{
  "schema": "ferrofinder.endpoint_parent_recovery.v4_variable_cell",
  "status": "complete",
  "input_atom_count": 8,
  "input_formula": "I6P2",
  "input_spacegroup": "P6_3",
  "input_pointgroup": "6",
  "input_is_polar_point_group": true,
  "input_energy_eV": -21.50515155177238,
  "input_cartesian_polarization_e_A2": [
    -1.7151476096230873e-11,
    0.00242342619980116,
    6.861840201163561e-11
  ],
  "input_reduced_polarization": [
    1.2247193611726476e-09,
    0.1169504417176473,
    4.319494792210162e-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": [
        0.0,
        0.5,
        0.5
      ],
      "target_reduced_polarization": [
        0.0,
        0.5,
        0.5
      ]
    }
  ],
  "parent_candidates": [
    {
      "candidate_id": "inversion_parent_endpoint_00",
      "source": "same_species_inversion_center_projection_from_endpoint",
      "spacegroup": "P6_3/m",
      "spacegroup_number": 176,
      "pointgroup": "6/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": 2.4305258513885067e-16,
      "parent_symmetrization_rmsd_A": 0.9068812780409947,
      "parent_cell_rmsd_A": 0.0,
      "energy_eV": -17.783894781161106,
      "reduced_polarization": [
        2.4210228957966455e-16,
        -4.62255910645128e-19,
        -2.146687779896211e-17
      ],
      "cartesian_polarization_e_A2": [
        4.6378365373293626e-18,
        -9.578784555384088e-21,
        -3.4101739245068843e-19
      ],
      "ranking_score": 0.9068812780409952
    },
    {
      "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": 5.0642962153391745e-15,
      "parent_symmetrization_rmsd_A": 1.1973700938824678,
      "parent_cell_rmsd_A": 0.0,
      "energy_eV": -5.429702038008612,
      "reduced_polarization": [
        3.974566563987154e-15,
        -1.0445599302683426e-18,
        -3.1384575342082603e-15
      ],
      "cartesian_polarization_e_A2": [
        1.0169138642879529e-16,
        -2.1645184619194084e-20,
        -4.985674277629065e-17
      ],
      "ranking_score": 1.197370093882478
    },
    {
      "candidate_id": "inversion_parent_endpoint_02",
      "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": 2.334268090414764e-15,
      "parent_symmetrization_rmsd_A": 1.1973715454703122,
      "parent_cell_rmsd_A": 0.0,
      "energy_eV": -5.429709132637747,
      "reduced_polarization": [
        1.0077412169845002e-15,
        -1.541650233681753e-17,
        2.1054755968604543e-15
      ],
      "cartesian_polarization_e_A2": [
        -8.253824758146739e-19,
        -3.194580125019043e-19,
        3.3447052926561276e-17
      ],
      "ranking_score": 1.1973715454703169
    },
    {
      "candidate_id": "bec_projection_00",
      "source": "MACEField_BEC_backprojection",
      "spacegroup": "P6_3",
      "spacegroup_number": 173,
      "pointgroup": "6",
      "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": 0.0005095372297643785,
      "parent_symmetrization_rmsd_A": 0.17313541459632692,
      "parent_cell_rmsd_A": 0.34285511175307276,
      "energy_eV": -19.580946161560576,
      "reduced_polarization": [
        1.1858553764871823e-10,
        -0.0005095372297641789,
        4.351130736268607e-10
      ],
      "cartesian_polarization_e_A2": [
        -1.6979213033388013e-12,
        -9.8065926004752e-06,
        6.4625420966920305e-12
      ],
      "ranking_score": 0.7598682669941239
    },
    {
      "candidate_id": "inversion_parent_bec_00_00",
      "source": "same_species_inversion_center_projection_after_BEC",
      "spacegroup": "P6_3/m",
      "spacegroup_number": 176,
      "pointgroup": "6/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": 4.0699967101369195e-16,
      "parent_symmetrization_rmsd_A": 0.9115645187428394,
      "parent_cell_rmsd_A": 0.34285511175307276,
      "energy_eV": -18.569501543712825,
      "reduced_polarization": [
        1.6412820421534967e-17,
        -3.0914814281868427e-17,
        4.05491831963335e-16
      ],
      "cartesian_polarization_e_A2": [
        -3.198105004301996e-18,
        -5.949888832646487e-19,
        6.027197892722993e-18
      ],
      "ranking_score": 0.9972782966811083
    },
    {
      "candidate_id": "inversion_parent_bec_00_01",
      "source": "same_species_inversion_center_projection_after_BEC",
      "spacegroup": "P-1",
      "spacegroup_number": 2,
      "pointgroup": "-1",
      "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": 2.7707801112312103e-15,
      "parent_symmetrization_rmsd_A": 1.4330323444792334,
      "parent_cell_rmsd_A": 0.34285511175307276,
      "energy_eV": -14.315724857281653,
      "reduced_polarization": [
        6.187595959740095e-16,
        -2.5197001454762423e-15,
        9.723529009940389e-16
      ],
      "cartesian_polarization_e_A2": [
        2.2755747145994975e-18,
        -4.8494342228694693e-17,
        1.4452974538672485e-17
      ],
      "ranking_score": 1.5187461224175072
    },
    {
      "candidate_id": "bec_projection_01",
      "source": "MACEField_BEC_backprojection",
      "spacegroup": "P6_3",
      "spacegroup_number": 173,
      "pointgroup": "6",
      "has_inversion": false,
      "is_polar_point_group": true,
      "nonpolar_parent_hypothesis": false,
      "symmetry_tolerance_A": null,
      "target_reduced_polarization": [
        0.0,
        0.5,
        0.0
      ],
      "formal_class": [
        0.0,
        0.5,
        0.0
      ],
      "target_residual": 0.28997955848067714,
      "parent_symmetrization_rmsd_A": 0.08608133607331961,
      "parent_cell_rmsd_A": 0.7427629408419644,
      "energy_eV": -20.13338553751926,
      "reduced_polarization": [
        6.40211887516205e-10,
        0.2100204415193229,
        1.754628373617254e-09
      ],
      "cartesian_polarization_e_A2": [
        -5.353230959681772e-12,
        0.005136942442433462,
        3.125190000215813e-11
      ],
      "ranking_score": 1.351731188245165
    },
    {
      "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": 0.328948145881196,
      "parent_symmetrization_rmsd_A": 0.19976359232995589,
      "parent_cell_rmsd_A": 0.9204340606065583,
      "energy_eV": -18.190149783303465,
      "reduced_polarization": [
        0.0004907006615568173,
        0.05751818784300863,
        0.17611992966717804
      ],
      "cartesian_polarization_e_A2": [
        -0.0014044599081175387,
        0.0008339359835711113,
        0.002494693561302036
      ],
      "ranking_score": 1.5877683992439873
    },
    {
      "candidate_id": "bec_projection_03",
      "source": "MACEField_BEC_backprojection",
      "spacegroup": "P1",
      "spacegroup_number": 1,
      "pointgroup": "1",
      "has_inversion": false,
      "is_polar_point_group": true,
      "nonpolar_parent_hypothesis": false,
      "symmetry_tolerance_A": null,
      "target_reduced_polarization": [
        0.0,
        0.5,
        0.5
      ],
      "formal_class": [
        0.0,
        0.5,
        0.5
      ],
      "target_residual": 0.4522843572097011,
      "parent_symmetrization_rmsd_A": 0.20892768813364593,
      "parent_cell_rmsd_A": 0.7760614529670984,
      "energy_eV": -19.0346518451324,
      "reduced_polarization": [
        0.005008059507637572,
        0.21254854078511445,
        0.1508471427701136
      ],
      "cartesian_polarization_e_A2": [
        -0.0014338763104913166,
        0.0050431885997274314,
        0.0026241079212947957
      ],
      "ranking_score": 1.8075117657948228
    }
  ],
  "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": [
              1.2247193611726476e-09,
              0.1169504417176473,
              4.319494792210162e-09
            ],
            "branch_aligned_reduced_polarization": [
              1.2247193611726476e-09,
              0.1169504417176473,
              4.319494792210162e-09
            ],
            "target_residual": 0.11695044171764739,
            "energy_eV": -21.50515155177238,
            "max_atomic_step_A": 0.05128458806347862,
            "max_log_strain_component": 0.02,
            "step_scale": 0.35860330107913563,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 2.792517141667799,
            "cell_principal_stretches": [
              1.0202013513898491,
              1.0202012577447594,
              1.0161250357466476
            ],
            "cell_volume_ratio": 1.0575938116135042,
            "cell_rmsd_from_input_A": 0.18266384536557123
          },
          {
            "iteration": 1,
            "reduced_polarization": [
              7.411594841823189e-10,
              0.06392324171231777,
              2.5883763371097374e-09
            ],
            "branch_aligned_reduced_polarization": [
              7.411594841823189e-10,
              0.06392324171231777,
              2.5883763371097374e-09
            ],
            "target_residual": 0.06392324171231782,
            "energy_eV": -20.989181142077513,
            "max_atomic_step_A": 0.08397127269269192,
            "max_log_strain_component": 0.016940114826651493,
            "step_scale": 1.0,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 2.792517141667799,
            "cell_principal_stretches": [
              1.0376309016186513,
              1.0376307257006665,
              1.029986255424311
            ],
            "cell_volume_ratio": 1.1089632381414631,
            "cell_rmsd_from_input_A": 0.34285511175307276
          },
          {
            "iteration": 2,
            "reduced_polarization": [
              1.1858553764871823e-10,
              -0.0005095372297641789,
              4.351130736268607e-10
            ],
            "branch_aligned_reduced_polarization": [
              1.1858553764871823e-10,
              -0.0005095372297641789,
              4.351130736268607e-10
            ],
            "target_residual": 0.0005095372297643785,
            "energy_eV": -19.580946161560576
          }
        ],
        "iterations": 2
      },
      "parent": {
        "candidate_id": "bec_projection_00",
        "source": "MACEField_BEC_backprojection",
        "spacegroup": "P6_3",
        "spacegroup_number": 173,
        "pointgroup": "6",
        "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": 0.0005095372297643785,
        "parent_symmetrization_rmsd_A": 0.17313541459632692,
        "parent_cell_rmsd_A": 0.34285511175307276,
        "energy_eV": -19.580946161560576,
        "reduced_polarization": [
          1.1858553764871823e-10,
          -0.0005095372297641789,
          4.351130736268607e-10
        ],
        "cartesian_polarization_e_A2": [
          -1.6979213033388013e-12,
          -9.8065926004752e-06,
          6.4625420966920305e-12
        ],
        "ranking_score": 0.7598682669941239
      },
      "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": [
          -21.505151551772382,
          -21.44713760785877,
          -21.331446546784292,
          -21.160890231653703,
          -20.937910548330372,
          -20.66507369808079,
          -20.345391991983355,
          -19.982547109722905,
          -19.58094616156056
        ],
        "cartesian_polarizations_e_A2": [
          [
            -1.7151474732161304e-11,
            0.0024234261998011637,
            6.861840095448169e-11
          ],
          [
            -1.4995927497695667e-11,
            0.002158473142062919,
            6.030985595003164e-11
          ],
          [
            -1.2736160620637124e-11,
            0.0018593856373238864,
            5.1680791846465353e-11
          ],
          [
            -1.046231551648213e-11,
            0.0015337666093497163,
            4.2899095498912096e-11
          ],
          [
            -8.261669280940944e-12,
            0.0011925294231886218,
            3.41875475735257e-11
          ],
          [
            -6.221051027600554e-12,
            0.0008505498618705559,
            2.5847016124439235e-11
          ],
          [
            -4.4181033752627606e-12,
            0.0005253088810058098,
            1.8233778641517376e-11
          ],
          [
            -2.905510592352057e-12,
            0.00023406854582774345,
            1.1691139878161803e-11
          ],
          [
            -1.6979174287115845e-12,
            -9.806592600476554e-06,
            6.462544952692052e-12
          ]
        ],
        "raw_reduced_polarization": [
          [
            1.2247194022624402e-09,
            0.1169504417176475,
            4.31949472566284e-09
          ],
          [
            1.0865761302535783e-09,
            0.1051306699120046,
            3.819550748620414e-09
          ],
          [
            9.42443096443069e-10,
            0.0914035302628275,
            3.292845376289719e-09
          ],
          [
            7.926993070175378e-10,
            0.0760962913873708,
            2.7499771758844976e-09
          ],
          [
            6.396207135095067e-10,
            0.059715081725328356,
            2.2053027235158348e-09
          ],
          [
            4.880525026329522e-10,
            0.0429858403393435,
            1.6785256121074784e-09
          ],
          [
            3.4524705631910925e-10,
            0.026794835866208677,
            1.1933596978036016e-09
          ],
          [
            2.1960123999400593e-10,
            0.01205008554449172,
            7.731478544474188e-10
          ],
          [
            1.1858585946999626e-10,
            -0.0005095372297642492,
            4.3511326577001295e-10
          ]
        ],
        "unwrapped_reduced_polarization": [
          [
            1.2247194022624402e-09,
            0.1169504417176475,
            4.31949472566284e-09
          ],
          [
            1.0865761302535783e-09,
            0.1051306699120046,
            3.819550748620414e-09
          ],
          [
            9.42443096443069e-10,
            0.0914035302628275,
            3.292845376289719e-09
          ],
          [
            7.926993070175378e-10,
            0.0760962913873708,
            2.7499771758844976e-09
          ],
          [
            6.396207135095067e-10,
            0.059715081725328356,
            2.2053027235158348e-09
          ],
          [
            4.880525026329522e-10,
            0.0429858403393435,
            1.6785256121074784e-09
          ],
          [
            3.4524705631910925e-10,
            0.026794835866208677,
            1.1933596978036016e-09
          ],
          [
            2.1960123999400593e-10,
            0.01205008554449172,
            7.731478544474188e-10
          ],
          [
            1.1858585946999626e-10,
            -0.0005095372297642484,
            4.3511326577001295e-10
          ]
        ],
        "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": [
          [
            1.2247194369763292e-09,
            0.11695044171764746,
            4.3194947618729884e-09
          ],
          [
            1.0865761623790604e-09,
            0.10513066991200459,
            3.8195507867655465e-09
          ],
          [
            9.424431235416364e-10,
            0.09140353026282755,
            3.292845329738725e-09
          ],
          [
            7.926993506046642e-10,
            0.07609629138737084,
            2.749977134897108e-09
          ],
          [
            6.39620689746323e-10,
            0.059715081725328356,
            2.2053027182167284e-09
          ],
          [
            4.880524873129843e-10,
            0.042985840339343495,
            1.6785256518048186e-09
          ],
          [
            3.452470531684071e-10,
            0.026794835866208677,
            1.1933597443558597e-09
          ],
          [
            2.1960122609243626e-10,
            0.012050085544491718,
            7.731478790518054e-10
          ],
          [
            1.18585807840077e-10,
            -0.0005095372297642675,
            4.3511327874057315e-10
          ]
        ]
      },
      "reflected": {
        "reached": true,
        "construction": "reflect_displacements_about_reconstructed_parent",
        "energies_eV": [
          -19.580946161560565,
          -19.48845320815014,
          -19.389260394758075,
          -19.283653354129342,
          -19.171893770546284,
          -19.05430701974757,
          -18.93135673897317,
          -18.80366341171582,
          -18.671980022613475
        ],
        "cartesian_polarizations_e_A2": [
          [
            -1.6979270845286167e-12,
            -9.806592600479414e-06,
            6.46253596570948e-12
          ],
          [
            -1.487409138942658e-12,
            -3.0126123181555955e-05,
            5.2877597066576976e-12
          ],
          [
            -1.2330639723001607e-12,
            -4.325144900323642e-05,
            4.3046434654392955e-12
          ],
          [
            -9.467310116957546e-13,
            -4.826035333609206e-05,
            3.4804918993190592e-12
          ],
          [
            -6.277252531309181e-13,
            -4.3650941620571775e-05,
            2.7873541473512487e-12
          ],
          [
            -2.6709333825679164e-13,
            -2.7702290267130654e-05,
            2.213065188867245e-12
          ],
          [
            1.3937357220896115e-13,
            9.993834850210192e-07,
            1.7509538049539036e-12
          ],
          [
            5.856306752505371e-13,
            4.3226794701161176e-05,
            1.3865898292128886e-12
          ],
          [
            1.057988658970375e-12,
            9.90058177193034e-05,
            1.0934622941344033e-12
          ]
        ],
        "raw_reduced_polarization": [
          [
            1.1858499457873823e-10,
            -0.0005095372297643978,
            4.3511266115267424e-10
          ],
          [
            9.078150918982318e-11,
            -0.001550923299744858,
            3.5368686840175115e-10
          ],
          [
            7.215387432873307e-11,
            -0.0022061600687169757,
            2.8591102602148106e-10
          ],
          [
            6.076030193544663e-11,
            -0.002439024372613765,
            2.29387908921877e-10
          ],
          [
            5.5581824683302364e-11,
            -0.002185790552060612,
            1.8210836290102998e-10
          ],
          [
            5.6609744087268866e-11,
            -0.0013744213359546693,
            1.431656491136099e-10
          ],
          [
            6.375697274332337e-11,
            4.9127613327571896e-05,
            1.1206099127457426e-10
          ],
          [
            7.613601281742241e-11,
            0.002105405805855191,
            8.784118592118998e-11
          ],
          [
            9.209363338065448e-11,
            0.00477785299005162,
            6.88329157561964e-11
          ]
        ],
        "unwrapped_reduced_polarization": [
          [
            1.1858499457873823e-10,
            -0.0005095372297643978,
            4.3511266115267424e-10
          ],
          [
            9.078150918982318e-11,
            -0.001550923299744858,
            3.5368686840175115e-10
          ],
          [
            7.215387432873307e-11,
            -0.0022061600687169757,
            2.8591102602148106e-10
          ],
          [
            6.076030193544663e-11,
            -0.002439024372613765,
            2.29387908921877e-10
          ],
          [
            5.5581824683302364e-11,
            -0.002185790552060612,
            1.8210836290102998e-10
          ],
          [
            5.6609744087268866e-11,
            -0.0013744213359546693,
            1.431656491136099e-10
          ],
          [
            6.375697274332337e-11,
            4.912761332757183e-05,
            1.1206099127457426e-10
          ],
          [
            7.613601281742241e-11,
            0.002105405805855191,
            8.784118592118998e-11
          ],
          [
            9.209363338065448e-11,
            0.00477785299005162,
            6.88329157561964e-11
          ]
        ],
        "gauge_integer_shift": [
          0,
          0,
          0
        ],
        "expected_opposite_endpoint_reduced_polarization": [
          -1.0030323303154195e-09,
          -0.11789694079937307,
          -3.5058666477940534e-09
        ],
        "actual_opposite_endpoint_branch_residual": 0.12267479378942475
      },
      "pnp_branch": {
        "construction": "incoming_path_concatenated_with_parent_reflection",
        "reduced_polarization": [
          [
            1.2247194022624402e-09,
            0.1169504417176475,
            4.31949472566284e-09
          ],
          [
            1.0865761302535783e-09,
            0.1051306699120046,
            3.819550748620414e-09
          ],
          [
            9.42443096443069e-10,
            0.0914035302628275,
            3.292845376289719e-09
          ],
          [
            7.926993070175378e-10,
            0.0760962913873708,
            2.7499771758844976e-09
          ],
          [
            6.396207135095067e-10,
            0.059715081725328356,
            2.2053027235158348e-09
          ],
          [
            4.880525026329522e-10,
            0.0429858403393435,
            1.6785256121074784e-09
          ],
          [
            3.4524705631910925e-10,
            0.026794835866208677,
            1.1933596978036016e-09
          ],
          [
            2.1960123999400593e-10,
            0.01205008554449172,
            7.731478544474188e-10
          ],
          [
            1.1858585946999626e-10,
            -0.0005095372297642492,
            4.3511326577001295e-10
          ],
          [
            9.078150918982318e-11,
            -0.001550923299744858,
            3.5368686840175115e-10
          ],
          [
            7.215387432873307e-11,
            -0.0022061600687169757,
            2.8591102602148106e-10
          ],
          [
            6.076030193544663e-11,
            -0.002439024372613765,
            2.29387908921877e-10
          ],
          [
            5.5581824683302364e-11,
            -0.002185790552060612,
            1.8210836290102998e-10
          ],
          [
            5.6609744087268866e-11,
            -0.0013744213359546693,
            1.431656491136099e-10
          ],
          [
            6.375697274332337e-11,
            4.9127613327571896e-05,
            1.1206099127457426e-10
          ],
          [
            7.613601281742241e-11,
            0.002105405805855191,
            8.784118592118998e-11
          ],
          [
            9.209363338065448e-11,
            0.00477785299005162,
            6.88329157561964e-11
          ]
        ],
        "unwrapped_reduced_polarization": [
          [
            1.2247194022624402e-09,
            0.1169504417176475,
            4.31949472566284e-09
          ],
          [
            1.0865761302535783e-09,
            0.1051306699120046,
            3.819550748620414e-09
          ],
          [
            9.42443096443069e-10,
            0.0914035302628275,
            3.292845376289719e-09
          ],
          [
            7.926993070175378e-10,
            0.0760962913873708,
            2.7499771758844976e-09
          ],
          [
            6.396207135095067e-10,
            0.059715081725328356,
            2.2053027235158348e-09
          ],
          [
            4.880525026329522e-10,
            0.0429858403393435,
            1.6785256121074784e-09
          ],
          [
            3.4524705631910925e-10,
            0.026794835866208677,
            1.1933596978036016e-09
          ],
          [
            2.1960123999400593e-10,
            0.01205008554449172,
            7.731478544474188e-10
          ],
          [
            1.1858585946999626e-10,
            -0.0005095372297642484,
            4.3511326577001295e-10
          ],
          [
            9.078150918982318e-11,
            -0.001550923299744858,
            3.5368686840175115e-10
          ],
          [
            7.215387432873307e-11,
            -0.0022061600687169757,
            2.8591102602148106e-10
          ],
          [
            6.076030193544663e-11,
            -0.002439024372613765,
            2.29387908921877e-10
          ],
          [
            5.5581824683302364e-11,
            -0.002185790552060612,
            1.8210836290102998e-10
          ],
          [
            5.6609744087268866e-11,
            -0.0013744213359546693,
            1.431656491136099e-10
          ],
          [
            6.375697274332337e-11,
            4.912761332757183e-05,
            1.1206099127457426e-10
          ],
          [
            7.613601281742241e-11,
            0.002105405805855191,
            8.784118592118998e-11
          ],
          [
            9.209363338065448e-11,
            0.00477785299005162,
            6.88329157561964e-11
          ]
        ],
        "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": [
          [
            1.2247194369763292e-09,
            0.11695044171764746,
            4.3194947618729884e-09
          ],
          [
            1.0865761623790604e-09,
            0.10513066991200459,
            3.8195507867655465e-09
          ],
          [
            9.424431235416364e-10,
            0.09140353026282755,
            3.292845329738725e-09
          ],
          [
            7.926993506046642e-10,
            0.07609629138737084,
            2.749977134897108e-09
          ],
          [
            6.39620689746323e-10,
            0.059715081725328356,
            2.2053027182167284e-09
          ],
          [
            4.880524873129843e-10,
            0.042985840339343495,
            1.6785256518048186e-09
          ],
          [
            3.452470531684071e-10,
            0.026794835866208677,
            1.1933597443558597e-09
          ],
          [
            2.1960122609243626e-10,
            0.012050085544491718,
            7.731478790518054e-10
          ],
          [
            1.18585807840077e-10,
            -0.0005095372297642675,
            4.3511327874057315e-10
          ],
          [
            9.078149343366704e-11,
            -0.0015509232997448774,
            3.5368685757930507e-10
          ],
          [
            7.215383845959877e-11,
            -0.002206160068716989,
            2.8591107259501314e-10
          ],
          [
            6.076028569168557e-11,
            -0.002439024372613785,
            2.2938795307680948e-10
          ],
          [
            5.558187243792645e-11,
            -0.0021857905520605847,
            1.8210832841702995e-10
          ],
          [
            5.660971691412442e-11,
            -0.0013744213359546675,
            1.431657015160681e-10
          ],
          [
            6.375699967975379e-11,
            4.912761332753757e-05,
            1.1206102712435495e-10
          ],
          [
            7.613598640432429e-11,
            0.002105405805855165,
            8.784117877524977e-11
          ],
          [
            9.209366602647151e-11,
            0.004777852990051623,
            6.883293934834e-11
          ]
        ]
      },
      "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": false,
        "history": [
          {
            "iteration": 0,
            "reduced_polarization": [
              1.2247193611726476e-09,
              0.1169504417176473,
              4.319494792210162e-09
            ],
            "branch_aligned_reduced_polarization": [
              1.2247193611726476e-09,
              0.11695044171764729,
              4.319494792210162e-09
            ],
            "target_residual": 0.38304955828235276,
            "energy_eV": -21.50515155177238,
            "max_atomic_step_A": 0.05128458793990194,
            "max_log_strain_component": 0.02,
            "step_scale": 0.10948665402636365,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 2.792517141667799,
            "cell_principal_stretches": [
              0.9841308547871779,
              0.9801987523624346,
              0.980198662389215
            ],
            "cell_volume_ratio": 0.9455425977524993,
            "cell_rmsd_from_input_A": 0.17591532374849453
          },
          {
            "iteration": 1,
            "reduced_polarization": [
              1.0265556136734577e-09,
              0.14601355706304237,
              3.5443435203799097e-09
            ],
            "branch_aligned_reduced_polarization": [
              1.0265556136734577e-09,
              0.14601355706304237,
              3.5443435203799097e-09
            ],
            "target_residual": 0.35398644293695763,
            "energy_eV": -21.162327317688312,
            "max_atomic_step_A": 0.025287900118669524,
            "max_log_strain_component": 0.02,
            "step_scale": 0.0758691870594843,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 2.792517141667799,
            "cell_principal_stretches": [
              0.9685135393441416,
              0.9607895941328736,
              0.9607894177496065
            ],
            "cell_volume_ratio": 0.8940508041645444,
            "cell_rmsd_from_input_A": 0.3453353973004859
          },
          {
            "iteration": 2,
            "reduced_polarization": [
              9.400524368991307e-10,
              0.16437434258662523,
              3.0223779871451077e-09
            ],
            "branch_aligned_reduced_polarization": [
              9.400524368991307e-10,
              0.1643743425866252,
              3.0223779871451077e-09
            ],
            "target_residual": 0.33562565741337486,
            "energy_eV": -20.757798623882813,
            "max_atomic_step_A": 0.034358630008369334,
            "max_log_strain_component": 0.02,
            "step_scale": 0.07972077483171482,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 2.792517141667799,
            "cell_principal_stretches": [
              0.9531440573477057,
              0.9417647614518528,
              0.9417645021158768
            ],
            "cell_volume_ratio": 0.8453631198924542,
            "cell_rmsd_from_input_A": 0.5085038439057352
          },
          {
            "iteration": 3,
            "reduced_polarization": [
              8.213040753433658e-10,
              0.18214952437354756,
              2.444207214989654e-09
            ],
            "branch_aligned_reduced_polarization": [
              8.213040753433658e-10,
              0.1821495243735476,
              2.444207214989654e-09
            ],
            "target_residual": 0.3178504756264524,
            "energy_eV": -20.39633885086956,
            "max_atomic_step_A": 0.028077538938356128,
            "max_log_strain_component": 0.02,
            "step_scale": 0.0819220989207059,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 2.792517141667799,
            "cell_principal_stretches": [
              0.9380184758929172,
              0.9231166441940124,
              0.9231163052596278
            ],
            "cell_volume_ratio": 0.7993268404272686,
            "cell_rmsd_from_input_A": 0.6656550107712337
          },
          {
            "iteration": 4,
            "reduced_polarization": [
              6.776037295046275e-10,
              0.1972622008500501,
              1.8549314333168738e-09
            ],
            "branch_aligned_reduced_polarization": [
              6.776037295046275e-10,
              0.19726220085005008,
              1.8549314333168738e-09
            ],
            "target_residual": 0.3027377991499499,
            "energy_eV": -20.022506239406926,
            "max_atomic_step_A": 0.016187657778418997,
            "max_log_strain_component": 0.02,
            "step_scale": 0.04162664439866072,
            "strain_jacobian_refreshed": true,
            "strain_jacobian_frobenius_norm": 2.310643943970665,
            "cell_principal_stretches": [
              0.9204336633974223,
              0.9204332648964298,
              0.9194444656074614
            ],
            "cell_volume_ratio": 0.7789512934737246,
            "cell_rmsd_from_input_A": 0.7427629408419644
          },
          {
            "iteration": 5,
            "reduced_polarization": [
              6.40211887516205e-10,
              0.2100204415193229,
              1.754628373617254e-09
            ],
            "branch_aligned_reduced_polarization": [
              6.40211887516205e-10,
              0.21002044151932286,
              1.754628373617254e-09
            ],
            "target_residual": 0.28997955848067714,
            "energy_eV": -20.13338553751926
          }
        ],
        "iterations": 5
      },
      "parent": {
        "candidate_id": "bec_projection_01",
        "source": "MACEField_BEC_backprojection",
        "spacegroup": "P6_3",
        "spacegroup_number": 173,
        "pointgroup": "6",
        "has_inversion": false,
        "is_polar_point_group": true,
        "nonpolar_parent_hypothesis": false,
        "symmetry_tolerance_A": null,
        "target_reduced_polarization": [
          0.0,
          0.5,
          0.0
        ],
        "formal_class": [
          0.0,
          0.5,
          0.0
        ],
        "target_residual": 0.28997955848067714,
        "parent_symmetrization_rmsd_A": 0.08608133607331961,
        "parent_cell_rmsd_A": 0.7427629408419644,
        "energy_eV": -20.13338553751926,
        "reduced_polarization": [
          6.40211887516205e-10,
          0.2100204415193229,
          1.754628373617254e-09
        ],
        "cartesian_polarization_e_A2": [
          -5.353230959681772e-12,
          0.005136942442433462,
          3.125190000215813e-11
        ],
        "ranking_score": 1.351731188245165
      },
      "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
        ],
        [
          0.5,
          0.0,
          0.0
        ],
        [
          0.5,
          0.0,
          0.5
        ]
      ],
      "target_reduced_polarization": [
        0.0,
        0.0,
        0.5
      ],
      "bec_backprojection": {
        "converged_to_target": false,
        "history": [
          {
            "iteration": 0,
            "reduced_polarization": [
              1.2247193611726476e-09,
              0.1169504417176473,
              4.319494792210162e-09
            ],
            "branch_aligned_reduced_polarization": [
              1.2247193611726476e-09,
              0.1169504417176473,
              4.31949481738414e-09
            ],
            "target_residual": 0.5134952789446637,
            "energy_eV": -21.50515155177238,
            "max_atomic_step_A": 0.11789613826284166,
            "max_log_strain_component": 0.02,
            "step_scale": 0.3127664890876953,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 2.792517141667799,
            "cell_principal_stretches": [
              1.0397664448008879,
              1.017596581135017,
              0.9924280090441154
            ],
            "cell_volume_ratio": 1.0500511376118569,
            "cell_rmsd_from_input_A": 0.2618514194309795
          },
          {
            "iteration": 1,
            "reduced_polarization": [
              -0.002031517222831736,
              0.08001738481325538,
              0.11598741195490293
            ],
            "branch_aligned_reduced_polarization": [
              -0.002031517222831736,
              0.08001738481325538,
              0.11598741195490292
            ],
            "target_residual": 0.3922659515069753,
            "energy_eV": -20.64209456751115,
            "max_atomic_step_A": 0.06974307793445436,
            "max_log_strain_component": 0.02,
            "step_scale": 0.17542372266039166,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 2.792517141667799,
            "cell_principal_stretches": [
              1.0722605252220765,
              1.026118094279898,
              0.97690633130831
            ],
            "cell_volume_ratio": 1.0748567499281871,
            "cell_rmsd_from_input_A": 0.4880986816866402
          },
          {
            "iteration": 2,
            "reduced_polarization": [
              -0.0022128346286978857,
              0.06916920063127045,
              0.14850556494706607
            ],
            "branch_aligned_reduced_polarization": [
              -0.0022128346286978857,
              0.06916920063127045,
              0.14850556494706607
            ],
            "target_residual": 0.3582423939544901,
            "energy_eV": -19.732664007750454,
            "max_atomic_step_A": 0.03406748555077907,
            "max_log_strain_component": 0.02,
            "step_scale": 0.13332723574509409,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 2.792517141667799,
            "cell_principal_stretches": [
              1.1053923291882586,
              1.03381504568704,
              0.9604574454566059
            ],
            "cell_volume_ratio": 1.0975831279529131,
            "cell_rmsd_from_input_A": 0.7296643099113014
          },
          {
            "iteration": 3,
            "reduced_polarization": [
              -0.0014503143328874332,
              0.06347459480695784,
              0.16043392101709172
            ],
            "branch_aligned_reduced_polarization": [
              -0.0014503143328874332,
              0.06347459480695784,
              0.16043392101709175
            ],
            "target_residual": 0.3454507918552197,
            "energy_eV": -19.010971999261734,
            "max_atomic_step_A": 0.024264399001795656,
            "max_log_strain_component": 0.02,
            "step_scale": 0.13586162126808699,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 2.792517141667799,
            "cell_principal_stretches": [
              1.1390372974039187,
              1.0408321522191195,
              0.9435050771467192
            ],
            "cell_volume_ratio": 1.118569275652129,
            "cell_rmsd_from_input_A": 0.9825354111748578
          },
          {
            "iteration": 4,
            "reduced_polarization": [
              -0.00020759893613787037,
              0.05995838251622629,
              0.16699115148493654
            ],
            "branch_aligned_reduced_polarization": [
              -0.00020759893613787037,
              0.05995838251622629,
              0.16699115148493654
            ],
            "target_residual": 0.3383636267694991,
            "energy_eV": -18.39075059036009,
            "max_atomic_step_A": 0.09571011684942267,
            "max_log_strain_component": 0.02,
            "step_scale": 0.08993852288137529,
            "strain_jacobian_refreshed": true,
            "strain_jacobian_frobenius_norm": 1.7963657369808272,
            "cell_principal_stretches": [
              1.1256949733678259,
              1.0575668861820042,
              0.9344481595124187
            ],
            "cell_volume_ratio": 1.1124584106233886,
            "cell_rmsd_from_input_A": 0.9204340606065583
          },
          {
            "iteration": 5,
            "reduced_polarization": [
              0.0004907006615568173,
              0.05751818784300863,
              0.17611992966717804
            ],
            "branch_aligned_reduced_polarization": [
              0.0004907006615568173,
              0.05751818784300863,
              0.17611992966717804
            ],
            "target_residual": 0.328948145881196,
            "energy_eV": -18.190149783303465
          }
        ],
        "iterations": 5
      },
      "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": 0.328948145881196,
        "parent_symmetrization_rmsd_A": 0.19976359232995589,
        "parent_cell_rmsd_A": 0.9204340606065583,
        "energy_eV": -18.190149783303465,
        "reduced_polarization": [
          0.0004907006615568173,
          0.05751818784300863,
          0.17611992966717804
        ],
        "cartesian_polarization_e_A2": [
          -0.0014044599081175387,
          0.0008339359835711113,
          0.002494693561302036
        ],
        "ranking_score": 1.5877683992439873
      },
      "branch_status": "awaiting_branch_sampling"
    },
    {
      "orbit_id": 3,
      "formal_class": [
        0.0,
        0.5,
        0.5
      ],
      "formal_classes_in_orbit": [
        [
          0.0,
          0.5,
          0.5
        ],
        [
          0.5,
          0.5,
          0.0
        ],
        [
          0.5,
          0.5,
          0.5
        ]
      ],
      "target_reduced_polarization": [
        0.0,
        0.5,
        0.5
      ],
      "bec_backprojection": {
        "converged_to_target": false,
        "history": [
          {
            "iteration": 0,
            "reduced_polarization": [
              1.2247193611726476e-09,
              0.1169504417176473,
              4.319494792210162e-09
            ],
            "branch_aligned_reduced_polarization": [
              1.2247193611726476e-09,
              0.11695044171764729,
              4.31949481738414e-09
            ],
            "target_residual": 0.6298626515207985,
            "energy_eV": -21.50515155177238,
            "max_atomic_step_A": 0.07659753837885043,
            "max_log_strain_component": 0.02,
            "step_scale": 0.10948665440622057,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 2.792517141667799,
            "cell_principal_stretches": [
              0.9904235868494822,
              0.9801987166782985,
              0.9739709305364523
            ],
            "cell_volume_ratio": 0.9455425976670608,
            "cell_rmsd_from_input_A": 0.1877691390616077
          },
          {
            "iteration": 1,
            "reduced_polarization": [
              0.0005760503462786396,
              0.14590368998201383,
              0.056067213701858666
            ],
            "branch_aligned_reduced_polarization": [
              0.0005760503462786396,
              0.14590368998201386,
              0.05606721370185869
            ],
            "target_residual": 0.5678563615499842,
            "energy_eV": -21.069406491508442,
            "max_atomic_step_A": 0.041221515982627535,
            "max_log_strain_component": 0.02,
            "step_scale": 0.07562298270181646,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 2.792517141667799,
            "cell_principal_stretches": [
              0.9788527836593167,
              0.9607895224716718,
              0.9506410405542849
            ],
            "cell_volume_ratio": 0.8940508040237369,
            "cell_rmsd_from_input_A": 0.3614900800558784
          },
          {
            "iteration": 2,
            "reduced_polarization": [
              0.001525143065372086,
              0.16411975831340922,
              0.08712885383206913
            ],
            "branch_aligned_reduced_polarization": [
              0.001525143065372086,
              0.1641197583134092,
              0.08712885383206914
            ],
            "target_residual": 0.5322409662500938,
            "energy_eV": -20.497637681597062,
            "max_atomic_step_A": 0.05245218456626962,
            "max_log_strain_component": 0.02,
            "step_scale": 0.08167240306241542,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 2.792517141667799,
            "cell_principal_stretches": [
              0.968685248917603,
              0.9417646526268,
              0.9266553228976105
            ],
            "cell_volume_ratio": 0.845363119688269,
            "cell_rmsd_from_input_A": 0.5308067818899903
          },
          {
            "iteration": 3,
            "reduced_polarization": [
              0.002648616646067642,
              0.18238151985184625,
              0.11460808041082059
            ],
            "branch_aligned_reduced_polarization": [
              0.002648616646067642,
              0.18238151985184625,
              0.1146080804108206
            ],
            "target_residual": 0.4994151036826915,
            "energy_eV": -19.87036294184758,
            "max_atomic_step_A": 0.05153719366431001,
            "max_log_strain_component": 0.02,
            "step_scale": 0.08697447368134634,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 2.792517141667799,
            "cell_principal_stretches": [
              0.9603951588520944,
              0.9231164955474405,
              0.9016083441077581
            ],
            "cell_volume_ratio": 0.799326840147569,
            "cell_rmsd_from_input_A": 0.6961579906435301
          },
          {
            "iteration": 4,
            "reduced_polarization": [
              0.004900926907019643,
              0.19808775038605858,
              0.13676693003715407
            ],
            "branch_aligned_reduced_polarization": [
              0.004900926907019643,
              0.19808775038605858,
              0.13676693003715407
            ],
            "target_residual": 0.4723486939392683,
            "energy_eV": -19.095117517735787,
            "max_atomic_step_A": 0.05102253195375906,
            "max_log_strain_component": 0.02,
            "step_scale": 0.05092002580502402,
            "strain_jacobian_refreshed": true,
            "strain_jacobian_frobenius_norm": 2.125598489288722,
            "cell_principal_stretches": [
              0.9608077551973812,
              0.9229913215843784,
              0.8828653109958783
            ],
            "cell_volume_ratio": 0.7829401605182802,
            "cell_rmsd_from_input_A": 0.7760614529670984
          },
          {
            "iteration": 5,
            "reduced_polarization": [
              0.005008059507637572,
              0.21254854078511445,
              0.1508471427701136
            ],
            "branch_aligned_reduced_polarization": [
              0.005008059507637572,
              0.21254854078511443,
              0.15084714277011357
            ],
            "target_residual": 0.4522843572097011,
            "energy_eV": -19.0346518451324
          }
        ],
        "iterations": 5
      },
      "parent": {
        "candidate_id": "bec_projection_03",
        "source": "MACEField_BEC_backprojection",
        "spacegroup": "P1",
        "spacegroup_number": 1,
        "pointgroup": "1",
        "has_inversion": false,
        "is_polar_point_group": true,
        "nonpolar_parent_hypothesis": false,
        "symmetry_tolerance_A": null,
        "target_reduced_polarization": [
          0.0,
          0.5,
          0.5
        ],
        "formal_class": [
          0.0,
          0.5,
          0.5
        ],
        "target_residual": 0.4522843572097011,
        "parent_symmetrization_rmsd_A": 0.20892768813364593,
        "parent_cell_rmsd_A": 0.7760614529670984,
        "energy_eV": -19.0346518451324,
        "reduced_polarization": [
          0.005008059507637572,
          0.21254854078511445,
          0.1508471427701136
        ],
        "cartesian_polarization_e_A2": [
          -0.0014338763104913166,
          0.0050431885997274314,
          0.0026241079212947957
        ],
        "ranking_score": 1.8075117657948228
      },
      "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
        ],
        "endpoint_rmsd_A": 0.17313541459632692,
        "minimum_distance_A_by_image": [
          2.4850224702728494,
          2.517220026189339,
          2.5497094707187435,
          2.5824909905493043,
          2.615564817064095,
          2.648931225186875,
          2.682590532263093,
          2.7165430969756894,
          2.7507893182952863
        ],
        "minimum_distance_A": 2.4850224702728494,
        "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": [
          406.95249318760756,
          412.24781002282134,
          417.61203018423225,
          423.0460502505571,
          428.55077846690307,
          434.1271348965792,
          439.77605157487284,
          445.49847266483135,
          451.2953546150714
        ],
        "cell_deformation_log_strain_norm": 0.060017237222626876
      },
      "parent_reduced_polarization": [
        1.1858585946999626e-10,
        -0.0005095372297642492,
        4.3511326577001295e-10
      ],
      "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": [
          -21.505151551772382,
          -21.44713760785877,
          -21.331446546784292,
          -21.160890231653703,
          -20.937910548330372,
          -20.66507369808079,
          -20.345391991983355,
          -19.982547109722905,
          -19.58094616156056
        ],
        "cartesian_polarizations_e_A2": [
          [
            -1.7151474732161304e-11,
            0.0024234261998011637,
            6.861840095448169e-11
          ],
          [
            -1.4995927497695667e-11,
            0.002158473142062919,
            6.030985595003164e-11
          ],
          [
            -1.2736160620637124e-11,
            0.0018593856373238864,
            5.1680791846465353e-11
          ],
          [
            -1.046231551648213e-11,
            0.0015337666093497163,
            4.2899095498912096e-11
          ],
          [
            -8.261669280940944e-12,
            0.0011925294231886218,
            3.41875475735257e-11
          ],
          [
            -6.221051027600554e-12,
            0.0008505498618705559,
            2.5847016124439235e-11
          ],
          [
            -4.4181033752627606e-12,
            0.0005253088810058098,
            1.8233778641517376e-11
          ],
          [
            -2.905510592352057e-12,
            0.00023406854582774345,
            1.1691139878161803e-11
          ],
          [
            -1.6979174287115845e-12,
            -9.806592600476554e-06,
            6.462544952692052e-12
          ]
        ],
        "raw_reduced_polarization": [
          [
            1.2247194022624402e-09,
            0.1169504417176475,
            4.31949472566284e-09
          ],
          [
            1.0865761302535783e-09,
            0.1051306699120046,
            3.819550748620414e-09
          ],
          [
            9.42443096443069e-10,
            0.0914035302628275,
            3.292845376289719e-09
          ],
          [
            7.926993070175378e-10,
            0.0760962913873708,
            2.7499771758844976e-09
          ],
          [
            6.396207135095067e-10,
            0.059715081725328356,
            2.2053027235158348e-09
          ],
          [
            4.880525026329522e-10,
            0.0429858403393435,
            1.6785256121074784e-09
          ],
          [
            3.4524705631910925e-10,
            0.026794835866208677,
            1.1933596978036016e-09
          ],
          [
            2.1960123999400593e-10,
            0.01205008554449172,
            7.731478544474188e-10
          ],
          [
            1.1858585946999626e-10,
            -0.0005095372297642492,
            4.3511326577001295e-10
          ]
        ],
        "unwrapped_reduced_polarization": [
          [
            1.2247194022624402e-09,
            0.1169504417176475,
            4.31949472566284e-09
          ],
          [
            1.0865761302535783e-09,
            0.1051306699120046,
            3.819550748620414e-09
          ],
          [
            9.42443096443069e-10,
            0.0914035302628275,
            3.292845376289719e-09
          ],
          [
            7.926993070175378e-10,
            0.0760962913873708,
            2.7499771758844976e-09
          ],
          [
            6.396207135095067e-10,
            0.059715081725328356,
            2.2053027235158348e-09
          ],
          [
            4.880525026329522e-10,
            0.0429858403393435,
            1.6785256121074784e-09
          ],
          [
            3.4524705631910925e-10,
            0.026794835866208677,
            1.1933596978036016e-09
          ],
          [
            2.1960123999400593e-10,
            0.01205008554449172,
            7.731478544474188e-10
          ],
          [
            1.1858585946999626e-10,
            -0.0005095372297642484,
            4.3511326577001295e-10
          ]
        ],
        "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": [
          [
            1.2247194369763292e-09,
            0.11695044171764746,
            4.3194947618729884e-09
          ],
          [
            1.0865761623790604e-09,
            0.10513066991200459,
            3.8195507867655465e-09
          ],
          [
            9.424431235416364e-10,
            0.09140353026282755,
            3.292845329738725e-09
          ],
          [
            7.926993506046642e-10,
            0.07609629138737084,
            2.749977134897108e-09
          ],
          [
            6.39620689746323e-10,
            0.059715081725328356,
            2.2053027182167284e-09
          ],
          [
            4.880524873129843e-10,
            0.042985840339343495,
            1.6785256518048186e-09
          ],
          [
            3.452470531684071e-10,
            0.026794835866208677,
            1.1933597443558597e-09
          ],
          [
            2.1960122609243626e-10,
            0.012050085544491718,
            7.731478790518054e-10
          ],
          [
            1.18585807840077e-10,
            -0.0005095372297642675,
            4.3511327874057315e-10
          ]
        ]
      },
      "reflected": {
        "reached": true,
        "construction": "reflect_displacements_about_reconstructed_parent",
        "energies_eV": [
          -19.580946161560565,
          -19.48845320815014,
          -19.389260394758075,
          -19.283653354129342,
          -19.171893770546284,
          -19.05430701974757,
          -18.93135673897317,
          -18.80366341171582,
          -18.671980022613475
        ],
        "cartesian_polarizations_e_A2": [
          [
            -1.6979270845286167e-12,
            -9.806592600479414e-06,
            6.46253596570948e-12
          ],
          [
            -1.487409138942658e-12,
            -3.0126123181555955e-05,
            5.2877597066576976e-12
          ],
          [
            -1.2330639723001607e-12,
            -4.325144900323642e-05,
            4.3046434654392955e-12
          ],
          [
            -9.467310116957546e-13,
            -4.826035333609206e-05,
            3.4804918993190592e-12
          ],
          [
            -6.277252531309181e-13,
            -4.3650941620571775e-05,
            2.7873541473512487e-12
          ],
          [
            -2.6709333825679164e-13,
            -2.7702290267130654e-05,
            2.213065188867245e-12
          ],
          [
            1.3937357220896115e-13,
            9.993834850210192e-07,
            1.7509538049539036e-12
          ],
          [
            5.856306752505371e-13,
            4.3226794701161176e-05,
            1.3865898292128886e-12
          ],
          [
            1.057988658970375e-12,
            9.90058177193034e-05,
            1.0934622941344033e-12
          ]
        ],
        "raw_reduced_polarization": [
          [
            1.1858499457873823e-10,
            -0.0005095372297643978,
            4.3511266115267424e-10
          ],
          [
            9.078150918982318e-11,
            -0.001550923299744858,
            3.5368686840175115e-10
          ],
          [
            7.215387432873307e-11,
            -0.0022061600687169757,
            2.8591102602148106e-10
          ],
          [
            6.076030193544663e-11,
            -0.002439024372613765,
            2.29387908921877e-10
          ],
          [
            5.5581824683302364e-11,
            -0.002185790552060612,
            1.8210836290102998e-10
          ],
          [
            5.6609744087268866e-11,
            -0.0013744213359546693,
            1.431656491136099e-10
          ],
          [
            6.375697274332337e-11,
            4.9127613327571896e-05,
            1.1206099127457426e-10
          ],
          [
            7.613601281742241e-11,
            0.002105405805855191,
            8.784118592118998e-11
          ],
          [
            9.209363338065448e-11,
            0.00477785299005162,
            6.88329157561964e-11
          ]
        ],
        "unwrapped_reduced_polarization": [
          [
            1.1858499457873823e-10,
            -0.0005095372297643978,
            4.3511266115267424e-10
          ],
          [
            9.078150918982318e-11,
            -0.001550923299744858,
            3.5368686840175115e-10
          ],
          [
            7.215387432873307e-11,
            -0.0022061600687169757,
            2.8591102602148106e-10
          ],
          [
            6.076030193544663e-11,
            -0.002439024372613765,
            2.29387908921877e-10
          ],
          [
            5.5581824683302364e-11,
            -0.002185790552060612,
            1.8210836290102998e-10
          ],
          [
            5.6609744087268866e-11,
            -0.0013744213359546693,
            1.431656491136099e-10
          ],
          [
            6.375697274332337e-11,
            4.912761332757183e-05,
            1.1206099127457426e-10
          ],
          [
            7.613601281742241e-11,
            0.002105405805855191,
            8.784118592118998e-11
          ],
          [
            9.209363338065448e-11,
            0.00477785299005162,
            6.88329157561964e-11
          ]
        ],
        "gauge_integer_shift": [
          0,
          0,
          0
        ],
        "expected_opposite_endpoint_reduced_polarization": [
          -1.0030323303154195e-09,
          -0.11789694079937307,
          -3.5058666477940534e-09
        ],
        "actual_opposite_endpoint_branch_residual": 0.12267479378942475
      },
      "pnp_branch": {
        "construction": "incoming_path_concatenated_with_parent_reflection",
        "reduced_polarization": [
          [
            1.2247194022624402e-09,
            0.1169504417176475,
            4.31949472566284e-09
          ],
          [
            1.0865761302535783e-09,
            0.1051306699120046,
            3.819550748620414e-09
          ],
          [
            9.42443096443069e-10,
            0.0914035302628275,
            3.292845376289719e-09
          ],
          [
            7.926993070175378e-10,
            0.0760962913873708,
            2.7499771758844976e-09
          ],
          [
            6.396207135095067e-10,
            0.059715081725328356,
            2.2053027235158348e-09
          ],
          [
            4.880525026329522e-10,
            0.0429858403393435,
            1.6785256121074784e-09
          ],
          [
            3.4524705631910925e-10,
            0.026794835866208677,
            1.1933596978036016e-09
          ],
          [
            2.1960123999400593e-10,
            0.01205008554449172,
            7.731478544474188e-10
          ],
          [
            1.1858585946999626e-10,
            -0.0005095372297642492,
            4.3511326577001295e-10
          ],
          [
            9.078150918982318e-11,
            -0.001550923299744858,
            3.5368686840175115e-10
          ],
          [
            7.215387432873307e-11,
            -0.0022061600687169757,
            2.8591102602148106e-10
          ],
          [
            6.076030193544663e-11,
            -0.002439024372613765,
            2.29387908921877e-10
          ],
          [
            5.5581824683302364e-11,
            -0.002185790552060612,
            1.8210836290102998e-10
          ],
          [
            5.6609744087268866e-11,
            -0.0013744213359546693,
            1.431656491136099e-10
          ],
          [
            6.375697274332337e-11,
            4.9127613327571896e-05,
            1.1206099127457426e-10
          ],
          [
            7.613601281742241e-11,
            0.002105405805855191,
            8.784118592118998e-11
          ],
          [
            9.209363338065448e-11,
            0.00477785299005162,
            6.88329157561964e-11
          ]
        ],
        "unwrapped_reduced_polarization": [
          [
            1.2247194022624402e-09,
            0.1169504417176475,
            4.31949472566284e-09
          ],
          [
            1.0865761302535783e-09,
            0.1051306699120046,
            3.819550748620414e-09
          ],
          [
            9.42443096443069e-10,
            0.0914035302628275,
            3.292845376289719e-09
          ],
          [
            7.926993070175378e-10,
            0.0760962913873708,
            2.7499771758844976e-09
          ],
          [
            6.396207135095067e-10,
            0.059715081725328356,
            2.2053027235158348e-09
          ],
          [
            4.880525026329522e-10,
            0.0429858403393435,
            1.6785256121074784e-09
          ],
          [
            3.4524705631910925e-10,
            0.026794835866208677,
            1.1933596978036016e-09
          ],
          [
            2.1960123999400593e-10,
            0.01205008554449172,
            7.731478544474188e-10
          ],
          [
            1.1858585946999626e-10,
            -0.0005095372297642484,
            4.3511326577001295e-10
          ],
          [
            9.078150918982318e-11,
            -0.001550923299744858,
            3.5368686840175115e-10
          ],
          [
            7.215387432873307e-11,
            -0.0022061600687169757,
            2.8591102602148106e-10
          ],
          [
            6.076030193544663e-11,
            -0.002439024372613765,
            2.29387908921877e-10
          ],
          [
            5.5581824683302364e-11,
            -0.002185790552060612,
            1.8210836290102998e-10
          ],
          [
            5.6609744087268866e-11,
            -0.0013744213359546693,
            1.431656491136099e-10
          ],
          [
            6.375697274332337e-11,
            4.912761332757183e-05,
            1.1206099127457426e-10
          ],
          [
            7.613601281742241e-11,
            0.002105405805855191,
            8.784118592118998e-11
          ],
          [
            9.209363338065448e-11,
            0.00477785299005162,
            6.88329157561964e-11
          ]
        ],
        "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": [
          [
            1.2247194369763292e-09,
            0.11695044171764746,
            4.3194947618729884e-09
          ],
          [
            1.0865761623790604e-09,
            0.10513066991200459,
            3.8195507867655465e-09
          ],
          [
            9.424431235416364e-10,
            0.09140353026282755,
            3.292845329738725e-09
          ],
          [
            7.926993506046642e-10,
            0.07609629138737084,
            2.749977134897108e-09
          ],
          [
            6.39620689746323e-10,
            0.059715081725328356,
            2.2053027182167284e-09
          ],
          [
            4.880524873129843e-10,
            0.042985840339343495,
            1.6785256518048186e-09
          ],
          [
            3.452470531684071e-10,
            0.026794835866208677,
            1.1933597443558597e-09
          ],
          [
            2.1960122609243626e-10,
            0.012050085544491718,
            7.731478790518054e-10
          ],
          [
            1.18585807840077e-10,
            -0.0005095372297642675,
            4.3511327874057315e-10
          ],
          [
            9.078149343366704e-11,
            -0.0015509232997448774,
            3.5368685757930507e-10
          ],
          [
            7.215383845959877e-11,
            -0.002206160068716989,
            2.8591107259501314e-10
          ],
          [
            6.076028569168557e-11,
            -0.002439024372613785,
            2.2938795307680948e-10
          ],
          [
            5.558187243792645e-11,
            -0.0021857905520605847,
            1.8210832841702995e-10
          ],
          [
            5.660971691412442e-11,
            -0.0013744213359546675,
            1.431657015160681e-10
          ],
          [
            6.375699967975379e-11,
            4.912761332753757e-05,
            1.1206102712435495e-10
          ],
          [
            7.613598640432429e-11,
            0.002105405805855165,
            8.784117877524977e-11
          ],
          [
            9.209366602647151e-11,
            0.004777852990051623,
            6.883293934834e-11
          ]
        ]
      },
      "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": "P6_3",
        "spacegroup_number": 173,
        "pointgroup": "6",
        "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": 0.0005095372297643785,
        "parent_symmetrization_rmsd_A": 0.17313541459632692,
        "parent_cell_rmsd_A": 0.34285511175307276,
        "energy_eV": -19.580946161560576,
        "reduced_polarization": [
          1.1858553764871823e-10,
          -0.0005095372297641789,
          4.351130736268607e-10
        ],
        "cartesian_polarization_e_A2": [
          -1.6979213033388013e-12,
          -9.8065926004752e-06,
          6.4625420966920305e-12
        ],
        "ranking_score": 0.7598682669941239
      }
    }
  ],
  "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": 89,
      "full_response": 18,
      "energy_polarization": 71
    },
    "model_evaluations_for_recovery_and_path_properties": {
      "total": 114,
      "full_response": 43,
      "energy_polarization": 71
    },
    "elapsed_seconds": 71.08947998302756
  }
}
