{
  "schema": "ferrofinder.endpoint_parent_recovery.v4_variable_cell",
  "status": "complete",
  "input_atom_count": 32,
  "input_formula": "Cu6S16Ta4Tl6",
  "input_spacegroup": "C2",
  "input_pointgroup": "2",
  "input_is_polar_point_group": true,
  "input_energy_eV": -167.01075439031533,
  "input_cartesian_polarization_e_A2": [
    2.7689344519303613e-11,
    -8.334537114474861e-05,
    -2.0881567721612543e-11
  ],
  "input_reduced_polarization": [
    1.0508188435288705e-09,
    -0.012297970264981235,
    -2.3217809187786937e-09
  ],
  "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": "C2/m",
      "spacegroup_number": 12,
      "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": 3.386229083661536e-15,
      "parent_symmetrization_rmsd_A": 1.1327030383761427,
      "parent_cell_rmsd_A": 0.0,
      "energy_eV": -119.1854332365001,
      "reduced_polarization": [
        1.0447716377930738e-15,
        1.0809500967933886e-15,
        -3.0342291475992365e-15
      ],
      "cartesian_polarization_e_A2": [
        2.826497926149811e-17,
        7.325776942455015e-18,
        -2.7289164501279724e-17
      ],
      "ranking_score": 1.1327030383761496
    },
    {
      "candidate_id": "inversion_parent_endpoint_01",
      "source": "same_species_inversion_center_projection_from_endpoint",
      "spacegroup": "C2/m",
      "spacegroup_number": 12,
      "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": 2.8327859613398124e-15,
      "parent_symmetrization_rmsd_A": 1.1888425510306118,
      "parent_cell_rmsd_A": 0.0,
      "energy_eV": -118.52603778509966,
      "reduced_polarization": [
        -2.079183424718925e-15,
        1.9239149219190174e-15,
        -1.4965371874718797e-17
      ],
      "cartesian_polarization_e_A2": [
        -5.011986501190647e-17,
        1.3038688479745257e-17,
        -1.345951393404672e-19
      ],
      "ranking_score": 1.1888425510306175
    },
    {
      "candidate_id": "bec_projection_00",
      "source": "MACEField_BEC_backprojection",
      "spacegroup": "C2",
      "spacegroup_number": 5,
      "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": 2.9410475474677804e-06,
      "parent_symmetrization_rmsd_A": 0.002028595265736744,
      "parent_cell_rmsd_A": 0.005993590614361183,
      "energy_eV": -167.00712302985545,
      "reduced_polarization": [
        -1.901687901680667e-12,
        -2.941047547467164e-06,
        1.0027300557962645e-13
      ],
      "cartesian_polarization_e_A2": [
        -4.5943669482393883e-14,
        -1.993096176279427e-08,
        8.892418087335407e-16
      ],
      "ranking_score": 0.503532875014422
    },
    {
      "candidate_id": "inversion_parent_bec_00_00",
      "source": "same_species_inversion_center_projection_after_BEC",
      "spacegroup": "C2/m",
      "spacegroup_number": 12,
      "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": 3.5818989769176154e-15,
      "parent_symmetrization_rmsd_A": 1.1327030923817416,
      "parent_cell_rmsd_A": 0.005993590614361183,
      "energy_eV": -119.08767770029883,
      "reduced_polarization": [
        -2.7690049539000176e-15,
        2.1741731570452073e-15,
        -6.599870675283717e-16
      ],
      "cartesian_polarization_e_A2": [
        -6.607598627959987e-17,
        1.4733988930052076e-17,
        -5.954913223772493e-18
      ],
      "ranking_score": 1.134201490035339
    },
    {
      "candidate_id": "inversion_parent_bec_00_01",
      "source": "same_species_inversion_center_projection_after_BEC",
      "spacegroup": "C2/m",
      "spacegroup_number": 12,
      "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": 1.8306365476493033e-15,
      "parent_symmetrization_rmsd_A": 1.1888426024859586,
      "parent_cell_rmsd_A": 0.005993590614361183,
      "energy_eV": -118.63953486661795,
      "reduced_polarization": [
        -1.5670428146115566e-15,
        -6.304768029312993e-16,
        -7.0576624156244435e-16
      ],
      "cartesian_polarization_e_A2": [
        -3.7058400655284755e-17,
        -4.272630373250901e-18,
        -6.358636154197747e-18
      ],
      "ranking_score": 1.1903410001395525
    },
    {
      "candidate_id": "bec_projection_01",
      "source": "MACEField_BEC_backprojection",
      "spacegroup": "C2",
      "spacegroup_number": 5,
      "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": 9.184284927299464e-06,
      "parent_symmetrization_rmsd_A": 0.0809594230522663,
      "parent_cell_rmsd_A": 0.2418955746543413,
      "energy_eV": -166.13775920653148,
      "reduced_polarization": [
        2.96057667536036e-13,
        -0.4999908157150727,
        1.116380547005316e-12
      ],
      "cartesian_polarization_e_A2": [
        -1.2199601239067056e-12,
        -0.003395298500228731,
        1.7420352761417598e-14
      ],
      "ranking_score": 0.6414516852857062
    },
    {
      "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": 0.0008139527798089765,
      "parent_symmetrization_rmsd_A": 0.07188815929067191,
      "parent_cell_rmsd_A": 0.19149414752105387,
      "energy_eV": -165.31750198016985,
      "reduced_polarization": [
        7.409064130515776e-05,
        -0.000681169493069481,
        -0.4995606392981374
      ],
      "cartesian_polarization_e_A2": [
        0.0005000366347439519,
        0.00010893011435004188,
        -0.004496446854180267
      ],
      "ranking_score": 0.6213896017305534
    },
    {
      "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": 0.011150243027013177,
      "parent_symmetrization_rmsd_A": 0.2670516559888016,
      "parent_cell_rmsd_A": 0.637444540703041,
      "energy_eV": -150.30416378888071,
      "reduced_polarization": [
        0.49911623846388997,
        0.00850981663423097,
        -0.0071505178805814015
      ],
      "cartesian_polarization_e_A2": [
        0.012292085509004248,
        -0.0008388216311576007,
        -5.4868405915421925e-05
      ],
      "ranking_score": 0.9487132772185882
    },
    {
      "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": 0.0005005092806825083,
      "parent_symmetrization_rmsd_A": 0.107694417011009,
      "parent_cell_rmsd_A": 0.3163942209370138,
      "energy_eV": -163.911403451044,
      "reduced_polarization": [
        -1.342039107345301e-05,
        -0.4996053596675783,
        -0.499692447661074
      ],
      "cartesian_polarization_e_A2": [
        0.0006379434162914039,
        -0.0032902660300104503,
        -0.004390385780517366
      ],
      "ranking_score": 0.6877939908066275
    },
    {
      "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": 0.12671273383576748,
      "parent_symmetrization_rmsd_A": 0.26526674101870323,
      "parent_cell_rmsd_A": 0.5521694130251474,
      "energy_eV": -151.10607575207962,
      "reduced_polarization": [
        0.43854208803904426,
        -0.3894838337215102,
        -0.008075825941577651
      ],
      "cartesian_polarization_e_A2": [
        0.0112288461033656,
        -0.003439377328696932,
        -0.0003045833019944242
      ],
      "ranking_score": 1.156734561946525
    },
    {
      "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": 0.10752880272178421,
      "parent_symmetrization_rmsd_A": 0.22488727747157652,
      "parent_cell_rmsd_A": 0.6657765566986784,
      "energy_eV": -155.22147631623045,
      "reduced_polarization": [
        0.43374400056963514,
        0.03914269524266729,
        -0.42489716807334393
      ],
      "cartesian_polarization_e_A2": [
        0.011146805404750326,
        -0.0006823386788395979,
        -0.003840822322356028
      ],
      "ranking_score": 1.1063890220898145
    },
    {
      "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": 0.2424194761189913,
      "parent_symmetrization_rmsd_A": 0.22307689538266987,
      "parent_cell_rmsd_A": 0.5780537789661694,
      "energy_eV": -157.07289520354453,
      "reduced_polarization": [
        0.3828191808522088,
        -0.32119275688682836,
        -0.38570289664245216
      ],
      "cartesian_polarization_e_A2": [
        0.010233975327739182,
        -0.0030433646424804207,
        -0.0036425164508185584
      ],
      "ranking_score": 1.3524292923621948
    }
  ],
  "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": [
              1.0508188435288705e-09,
              -0.012297970264981235,
              -2.3217809187786937e-09
            ],
            "branch_aligned_reduced_polarization": [
              1.0508188435288705e-09,
              -0.012297970264981235,
              -2.3217809187786937e-09
            ],
            "target_residual": 0.0122979702649815,
            "energy_eV": -167.01075439031533,
            "max_atomic_step_A": 0.0018447600323088812,
            "max_log_strain_component": 0.0002876384729643695,
            "step_scale": 1.0,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 5.668130719880383,
            "cell_principal_stretches": [
              1.0004073247313323,
              1.0001044926042078,
              0.999643101201394
            ],
            "cell_volume_ratio": 1.0001547784171734,
            "cell_rmsd_from_input_A": 0.005993590614361183
          },
          {
            "iteration": 1,
            "reduced_polarization": [
              -1.901687901680667e-12,
              -2.941047547467164e-06,
              1.0027300557962645e-13
            ],
            "branch_aligned_reduced_polarization": [
              -1.901687901680667e-12,
              -2.941047547467164e-06,
              1.0027300557962645e-13
            ],
            "target_residual": 2.9410475474677804e-06,
            "energy_eV": -167.00712302985545
          }
        ],
        "iterations": 1
      },
      "parent": {
        "candidate_id": "bec_projection_00",
        "source": "MACEField_BEC_backprojection",
        "spacegroup": "C2",
        "spacegroup_number": 5,
        "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": 2.9410475474677804e-06,
        "parent_symmetrization_rmsd_A": 0.002028595265736744,
        "parent_cell_rmsd_A": 0.005993590614361183,
        "energy_eV": -167.00712302985545,
        "reduced_polarization": [
          -1.901687901680667e-12,
          -2.941047547467164e-06,
          1.0027300557962645e-13
        ],
        "cartesian_polarization_e_A2": [
          -4.5943669482393883e-14,
          -1.993096176279427e-08,
          8.892418087335407e-16
        ],
        "ranking_score": 0.503532875014422
      },
      "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": [
          -167.01075439031536,
          -167.0103662088925,
          -167.00995923795202,
          -167.00953348106836,
          -167.00908894177644,
          -167.00862562357193,
          -167.0081435299117,
          -167.00764266421336,
          -167.00712302985545
        ],
        "cartesian_polarizations_e_A2": [
          [
            2.768933637629768e-11,
            -8.334537114474963e-05,
            -2.088156519795368e-11
          ],
          [
            2.4221237293322043e-11,
            -7.292771797053017e-05,
            -1.8270620092366643e-11
          ],
          [
            2.0753400514638002e-11,
            -6.251061387394133e-05,
            -1.5659868328350532e-11
          ],
          [
            1.728615980548935e-11,
            -5.2094066196157665e-05,
            -1.3049271439286743e-11
          ],
          [
            1.381895317665899e-11,
            -4.167808227694755e-05,
            -1.0438831151896259e-11
          ],
          [
            1.0352285582178639e-11,
            -3.1262669456199026e-05,
            -7.828646823683365e-12
          ],
          [
            6.885815701001694e-12,
            -2.0847835071918657e-05,
            -5.218553280011391e-12
          ],
          [
            3.419731462205488e-12,
            -1.0433586461683034e-05,
            -2.6087255189960587e-12
          ],
          [
            -4.6028518584938256e-14,
            -1.993096174995924e-08,
            8.88510060922145e-16
          ]
        ],
        "raw_reduced_polarization": [
          [
            1.050818517608761e-09,
            -0.012297970264981384,
            -2.321780638177971e-09
          ],
          [
            9.193556418699434e-10,
            -0.010760868078191687,
            -2.0315369541886123e-09
          ],
          [
            7.878531727653761e-10,
            -0.009223827589551373,
            -1.741296945096231e-09
          ],
          [
            6.563251340250573e-10,
            -0.007686849883648389,
            -1.4510563333862956e-09
          ],
          [
            5.247482091036166e-10,
            -0.006149936044890451,
            -1.1608153018768224e-09
          ],
          [
            3.9314288007123944e-10,
            -0.004613087157730181,
            -8.705848997629341e-10
          ],
          [
            2.614957602754502e-10,
            -0.0030763043063698186,
            -5.803467538222813e-10
          ],
          [
            1.2981383057421652e-10,
            -0.0015395885749753938,
            -2.9012031983333976e-10
          ],
          [
            -1.9052114145723965e-12,
            -2.9410475455732053e-06,
            1.0019427463423541e-13
          ]
        ],
        "unwrapped_reduced_polarization": [
          [
            1.050818517608761e-09,
            -0.012297970264981384,
            -2.321780638177971e-09
          ],
          [
            9.193556418699434e-10,
            -0.010760868078191687,
            -2.0315369541886123e-09
          ],
          [
            7.878531727653761e-10,
            -0.009223827589551373,
            -1.741296945096231e-09
          ],
          [
            6.563251340250573e-10,
            -0.007686849883648389,
            -1.4510563333862956e-09
          ],
          [
            5.247482091036166e-10,
            -0.006149936044890451,
            -1.1608153018768224e-09
          ],
          [
            3.9314288007123944e-10,
            -0.004613087157730181,
            -8.705848997629341e-10
          ],
          [
            2.614957602754502e-10,
            -0.0030763043063698186,
            -5.803467538222813e-10
          ],
          [
            1.2981383057421652e-10,
            -0.0015395885749753938,
            -2.9012031983333976e-10
          ],
          [
            -1.9052114145724066e-12,
            -2.9410475455731756e-06,
            1.0019427463422607e-13
          ]
        ],
        "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": [
          [
            1.0508185432911432e-09,
            -0.012297970264981362,
            -2.321780656622252e-09
          ],
          [
            9.193555916553464e-10,
            -0.01076086807819171,
            -2.0315369386736393e-09
          ],
          [
            7.878532271021754e-10,
            -0.00922382758955137,
            -1.741296939972159e-09
          ],
          [
            6.563251053748331e-10,
            -0.007686849883648372,
            -1.451056330648015e-09
          ],
          [
            5.247482448567098e-10,
            -0.006149936044890447,
            -1.1608152772346614e-09
          ],
          [
            3.931428516068536e-10,
            -0.004613087157730178,
            -8.705848819623441e-10
          ],
          [
            2.6149571397127147e-10,
            -0.0030763043063697926,
            -5.803467706400056e-10
          ],
          [
            1.298138263550186e-10,
            -0.0015395885749753813,
            -2.901203166594257e-10
          ],
          [
            -1.905198221408e-12,
            -2.9410475455571294e-06,
            1.0014211682118912e-13
          ]
        ]
      },
      "reflected": {
        "reached": true,
        "construction": "reflect_displacements_about_reconstructed_parent",
        "energies_eV": [
          -167.00712302985545,
          -167.00715548359898,
          -167.00717847855498,
          -167.00719201438744,
          -167.0071960907589,
          -167.0071907073302,
          -167.0071758637607,
          -167.00715155970784,
          -167.0071177948278
        ],
        "cartesian_polarizations_e_A2": [
          [
            -4.5983907201126266e-14,
            -1.993096168278984e-08,
            8.647745169708937e-16
          ],
          [
            -1.8675763825242856e-12,
            6.708422375909122e-06,
            1.6409004459514472e-12
          ],
          [
            -3.690581298512882e-12,
            1.3436807918313596e-05,
            3.28200929850352e-12
          ],
          [
            -5.514869267096698e-12,
            2.0165224744962828e-05,
            4.924128862399177e-12
          ],
          [
            -7.340810401394221e-12,
            2.689367193283141e-05,
            6.5671603419754064e-12
          ],
          [
            -9.16819214732529e-12,
            3.3622148556481486e-05,
            8.211339114257224e-12
          ],
          [
            -1.0997086995833237e-11,
            4.035065368863801e-05,
            9.856520997227078e-12
          ],
          [
            -1.282736474710936e-11,
            4.707918639947782e-05,
            1.150278909085185e-11
          ],
          [
            -1.4659135578185095e-11,
            5.3807745756629574e-05,
            1.3150029227113536e-11
          ]
        ],
        "raw_reduced_polarization": [
          [
            -1.9034711808420063e-12,
            -2.941047535661571e-06,
            9.755413873126717e-14
          ],
          [
            -6.989602160350718e-11,
            0.000989900307433973,
            1.8247940355028262e-10
          ],
          [
            -1.3791183718752772e-10,
            0.001982733934740784,
            3.6497212006849745e-10
          ],
          [
            -2.0594583147553983e-10,
            0.0029755596985747905,
            5.47568749540858e-10
          ],
          [
            -2.7401380765555764e-10,
            0.003968377462766787,
            7.302583083268121e-10
          ],
          [
            -3.4210584042283213e-10,
            0.004961187090795019,
            9.130669537586273e-10
          ],
          [
            -4.102255981719261e-10,
            0.005953988445870074,
            1.0959786493601009e-09
          ],
          [
            -4.783672824015465e-10,
            0.0069467813908299925,
            1.2790026263132582e-09
          ],
          [
            -5.465359850446067e-10,
            0.007939565788140287,
            1.4621261845821123e-09
          ]
        ],
        "unwrapped_reduced_polarization": [
          [
            -1.9034711808420063e-12,
            -2.941047535661571e-06,
            9.755413873126717e-14
          ],
          [
            -6.989602160350718e-11,
            0.000989900307433973,
            1.8247940355028262e-10
          ],
          [
            -1.3791183718752772e-10,
            0.001982733934740784,
            3.6497212006849745e-10
          ],
          [
            -2.0594583147553983e-10,
            0.0029755596985747905,
            5.47568749540858e-10
          ],
          [
            -2.7401380765555764e-10,
            0.003968377462766787,
            7.302583083268121e-10
          ],
          [
            -3.4210584042283213e-10,
            0.004961187090795019,
            9.130669537586273e-10
          ],
          [
            -4.102255981719261e-10,
            0.005953988445870074,
            1.0959786493601009e-09
          ],
          [
            -4.783672824015465e-10,
            0.0069467813908299925,
            1.2790026263132582e-09
          ],
          [
            -5.465359850446067e-10,
            0.007939565788140287,
            1.4621261845821123e-09
          ]
        ],
        "gauge_integer_shift": [
          0,
          0,
          0
        ],
        "expected_opposite_endpoint_reduced_polarization": [
          -1.0546279798375916e-09,
          0.012292088465630397,
          2.321978221590586e-09
        ],
        "actual_opposite_endpoint_branch_residual": 0.004352522677490225
      },
      "pnp_branch": {
        "construction": "incoming_path_concatenated_with_parent_reflection",
        "reduced_polarization": [
          [
            1.050818517608761e-09,
            -0.012297970264981384,
            -2.321780638177971e-09
          ],
          [
            9.193556418699434e-10,
            -0.010760868078191687,
            -2.0315369541886123e-09
          ],
          [
            7.878531727653761e-10,
            -0.009223827589551373,
            -1.741296945096231e-09
          ],
          [
            6.563251340250573e-10,
            -0.007686849883648389,
            -1.4510563333862956e-09
          ],
          [
            5.247482091036166e-10,
            -0.006149936044890451,
            -1.1608153018768224e-09
          ],
          [
            3.9314288007123944e-10,
            -0.004613087157730181,
            -8.705848997629341e-10
          ],
          [
            2.614957602754502e-10,
            -0.0030763043063698186,
            -5.803467538222813e-10
          ],
          [
            1.2981383057421652e-10,
            -0.0015395885749753938,
            -2.9012031983333976e-10
          ],
          [
            -1.9052114145723965e-12,
            -2.9410475455732053e-06,
            1.0019427463423541e-13
          ],
          [
            -6.989602160350718e-11,
            0.000989900307433973,
            1.8247940355028262e-10
          ],
          [
            -1.3791183718752772e-10,
            0.001982733934740784,
            3.6497212006849745e-10
          ],
          [
            -2.0594583147553983e-10,
            0.0029755596985747905,
            5.47568749540858e-10
          ],
          [
            -2.7401380765555764e-10,
            0.003968377462766787,
            7.302583083268121e-10
          ],
          [
            -3.4210584042283213e-10,
            0.004961187090795019,
            9.130669537586273e-10
          ],
          [
            -4.102255981719261e-10,
            0.005953988445870074,
            1.0959786493601009e-09
          ],
          [
            -4.783672824015465e-10,
            0.0069467813908299925,
            1.2790026263132582e-09
          ],
          [
            -5.465359850446067e-10,
            0.007939565788140287,
            1.4621261845821123e-09
          ]
        ],
        "unwrapped_reduced_polarization": [
          [
            1.050818517608761e-09,
            -0.012297970264981384,
            -2.321780638177971e-09
          ],
          [
            9.193556418699434e-10,
            -0.010760868078191687,
            -2.0315369541886123e-09
          ],
          [
            7.878531727653761e-10,
            -0.009223827589551373,
            -1.741296945096231e-09
          ],
          [
            6.563251340250573e-10,
            -0.007686849883648389,
            -1.4510563333862956e-09
          ],
          [
            5.247482091036166e-10,
            -0.006149936044890451,
            -1.1608153018768224e-09
          ],
          [
            3.9314288007123944e-10,
            -0.004613087157730181,
            -8.705848997629341e-10
          ],
          [
            2.614957602754502e-10,
            -0.0030763043063698186,
            -5.803467538222813e-10
          ],
          [
            1.2981383057421652e-10,
            -0.0015395885749753938,
            -2.9012031983333976e-10
          ],
          [
            -1.9052114145724066e-12,
            -2.9410475455731756e-06,
            1.0019427463422607e-13
          ],
          [
            -6.989602160350718e-11,
            0.000989900307433973,
            1.8247940355028262e-10
          ],
          [
            -1.3791183718752772e-10,
            0.001982733934740784,
            3.6497212006849745e-10
          ],
          [
            -2.0594583147553983e-10,
            0.0029755596985747905,
            5.47568749540858e-10
          ],
          [
            -2.7401380765555764e-10,
            0.003968377462766787,
            7.302583083268121e-10
          ],
          [
            -3.4210584042283213e-10,
            0.004961187090795019,
            9.130669537586273e-10
          ],
          [
            -4.102255981719261e-10,
            0.005953988445870074,
            1.0959786493601009e-09
          ],
          [
            -4.783672824015465e-10,
            0.0069467813908299925,
            1.2790026263132582e-09
          ],
          [
            -5.465359850446067e-10,
            0.007939565788140287,
            1.4621261845821123e-09
          ]
        ],
        "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": [
          [
            1.0508185432911432e-09,
            -0.012297970264981362,
            -2.321780656622252e-09
          ],
          [
            9.193555916553464e-10,
            -0.01076086807819171,
            -2.0315369386736393e-09
          ],
          [
            7.878532271021754e-10,
            -0.00922382758955137,
            -1.741296939972159e-09
          ],
          [
            6.563251053748331e-10,
            -0.007686849883648372,
            -1.451056330648015e-09
          ],
          [
            5.247482448567098e-10,
            -0.006149936044890447,
            -1.1608152772346614e-09
          ],
          [
            3.931428516068536e-10,
            -0.004613087157730178,
            -8.705848819623441e-10
          ],
          [
            2.6149571397127147e-10,
            -0.0030763043063697926,
            -5.803467706400056e-10
          ],
          [
            1.298138263550186e-10,
            -0.0015395885749753813,
            -2.901203166594257e-10
          ],
          [
            -1.905198221408e-12,
            -2.9410475455571294e-06,
            1.0014211682118912e-13
          ],
          [
            -6.989603340556982e-11,
            0.0009899003074339552,
            1.8247936495185968e-10
          ],
          [
            -1.3791184860778571e-10,
            0.001982733934740799,
            3.649721636023173e-10
          ],
          [
            -2.0594581595645423e-10,
            0.00297555969857477,
            5.475687681055774e-10
          ],
          [
            -2.740138116408275e-10,
            0.003968377462766792,
            7.302582982759986e-10
          ],
          [
            -3.421058436536839e-10,
            0.004961187090795072,
            9.130669553769621e-10
          ],
          [
            -4.102255757310047e-10,
            0.005953988445870029,
            1.0959786411746109e-09
          ],
          [
            -4.783672902242131e-10,
            0.006946781390829937,
            1.2790026815423516e-09
          ],
          [
            -5.465359831369199e-10,
            0.007939565788140257,
            1.4621261978930988e-09
          ]
        ]
      },
      "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": [
              1.0508188435288705e-09,
              -0.012297970264981235,
              -2.3217809187786937e-09
            ],
            "branch_aligned_reduced_polarization": [
              1.0508188435288705e-09,
              -0.01229797026498125,
              -2.3217809187786937e-09
            ],
            "target_residual": 0.48770202973501875,
            "energy_eV": -167.01075439031533,
            "max_atomic_step_A": 0.0731578532473822,
            "max_log_strain_component": 0.011406912203557681,
            "step_scale": 1.0,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 5.668130719880383,
            "cell_principal_stretches": [
              1.014256775359979,
              0.9958649143004283,
              0.9839796775211118
            ],
            "cell_volume_ratio": 0.9938812059070925,
            "cell_rmsd_from_input_A": 0.24134820247041233
          },
          {
            "iteration": 1,
            "reduced_polarization": [
              9.493424859417705e-11,
              -0.49892448521417654,
              -1.3410774467844725e-11
            ],
            "branch_aligned_reduced_polarization": [
              9.493424859417705e-11,
              -0.49892448521417654,
              -1.3410774467844725e-11
            ],
            "target_residual": 0.0010755147858234658,
            "energy_eV": -166.14196721590724,
            "max_atomic_step_A": 0.00016043840330958513,
            "max_log_strain_component": 2.548773726908788e-05,
            "step_scale": 1.0,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 5.668130719880383,
            "cell_principal_stretches": [
              1.0142888573788853,
              0.9958556939889552,
              0.9839441704421856
            ],
            "cell_volume_ratio": 0.9938675760092396,
            "cell_rmsd_from_input_A": 0.2418955746543413
          },
          {
            "iteration": 2,
            "reduced_polarization": [
              2.96057667536036e-13,
              -0.4999908157150727,
              1.116380547005316e-12
            ],
            "branch_aligned_reduced_polarization": [
              2.96057667536036e-13,
              -0.4999908157150727,
              1.116380547005316e-12
            ],
            "target_residual": 9.184284927299464e-06,
            "energy_eV": -166.13775920653148
          }
        ],
        "iterations": 2
      },
      "parent": {
        "candidate_id": "bec_projection_01",
        "source": "MACEField_BEC_backprojection",
        "spacegroup": "C2",
        "spacegroup_number": 5,
        "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": 9.184284927299464e-06,
        "parent_symmetrization_rmsd_A": 0.0809594230522663,
        "parent_cell_rmsd_A": 0.2418955746543413,
        "energy_eV": -166.13775920653148,
        "reduced_polarization": [
          2.96057667536036e-13,
          -0.4999908157150727,
          1.116380547005316e-12
        ],
        "cartesian_polarization_e_A2": [
          -1.2199601239067056e-12,
          -0.003395298500228731,
          1.7420352761417598e-14
        ],
        "ranking_score": 0.6414516852857062
      },
      "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": [
              1.0508188435288705e-09,
              -0.012297970264981235,
              -2.3217809187786937e-09
            ],
            "branch_aligned_reduced_polarization": [
              1.0508188435288705e-09,
              -0.012297970264981235,
              -2.3217809341780082e-09
            ],
            "target_residual": 0.500151214884916,
            "energy_eV": -167.01075439031533,
            "max_atomic_step_A": 0.06628184088072646,
            "max_log_strain_component": 0.02,
            "step_scale": 0.7584551025060455,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 5.668130719880383,
            "cell_principal_stretches": [
              1.025773759551231,
              0.9997650268487857,
              0.9752174266861253
            ],
            "cell_volume_ratio": 1.0001173901851068,
            "cell_rmsd_from_input_A": 0.1397516503816263
          },
          {
            "iteration": 1,
            "reduced_polarization": [
              0.0002202989183591795,
              -0.022348815855682106,
              -0.3724274626578066
            ],
            "branch_aligned_reduced_polarization": [
              0.0002202989183591795,
              -0.022348815855682106,
              -0.3724274626578066
            ],
            "target_residual": 0.12951552179445502,
            "energy_eV": -166.08256115056759,
            "max_atomic_step_A": 0.02417289408457241,
            "max_log_strain_component": 0.007190258441039447,
            "step_scale": 1.0,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 5.668130719880383,
            "cell_principal_stretches": [
              1.035689563863992,
              0.9988410772081284,
              0.9672168041559994
            ],
            "cell_volume_ratio": 1.0005754149707216,
            "cell_rmsd_from_input_A": 0.18919672144671104
          },
          {
            "iteration": 2,
            "reduced_polarization": [
              0.0004726863462328984,
              -0.008164195391813319,
              -0.4943712414454262
            ],
            "branch_aligned_reduced_polarization": [
              0.0004726863462328984,
              -0.008164195391813319,
              -0.4943712414454262
            ],
            "target_residual": 0.009927761159662759,
            "energy_eV": -165.3548367517779,
            "max_atomic_step_A": 0.0017038882424885579,
            "max_log_strain_component": 0.00043333712513327137,
            "step_scale": 1.0,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 5.668130719880383,
            "cell_principal_stretches": [
              1.03635144876854,
              0.9985799587949549,
              0.9669743051045961
            ],
            "cell_volume_ratio": 1.0007021629092212,
            "cell_rmsd_from_input_A": 0.19149414752105387
          },
          {
            "iteration": 3,
            "reduced_polarization": [
              7.409064130515776e-05,
              -0.000681169493069481,
              -0.4995606392981374
            ],
            "branch_aligned_reduced_polarization": [
              7.409064130515776e-05,
              -0.000681169493069481,
              -0.4995606392981374
            ],
            "target_residual": 0.0008139527798089765,
            "energy_eV": -165.31750198016985
          }
        ],
        "iterations": 3
      },
      "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": 0.0008139527798089765,
        "parent_symmetrization_rmsd_A": 0.07188815929067191,
        "parent_cell_rmsd_A": 0.19149414752105387,
        "energy_eV": -165.31750198016985,
        "reduced_polarization": [
          7.409064130515776e-05,
          -0.000681169493069481,
          -0.4995606392981374
        ],
        "cartesian_polarization_e_A2": [
          0.0005000366347439519,
          0.00010893011435004188,
          -0.004496446854180267
        ],
        "ranking_score": 0.6213896017305534
      },
      "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": false,
        "history": [
          {
            "iteration": 0,
            "reduced_polarization": [
              1.0508188435288705e-09,
              -0.012297970264981235,
              -2.3217809187786937e-09
            ],
            "branch_aligned_reduced_polarization": [
              1.0508188208468994e-09,
              -0.012297970264981235,
              -2.3217809187786937e-09
            ],
            "target_residual": 0.5001512161554938,
            "energy_eV": -167.01075439031533,
            "max_atomic_step_A": 0.05678916844512981,
            "max_log_strain_component": 0.02,
            "step_scale": 0.24283313091318065,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 5.668130719880383,
            "cell_principal_stretches": [
              1.0249213638603847,
              1.000090281851042,
              0.9756331960406052
            ],
            "cell_volume_ratio": 1.0000375830071258,
            "cell_rmsd_from_input_A": 0.17332075061284774
          },
          {
            "iteration": 1,
            "reduced_polarization": [
              0.12021875346182044,
              0.0021984269588615547,
              0.001688951593316385
            ],
            "branch_aligned_reduced_polarization": [
              0.12021875346182043,
              0.0021984269588615547,
              0.001688951593316385
            ],
            "target_residual": 0.37979136491061977,
            "energy_eV": -166.0346549198996,
            "max_atomic_step_A": 0.056799117532667955,
            "max_log_strain_component": 0.02,
            "step_scale": 0.3111256602324737,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 5.668130719880383,
            "cell_principal_stretches": [
              1.0503758877615867,
              0.9994302117800178,
              0.9523585662604067
            ],
            "cell_volume_ratio": 0.9997644957035124,
            "cell_rmsd_from_input_A": 0.349380156291287
          },
          {
            "iteration": 2,
            "reduced_polarization": [
              0.23292104952636497,
              0.022444991089168885,
              0.00881970493650931
            ],
            "branch_aligned_reduced_polarization": [
              0.23292104952636494,
              0.022444991089168885,
              0.00881970493650931
            ],
            "target_residual": 0.2681654910801507,
            "energy_eV": -163.13186047055194,
            "max_atomic_step_A": 0.05571386985750633,
            "max_log_strain_component": 0.02,
            "step_scale": 0.40457112666518347,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 5.668130719880383,
            "cell_principal_stretches": [
              1.0758580221041396,
              0.9977364923410904,
              0.9307412215615662
            ],
            "cell_volume_ratio": 0.9990788567159022,
            "cell_rmsd_from_input_A": 0.5326143062677335
          },
          {
            "iteration": 3,
            "reduced_polarization": [
              0.32707158492069827,
              0.04645944869899336,
              0.019972162905289643
            ],
            "branch_aligned_reduced_polarization": [
              0.32707158492069827,
              0.04645944869899336,
              0.019972162905289643
            ],
            "target_residual": 0.18017104208603862,
            "energy_eV": -158.70431207767123,
            "max_atomic_step_A": 0.05183748022127639,
            "max_log_strain_component": 0.02,
            "step_scale": 0.5343105649139106,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 5.668130719880383,
            "cell_principal_stretches": [
              1.101395020691213,
              0.9942720402473322,
              0.9110797625685314
            ],
            "cell_volume_ratio": 0.9977109428185693,
            "cell_rmsd_from_input_A": 0.7313346856151398
          },
          {
            "iteration": 4,
            "reduced_polarization": [
              0.39457458521788663,
              0.07099007722946699,
              0.026338855224254148
            ],
            "branch_aligned_reduced_polarization": [
              0.39457458521788663,
              0.07099007722946699,
              0.026338855224254148
            ],
            "target_residual": 0.129799246690998,
            "energy_eV": -153.80877622482078,
            "max_atomic_step_A": 0.08107978636167179,
            "max_log_strain_component": 0.016564902488253725,
            "step_scale": 1.0,
            "strain_jacobian_refreshed": true,
            "strain_jacobian_frobenius_norm": 4.6952532612202935,
            "cell_principal_stretches": [
              1.0833700274457472,
              0.9866450189736784,
              0.9066595251263595
            ],
            "cell_volume_ratio": 0.9691298544939936,
            "cell_rmsd_from_input_A": 0.637444540703041
          },
          {
            "iteration": 5,
            "reduced_polarization": [
              0.49911623846388997,
              0.00850981663423097,
              -0.0071505178805814015
            ],
            "branch_aligned_reduced_polarization": [
              0.49911623846388997,
              0.00850981663423097,
              -0.0071505178805814015
            ],
            "target_residual": 0.011150243027013177,
            "energy_eV": -150.30416378888071
          }
        ],
        "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": [
          0.5,
          0.0,
          0.0
        ],
        "formal_class": [
          0.5,
          0.0,
          0.0
        ],
        "target_residual": 0.011150243027013177,
        "parent_symmetrization_rmsd_A": 0.2670516559888016,
        "parent_cell_rmsd_A": 0.637444540703041,
        "energy_eV": -150.30416378888071,
        "reduced_polarization": [
          0.49911623846388997,
          0.00850981663423097,
          -0.0071505178805814015
        ],
        "cartesian_polarization_e_A2": [
          0.012292085509004248,
          -0.0008388216311576007,
          -5.4868405915421925e-05
        ],
        "ranking_score": 0.9487132772185882
      },
      "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": [
              1.0508188435288705e-09,
              -0.012297970264981235,
              -2.3217809187786937e-09
            ],
            "branch_aligned_reduced_polarization": [
              1.0508188435288705e-09,
              -0.01229797026498125,
              -2.3217809341780082e-09
            ],
            "target_residual": 0.6984649364756088,
            "energy_eV": -167.01075439031533,
            "max_atomic_step_A": 0.08375717377528256,
            "max_log_strain_component": 0.02,
            "step_scale": 0.7584551028715283,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 5.668130719880383,
            "cell_principal_stretches": [
              1.0200458288307983,
              1.0085001923764696,
              0.9675705733457358
            ],
            "cell_volume_ratio": 0.9953557310930863,
            "cell_rmsd_from_input_A": 0.2308201995810562
          },
          {
            "iteration": 1,
            "reduced_polarization": [
              -0.004401832736449409,
              -0.3892866359062593,
              -0.37633770582484627
            ],
            "branch_aligned_reduced_polarization": [
              -0.004401832736449409,
              -0.3892866359062593,
              -0.37633770582484627
            ],
            "target_residual": 0.1660397185045046,
            "energy_eV": -165.2986964095848,
            "max_atomic_step_A": 0.024644795042498023,
            "max_log_strain_component": 0.006389561615681601,
            "step_scale": 1.0,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 5.668130719880383,
            "cell_principal_stretches": [
              1.0276382425454327,
              1.0102679165263848,
              0.9573391721407044
            ],
            "cell_volume_ratio": 0.9938999036574477,
            "cell_rmsd_from_input_A": 0.31211059597807445
          },
          {
            "iteration": 2,
            "reduced_polarization": [
              -0.0004945552481686197,
              -0.49486906105495565,
              -0.4943513352954802
            ],
            "branch_aligned_reduced_polarization": [
              -0.0004945552481686197,
              -0.49486906105495565,
              -0.4943513352954802
            ],
            "target_residual": 0.007647125753860186,
            "energy_eV": -163.97827633987146,
            "max_atomic_step_A": 0.001256980415625162,
            "max_log_strain_component": 0.00035878907421477266,
            "step_scale": 1.0,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 5.668130719880383,
            "cell_principal_stretches": [
              1.028035848125612,
              1.0103107730907657,
              0.9568580379072833
            ],
            "cell_volume_ratio": 0.9938269108114864,
            "cell_rmsd_from_input_A": 0.3163942209370138
          },
          {
            "iteration": 3,
            "reduced_polarization": [
              -1.342039107345301e-05,
              -0.4996053596675783,
              -0.499692447661074
            ],
            "branch_aligned_reduced_polarization": [
              -1.342039107345301e-05,
              -0.4996053596675783,
              -0.499692447661074
            ],
            "target_residual": 0.0005005092806825083,
            "energy_eV": -163.911403451044
          }
        ],
        "iterations": 3
      },
      "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": 0.0005005092806825083,
        "parent_symmetrization_rmsd_A": 0.107694417011009,
        "parent_cell_rmsd_A": 0.3163942209370138,
        "energy_eV": -163.911403451044,
        "reduced_polarization": [
          -1.342039107345301e-05,
          -0.4996053596675783,
          -0.499692447661074
        ],
        "cartesian_polarization_e_A2": [
          0.0006379434162914039,
          -0.0032902660300104503,
          -0.004390385780517366
        ],
        "ranking_score": 0.6877939908066275
      },
      "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": [
              1.0508188435288705e-09,
              -0.012297970264981235,
              -2.3217809187786937e-09
            ],
            "branch_aligned_reduced_polarization": [
              1.0508188208468994e-09,
              -0.01229797026498125,
              -2.3217809187786937e-09
            ],
            "target_residual": 0.698464937385434,
            "energy_eV": -167.01075439031533,
            "max_atomic_step_A": 0.05757544534723455,
            "max_log_strain_component": 0.02,
            "step_scale": 0.24283313113354027,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 5.668130719880383,
            "cell_principal_stretches": [
              1.026152564968107,
              0.9964366145285298,
              0.9765424133981354
            ],
            "cell_volume_ratio": 0.998510699642086,
            "cell_rmsd_from_input_A": 0.1860811783746314
          },
          {
            "iteration": 1,
            "reduced_polarization": [
              0.11905045621018526,
              -0.11671216926764974,
              0.003914502354834873
            ],
            "branch_aligned_reduced_polarization": [
              0.11905045621018528,
              -0.11671216926764971,
              0.003914502354834873
            ],
            "target_residual": 0.5404141369633707,
            "energy_eV": -166.05682341295838,
            "max_atomic_step_A": 0.05871623788979781,
            "max_log_strain_component": 0.02,
            "step_scale": 0.2951239102552594,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 5.668130719880383,
            "cell_principal_stretches": [
              1.0525263087406136,
              0.9919836267420274,
              0.9546185436866543
            ],
            "cell_volume_ratio": 0.9967065917723036,
            "cell_rmsd_from_input_A": 0.3846114556217036
          },
          {
            "iteration": 2,
            "reduced_polarization": [
              0.22400428828907434,
              -0.19534981227528728,
              0.010970514825831912
            ],
            "branch_aligned_reduced_polarization": [
              0.22400428828907437,
              -0.19534981227528725,
              0.010970514825831912
            ],
            "target_residual": 0.41122466117569706,
            "energy_eV": -163.37426598186144,
            "max_atomic_step_A": 0.05187020074557699,
            "max_log_strain_component": 0.02,
            "step_scale": 0.3513665653157763,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 5.668130719880383,
            "cell_principal_stretches": [
              1.0790836804365718,
              0.9858922097845826,
              0.9346330702877963
            ],
            "cell_volume_ratio": 0.9943189197070655,
            "cell_rmsd_from_input_A": 0.604314367798643
          },
          {
            "iteration": 3,
            "reduced_polarization": [
              0.3039140460320962,
              -0.24019768782608047,
              0.01843323123834086
            ],
            "branch_aligned_reduced_polarization": [
              0.3039140460320962,
              -0.24019768782608047,
              0.01843323123834086
            ],
            "target_residual": 0.32601645168350596,
            "energy_eV": -159.45771891793447,
            "max_atomic_step_A": 0.04590851145268432,
            "max_log_strain_component": 0.02,
            "step_scale": 0.3987688843356834,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 5.668130719880383,
            "cell_principal_stretches": [
              1.1063481702604065,
              0.9774380904249781,
              0.9164726877948192
            ],
            "cell_volume_ratio": 0.991061506444312,
            "cell_rmsd_from_input_A": 0.8582043945482606
          },
          {
            "iteration": 4,
            "reduced_polarization": [
              0.35255941285607956,
              -0.2529322538345461,
              0.019558843344816914
            ],
            "branch_aligned_reduced_polarization": [
              0.35255941285607956,
              -0.2529322538345461,
              0.019558843344816914
            ],
            "target_residual": 0.2883812516194634,
            "energy_eV": -154.96665168747816,
            "max_atomic_step_A": 0.07749353030760332,
            "max_log_strain_component": 0.02,
            "step_scale": 0.5905575555888426,
            "strain_jacobian_refreshed": true,
            "strain_jacobian_frobenius_norm": 5.301055891811357,
            "cell_principal_stretches": [
              1.070961213728419,
              0.9712061926792032,
              0.9161465942962117
            ],
            "cell_volume_ratio": 0.9529062094789573,
            "cell_rmsd_from_input_A": 0.5521694130251474
          },
          {
            "iteration": 5,
            "reduced_polarization": [
              0.43854208803904426,
              -0.3894838337215102,
              -0.008075825941577651
            ],
            "branch_aligned_reduced_polarization": [
              0.43854208803904426,
              -0.3894838337215102,
              -0.008075825941577651
            ],
            "target_residual": 0.12671273383576748,
            "energy_eV": -151.10607575207962
          }
        ],
        "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": 0.12671273383576748,
        "parent_symmetrization_rmsd_A": 0.26526674101870323,
        "parent_cell_rmsd_A": 0.5521694130251474,
        "energy_eV": -151.10607575207962,
        "reduced_polarization": [
          0.43854208803904426,
          -0.3894838337215102,
          -0.008075825941577651
        ],
        "cartesian_polarization_e_A2": [
          0.0112288461033656,
          -0.003439377328696932,
          -0.0003045833019944242
        ],
        "ranking_score": 1.156734561946525
      },
      "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": false,
        "history": [
          {
            "iteration": 0,
            "reduced_polarization": [
              1.0508188435288705e-09,
              -0.012297970264981235,
              -2.3217809187786937e-09
            ],
            "branch_aligned_reduced_polarization": [
              1.0508188208468994e-09,
              -0.012297970264981235,
              -2.3217809341780082e-09
            ],
            "target_residual": 0.707213713597268,
            "energy_eV": -167.01075439031533,
            "max_atomic_step_A": 0.059944725198041754,
            "max_log_strain_component": 0.02,
            "step_scale": 0.19469099886104455,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 5.668130719880383,
            "cell_principal_stretches": [
              1.0211991789829797,
              1.0000779031283575,
              0.9791941211260681
            ],
            "cell_volume_ratio": 1.0000301319660259,
            "cell_rmsd_from_input_A": 0.16765657374105863
          },
          {
            "iteration": 1,
            "reduced_polarization": [
              0.09641693758462412,
              0.005156634446327849,
              -0.09571369758830384
            ],
            "branch_aligned_reduced_polarization": [
              0.09641693758462411,
              0.005156634446327849,
              -0.09571369758830384
            ],
            "target_residual": 0.5712733964268839,
            "energy_eV": -166.36391055534574,
            "max_atomic_step_A": 0.05966750899246546,
            "max_log_strain_component": 0.02,
            "step_scale": 0.2352350355934043,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 5.668130719880383,
            "cell_principal_stretches": [
              1.0431047090843613,
              0.9992008896750066,
              0.9591461872313711
            ],
            "cell_volume_ratio": 0.9996904027885355,
            "cell_rmsd_from_input_A": 0.3384370559046142
          },
          {
            "iteration": 2,
            "reduced_polarization": [
              0.1867744121800531,
              0.030654118720669907,
              -0.18448036082312125
            ],
            "branch_aligned_reduced_polarization": [
              0.18677441218005308,
              0.030654118720669907,
              -0.18448036082312125
            ],
            "target_residual": 0.4456485011373874,
            "energy_eV": -164.45536110206987,
            "max_atomic_step_A": 0.05847338592633631,
            "max_log_strain_component": 0.02,
            "step_scale": 0.28040556631255426,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 5.668130719880383,
            "cell_principal_stretches": [
              1.065734576538991,
              0.9971744218332124,
              0.9399447190495293
            ],
            "cell_volume_ratio": 0.9989011162247451,
            "cell_rmsd_from_input_A": 0.5176279353129883
          },
          {
            "iteration": 3,
            "reduced_polarization": [
              0.2632293518906576,
              0.06061510303999121,
              -0.2587790111309296
            ],
            "branch_aligned_reduced_polarization": [
              0.2632293518906576,
              0.06061510303999121,
              -0.2587790111309296
            ],
            "target_residual": 0.34339786835919495,
            "energy_eV": -161.50972362752867,
            "max_atomic_step_A": 0.0548975772012333,
            "max_log_strain_component": 0.02,
            "step_scale": 0.32496175116844633,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 5.668130719880383,
            "cell_principal_stretches": [
              1.0891934778980197,
              0.9937478551739787,
              0.9216274800848221
            ],
            "cell_volume_ratio": 0.9975545458156474,
            "cell_rmsd_from_input_A": 0.7118863011893954
          },
          {
            "iteration": 4,
            "reduced_polarization": [
              0.3193392237310778,
              0.08913763562840775,
              -0.3171411633415968
            ],
            "branch_aligned_reduced_polarization": [
              0.3193392237310778,
              0.08913763562840775,
              -0.3171411633415968
            ],
            "target_residual": 0.27206835227857157,
            "energy_eV": -158.09329796007785,
            "max_atomic_step_A": 0.10437170473948199,
            "max_log_strain_component": 0.02,
            "step_scale": 0.6157137276302314,
            "strain_jacobian_refreshed": true,
            "strain_jacobian_frobenius_norm": 5.214620780567246,
            "cell_principal_stretches": [
              1.0716211143069392,
              0.9826047054699668,
              0.9123401619496122
            ],
            "cell_volume_ratio": 0.9606758975643486,
            "cell_rmsd_from_input_A": 0.6657765566986784
          },
          {
            "iteration": 5,
            "reduced_polarization": [
              0.43374400056963514,
              0.03914269524266729,
              -0.42489716807334393
            ],
            "branch_aligned_reduced_polarization": [
              0.43374400056963514,
              0.03914269524266729,
              -0.42489716807334393
            ],
            "target_residual": 0.10752880272178421,
            "energy_eV": -155.22147631623045
          }
        ],
        "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": [
          0.5,
          0.0,
          -0.5
        ],
        "formal_class": [
          0.5,
          0.0,
          0.5
        ],
        "target_residual": 0.10752880272178421,
        "parent_symmetrization_rmsd_A": 0.22488727747157652,
        "parent_cell_rmsd_A": 0.6657765566986784,
        "energy_eV": -155.22147631623045,
        "reduced_polarization": [
          0.43374400056963514,
          0.03914269524266729,
          -0.42489716807334393
        ],
        "cartesian_polarization_e_A2": [
          0.011146805404750326,
          -0.0006823386788395979,
          -0.003840822322356028
        ],
        "ranking_score": 1.1063890220898145
      },
      "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": [
              1.0508188435288705e-09,
              -0.012297970264981235,
              -2.3217809187786937e-09
            ],
            "branch_aligned_reduced_polarization": [
              1.0508188208468994e-09,
              -0.01229797026498125,
              -2.3217809341780082e-09
            ],
            "target_residual": 0.8589838569117917,
            "energy_eV": -167.01075439031533,
            "max_atomic_step_A": 0.060061847477578985,
            "max_log_strain_component": 0.02,
            "step_scale": 0.19469099900269168,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 5.668130719880383,
            "cell_principal_stretches": [
              1.0222730787475816,
              0.996917179754181,
              0.9800653672401208
            ],
            "cell_volume_ratio": 0.998805779877576,
            "cell_rmsd_from_input_A": 0.17639562015373417
          },
          {
            "iteration": 1,
            "reduced_polarization": [
              0.0953459870298939,
              -0.09074173192584639,
              -0.09475291750445311
            ],
            "branch_aligned_reduced_polarization": [
              0.09534598702989389,
              -0.09074173192584639,
              -0.09475291750445314
            ],
            "target_residual": 0.7038908992670804,
            "energy_eV": -166.39519170240817,
            "max_atomic_step_A": 0.05808947725479379,
            "max_log_strain_component": 0.02,
            "step_scale": 0.22655665677733616,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 5.668130719880383,
            "cell_principal_stretches": [
              1.0452885673661723,
              0.9929356392295411,
              0.9608320467877183
            ],
            "cell_volume_ratio": 0.9972516858597036,
            "cell_rmsd_from_input_A": 0.3643082701034962
          },
          {
            "iteration": 2,
            "reduced_polarization": [
              0.18070924468092192,
              -0.14907568025923423,
              -0.17932111289145727
            ],
            "branch_aligned_reduced_polarization": [
              0.18070924468092192,
              -0.14907568025923423,
              -0.17932111289145725
            ],
            "target_residual": 0.5726512143136694,
            "energy_eV": -164.65891008331604,
            "max_atomic_step_A": 0.05541547090745719,
            "max_log_strain_component": 0.02,
            "step_scale": 0.254480560018775,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 5.668130719880383,
            "cell_principal_stretches": [
              1.0691647314266133,
              0.9877347903481194,
              0.9423761938559023
            ],
            "cell_volume_ratio": 0.9951975121100111,
            "cell_rmsd_from_input_A": 0.5703388140707175
          },
          {
            "iteration": 3,
            "reduced_polarization": [
              0.24789083025053088,
              -0.1827035224330605,
              -0.24704599190807722
            ],
            "branch_aligned_reduced_polarization": [
              0.24789083025053088,
              -0.18270352243306054,
              -0.2470459919080772
            ],
            "target_residual": 0.4777256727013135,
            "energy_eV": -162.1099162621394,
            "max_atomic_step_A": 0.05109734188080171,
            "max_log_strain_component": 0.02,
            "step_scale": 0.270387217947205,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 5.668130719880383,
            "cell_principal_stretches": [
              1.094133928075517,
              0.9810439030622776,
              0.9246582245042064
            ],
            "cell_volume_ratio": 0.9925220532586084,
            "cell_rmsd_from_input_A": 0.8023455787282803
          },
          {
            "iteration": 4,
            "reduced_polarization": [
              0.2917490054429219,
              -0.1931375744310938,
              -0.2977584829748811
            ],
            "branch_aligned_reduced_polarization": [
              0.2917490054429219,
              -0.1931375744310938,
              -0.2977584829748811
            ],
            "target_residual": 0.42241526507533567,
            "energy_eV": -159.16999587849796,
            "max_atomic_step_A": 0.08610432935215837,
            "max_log_strain_component": 0.02,
            "step_scale": 0.4161203950425572,
            "strain_jacobian_refreshed": true,
            "strain_jacobian_frobenius_norm": 5.589367837425369,
            "cell_principal_stretches": [
              1.0644340387301887,
              0.968893960607562,
              0.921604534117436
            ],
            "cell_volume_ratio": 0.9504726087449,
            "cell_rmsd_from_input_A": 0.5780537789661694
          },
          {
            "iteration": 5,
            "reduced_polarization": [
              0.3828191808522088,
              -0.32119275688682836,
              -0.38570289664245216
            ],
            "branch_aligned_reduced_polarization": [
              0.3828191808522088,
              -0.32119275688682836,
              -0.38570289664245216
            ],
            "target_residual": 0.2424194761189913,
            "energy_eV": -157.07289520354453
          }
        ],
        "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": 0.2424194761189913,
        "parent_symmetrization_rmsd_A": 0.22307689538266987,
        "parent_cell_rmsd_A": 0.5780537789661694,
        "energy_eV": -157.07289520354453,
        "reduced_polarization": [
          0.3828191808522088,
          -0.32119275688682836,
          -0.38570289664245216
        ],
        "cartesian_polarization_e_A2": [
          0.010233975327739182,
          -0.0030433646424804207,
          -0.0036425164508185584
        ],
        "ranking_score": 1.3524292923621948
      },
      "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": 0.002028595265736744,
        "minimum_distance_A_by_image": [
          2.2868200509120684,
          2.2865016288631566,
          2.2861832190680023,
          2.2858648215310753,
          2.285546436256848,
          2.2852280632497846,
          2.2849097025143705,
          2.2845913540550673,
          2.284273017876367
        ],
        "minimum_distance_A": 2.284273017876367,
        "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": [
          824.8611577397129,
          824.8771154972025,
          824.8930735634121,
          824.9090319383464,
          824.9249906220113,
          824.9409496144127,
          824.9569089155567,
          824.9728685254493,
          824.9888284440947
        ],
        "cell_deformation_log_strain_norm": 0.0005515303008781093
      },
      "parent_reduced_polarization": [
        -1.9052114145723965e-12,
        -2.9410475455732053e-06,
        1.0019427463423541e-13
      ],
      "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": [
          -167.01075439031536,
          -167.0103662088925,
          -167.00995923795202,
          -167.00953348106836,
          -167.00908894177644,
          -167.00862562357193,
          -167.0081435299117,
          -167.00764266421336,
          -167.00712302985545
        ],
        "cartesian_polarizations_e_A2": [
          [
            2.768933637629768e-11,
            -8.334537114474963e-05,
            -2.088156519795368e-11
          ],
          [
            2.4221237293322043e-11,
            -7.292771797053017e-05,
            -1.8270620092366643e-11
          ],
          [
            2.0753400514638002e-11,
            -6.251061387394133e-05,
            -1.5659868328350532e-11
          ],
          [
            1.728615980548935e-11,
            -5.2094066196157665e-05,
            -1.3049271439286743e-11
          ],
          [
            1.381895317665899e-11,
            -4.167808227694755e-05,
            -1.0438831151896259e-11
          ],
          [
            1.0352285582178639e-11,
            -3.1262669456199026e-05,
            -7.828646823683365e-12
          ],
          [
            6.885815701001694e-12,
            -2.0847835071918657e-05,
            -5.218553280011391e-12
          ],
          [
            3.419731462205488e-12,
            -1.0433586461683034e-05,
            -2.6087255189960587e-12
          ],
          [
            -4.6028518584938256e-14,
            -1.993096174995924e-08,
            8.88510060922145e-16
          ]
        ],
        "raw_reduced_polarization": [
          [
            1.050818517608761e-09,
            -0.012297970264981384,
            -2.321780638177971e-09
          ],
          [
            9.193556418699434e-10,
            -0.010760868078191687,
            -2.0315369541886123e-09
          ],
          [
            7.878531727653761e-10,
            -0.009223827589551373,
            -1.741296945096231e-09
          ],
          [
            6.563251340250573e-10,
            -0.007686849883648389,
            -1.4510563333862956e-09
          ],
          [
            5.247482091036166e-10,
            -0.006149936044890451,
            -1.1608153018768224e-09
          ],
          [
            3.9314288007123944e-10,
            -0.004613087157730181,
            -8.705848997629341e-10
          ],
          [
            2.614957602754502e-10,
            -0.0030763043063698186,
            -5.803467538222813e-10
          ],
          [
            1.2981383057421652e-10,
            -0.0015395885749753938,
            -2.9012031983333976e-10
          ],
          [
            -1.9052114145723965e-12,
            -2.9410475455732053e-06,
            1.0019427463423541e-13
          ]
        ],
        "unwrapped_reduced_polarization": [
          [
            1.050818517608761e-09,
            -0.012297970264981384,
            -2.321780638177971e-09
          ],
          [
            9.193556418699434e-10,
            -0.010760868078191687,
            -2.0315369541886123e-09
          ],
          [
            7.878531727653761e-10,
            -0.009223827589551373,
            -1.741296945096231e-09
          ],
          [
            6.563251340250573e-10,
            -0.007686849883648389,
            -1.4510563333862956e-09
          ],
          [
            5.247482091036166e-10,
            -0.006149936044890451,
            -1.1608153018768224e-09
          ],
          [
            3.9314288007123944e-10,
            -0.004613087157730181,
            -8.705848997629341e-10
          ],
          [
            2.614957602754502e-10,
            -0.0030763043063698186,
            -5.803467538222813e-10
          ],
          [
            1.2981383057421652e-10,
            -0.0015395885749753938,
            -2.9012031983333976e-10
          ],
          [
            -1.9052114145724066e-12,
            -2.9410475455731756e-06,
            1.0019427463422607e-13
          ]
        ],
        "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": [
          [
            1.0508185432911432e-09,
            -0.012297970264981362,
            -2.321780656622252e-09
          ],
          [
            9.193555916553464e-10,
            -0.01076086807819171,
            -2.0315369386736393e-09
          ],
          [
            7.878532271021754e-10,
            -0.00922382758955137,
            -1.741296939972159e-09
          ],
          [
            6.563251053748331e-10,
            -0.007686849883648372,
            -1.451056330648015e-09
          ],
          [
            5.247482448567098e-10,
            -0.006149936044890447,
            -1.1608152772346614e-09
          ],
          [
            3.931428516068536e-10,
            -0.004613087157730178,
            -8.705848819623441e-10
          ],
          [
            2.6149571397127147e-10,
            -0.0030763043063697926,
            -5.803467706400056e-10
          ],
          [
            1.298138263550186e-10,
            -0.0015395885749753813,
            -2.901203166594257e-10
          ],
          [
            -1.905198221408e-12,
            -2.9410475455571294e-06,
            1.0014211682118912e-13
          ]
        ]
      },
      "reflected": {
        "reached": true,
        "construction": "reflect_displacements_about_reconstructed_parent",
        "energies_eV": [
          -167.00712302985545,
          -167.00715548359898,
          -167.00717847855498,
          -167.00719201438744,
          -167.0071960907589,
          -167.0071907073302,
          -167.0071758637607,
          -167.00715155970784,
          -167.0071177948278
        ],
        "cartesian_polarizations_e_A2": [
          [
            -4.5983907201126266e-14,
            -1.993096168278984e-08,
            8.647745169708937e-16
          ],
          [
            -1.8675763825242856e-12,
            6.708422375909122e-06,
            1.6409004459514472e-12
          ],
          [
            -3.690581298512882e-12,
            1.3436807918313596e-05,
            3.28200929850352e-12
          ],
          [
            -5.514869267096698e-12,
            2.0165224744962828e-05,
            4.924128862399177e-12
          ],
          [
            -7.340810401394221e-12,
            2.689367193283141e-05,
            6.5671603419754064e-12
          ],
          [
            -9.16819214732529e-12,
            3.3622148556481486e-05,
            8.211339114257224e-12
          ],
          [
            -1.0997086995833237e-11,
            4.035065368863801e-05,
            9.856520997227078e-12
          ],
          [
            -1.282736474710936e-11,
            4.707918639947782e-05,
            1.150278909085185e-11
          ],
          [
            -1.4659135578185095e-11,
            5.3807745756629574e-05,
            1.3150029227113536e-11
          ]
        ],
        "raw_reduced_polarization": [
          [
            -1.9034711808420063e-12,
            -2.941047535661571e-06,
            9.755413873126717e-14
          ],
          [
            -6.989602160350718e-11,
            0.000989900307433973,
            1.8247940355028262e-10
          ],
          [
            -1.3791183718752772e-10,
            0.001982733934740784,
            3.6497212006849745e-10
          ],
          [
            -2.0594583147553983e-10,
            0.0029755596985747905,
            5.47568749540858e-10
          ],
          [
            -2.7401380765555764e-10,
            0.003968377462766787,
            7.302583083268121e-10
          ],
          [
            -3.4210584042283213e-10,
            0.004961187090795019,
            9.130669537586273e-10
          ],
          [
            -4.102255981719261e-10,
            0.005953988445870074,
            1.0959786493601009e-09
          ],
          [
            -4.783672824015465e-10,
            0.0069467813908299925,
            1.2790026263132582e-09
          ],
          [
            -5.465359850446067e-10,
            0.007939565788140287,
            1.4621261845821123e-09
          ]
        ],
        "unwrapped_reduced_polarization": [
          [
            -1.9034711808420063e-12,
            -2.941047535661571e-06,
            9.755413873126717e-14
          ],
          [
            -6.989602160350718e-11,
            0.000989900307433973,
            1.8247940355028262e-10
          ],
          [
            -1.3791183718752772e-10,
            0.001982733934740784,
            3.6497212006849745e-10
          ],
          [
            -2.0594583147553983e-10,
            0.0029755596985747905,
            5.47568749540858e-10
          ],
          [
            -2.7401380765555764e-10,
            0.003968377462766787,
            7.302583083268121e-10
          ],
          [
            -3.4210584042283213e-10,
            0.004961187090795019,
            9.130669537586273e-10
          ],
          [
            -4.102255981719261e-10,
            0.005953988445870074,
            1.0959786493601009e-09
          ],
          [
            -4.783672824015465e-10,
            0.0069467813908299925,
            1.2790026263132582e-09
          ],
          [
            -5.465359850446067e-10,
            0.007939565788140287,
            1.4621261845821123e-09
          ]
        ],
        "gauge_integer_shift": [
          0,
          0,
          0
        ],
        "expected_opposite_endpoint_reduced_polarization": [
          -1.0546279798375916e-09,
          0.012292088465630397,
          2.321978221590586e-09
        ],
        "actual_opposite_endpoint_branch_residual": 0.004352522677490225
      },
      "pnp_branch": {
        "construction": "incoming_path_concatenated_with_parent_reflection",
        "reduced_polarization": [
          [
            1.050818517608761e-09,
            -0.012297970264981384,
            -2.321780638177971e-09
          ],
          [
            9.193556418699434e-10,
            -0.010760868078191687,
            -2.0315369541886123e-09
          ],
          [
            7.878531727653761e-10,
            -0.009223827589551373,
            -1.741296945096231e-09
          ],
          [
            6.563251340250573e-10,
            -0.007686849883648389,
            -1.4510563333862956e-09
          ],
          [
            5.247482091036166e-10,
            -0.006149936044890451,
            -1.1608153018768224e-09
          ],
          [
            3.9314288007123944e-10,
            -0.004613087157730181,
            -8.705848997629341e-10
          ],
          [
            2.614957602754502e-10,
            -0.0030763043063698186,
            -5.803467538222813e-10
          ],
          [
            1.2981383057421652e-10,
            -0.0015395885749753938,
            -2.9012031983333976e-10
          ],
          [
            -1.9052114145723965e-12,
            -2.9410475455732053e-06,
            1.0019427463423541e-13
          ],
          [
            -6.989602160350718e-11,
            0.000989900307433973,
            1.8247940355028262e-10
          ],
          [
            -1.3791183718752772e-10,
            0.001982733934740784,
            3.6497212006849745e-10
          ],
          [
            -2.0594583147553983e-10,
            0.0029755596985747905,
            5.47568749540858e-10
          ],
          [
            -2.7401380765555764e-10,
            0.003968377462766787,
            7.302583083268121e-10
          ],
          [
            -3.4210584042283213e-10,
            0.004961187090795019,
            9.130669537586273e-10
          ],
          [
            -4.102255981719261e-10,
            0.005953988445870074,
            1.0959786493601009e-09
          ],
          [
            -4.783672824015465e-10,
            0.0069467813908299925,
            1.2790026263132582e-09
          ],
          [
            -5.465359850446067e-10,
            0.007939565788140287,
            1.4621261845821123e-09
          ]
        ],
        "unwrapped_reduced_polarization": [
          [
            1.050818517608761e-09,
            -0.012297970264981384,
            -2.321780638177971e-09
          ],
          [
            9.193556418699434e-10,
            -0.010760868078191687,
            -2.0315369541886123e-09
          ],
          [
            7.878531727653761e-10,
            -0.009223827589551373,
            -1.741296945096231e-09
          ],
          [
            6.563251340250573e-10,
            -0.007686849883648389,
            -1.4510563333862956e-09
          ],
          [
            5.247482091036166e-10,
            -0.006149936044890451,
            -1.1608153018768224e-09
          ],
          [
            3.9314288007123944e-10,
            -0.004613087157730181,
            -8.705848997629341e-10
          ],
          [
            2.614957602754502e-10,
            -0.0030763043063698186,
            -5.803467538222813e-10
          ],
          [
            1.2981383057421652e-10,
            -0.0015395885749753938,
            -2.9012031983333976e-10
          ],
          [
            -1.9052114145724066e-12,
            -2.9410475455731756e-06,
            1.0019427463422607e-13
          ],
          [
            -6.989602160350718e-11,
            0.000989900307433973,
            1.8247940355028262e-10
          ],
          [
            -1.3791183718752772e-10,
            0.001982733934740784,
            3.6497212006849745e-10
          ],
          [
            -2.0594583147553983e-10,
            0.0029755596985747905,
            5.47568749540858e-10
          ],
          [
            -2.7401380765555764e-10,
            0.003968377462766787,
            7.302583083268121e-10
          ],
          [
            -3.4210584042283213e-10,
            0.004961187090795019,
            9.130669537586273e-10
          ],
          [
            -4.102255981719261e-10,
            0.005953988445870074,
            1.0959786493601009e-09
          ],
          [
            -4.783672824015465e-10,
            0.0069467813908299925,
            1.2790026263132582e-09
          ],
          [
            -5.465359850446067e-10,
            0.007939565788140287,
            1.4621261845821123e-09
          ]
        ],
        "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": [
          [
            1.0508185432911432e-09,
            -0.012297970264981362,
            -2.321780656622252e-09
          ],
          [
            9.193555916553464e-10,
            -0.01076086807819171,
            -2.0315369386736393e-09
          ],
          [
            7.878532271021754e-10,
            -0.00922382758955137,
            -1.741296939972159e-09
          ],
          [
            6.563251053748331e-10,
            -0.007686849883648372,
            -1.451056330648015e-09
          ],
          [
            5.247482448567098e-10,
            -0.006149936044890447,
            -1.1608152772346614e-09
          ],
          [
            3.931428516068536e-10,
            -0.004613087157730178,
            -8.705848819623441e-10
          ],
          [
            2.6149571397127147e-10,
            -0.0030763043063697926,
            -5.803467706400056e-10
          ],
          [
            1.298138263550186e-10,
            -0.0015395885749753813,
            -2.901203166594257e-10
          ],
          [
            -1.905198221408e-12,
            -2.9410475455571294e-06,
            1.0014211682118912e-13
          ],
          [
            -6.989603340556982e-11,
            0.0009899003074339552,
            1.8247936495185968e-10
          ],
          [
            -1.3791184860778571e-10,
            0.001982733934740799,
            3.649721636023173e-10
          ],
          [
            -2.0594581595645423e-10,
            0.00297555969857477,
            5.475687681055774e-10
          ],
          [
            -2.740138116408275e-10,
            0.003968377462766792,
            7.302582982759986e-10
          ],
          [
            -3.421058436536839e-10,
            0.004961187090795072,
            9.130669553769621e-10
          ],
          [
            -4.102255757310047e-10,
            0.005953988445870029,
            1.0959786411746109e-09
          ],
          [
            -4.783672902242131e-10,
            0.006946781390829937,
            1.2790026815423516e-09
          ],
          [
            -5.465359831369199e-10,
            0.007939565788140257,
            1.4621261978930988e-09
          ]
        ]
      },
      "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": "C2",
        "spacegroup_number": 5,
        "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": 2.9410475474677804e-06,
        "parent_symmetrization_rmsd_A": 0.002028595265736744,
        "parent_cell_rmsd_A": 0.005993590614361183,
        "energy_eV": -167.00712302985545,
        "reduced_polarization": [
          -1.901687901680667e-12,
          -2.941047547467164e-06,
          1.0027300557962645e-13
        ],
        "cartesian_polarization_e_A2": [
          -4.5943669482393883e-14,
          -1.993096176279427e-08,
          8.892418087335407e-16
        ],
        "ranking_score": 0.503532875014422
      }
    }
  ],
  "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": 112,
      "full_response": 30,
      "energy_polarization": 82
    },
    "model_evaluations_for_recovery_and_path_properties": {
      "total": 137,
      "full_response": 55,
      "energy_polarization": 82
    },
    "elapsed_seconds": 517.9578481870121
  }
}