210041,
            9.501281683566664e-07
          ],
          [
            -3.651768952842632e-07,
            -0.12730355633737758,
            1.4974047887141138e-06
          ],
          [
            -2.6873901278538655e-07,
            -0.09406698783187364,
            1.9852883837567254e-06
          ],
          [
            -1.866865205065936e-07,
            -0.06037208162488953,
            2.4149659772398597e-06
          ],
          [
            -1.131041831697687e-07,
            -0.02761079242235382,
            2.814474405325359e-06
          ]
        ],
        "gauge_integer_shift": [
          0,
          0,
          0
        ],
        "expected_opposite_endpoint_reduced_polarization": [
          -1.1310417099278154e-07,
          -0.02761079242235554,
          2.814474401742555e-06
        ],
        "actual_opposite_endpoint_branch_residual": 1.2809247112382252e-14
      },
      "pnp_branch": {
        "construction": "incoming_path_concatenated_with_parent_reflection",
        "reduced_polarization": [
          [
            1.1310417596453431e-07,
            0.027610792422356745,
            -2.814474404370032e-06
          ],
          [
            1.8668651839238606e-07,
            0.06037208162489325,
            -2.4149659807460806e-06
          ],
          [
            2.6873901053447193e-07,
            0.09406698783187066,
            -1.985288384895853e-06
          ],
          [
            3.651768942119698e-07,
            0.12730355633737897,
            -1.4974047925476753e-06
          ],
          [
            4.895695012401657e-07,
            0.153795647722101,
            -9.501281631148398e-07
          ],
          [
            5.786850667866362e-07,
            0.16203290867585796,
            -4.019787755056286e-07
          ],
          [
            5.562966557936849e-07,
            0.13932004665165834,
            2.0144730217651805e-08
          ],
          [
            3.4822883176430063e-07,
            0.08119482853644418,
            1.5167338719771918e-07
          ],
          [
            2.4858763892847465e-15,
            6.013774933110639e-16,
            -1.3137387746607351e-15
          ],
          [
            -3.4822882873729837e-07,
            -0.0811948285364456,
            -1.516733849811679e-07
          ],
          [
            -5.562966558902459e-07,
            -0.13932004665165698,
            -2.0144736080462718e-08
          ],
          [
            -5.786850727329821e-07,
            -0.16203290867586106,
            4.0197877458137266e-07
          ],
          [
            -4.895694990949133e-07,
            -0.15379564772210041,
            9.501281683566664e-07
          ],
          [
            -3.651768952842632e-07,
            -0.12730355633737758,
            1.4974047887141138e-06
          ],
          [
            -2.6873901278538655e-07,
            -0.09406698783187364,
            1.9852883837567254e-06
          ],
          [
            -1.866865205065936e-07,
            -0.06037208162488953,
            2.4149659772398597e-06
          ],
          [
            -1.131041831697687e-07,
            -0.02761079242235382,
            2.814474405325359e-06
          ]
        ],
        "unwrapped_reduced_polarization": [
          [
            1.1310417596453431e-07,
            0.027610792422356745,
            -2.814474404370032e-06
          ],
          [
            1.8668651839238606e-07,
            0.06037208162489324,
            -2.4149659807460806e-06
          ],
          [
            2.6873901053447193e-07,
            0.09406698783187066,
            -1.985288384895853e-06
          ],
          [
            3.651768942119698e-07,
            0.12730355633737897,
            -1.4974047925476753e-06
          ],
          [
            4.895695012401657e-07,
            0.153795647722101,
            -9.501281631148398e-07
          ],
          [
            5.786850667866362e-07,
            0.16203290867585796,
            -4.019787755056286e-07
          ],
          [
            5.562966557936849e-07,
            0.13932004665165834,
            2.0144730217651812e-08
          ],
          [
            3.4822883176430063e-07,
            0.08119482853644418,
            1.5167338719771918e-07
          ],
          [
            2.4858763699479793e-15,
            5.967448757360216e-16,
            -1.313738783829e-15
          ],
          [
            -3.4822882873729837e-07,
            -0.0811948285364456,
            -1.516733849811679e-07
          ],
          [
            -5.562966558902459e-07,
            -0.13932004665165698,
            -2.0144736080462725e-08
          ],
          [
            -5.786850727329821e-07,
            -0.16203290867586106,
            4.0197877458137266e-07
          ],
          [
            -4.895694990949133e-07,
            -0.15379564772210041,
            9.501281683566664e-07
          ],
          [
            -3.651768952842632e-07,
            -0.12730355633737758,
            1.4974047887141138e-06
          ],
          [
            -2.6873901278538655e-07,
            -0.09406698783187364,
            1.9852883837567254e-06
          ],
          [
            -1.866865205065936e-07,
            -0.06037208162488953,
            2.4149659772398597e-06
          ],
          [
            -1.131041831697687e-07,
            -0.02761079242235382,
            2.814474405325359e-06
          ]
        ],
        "berry_integer_shifts": [
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ]
        ],
        "folded_reduced_polarization": [
          [
            1.1310417591392508e-07,
            0.027610792422356756,
            -2.8144744043667735e-06
          ],
          [
            1.866865183552946e-07,
            0.06037208162489327,
            -2.4149659807459756e-06
          ],
          [
            2.6873901048940496e-07,
            0.09406698783187062,
            -1.9852883849091896e-06
          ],
          [
            3.65176894168151e-07,
            0.127303556337379,
            -1.4974047925497835e-06
          ],
          [
            4.895695012718804e-07,
            0.15379564772210097,
            -9.501281630908132e-07
          ],
          [
            5.78685066754403e-07,
            0.16203290867585796,
            -4.0197877548830974e-07
          ],
          [
            5.562966557404181e-07,
            0.1393200466516583,
            2.0144730217275253e-08
          ],
          [
            3.4822883177021424e-07,
            0.08119482853644422,
            1.5167338718313772e-07
          ],
          [
            2.4424906541753444e-15,
            5.551115123125783e-16,
            -1.3322676295501878e-15
          ],
          [
            -3.482288287171009e-07,
            -0.0811948285364456,
            -1.5167338496269167e-07
          ],
          [
            -5.562966559069515e-07,
            -0.13932004665165698,
            -2.0144736101457283e-08
          ],
          [
            -5.786850727496073e-07,
            -0.16203290867586106,
            4.019787746001313e-07
          ],
          [
            -4.895694991069455e-07,
            -0.15379564772210041,
            9.501281683643725e-07
          ],
          [
            -3.6517689527837405e-07,
            -0.12730355633737755,
            1.497404788719514e-06
          ],
          [
            -2.6873901276536216e-07,
            -0.09406698783187362,
            1.9852883837989665e-06
          ],
          [
            -1.866865205202295e-07,
            -0.06037208162488955,
            2.414965977193262e-06
          ],
          [
            -1.1310418318588589e-07,
            -0.027610792422353814,
            2.814474405310463e-06
          ]
        ]
      },
      "incoming_structure_ids": [
        "incoming_00_000",
        "incoming_00_001",
        "incoming_00_002",
        "incoming_00_003",
        "incoming_00_004",
        "incoming_00_005",
        "incoming_00_006",
        "incoming_00_007",
        "incoming_00_008"
      ],
      "reflected_structure_ids": [
        "reflected_00_001",
        "reflected_00_002",
        "reflected_00_003",
        "reflected_00_004",
        "reflected_00_005",
        "reflected_00_006",
        "reflected_00_007",
        "reflected_00_008"
      ]
    },
    {
      "orbit_id": 1,
      "formal_class": [
        0.0,
        0.5,
        0.0
      ],
      "formal_classes_in_orbit": [
        [
          0.0,
          0.5,
          0.0
        ]
      ],
      "target_reduced_polarization": [
        0.0,
        0.5,
        0.0
      ],
      "bec_backprojection": {
        "converged_to_target": true,
        "history": [
          {
            "iteration": 0,
            "reduced_polarization": [
              1.1310417829330154e-07,
              0.027610792422356867,
              -2.814474404178354e-06
            ],
            "branch_aligned_reduced_polarization": [
              1.1310417829330154e-07,
              0.027610792422356867,
              -2.814474404178354e-06
            ],
            "target_residual": 0.47238920758604097,
            "energy_eV": -168.93082887422793,
            "max_atomic_step_A": 0.09284962907265819,
            "max_log_strain_component": 0.000928859025539239,
            "step_scale": 1.0,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 0.3670433138065003,
            "cell_principal_stretches": [
              0.9998714176094543,
              0.9997719453718701,
              0.9987455946500242
            ],
            "cell_volume_ratio": 0.998389434285758,
            "cell_rmsd_from_input_A": 0.006262280316534061
          },
          {
            "iteration": 1,
            "reduced_polarization": [
              3.601105368786957e-08,
              0.4990604969614338,
              2.5212645270614402e-08
            ],
            "branch_aligned_reduced_polarization": [
              3.601105368786957e-08,
              0.4990604969614338,
              2.5212645270614402e-08
            ],
            "target_residual": 0.0009395030395946692,
            "energy_eV": -167.68398907544352
          }
        ],
        "iterations": 1
      },
      "parent": {
        "candidate_id": "bec_projection_01",
        "source": "MACEField_BEC_backprojection",
        "spacegroup": "P2_1",
        "spacegroup_number": 4,
        "pointgroup": "2",
        "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": 0.0009395030395946692,
        "parent_symmetrization_rmsd_A": 0.08891505979238344,
        "parent_cell_rmsd_A": 0.006262280316534061,
        "energy_eV": -167.68398907544352,
        "reduced_polarization": [
          3.601105368786957e-08,
          0.4990604969614338,
          2.5212645270614402e-08
        ],
        "cartesian_polarization_e_A2": [
          5.408703379162758e-10,
          0.011826372819032161,
          6.627543387846081e-10
        ],
        "ranking_score": 0.5923596359507063
      },
      "branch_status": "awaiting_branch_sampling"
    },
    {
      "orbit_id": 2,
      "formal_class": [
        0.0,
        0.0,
        0.5
      ],
      "formal_classes_in_orbit": [
        [
          0.0,
          0.0,
          0.5
        ]
      ],
      "target_reduced_polarization": [
        0.0,
        0.0,
        -0.5
      ],
      "bec_backprojection": {
        "converged_to_target": true,
        "history": [
          {
            "iteration": 0,
            "reduced_polarization": [
              1.1310417829330154e-07,
              0.027610792422356867,
              -2.814474404178354e-06
            ],
            "branch_aligned_reduced_polarization": [
              1.1310417829330154e-07,
              0.027610792422356867,
              -2.81447440420024e-06
            ],
            "target_residual": 0.5007589653632977,
            "energy_eV": -168.93082887422793,
            "max_atomic_step_A": 0.09931286417995681,
            "max_log_strain_component": 0.0013722443106462202,
            "step_scale": 1.0,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 0.3670433138065003,
            "cell_principal_stretches": [
              1.0015146933224253,
              1.0000163004897649,
              0.99856537941478
            ],
            "cell_volume_ratio": 1.0000942014865524,
            "cell_rmsd_from_input_A": 0.011726341521588251
          },
          {
            "iteration": 1,
            "reduced_polarization": [
              0.0005773880630664227,
              0.0005604010510512905,
              -0.4983867951521621
            ],
            "branch_aligned_reduced_polarization": [
              0.0005773880630664227,
              0.0005604010510512905,
              -0.4983867951521621
            ],
            "target_residual": 0.0018027357528153307,
            "energy_eV": -167.45986512341017,
            "max_atomic_step_A": 0.00035233788651916015,
            "max_log_strain_component": 5.134195590390248e-06,
            "step_scale": 1.0,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 0.3670433138065003,
            "cell_principal_stretches": [
              1.0015213227539268,
              1.00001662071467,
              0.9985603725292999
            ],
            "cell_volume_ratio": 1.0000961271813005,
            "cell_rmsd_from_input_A": 0.011771544691336044
          },
          {
            "iteration": 2,
            "reduced_polarization": [
              1.1376470880649154e-07,
              1.5079108098447817e-07,
              -0.4999997592404408
            ],
            "branch_aligned_reduced_polarization": [
              1.1376470880649154e-07,
              1.5079108098447817e-07,
              -0.4999997592404408
            ],
            "target_residual": 3.0601556236552106e-07,
            "energy_eV": -167.450134546524
          }
        ],
        "iterations": 2
      },
      "parent": {
        "candidate_id": "bec_projection_02",
        "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,
          0.0,
          -0.5
        ],
        "formal_class": [
          0.0,
          0.0,
          0.5
        ],
        "target_residual": 3.0601556236552106e-07,
        "parent_symmetrization_rmsd_A": 0.09420322074386638,
        "parent_cell_rmsd_A": 0.011771544691336044,
        "energy_eV": -167.450134546524,
        "reduced_polarization": [
          1.1376470880649154e-07,
          1.5079108098447817e-07,
          -0.4999997592404408
        ],
        "cartesian_polarization_e_A2": [
          1.7498635857787101e-06,
          -1.6322233825510976e-05,
          -0.011853858557587983
        ],
        "ranking_score": 0.5971467189478251
      },
      "branch_status": "awaiting_branch_sampling"
    },
    {
      "orbit_id": 3,
      "formal_class": [
        0.5,
        0.0,
        0.0
      ],
      "formal_classes_in_orbit": [
        [
          0.5,
          0.0,
          0.0
        ]
      ],
      "target_reduced_polarization": [
        0.5,
        0.0,
        0.0
      ],
      "bec_backprojection": {
        "converged_to_target": true,
        "history": [
          {
            "iteration": 0,
            "reduced_polarization": [
              1.1310417829330154e-07,
              0.027610792422356867,
              -2.814474404178354e-06
            ],
            "branch_aligned_reduced_polarization": [
              1.1310417830090458e-07,
              0.027610792422356867,
              -2.814474404178354e-06
            ],
            "target_residual": 0.5007616626319813,
            "energy_eV": -168.93082887422793,
            "max_atomic_step_A": 0.06079692841353599,
            "max_log_strain_component": 0.0008956102999245448,
            "step_scale": 1.0,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 0.3670433138065003,
            "cell_principal_stretches": [
              1.001085623760253,
              1.0000234978654179,
              0.9989861961296821
            ],
            "cell_volume_ratio": 1.0000942188075355,
            "cell_rmsd_from_input_A": 0.006724062966784372
          },
          {
            "iteration": 1,
            "reduced_polarization": [
              0.49838296114178593,
              1.6065791559640943e-06,
              0.00011139982311810747
            ],
            "branch_aligned_reduced_polarization": [
              0.49838296114178593,
              1.6065791559640943e-06,
              0.00011139982311810747
            ],
            "target_residual": 0.0016208723486633965,
            "energy_eV": -168.1556824704127,
            "max_atomic_step_A": 0.00019754367789175865,
            "max_log_strain_component": 2.8305642717395273e-06,
            "step_scale": 1.0,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 0.3670433138065003,
            "cell_principal_stretches": [
              1.001088813934919,
              1.0000235057013542,
              0.9989830018777816
            ],
            "cell_volume_ratio": 1.0000942158543809,
            "cell_rmsd_from_input_A": 0.006743956759454403
          },
          {
            "iteration": 2,
            "reduced_polarization": [
              0.49999997542490504,
              6.263224299902168e-07,
              1.1213384477774574e-08
            ],
            "branch_aligned_reduced_polarization": [
              0.49999997542490504,
              6.263224299902168e-07,
              1.1213384477774574e-08
            ],
            "target_residual": 6.269046670687185e-07,
            "energy_eV": -168.15054282063537
          }
        ],
        "iterations": 2
      },
      "parent": {
        "candidate_id": "bec_projection_03",
        "source": "MACEField_BEC_backprojection",
        "spacegroup": "P1",
        "spacegroup_number": 1,
        "pointgroup": "1",
        "has_inversion": false,
        "is_polar_point_group": true,
        "nonpolar_parent_hypothesis": false,
        "symmetry_tolerance_A": null,
        "target_reduced_polarization": [
          0.5,
          0.0,
          0.0
        ],
        "formal_class": [
          0.5,
          0.0,
          0.0
        ],
        "target_residual": 6.269046670687185e-07,
        "parent_symmetrization_rmsd_A": 0.06777111184665542,
        "parent_cell_rmsd_A": 0.006743956759454403,
        "energy_eV": -168.15054282063537,
        "reduced_polarization": [
          0.49999997542490504,
          6.263224299902168e-07,
          1.1213384477774574e-08
        ],
        "cartesian_polarization_e_A2": [
          0.007970260209765411,
          -7.145959569582467e-06,
          2.2499762491085386e-07
        ],
        "ranking_score": 0.5694583548458532
      },
      "branch_status": "awaiting_branch_sampling"
    },
    {
      "orbit_id": 4,
      "formal_class": [
        0.0,
        0.5,
        0.5
      ],
      "formal_classes_in_orbit": [
        [
          0.0,
          0.5,
          0.5
        ]
      ],
      "target_reduced_polarization": [
        0.0,
        0.5,
        -0.5
      ],
      "bec_backprojection": {
        "converged_to_target": true,
        "history": [
          {
            "iteration": 0,
            "reduced_polarization": [
              1.1310417829330154e-07,
              0.027610792422356867,
              -2.814474404178354e-06
            ],
            "branch_aligned_reduced_polarization": [
              1.1310417829330154e-07,
              0.027610792422356867,
              -2.81447440420024e-06
            ],
            "target_residual": 0.6878580878127141,
            "energy_eV": -168.93082887422793,
            "max_atomic_step_A": 0.12,
            "max_log_strain_component": 0.0011800937507018498,
            "step_scale": 0.8599648251639854,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 0.3670433138065003,
            "cell_principal_stretches": [
              1.0007886070691068,
              0.9997627488220834,
              0.9980646986961234
            ],
            "cell_volume_ratio": 0.9986148008116734,
            "cell_rmsd_from_input_A": 0.011412962007997482
          },
          {
            "iteration": 1,
            "reduced_polarization": [
              0.0016643664506819967,
              0.4328753205028841,
              -0.4303875116064626
            ],
            "branch_aligned_reduced_polarization": [
              0.0016643664506819967,
              0.4328753205028841,
              -0.4303875116064626
            ],
            "target_residual": 0.09671810199550583,
            "energy_eV": -166.67875893472126,
            "max_atomic_step_A": 0.020044128781522876,
            "max_log_strain_component": 0.00019813694881053704,
            "step_scale": 1.0,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 0.3670433138065003,
            "cell_principal_stretches": [
              1.0009220681581799,
              0.9997243398495618,
              0.9977376377748021
            ],
            "cell_volume_ratio": 0.9983823297710794,
            "cell_rmsd_from_input_A": 0.013333010260866744
          },
          {
            "iteration": 2,
            "reduced_polarization": [
              0.00020585439050056382,
              0.49987395808942675,
              -0.4999192105324641
            ],
            "branch_aligned_reduced_polarization": [
              0.00020585439050056382,
              0.49987395808942675,
              -0.4999192105324641
            ],
            "target_residual": 0.0002545378780732874,
            "energy_eV": -165.77011765140858
          }
        ],
        "iterations": 2
      },
      "parent": {
        "candidate_id": "bec_projection_04",
        "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": 0.0002545378780732874,
        "parent_symmetrization_rmsd_A": 0.1296672888085847,
        "parent_cell_rmsd_A": 0.013333010260866744,
        "energy_eV": -165.77011765140858,
        "reduced_polarization": [
          0.00020585439050056382,
          0.49987395808942675,
          -0.4999192105324641
        ],
        "cartesian_polarization_e_A2": [
          1.7541567253646057e-05,
          0.011829391501537504,
          -0.01184425145084193
        ],
        "ranking_score": 0.6335096171299479
      },
      "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": true,
        "history": [
          {
            "iteration": 0,
            "reduced_polarization": [
              1.1310417829330154e-07,
              0.027610792422356867,
              -2.814474404178354e-06
            ],
            "branch_aligned_reduced_polarization": [
              1.1310417830090458e-07,
              0.027610792422356867,
              -2.814474404178354e-06
            ],
            "target_residual": 0.6878600514200468,
            "energy_eV": -168.93082887422793,
            "max_atomic_step_A": 0.11411279076163666,
            "max_log_strain_component": 0.0009288571652985285,
            "step_scale": 1.0,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 0.3670433138065003,
            "cell_principal_stretches": [
              1.0005932440110166,
              0.9996264808038897,
              0.9981703348044537
            ],
            "cell_volume_ratio": 0.9983894364139194,
            "cell_rmsd_from_input_A": 0.009171234311715211
          },
          {
            "iteration": 1,
            "reduced_polarization": [
              0.49725670424509166,
              0.49809886177969476,
              -0.0013983141807082317
            ],
            "branch_aligned_reduced_polarization": [
              0.49725670424509166,
              0.49809886177969476,
              -0.0013983141807082317
            ],
            "target_residual": 0.0036187402061453955,
            "energy_eV": -166.88347597233403,
            "max_atomic_step_A": 0.0006277870127572994,
            "max_log_strain_component": 7.018593174093748e-06,
            "step_scale": 1.0,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 0.3670433138065003,
            "cell_principal_stretches": [
              1.0005992790330498,
              0.9996261673590627,
              0.9981579589327216
            ],
            "cell_volume_ratio": 0.9983827664259302,
            "cell_rmsd_from_input_A": 0.009237262858984394
          },
          {
            "iteration": 2,
            "reduced_polarization": [
              0.5000037227769447,
              0.5000015427792717,
              7.48643621529156e-07
            ],
            "branch_aligned_reduced_polarization": [
              0.5000037227769447,
              0.5000015427792717,
              7.48643621529156e-07
            ],
            "target_residual": 4.098744116585444e-06,
            "energy_eV": -166.86406719108052
          }
        ],
        "iterations": 2
      },
      "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": 4.098744116585444e-06,
        "parent_symmetrization_rmsd_A": 0.11219110820376091,
        "parent_cell_rmsd_A": 0.009237262858984394,
        "energy_eV": -166.86406719108052,
        "reduced_polarization": [
          0.5000037227769447,
          0.5000015427792717,
          7.48643621529156e-07
        ],
        "cartesian_polarization_e_A2": [
          0.00796859489842979,
          0.011841552678536958,
          -1.0361673190108705e-05
        ],
        "ranking_score": 0.6145086214067402
      },
      "branch_status": "awaiting_branch_sampling"
    },
    {
      "orbit_id": 6,
      "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": [
              1.1310417829330154e-07,
              0.027610792422356867,
              -2.814474404178354e-06
            ],
            "branch_aligned_reduced_polarization": [
              1.1310417830090458e-07,
              0.027610792422356867,
              -2.81447440420024e-06
            ],
            "target_residual": 0.7076435743278829,
            "energy_eV": -168.93082887422793,
            "max_atomic_step_A": 0.11454526186898391,
            "max_log_strain_component": 0.0008259736099485752,
            "step_scale": 1.0,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 0.3670433138065003,
            "cell_principal_stretches": [
              1.0009197021246588,
              1.000056157713817,
              0.9991191517614179
            ],
            "cell_volume_ratio": 1.000094203618348,
            "cell_rmsd_from_input_A": 0.007113282058637109
          },
          {
            "iteration": 1,
            "reduced_polarization": [
              0.4982527687833407,
              0.0028716316953458472,
              -0.4977052537709804
            ],
            "branch_aligned_reduced_polarization": [
              0.4982527687833407,
              0.0028716316953458472,
              -0.4977052537709804
            ],
            "target_residual": 0.004070005623311019,
            "energy_eV": -166.6538173581569,
            "max_atomic_step_A": 0.0007459412616963907,
            "max_log_strain_component": 5.775551467016534e-06,
            "step_scale": 1.0,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 0.3670433138065003,
            "cell_principal_stretches": [
              1.0009263277257021,
              1.0000620458645582,
              0.9991166690036316
            ],
            "cell_volume_ratio": 1.0001042269568992,
            "cell_rmsd_from_input_A": 0.007152447752607323
          },
          {
            "iteration": 2,
            "reduced_polarization": [
              0.49999852707245307,
              8.310935530116824e-07,
              -0.49999932727154095
            ],
            "branch_aligned_reduced_polarization": [
              0.49999852707245307,
              8.310935530116824e-07,
              -0.49999932727154095
            ],
            "target_residual": 1.820108686859215e-06,
            "energy_eV": -166.63498119199258
          }
        ],
        "iterations": 2
      },
      "parent": {
        "candidate_id": "bec_projection_06",
        "source": "MACEField_BEC_backprojection",
        "spacegroup": "P1",
        "spacegroup_number": 1,
        "pointgroup": "1",
        "has_inversion": false,
        "is_polar_point_group": true,
        "nonpolar_parent_hypothesis": false,
        "symmetry_tolerance_A": null,
        "target_reduced_polarization": [
          0.5,
          0.0,
          -0.5
        ],
        "formal_class": [
          0.5,
          0.0,
          0.5
        ],
        "target_residual": 1.820108686859215e-06,
        "parent_symmetrization_rmsd_A": 0.11690001641107371,
        "parent_cell_rmsd_A": 0.007152447752607323,
        "energy_eV": -166.63498119199258,
        "reduced_polarization": [
          0.49999852707245307,
          8.310935530116824e-07,
          -0.49999932727154095
        ],
        "cartesian_polarization_e_A2": [
          0.007971907801662874,
          -1.2675343089829138e-05,
          -0.011853555121512217
        ],
        "ranking_score": 0.6186917685665992
      },
      "branch_status": "awaiting_branch_sampling"
    },
    {
      "orbit_id": 7,
      "formal_class": [
        0.5,
        0.5,
        0.5
      ],
      "formal_classes_in_orbit": [
        [
          0.5,
          0.5,
          0.5
        ]
      ],
      "target_reduced_polarization": [
        0.5,
        0.5,
        -0.5
      ],
      "bec_backprojection": {
        "converged_to_target": true,
        "history": [
          {
            "iteration": 0,
            "reduced_polarization": [
              1.1310417829330154e-07,
              0.027610792422356867,
              -2.814474404178354e-06
            ],
            "branch_aligned_reduced_polarization": [
              1.1310417830090458e-07,
              0.027610792422356867,
              -2.81447440420024e-06
            ],
            "target_residual": 0.850381464911592,
            "energy_eV": -168.93082887422793,
            "max_atomic_step_A": 0.12,
            "max_log_strain_component": 0.0007276774676372289,
            "step_scale": 0.7834102865538963,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 0.3670433138065003,
            "cell_principal_stretches": [
              1.0005099149527759,
              0.9994071153536112,
              0.9988212096805898
            ],
            "cell_volume_ratio": 0.9987380358264748,
            "cell_rmsd_from_input_A": 0.007415661871854443
          },
          {
            "iteration": 1,
            "reduced_polarization": [
              0.3914330637873029,
              0.39774260351608,
              -0.3931602741506222
            ],
            "branch_aligned_reduced_polarization": [
              0.3914330637873029,
              0.39774260351608,
              -0.3931602741506222
            ],
            "target_residual": 0.1834613904718147,
            "energy_eV": -166.52632297569824,
            "max_atomic_step_A": 0.03520390155759031,
            "max_log_strain_component": 0.00020161948674239614,
            "step_scale": 1.0,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 0.3670433138065003,
            "cell_principal_stretches": [
              1.0006477721137963,
              0.9992412262216153,
              0.9984999879715145
            ],
            "cell_volume_ratio": 0.9983886620355383,
            "cell_rmsd_from_input_A": 0.009433719882538064
          },
          {
            "iteration": 2,
            "reduced_polarization": [
              0.500565458334183,
              0.49989541985467345,
              -0.49994902470250385
            ],
            "branch_aligned_reduced_polarization": [
              0.500565458334183,
              0.49989541985467345,
              -0.49994902470250385
            ],
            "target_residual": 0.0005773028801663222,
            "energy_eV": -164.79852629554756
          }
        ],
        "iterations": 2
      },
      "parent": {
        "candidate_id": "bec_projection_07",
        "source": "MACEField_BEC_backprojection",
        "spacegroup": "P1",
        "spacegroup_number": 1,
        "pointgroup": "1",
        "has_inversion": false,
        "is_polar_point_group": true,
        "nonpolar_parent_hypothesis": false,
        "symmetry_tolerance_A": null,
        "target_reduced_polarization": [
          0.5,
          0.5,
          -0.5
        ],
        "formal_class": [
          0.5,
          0.5,
          0.5
        ],
        "target_residual": 0.0005773028801663222,
        "parent_symmetrization_rmsd_A": 0.14618073451456756,
        "parent_cell_rmsd_A": 0.009433719882538064,
        "energy_eV": -164.79852629554756,
        "reduced_polarization": [
          0.500565458334183,
          0.49989541985467345,
          -0.49994902470250385
        ],
        "cartesian_polarization_e_A2": [
          0.007991728191020545,
          0.01183356669265908,
          -0.01185534486108565
        ],
        "ranking_score": 0.6496937702455348
      },
      "branch_status": "awaiting_branch_sampling"
    }
  ],
  "sampled_polarization_branches": [
    {
      "orbit_id": 0,
      "candidate_id": "inversion_parent_endpoint_00",
      "formal_class": [
        0.0,
        0.0,
        0.0
      ],
      "construction": "MACEField-BEC-parent plus variable-cell P-N-P path and symmetric log-strain continuation beyond both polar endpoints",
      "geometry_diagnostics": {
        "collision_aware": false,
        "permutations_tested": 1,
        "selected_order": [
          0,
          1,
          2,
          3,
          4,
          5,
          6,
          7,
          8,
          9,
          10,
          11,
          12,
          13,
          14,
          15,
          16,
          17,
          18,
          19,
          20,
          21,
          22,
          23
        ],
        "endpoint_rmsd_A": 0.4831736928107981,
        "minimum_distance_A_by_image": [
          1.6149949741291294,
          1.6149949268762975,
          1.6149948859253604,
          1.6102862476577735,
          1.5817728074711852,
          1.559769062349523,
          1.5445532492012286,
          1.536327064697277,
          1.5352028719920232
        ],
        "minimum_distance_A": 1.5352028719920232,
        "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": [
          334.3910918673359,
          334.3910918673359,
          334.3910918673359,
          334.3910918673359,
          334.3910918673359,
          334.3910918673359,
          334.3910918673359,
          334.3910918673359,
          334.3910918673359
        ],
        "cell_deformation_log_strain_norm": 0.0
      },
      "parent_reduced_polarization": [
        2.4858763892847465e-15,
        6.013774933110639e-16,
        -1.3137387746607351e-15
      ],
      "incoming": {
        "reached": true,
        "construction": "variable_cell_linear_interpolation",
        "continuation_fractions": [
          0.0,
          0.125,
          0.25,
          0.375,
          0.5,
          0.625,
          0.75,
          0.875,
          1.0
        ],
        "energies_eV": [
          -168.93082887422796,
          -168.56184981965447,
          -167.69454608535105,
          -166.55001249669078,
          -165.3075731277825,
          -164.13269822550902,
          -163.18063613342935,
          -162.57743735839404,
          -162.37622735832988
        ],
        "cartesian_polarizations_e_A2": [
          [
            1.8148191648879607e-09,
            0.0006533306975140298,
            -6.672744949463752e-08
          ],
          [
            2.986161508910642e-09,
            0.0014285332197285323,
            -5.7255635461204714e-08
          ],
          [
            4.292404590700929e-09,
            0.0022258271270576635,
            -4.706855042978449e-08
          ],
          [
            5.827729000199205e-09,
            0.00301227577918306,
            -3.550147853986896e-08
          ],
          [
            7.80844527801707e-09,
            0.0036391356055229702,
            -2.2526276635963588e-08
          ],
          [
            9.226788946491755e-09,
            0.0038340469055031016,
            -9.5303827950327e-09
          ],
          [
            8.868118949887625e-09,
            0.0032966117692049142,
            4.776047940227528e-10
          ],
          [
            5.550655718223897e-09,
            0.0019212441696999018,
            3.5959745337182253e-09
          ],
          [
            3.9634092171692256e-17,
            1.4229884139653387e-17,
            -3.11470012302147e-17
          ]
        ],
        "raw_reduced_polarization": [
          [
            1.1310417596453431e-07,
            0.027610792422356745,
            -2.814474404370032e-06
          ],
          [
            1.8668651839238606e-07,
            0.06037208162489325,
            -2.4149659807460806e-06
          ],
          [
            2.6873901053447193e-07,
            0.09406698783187066,
            -1.985288384895853e-06
          ],
          [
            3.651768942119698e-07,
            0.12730355633737897,
            -1.4974047925476753e-06
          ],
          [
            4.895695012401657e-07,
            0.153795647722101,
            -9.501281631148398e-07
          ],
          [
            5.786850667866362e-07,
            0.16203290867585796,
            -4.019787755056286e-07
          ],
          [
            5.562966557936849e-07,
            0.13932004665165834,
            2.0144730217651805e-08
          ],
          [
            3.4822883176430063e-07,
            0.08119482853644418,
            1.5167338719771918e-07
          ],
          [
            2.4858763892847465e-15,
            6.013774933110639e-16,
            -1.3137387746607351e-15
          ]
        ],
        "unwrapped_reduced_polarization": [
          [
            1.1310417596453431e-07,
            0.027610792422356745,
            -2.814474404370032e-06
          ],
          [
            1.8668651839238606e-07,
            0.06037208162489324,
            -2.4149659807460806e-06
          ],
          [
            2.6873901053447193e-07,
            0.09406698783187066,
            -1.985288384895853e-06
          ],
          [
            3.651768942119698e-07,
            0.12730355633737897,
            -1.4974047925476753e-06
          ],
          [
            4.895695012401657e-07,
            0.153795647722101,
            -9.501281631148398e-07
          ],
          [
            5.786850667866362e-07,
            0.16203290867585796,
            -4.019787755056286e-07
          ],
          [
            5.562966557936849e-07,
            0.13932004665165834,
            2.0144730217651812e-08
          ],
          [
            3.4822883176430063e-07,
            0.08119482853644418,
            1.5167338719771918e-07
          ],
          [
            2.4858763699479793e-15,
            5.967448757360216e-16,
            -1.313738783829e-15
          ]
        ],
        "berry_integer_shifts": [
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ]
        ],
        "folded_reduced_polarization": [
          [
            1.1310417591392508e-07,
            0.027610792422356756,
            -2.8144744043667735e-06
          ],
          [
            1.866865183552946e-07,
            0.06037208162489327,
            -2.4149659807459756e-06
          ],
          [
            2.6873901048940496e-07,
            0.09406698783187062,
            -1.9852883849091896e-06
          ],
          [
            3.65176894168151e-07,
            0.127303556337379,
            -1.4974047925497835e-06
          ],
          [
            4.895695012718804e-07,
            0.15379564772210097,
            -9.501281630908132e-07
          ],
          [
            5.78685066754403e-07,
            0.16203290867585796,
            -4.0197877548830974e-07
          ],
          [
            5.562966557404181e-07,
            0.1393200466516583,
            2.0144730217275253e-08
          ],
          [
            3.4822883177021424e-07,
            0.08119482853644422,
            1.5167338718313772e-07
          ],
          [
            2.4424906541753444e-15,
            5.551115123125783e-16,
            -1.3322676295501878e-15
          ]
        ]
      },
      "reflected": {
        "reached": true,
        "construction": "reflect_displacements_about_reconstructed_parent",
        "energies_eV": [
          -162.37622735832988,
          -162.57743735839404,
          -163.18063613342935,
          -164.132698225509,
          -165.3075731277825,
          -166.55001249669075,
          -167.69454608535102,
          -168.5618498196545,
          -168.93082887422798
        ],
        "cartesian_polarizations_e_A2": [
          [
            -4.76024122732262e-17,
            -1.0416918466067807e-17,
            -3.820228465344788e-17
          ],
          [
            -5.550655669978209e-09,
            -0.0019212441696999356,
            -3.595974481166739e-09
          ],
          [
            -8.868118951402436e-09,
            -0.0032966117692048826,
            -4.776049330222116e-10
          ],
          [
            -9.226789041281563e-09,
            -0.0038340469055031753,
            9.530382773119821e-09
          ],
          [
            -7.808445243840448e-09,
            -0.0036391356055229564,
            2.252627676024033e-08
          ],
          [
            -5.827729017277141e-09,
            -0.003012275779183027,
            3.550147844898031e-08
          ],
          [
            -4.29240462657912e-09,
            -0.002225827127057734,
            4.706855040277728e-08
          ],
          [
            -2.98616154259962e-09,
            -0.0014285332197284445,
            5.7255635378076874e-08
          ],
          [
            -1.8148192797542002e-09,
            -0.0006533306975139606,
            6.672744951728704e-08
          ]
        ],
        "raw_reduced_polarization": [
          [
            -2.9864912256391634e-15,
            -4.4023551096194537e-16,
            -1.6113211753167311e-15
          ],
          [
            -3.4822882873729837e-07,
            -0.0811948285364456,
            -1.516733849811679e-07
          ],
          [
            -5.562966558902459e-07,
            -0.13932004665165698,
            -2.0144736080462718e-08
          ],
          [
            -5.786850727329821e-07,
            -0.16203290867586106,
            4.0197877458137266e-07
          ],
          [
            -4.895694990949133e-07,
            -0.15379564772210041,
            9.501281683566664e-07
          ],
          [
            -3.651768952842632e-07,
            -0.12730355633737758,
            1.4974047887141138e-06
          ],
          [
            -2.6873901278538655e-07,
            -0.09406698783187364,
            1.9852883837567254e-06
          ],
          [
            -1.866865205065936e-07,
            -0.06037208162488953,
            2.4149659772398597e-06
          ],
          [
            -1.131041831697687e-07,
            -0.02761079242235382,
            2.814474405325359e-06
          ]
        ],
        "unwrapped_reduced_polarization": [
          [
            -2.9864912256391634e-15,
            -4.4023551096194537e-16,
            -1.6113211753167311e-15
          ],
          [
            -3.4822882873729837e-07,
            -0.0811948285364456,
            -1.516733849811679e-07
          ],
          [
            -5.562966558902459e-07,
            -0.13932004665165698,
            -2.0144736080462725e-08
          ],
          [
            -5.786850727329821e-07,
            -0.16203290867586106,
            4.0197877458137266e-07
          ],
          [
            -4.895694990949133e-07,
            -0.15379564772210041,
            9.501281683566664e-07
          ],
          [
            -3.651768952842632e-07,
            -0.12730355633737758,
            1.4974047887141138e-06
          ],
          [
            -2.6873901278538655e-07,
            -0.09406698783187364,
            1.9852883837567254e-06
          ],
          [
            -1.866865205065936e-07,
            -0.06037208162488953,
            2.4149659772398597e-06
          ],
          [
            -1.131041831697687e-07,
            -0.02761079242235382,
            2.814474405325359e-06
          ]
        ],
        "gauge_integer_shift": [
          0,
          0,
          0
        ],
        "expected_opposite_endpoint_reduced_polarization": [
          -1.1310417099278154e-07,
          -0.02761079242235554,
          2.814474401742555e-06
        ],
        "actual_opposite_endpoint_branch_residual": 1.2809247112382252e-14
      },
      "pnp_branch": {
        "construction": "incoming_path_concatenated_with_parent_reflection",
        "reduced_polarization": [
          [
            1.1310417596453431e-07,
            0.027610792422356745,
            -2.814474404370032e-06
          ],
          [
            1.8668651839238606e-07,
            0.06037208162489325,
            -2.4149659807460806e-06
          ],
          [
            2.6873901053447193e-07,
            0.09406698783187066,
            -1.985288384895853e-06
          ],
          [
            3.651768942119698e-07,
            0.12730355633737897,
            -1.4974047925476753e-06
          ],
          [
            4.895695012401657e-07,
            0.153795647722101,
            -9.501281631148398e-07
          ],
          [
            5.786850667866362e-07,
            0.16203290867585796,
            -4.019787755056286e-07
          ],
          [
            5.562966557936849e-07,
            0.13932004665165834,
            2.0144730217651805e-08
          ],
          [
            3.4822883176430063e-07,
            0.08119482853644418,
            1.5167338719771918e-07
          ],
          [
            2.4858763892847465e-15,
            6.013774933110639e-16,
            -1.3137387746607351e-15
          ],
          [
            -3.4822882873729837e-07,
            -0.0811948285364456,
            -1.516733849811679e-07
          ],
          [
            -5.562966558902459e-07,
            -0.13932004665165698,
            -2.0144736080462718e-08
          ],
          [
            -5.786850727329821e-07,
            -0.16203290867586106,
            4.0197877458137266e-07
          ],
          [
            -4.895694990949133e-07,
            -0.15379564772210041,
            9.501281683566664e-07
          ],
          [
            -3.651768952842632e-07,
            -0.12730355633737758,
            1.4974047887141138e-06
          ],
          [
            -2.6873901278538655e-07,
            -0.09406698783187364,
            1.9852883837567254e-06
          ],
          [
            -1.866865205065936e-07,
            -0.06037208162488953,
            2.4149659772398597e-06
          ],
          [
            -1.131041831697687e-07,
            -0.02761079242235382,
            2.814474405325359e-06
          ]
        ],
        "unwrapped_reduced_polarization": [
          [
            1.1310417596453431e-07,
            0.027610792422356745,
            -2.814474404370032e-06
          ],
          [
            1.8668651839238606e-07,
            0.06037208162489324,
            -2.4149659807460806e-06
          ],
          [
            2.6873901053447193e-07,
            0.09406698783187066,
            -1.985288384895853e-06
          ],
          [
            3.651768942119698e-07,
            0.12730355633737897,
            -1.4974047925476753e-06
          ],
          [
            4.895695012401657e-07,
            0.153795647722101,
            -9.501281631148398e-07
          ],
          [
            5.786850667866362e-07,
            0.16203290867585796,
            -4.019787755056286e-07
          ],
          [
            5.562966557936849e-07,
            0.13932004665165834,
            2.0144730217651812e-08
          ],
          [
            3.4822883176430063e-07,
            0.08119482853644418,
            1.5167338719771918e-07
          ],
          [
            2.4858763699479793e-15,
            5.967448757360216e-16,
            -1.313738783829e-15
          ],
          [
            -3.4822882873729837e-07,
            -0.0811948285364456,
            -1.516733849811679e-07
          ],
          [
            -5.562966558902459e-07,
            -0.13932004665165698,
            -2.0144736080462725e-08
          ],
          [
            -5.786850727329821e-07,
            -0.16203290867586106,
            4.0197877458137266e-07
          ],
          [
            -4.895694990949133e-07,
            -0.15379564772210041,
            9.501281683566664e-07
          ],
          [
            -3.651768952842632e-07,
            -0.12730355633737758,
            1.4974047887141138e-06
          ],
          [
            -2.6873901278538655e-07,
            -0.09406698783187364,
            1.9852883837567254e-06
          ],
          [
            -1.866865205065936e-07,
            -0.06037208162488953,
            2.4149659772398597e-06
          ],
          [
            -1.131041831697687e-07,
            -0.02761079242235382,
            2.814474405325359e-06
          ]
        ],
        "berry_integer_shifts": [
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ]
        ],
        "folded_reduced_polarization": [
          [
            1.1310417591392508e-07,
            0.027610792422356756,
            -2.8144744043667735e-06
          ],
          [
            1.866865183552946e-07,
            0.06037208162489327,
            -2.4149659807459756e-06
          ],
          [
            2.6873901048940496e-07,
            0.09406698783187062,
            -1.9852883849091896e-06
          ],
          [
            3.65176894168151e-07,
            0.127303556337379,
            -1.4974047925497835e-06
          ],
          [
            4.895695012718804e-07,
            0.15379564772210097,
            -9.501281630908132e-07
          ],
          [
            5.78685066754403e-07,
            0.16203290867585796,
            -4.0197877548830974e-07
          ],
          [
            5.562966557404181e-07,
            0.1393200466516583,
            2.0144730217275253e-08
          ],
          [
            3.4822883177021424e-07,
            0.08119482853644422,
            1.5167338718313772e-07
          ],
          [
            2.4424906541753444e-15,
            5.551115123125783e-16,
            -1.3322676295501878e-15
          ],
          [
            -3.482288287171009e-07,
            -0.0811948285364456,
            -1.5167338496269167e-07
          ],
          [
            -5.562966559069515e-07,
            -0.13932004665165698,
            -2.0144736101457283e-08
          ],
          [
            -5.786850727496073e-07,
            -0.16203290867586106,
            4.019787746001313e-07
          ],
          [
            -4.895694991069455e-07,
            -0.15379564772210041,
            9.501281683643725e-07
          ],
          [
            -3.6517689527837405e-07,
            -0.12730355633737755,
            1.497404788719514e-06
          ],
          [
            -2.6873901276536216e-07,
            -0.09406698783187362,
            1.9852883837989665e-06
          ],
          [
            -1.866865205202295e-07,
            -0.06037208162488955,
            2.414965977193262e-06
          ],
          [
            -1.1310418318588589e-07,
            -0.027610792422353814,
            2.814474405310463e-06
          ]
        ]
      },
      "incoming_structure_ids": [
        "incoming_00_000",
        "incoming_00_001",
        "incoming_00_002",
        "incoming_00_003",
        "incoming_00_004",
        "incoming_00_005",
        "incoming_00_006",
        "incoming_00_007",
        "incoming_00_008"
      ],
      "reflected_structure_ids": [
        "reflected_00_001",
        "reflected_00_002",
        "reflected_00_003",
        "reflected_00_004",
        "reflected_00_005",
        "reflected_00_006",
        "reflected_00_007",
        "reflected_00_008"
      ],
      "positive_extension_structure_ids": [
        "extension_plus_00_000",
        "extension_plus_00_001",
        "extension_plus_00_002",
        "extension_plus_00_003"
      ],
      "negative_extension_structure_ids": [
        "extension_minus_00_000",
        "extension_minus_00_001",
        "extension_minus_00_002",
        "extension_minus_00_003"
      ],
      "extension": {
        "enabled": true,
        "fraction_beyond_polar_endpoint": 0.35,
        "images_per_side": 4,
        "construction": "continue fractional atomic displacements and symmetric log strain beyond +P; reflect these structures about N for the -P side",
        "positive_path_coordinates": [
          1.35,
          1.2625,
          1.175,
          1.0875
        ],
        "negative_path_coordinates": [
          -1.0875,
          -1.175,
          -1.2625,
          -1.35
        ]
      },
      "branch_coordinates": [
        1.35,
        1.2625,
        1.175,
        1.0875,
        1.0,
        0.875,
        0.75,
        0.625,
        0.5,
        0.375,
        0.25,
        0.125,
        0.0,
        -0.125,
        -0.25,
        -0.375,
        -0.5,
        -0.625,
        -0.75,
        -0.875,
        -1.0,
        -1.0875,
        -1.175,
        -1.2625,
        -1.35
      ],
      "parent": {
        "candidate_id": "inversion_parent_endpoint_00",
        "source": "same_species_inversion_center_projection_from_endpoint",
        "spacegroup": "P2_1/m",
        "spacegroup_number": 11,
        "pointgroup": "2/m",
        "has_inversion": true,
        "is_polar_point_group": false,
        "nonpolar_parent_hypothesis": true,
        "symmetry_tolerance_A": null,
        "target_reduced_polarization": [
          0.0,
          0.0,
          0.0
        ],
        "formal_class": [
          0.0,
          0.0,
          0.0
        ],
        "target_residual": 3.141425420828893e-15,
        "parent_symmetrization_rmsd_A": 0.4831736928107981,
        "parent_cell_rmsd_A": 0.0,
        "energy_eV": -162.37622735832988,
        "reduced_polarization": [
          2.2067989841903842e-16,
          2.1139197194696598e-15,
          -2.3132655439229333e-15
        ],
        "cartesian_polarization_e_A2": [
          3.527641711616589e-18,
          5.0019884387363447e-17,
          -5.4844453198839076e-17
        ],
        "ranking_score": 0.48317369281080436
      }
    }
  ],
  "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": 49,
      "full_response": 15,
      "energy_polarization": 34
    },
    "model_evaluations_for_recovery_and_path_properties": {
      "total": 74,
      "full_response": 40,
      "energy_polarization": 34
    },
    "elapsed_seconds": 514.8731985529885
  }
}
