{
  "schema": "ferrofinder.endpoint_parent_recovery.v4_variable_cell",
  "status": "complete",
  "input_atom_count": 78,
  "input_formula": "O46Rb12Si20",
  "input_spacegroup": "Amm2",
  "input_pointgroup": "mm2",
  "input_is_polar_point_group": true,
  "input_energy_eV": -530.008915134207,
  "input_cartesian_polarization_e_A2": [
    6.418174646255737e-18,
    5.823761687695768e-11,
    7.044639857895322e-05
  ],
  "input_reduced_polarization": [
    1.0076417930981045e-15,
    4.519596387496164e-09,
    0.009561000517746545
  ],
  "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,
        0.0,
        0.5
      ],
      "target_reduced_polarization": [
        0.0,
        0.0,
        0.5
      ]
    },
    {
      "orbit_id": 2,
      "representative_formal_class": [
        0.0,
        0.5,
        0.0
      ],
      "target_reduced_polarization": [
        0.0,
        0.5,
        0.0
      ]
    },
    {
      "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,
        0.0,
        0.5
      ],
      "target_reduced_polarization": [
        0.5,
        0.0,
        0.5
      ]
    },
    {
      "orbit_id": 6,
      "representative_formal_class": [
        0.5,
        0.5,
        0.0
      ],
      "target_reduced_polarization": [
        0.5,
        0.5,
        0.0
      ]
    },
    {
      "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": "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": 0.00023783019826602333,
      "parent_symmetrization_rmsd_A": 0.8434276244555661,
      "parent_cell_rmsd_A": 0.0,
      "energy_eV": "Infinity",
      "reduced_polarization": [
        -2.036683475591729e-06,
        0.00020282950790056738,
        -0.00012417425599732775
      ],
      "cartesian_polarization_e_A2": [
        -1.297265589322194e-08,
        2.613575673512534e-06,
        -9.149282143637486e-07
      ],
      "ranking_score": 0.8439032848520981
    },
    {
      "candidate_id": "inversion_parent_endpoint_01",
      "source": "same_species_inversion_center_projection_from_endpoint",
      "spacegroup": "P2_1/c",
      "spacegroup_number": 14,
      "pointgroup": "2/m",
      "has_inversion": true,
      "is_polar_point_group": false,
      "nonpolar_parent_hypothesis": true,
      "symmetry_tolerance_A": null,
      "target_reduced_polarization": [
        0.0,
        0.0,
        0.0
      ],
      "formal_class": [
        0.0,
        0.0,
        0.0
      ],
      "target_residual": 2.125051328189765e-15,
      "parent_symmetrization_rmsd_A": 0.8434276244555662,
      "parent_cell_rmsd_A": 0.0,
      "energy_eV": "Infinity",
      "reduced_polarization": [
        4.760000244493111e-16,
        1.1499242038262284e-15,
        1.7224811899176004e-15
      ],
      "cartesian_polarization_e_A2": [
        3.0318822715209053e-18,
        1.4817439319415183e-17,
        1.2691411973512204e-17
      ],
      "ranking_score": 0.8434276244555704
    },
    {
      "candidate_id": "inversion_parent_endpoint_02",
      "source": "same_species_inversion_center_projection_from_endpoint",
      "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": 0.0006346349476402298,
      "parent_symmetrization_rmsd_A": 0.8726154397251799,
      "parent_cell_rmsd_A": 0.0,
      "energy_eV": "Infinity",
      "reduced_polarization": [
        -0.00043045011939606034,
        0.0002757675339724042,
        -0.00037606711992011936
      ],
      "cartesian_polarization_e_A2": [
        -2.7417521402038264e-06,
        3.553424379889258e-06,
        -2.7708997790720573e-06
      ],
      "ranking_score": 0.8738847096204603
    },
    {
      "candidate_id": "bec_projection_00",
      "source": "MACEField_BEC_backprojection",
      "spacegroup": "Amm2",
      "spacegroup_number": 38,
      "pointgroup": "mm2",
      "has_inversion": false,
      "is_polar_point_group": true,
      "nonpolar_parent_hypothesis": false,
      "symmetry_tolerance_A": null,
      "target_reduced_polarization": [
        0.0,
        0.0,
        0.0
      ],
      "formal_class": [
        0.0,
        0.0,
        0.0
      ],
      "target_residual": 1.0431427701187283e-06,
      "parent_symmetrization_rmsd_A": 0.000471389707033928,
      "parent_cell_rmsd_A": 0.0022575809039229,
      "energy_eV": -530.0087912059823,
      "reduced_polarization": [
        -5.675115823208565e-16,
        3.0422306102394555e-12,
        -1.0431427701142922e-06
      ],
      "cartesian_polarization_e_A2": [
        -3.614566179339567e-18,
        3.920483661238817e-14,
        -7.685296522770607e-09
      ],
      "ranking_score": 0.5010378712185549
    },
    {
      "candidate_id": "inversion_parent_bec_00_00",
      "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": 0.0009311184797569738,
      "parent_symmetrization_rmsd_A": 0.8726154417547863,
      "parent_cell_rmsd_A": 0.0022575809039229,
      "energy_eV": "Infinity",
      "reduced_polarization": [
        -7.684865961187954e-06,
        0.0009153111717862075,
        -0.0001706693440060527
      ],
      "cartesian_polarization_e_A2": [
        -4.894607636048991e-08,
        1.1796025711134909e-05,
        -1.2573969266754276e-06
      ],
      "ranking_score": 0.875042073940281
    },
    {
      "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": 0.0010242443967616308,
      "parent_symmetrization_rmsd_A": 0.8726154417547862,
      "parent_cell_rmsd_A": 0.0022575809039229,
      "energy_eV": "Infinity",
      "reduced_polarization": [
        0.00044163114039938976,
        0.0009081228747725398,
        -0.0001713223991251274
      ],
      "cartesian_polarization_e_A2": [
        2.8128156860939634e-06,
        1.1703386902597159e-05,
        -1.262208274078338e-06
      ],
      "ranking_score": 0.8752283257742902
    },
    {
      "candidate_id": "bec_projection_01",
      "source": "MACEField_BEC_backprojection",
      "spacegroup": "Amm2",
      "spacegroup_number": 38,
      "pointgroup": "mm2",
      "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": 4.005284516939173e-06,
      "parent_symmetrization_rmsd_A": 0.024239465908917047,
      "parent_cell_rmsd_A": 0.1157980975265128,
      "energy_eV": -528.8100525204826,
      "reduced_polarization": [
        -3.2766416665812264e-16,
        3.68211512884519e-13,
        0.49999599471548306
      ],
      "cartesian_polarization_e_A2": [
        2.470076685666329e-17,
        8.420065447408331e-13,
        0.0037009623685365658
      ],
      "ranking_score": 0.5531970008595791
    },
    {
      "candidate_id": "bec_projection_02",
      "source": "MACEField_BEC_backprojection",
      "spacegroup": "Pm",
      "spacegroup_number": 6,
      "pointgroup": "m",
      "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": 1.0346705562166417e-05,
      "parent_symmetrization_rmsd_A": 0.039164920992552775,
      "parent_cell_rmsd_A": 0.3141667477423024,
      "energy_eV": -525.4784216430337,
      "reduced_polarization": [
        -2.4885871376136794e-15,
        0.4999923755658896,
        6.994449262548315e-06
      ],
      "cartesian_polarization_e_A2": [
        2.5963475528985604e-17,
        0.0064490171479085956,
        -0.00016347531831747313
      ],
      "ranking_score": 0.6177273013392527
    },
    {
      "candidate_id": "bec_projection_03",
      "source": "MACEField_BEC_backprojection",
      "spacegroup": "Cm",
      "spacegroup_number": 8,
      "pointgroup": "m",
      "has_inversion": false,
      "is_polar_point_group": true,
      "nonpolar_parent_hypothesis": false,
      "symmetry_tolerance_A": null,
      "target_reduced_polarization": [
        0.5,
        0.0,
        0.0
      ],
      "formal_class": [
        0.5,
        0.0,
        0.0
      ],
      "target_residual": 6.917545053305645e-06,
      "parent_symmetrization_rmsd_A": 0.02106107558206401,
      "parent_cell_rmsd_A": 0.03183008575264966,
      "energy_eV": -529.1788431746174,
      "reduced_polarization": [
        0.49999310021355436,
        -6.123815689582648e-14,
        4.95354993048566e-07
      ],
      "cartesian_polarization_e_A2": [
        0.0031846348215341736,
        -1.78380057870211e-14,
        1.6601088697817424e-05
      ],
      "ranking_score": 0.529032432110333
    },
    {
      "candidate_id": "bec_projection_04",
      "source": "MACEField_BEC_backprojection",
      "spacegroup": "Pm",
      "spacegroup_number": 6,
      "pointgroup": "m",
      "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": 9.680920496786864e-06,
      "parent_symmetrization_rmsd_A": 0.04539888665590686,
      "parent_cell_rmsd_A": 0.3168334619558985,
      "energy_eV": -523.8167202373735,
      "reduced_polarization": [
        2.6246535534396177e-15,
        0.4999947280660967,
        0.4999918804597061
      ],
      "cartesian_polarization_e_A2": [
        1.0909373627051875e-16,
        0.006309719047137636,
        0.003544031374428587
      ],
      "ranking_score": 0.624626613985875
    },
    {
      "candidate_id": "bec_projection_05",
      "source": "MACEField_BEC_backprojection",
      "spacegroup": "Cm",
      "spacegroup_number": 8,
      "pointgroup": "m",
      "has_inversion": false,
      "is_polar_point_group": true,
      "nonpolar_parent_hypothesis": false,
      "symmetry_tolerance_A": null,
      "target_reduced_polarization": [
        0.5,
        0.0,
        0.5
      ],
      "formal_class": [
        0.5,
        0.0,
        0.5
      ],
      "target_residual": 3.0862053855217666e-05,
      "parent_symmetrization_rmsd_A": 0.032312116183036185,
      "parent_cell_rmsd_A": 0.12117005890368908,
      "energy_eV": -528.0541685607567,
      "reduced_polarization": [
        0.4999748369000347,
        2.4995553919888466e-13,
        0.49998213145869697
      ],
      "cartesian_polarization_e_A2": [
        0.0032133790628668256,
        8.220724773604733e-13,
        0.003718032308722053
      ],
      "ranking_score": 0.5626663550166688
    },
    {
      "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,
        0.5,
        0.0
      ],
      "formal_class": [
        0.5,
        0.5,
        0.0
      ],
      "target_residual": 1.0954017269723053e-05,
      "parent_symmetrization_rmsd_A": 0.044592683335285495,
      "parent_cell_rmsd_A": 0.3162924913310569,
      "energy_eV": -524.6099819918131,
      "reduced_polarization": [
        0.5000034674880731,
        0.4999926438400197,
        7.338523771993432e-06
      ],
      "cartesian_polarization_e_A2": [
        0.003183662137926056,
        0.006448441552649926,
        -0.00014701588497370558
      ],
      "ranking_score": 0.6236877142025892
    },
    {
      "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": 1.0746474103224336e-05,
      "parent_symmetrization_rmsd_A": 0.05027857293999296,
      "parent_cell_rmsd_A": 0.31932483023135577,
      "energy_eV": -523.0235273440912,
      "reduced_polarization": [
        0.5000036197722607,
        0.4999953011649954,
        0.4999910386996462
      ],
      "cartesian_polarization_e_A2": [
        0.003212803792911518,
        0.0063089895266538135,
        0.0035611644615956483
      ],
      "ranking_score": 0.6301312734460384
    }
  ],
  "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": [
              1.0076417930981045e-15,
              4.519596387496164e-09,
              0.009561000517746545
            ],
            "branch_aligned_reduced_polarization": [
              1.0076417930981045e-15,
              4.519596387496164e-09,
              0.009561000517746545
            ],
            "target_residual": 0.009561000517747614,
            "energy_eV": -530.008915134207,
            "max_atomic_step_A": 0.0006775360445892697,
            "max_log_strain_component": 0.0001443202076393241,
            "step_scale": 1.0,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 4.362664515679049,
            "cell_principal_stretches": [
              1.0001443306223015,
              0.9999445097599848,
              0.9999104210907402
            ],
            "cell_volume_ratio": 0.9999992455065788,
            "cell_rmsd_from_input_A": 0.0022575809039229
          },
          {
            "iteration": 1,
            "reduced_polarization": [
              -5.675115823208565e-16,
              3.0422306102394555e-12,
              -1.0431427701142922e-06
            ],
            "branch_aligned_reduced_polarization": [
              -5.675115823208565e-16,
              3.0422306102394555e-12,
              -1.0431427701142922e-06
            ],
            "target_residual": 1.0431427701187283e-06,
            "energy_eV": -530.0087912059823
          }
        ],
        "iterations": 1
      },
      "parent": {
        "candidate_id": "bec_projection_00",
        "source": "MACEField_BEC_backprojection",
        "spacegroup": "Amm2",
        "spacegroup_number": 38,
        "pointgroup": "mm2",
        "has_inversion": false,
        "is_polar_point_group": true,
        "nonpolar_parent_hypothesis": false,
        "symmetry_tolerance_A": null,
        "target_reduced_polarization": [
          0.0,
          0.0,
          0.0
        ],
        "formal_class": [
          0.0,
          0.0,
          0.0
        ],
        "target_residual": 1.0431427701187283e-06,
        "parent_symmetrization_rmsd_A": 0.000471389707033928,
        "parent_cell_rmsd_A": 0.0022575809039229,
        "energy_eV": -530.0087912059823,
        "reduced_polarization": [
          -5.675115823208565e-16,
          3.0422306102394555e-12,
          -1.0431427701142922e-06
        ],
        "cartesian_polarization_e_A2": [
          -3.614566179339567e-18,
          3.920483661238817e-14,
          -7.685296522770607e-09
        ],
        "ranking_score": 0.5010378712185549
      },
      "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": [
          -530.0089151342067,
          -530.0089485729909,
          -530.0089680333314,
          -530.0089735144835,
          -530.0089650156979,
          -530.0089425362188,
          -530.0089060752849,
          -530.0088556321302,
          -530.0087912059823
        ],
        "cartesian_polarizations_e_A2": [
          [
            2.752559580054663e-18,
            5.8237626749629e-11,
            7.044639857895299e-05
          ],
          [
            -9.840340734291479e-18,
            5.096355215786202e-11,
            6.163917981594125e-05
          ],
          [
            1.9502152207228053e-17,
            4.368930070919169e-11,
            5.2832091191813295e-05
          ],
          [
            2.869471922963185e-17,
            3.641482843499598e-11,
            4.4025133105765186e-05
          ],
          [
            3.0970591733172965e-17,
            2.914014556088046e-11,
            3.52183059565358e-05
          ],
          [
            1.6039777491848544e-17,
            2.1865173599154635e-11,
            2.641161014300293e-05
          ],
          [
            1.8105168223930785e-18,
            1.4590047407769698e-11,
            1.7605046063937355e-05
          ],
          [
            2.7258094961962097e-17,
            7.31475961697792e-12,
            8.798614117899094e-06
          ],
          [
            2.3653871066050646e-17,
            3.9188640986319486e-14,
            -7.685296550117599e-09
          ]
        ],
        "raw_reduced_polarization": [
          [
            4.3214686787523274e-16,
            4.519597153676033e-09,
            0.009561000517746514
          ],
          [
            -1.5447491266148405e-15,
            3.9548761522066514e-09,
            0.008365775763418992
          ],
          [
            3.0621480855435684e-15,
            3.3902008973308743e-09,
            0.00717054212815114
          ],
          [
            4.505490924071416e-15,
            2.8255679759109798e-09,
            0.005975299666270017
          ],
          [
            4.862864672121758e-15,
            2.2609781805527237e-09,
            0.004780048432043001
          ],
          [
            2.518681630838705e-15,
            1.6964254197289443e-09,
            0.0035847884797587707
          ],
          [
            2.84563062029961e-16,
            1.131920157480124e-09,
            0.002389519863693878
          ],
          [
            4.279853485205878e-15,
            5.674618207431195e-10,
            0.0011942426380986784
          ],
          [
            3.7138180110567695e-15,
            3.0409739126167407e-12,
            -1.0431427738261615e-06
          ]
        ],
        "unwrapped_reduced_polarization": [
          [
            4.3214686787523274e-16,
            4.519597153676033e-09,
            0.009561000517746514
          ],
          [
            -1.5447491266148407e-15,
            3.9548761522066514e-09,
            0.008365775763418992
          ],
          [
            3.0621480855435684e-15,
            3.3902008973308743e-09,
            0.00717054212815114
          ],
          [
            4.505490924071416e-15,
            2.8255679759109798e-09,
            0.005975299666270017
          ],
          [
            4.862864672121758e-15,
            2.2609781805527237e-09,
            0.004780048432043001
          ],
          [
            2.518681630838705e-15,
            1.6964254197289443e-09,
            0.0035847884797587707
          ],
          [
            2.8456306202996105e-16,
            1.131920157480124e-09,
            0.002389519863693878
          ],
          [
            4.279853485205878e-15,
            5.674618207431195e-10,
            0.0011942426380986784
          ],
          [
            3.7138180110567695e-15,
            3.040973912616721e-12,
            -1.0431427738262326e-06
          ]
        ],
        "berry_integer_shifts": [
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ]
        ],
        "folded_reduced_polarization": [
          [
            4.440892098500626e-16,
            4.519597140983933e-09,
            0.009561000517746554
          ],
          [
            -1.5543122344752192e-15,
            3.954876204304014e-09,
            0.008365775763419014
          ],
          [
            3.1086244689504383e-15,
            3.3902008977904075e-09,
            0.007170542128151158
          ],
          [
            4.551914400963142e-15,
            2.8255680017963414e-09,
            0.005975299666269973
          ],
          [
            4.884981308350689e-15,
            2.2609781824556308e-09,
            0.004780048432043049
          ],
          [
            2.55351295663786e-15,
            1.6964254445639426e-09,
            0.003584788479758738
          ],
          [
            3.3306690738754696e-16,
            1.131920113195406e-09,
            0.0023895198636938453
          ],
          [
            4.3298697960381105e-15,
            5.674618552831134e-10,
            0.0011942426380986415
          ],
          [
            3.6637359812630166e-15,
            3.0410118867507663e-12,
            -1.0431427738266663e-06
          ]
        ]
      },
      "reflected": {
        "reached": true,
        "construction": "reflect_displacements_about_reconstructed_parent",
        "energies_eV": [
          -530.0087912059822,
          -530.0087648766214,
          -530.0087278159003,
          -530.0086800242486,
          -530.0086215020924,
          -530.0085522498539,
          -530.0084722679517,
          -530.0083815568003,
          -530.0082801168104
        ],
        "cartesian_polarizations_e_A2": [
          [
            1.727885466739744e-17,
            3.9210527865496727e-14,
            -7.685296514503916e-09
          ],
          [
            4.687632690763198e-17,
            -5.275744934174847e-12,
            -7.911870773406911e-06
          ],
          [
            1.8237119214525882e-18,
            -1.0589654422690336e-11,
            -1.5816285531468843e-05
          ],
          [
            7.966545085891722e-18,
            -1.5902504799581863e-11,
            -2.372092931175711e-05
          ],
          [
            9.068393259257302e-18,
            -2.12143880609697e-11,
            -3.162580185540195e-05
          ],
          [
            1.4737818253215546e-17,
            -2.6525317046080325e-11,
            -3.953090290348439e-05
          ],
          [
            3.3816139705960306e-17,
            -3.183517195574668e-11,
            -4.743623219711572e-05
          ],
          [
            2.3721263556700732e-17,
            -3.714406811349013e-11,
            -5.534178947740192e-05
          ],
          [
            6.924648793266873e-17,
            -4.245192990601275e-11,
            -6.324757448520135e-05
          ]
        ],
        "raw_reduced_polarization": [
          [
            2.7128971984628734e-15,
            3.0426722223279195e-12,
            -1.0431427689922355e-06
          ],
          [
            7.359691755631243e-15,
            -4.0925559833881716e-10,
            -0.001073884284288334
          ],
          [
            2.860585316701662e-16,
            -8.215226549210059e-10,
            -0.002146732721405128
          ],
          [
            1.2504351263181494e-15,
            -1.2337574759053296e-09,
            -0.003219588418333773
          ],
          [
            1.4233967768594793e-15,
            -1.6459671980652723e-09,
            -0.004292451339300211
          ],
          [
            2.313517493578547e-15,
            -2.0581528159633256e-09,
            -0.00536532144852529
          ],
          [
            5.308872719736929e-15,
            -2.470305031052037e-09,
            -0.0064381987102355214
          ],
          [
            3.724061870705479e-15,
            -2.8824327907395323e-09,
            -0.0075110830886583125
          ],
          [
            1.0871573167135084e-14,
            -3.2945302252120348e-09,
            -0.008583974547989008
          ]
        ],
        "unwrapped_reduced_polarization": [
          [
            2.7128971984628734e-15,
            3.0426722223279195e-12,
            -1.0431427689922355e-06
          ],
          [
            7.359691755631243e-15,
            -4.0925559833881716e-10,
            -0.001073884284288334
          ],
          [
            2.860585316701661e-16,
            -8.215226549210059e-10,
            -0.002146732721405128
          ],
          [
            1.2504351263181494e-15,
            -1.2337574759053296e-09,
            -0.003219588418333773
          ],
          [
            1.4233967768594793e-15,
            -1.6459671980652723e-09,
            -0.004292451339300211
          ],
          [
            2.313517493578547e-15,
            -2.0581528159633256e-09,
            -0.00536532144852529
          ],
          [
            5.308872719736929e-15,
            -2.470305031052037e-09,
            -0.0064381987102355214
          ],
          [
            3.724061870705479e-15,
            -2.8824327907395323e-09,
            -0.0075110830886583125
          ],
          [
            1.0871573167135085e-14,
            -3.2945302252120348e-09,
            -0.008583974547989008
          ]
        ],
        "gauge_integer_shift": [
          0,
          0,
          0
        ],
        "expected_opposite_endpoint_reduced_polarization": [
          6.995082950064171e-15,
          -4.51351459570987e-09,
          -0.009563086617980932
        ],
        "actual_opposite_endpoint_branch_residual": 0.0009791120699926832
      },
      "pnp_branch": {
        "construction": "incoming_path_concatenated_with_parent_reflection",
        "reduced_polarization": [
          [
            4.3214686787523274e-16,
            4.519597153676033e-09,
            0.009561000517746514
          ],
          [
            -1.5447491266148405e-15,
            3.9548761522066514e-09,
            0.008365775763418992
          ],
          [
            3.0621480855435684e-15,
            3.3902008973308743e-09,
            0.00717054212815114
          ],
          [
            4.505490924071416e-15,
            2.8255679759109798e-09,
            0.005975299666270017
          ],
          [
            4.862864672121758e-15,
            2.2609781805527237e-09,
            0.004780048432043001
          ],
          [
            2.518681630838705e-15,
            1.6964254197289443e-09,
            0.0035847884797587707
          ],
          [
            2.84563062029961e-16,
            1.131920157480124e-09,
            0.002389519863693878
          ],
          [
            4.279853485205878e-15,
            5.674618207431195e-10,
            0.0011942426380986784
          ],
          [
            3.7138180110567695e-15,
            3.0409739126167407e-12,
            -1.0431427738261615e-06
          ],
          [
            7.359691755631243e-15,
            -4.0925559833881716e-10,
            -0.001073884284288334
          ],
          [
            2.860585316701662e-16,
            -8.215226549210059e-10,
            -0.002146732721405128
          ],
          [
            1.2504351263181494e-15,
            -1.2337574759053296e-09,
            -0.003219588418333773
          ],
          [
            1.4233967768594793e-15,
            -1.6459671980652723e-09,
            -0.004292451339300211
          ],
          [
            2.313517493578547e-15,
            -2.0581528159633256e-09,
            -0.00536532144852529
          ],
          [
            5.308872719736929e-15,
            -2.470305031052037e-09,
            -0.0064381987102355214
          ],
          [
            3.724061870705479e-15,
            -2.8824327907395323e-09,
            -0.0075110830886583125
          ],
          [
            1.0871573167135084e-14,
            -3.2945302252120348e-09,
            -0.008583974547989008
          ]
        ],
        "unwrapped_reduced_polarization": [
          [
            4.3214686787523274e-16,
            4.519597153676033e-09,
            0.009561000517746514
          ],
          [
            -1.5447491266148407e-15,
            3.9548761522066514e-09,
            0.008365775763418992
          ],
          [
            3.0621480855435684e-15,
            3.3902008973308743e-09,
            0.00717054212815114
          ],
          [
            4.505490924071416e-15,
            2.8255679759109798e-09,
            0.005975299666270017
          ],
          [
            4.862864672121758e-15,
            2.2609781805527237e-09,
            0.004780048432043001
          ],
          [
            2.518681630838705e-15,
            1.6964254197289443e-09,
            0.0035847884797587707
          ],
          [
            2.8456306202996105e-16,
            1.131920157480124e-09,
            0.002389519863693878
          ],
          [
            4.279853485205878e-15,
            5.674618207431195e-10,
            0.0011942426380986784
          ],
          [
            3.7138180110567695e-15,
            3.040973912616721e-12,
            -1.0431427738262326e-06
          ],
          [
            7.359691755631243e-15,
            -4.0925559833881716e-10,
            -0.001073884284288334
          ],
          [
            2.860585316701661e-16,
            -8.215226549210059e-10,
            -0.002146732721405128
          ],
          [
            1.2504351263181494e-15,
            -1.2337574759053296e-09,
            -0.003219588418333773
          ],
          [
            1.4233967768594793e-15,
            -1.6459671980652723e-09,
            -0.004292451339300211
          ],
          [
            2.313517493578547e-15,
            -2.0581528159633256e-09,
            -0.00536532144852529
          ],
          [
            5.308872719736929e-15,
            -2.470305031052037e-09,
            -0.0064381987102355214
          ],
          [
            3.724061870705479e-15,
            -2.8824327907395323e-09,
            -0.0075110830886583125
          ],
          [
            1.0871573167135085e-14,
            -3.2945302252120348e-09,
            -0.008583974547989008
          ]
        ],
        "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": [
          [
            4.440892098500626e-16,
            4.519597140983933e-09,
            0.009561000517746554
          ],
          [
            -1.5543122344752192e-15,
            3.954876204304014e-09,
            0.008365775763419014
          ],
          [
            3.1086244689504383e-15,
            3.3902008977904075e-09,
            0.007170542128151158
          ],
          [
            4.551914400963142e-15,
            2.8255680017963414e-09,
            0.005975299666269973
          ],
          [
            4.884981308350689e-15,
            2.2609781824556308e-09,
            0.004780048432043049
          ],
          [
            2.55351295663786e-15,
            1.6964254445639426e-09,
            0.003584788479758738
          ],
          [
            3.3306690738754696e-16,
            1.131920113195406e-09,
            0.0023895198636938453
          ],
          [
            4.3298697960381105e-15,
            5.674618552831134e-10,
            0.0011942426380986415
          ],
          [
            3.6637359812630166e-15,
            3.0410118867507663e-12,
            -1.0431427738266663e-06
          ],
          [
            7.327471962526033e-15,
            -4.092555738743897e-10,
            -0.00107388428428834
          ],
          [
            3.3306690738754696e-16,
            -8.215226277030752e-10,
            -0.0021467327214051424
          ],
          [
            1.2212453270876722e-15,
            -1.2337574850640465e-09,
            -0.003219588418333752
          ],
          [
            1.4432899320127035e-15,
            -1.64596719587351e-09,
            -0.0042924513393002295
          ],
          [
            2.3314683517128287e-15,
            -2.0581528148433392e-09,
            -0.0053653214485253065
          ],
          [
            5.329070518200751e-15,
            -2.470305016100127e-09,
            -0.006438198710235543
          ],
          [
            3.774758283725532e-15,
            -2.8824327924503734e-09,
            -0.007511083088658332
          ],
          [
            1.0880185641326534e-14,
            -3.294530204200896e-09,
            -0.008583974547988982
          ]
        ]
      },
      "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,
        0.0,
        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": [
              1.0076417930981045e-15,
              4.519596387496164e-09,
              0.009561000517746545
            ],
            "branch_aligned_reduced_polarization": [
              1.0076417930981045e-15,
              4.519596387496164e-09,
              0.009561000517746554
            ],
            "target_residual": 0.4904389994822535,
            "energy_eV": -530.008915134207,
            "max_atomic_step_A": 0.034754740572008565,
            "max_log_strain_component": 0.007403017927707795,
            "step_scale": 1.0,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 4.362664515679049,
            "cell_principal_stretches": [
              1.0046058002753182,
              1.002850549350517,
              0.9926243169144765
            ],
            "cell_volume_ratio": 1.0000387030936873,
            "cell_rmsd_from_input_A": 0.11500065569327074
          },
          {
            "iteration": 1,
            "reduced_polarization": [
              -2.2007540769870458e-14,
              -1.6718454368501316e-10,
              0.49663985563849816
            ],
            "branch_aligned_reduced_polarization": [
              -2.2007540769870458e-14,
              -1.6718454368501316e-10,
              0.49663985563849816
            ],
            "target_residual": 0.0033601443615018417,
            "energy_eV": -528.8263930756558,
            "max_atomic_step_A": 0.00024326568623084778,
            "max_log_strain_component": 5.168903748674864e-05,
            "step_scale": 1.0,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 4.362664515679049,
            "cell_principal_stretches": [
              1.0046380331597526,
              1.0028704808735447,
              0.9925730104449517
            ],
            "cell_volume_ratio": 1.0000389733300505,
            "cell_rmsd_from_input_A": 0.1157980975265128
          },
          {
            "iteration": 2,
            "reduced_polarization": [
              -3.2766416665812264e-16,
              3.68211512884519e-13,
              0.49999599471548306
            ],
            "branch_aligned_reduced_polarization": [
              -3.2766416665812264e-16,
              3.68211512884519e-13,
              0.49999599471548306
            ],
            "target_residual": 4.005284516939173e-06,
            "energy_eV": -528.8100525204826
          }
        ],
        "iterations": 2
      },
      "parent": {
        "candidate_id": "bec_projection_01",
        "source": "MACEField_BEC_backprojection",
        "spacegroup": "Amm2",
        "spacegroup_number": 38,
        "pointgroup": "mm2",
        "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": 4.005284516939173e-06,
        "parent_symmetrization_rmsd_A": 0.024239465908917047,
        "parent_cell_rmsd_A": 0.1157980975265128,
        "energy_eV": -528.8100525204826,
        "reduced_polarization": [
          -3.2766416665812264e-16,
          3.68211512884519e-13,
          0.49999599471548306
        ],
        "cartesian_polarization_e_A2": [
          2.470076685666329e-17,
          8.420065447408331e-13,
          0.0037009623685365658
        ],
        "ranking_score": 0.5531970008595791
      },
      "branch_status": "awaiting_branch_sampling"
    },
    {
      "orbit_id": 2,
      "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": [
              1.0076417930981045e-15,
              4.519596387496164e-09,
              0.009561000517746545
            ],
            "branch_aligned_reduced_polarization": [
              1.0076417930981045e-15,
              4.519596363827816e-09,
              0.009561000517746545
            ],
            "target_residual": 0.5000913998573701,
            "energy_eV": -530.008915134207,
            "max_atomic_step_A": 0.04667893073373827,
            "max_log_strain_component": 0.02,
            "step_scale": 0.7916568802359734,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 4.362664515679049,
            "cell_principal_stretches": [
              1.0202236631620305,
              0.9999560705044581,
              0.9802197010155609
            ],
            "cell_volume_ratio": 0.9999994026744998,
            "cell_rmsd_from_input_A": 0.24707003316613915
          },
          {
            "iteration": 1,
            "reduced_polarization": [
              -1.534646817418415e-14,
              0.3955468335972508,
              0.02091014553390413
            ],
            "branch_aligned_reduced_polarization": [
              -1.534646817418415e-14,
              0.3955468335972508,
              0.02091014553390413
            ],
            "target_residual": 0.10652557513484481,
            "energy_eV": -527.1864475886637,
            "max_atomic_step_A": 0.01247524919279406,
            "max_log_strain_component": 0.0053589350992421896,
            "step_scale": 1.0,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 4.362664515679049,
            "cell_principal_stretches": [
              1.0258072193845456,
              0.9997647306319699,
              0.9750683226208516
            ],
            "cell_volume_ratio": 0.9999968007577784,
            "cell_rmsd_from_input_A": 0.3138063159154961
          },
          {
            "iteration": 2,
            "reduced_polarization": [
              5.650026672839146e-15,
              0.49965586024208414,
              0.0028520438366025852
            ],
            "branch_aligned_reduced_polarization": [
              5.650026672839146e-15,
              0.49965586024208414,
              0.0028520438366025852
            ],
            "target_residual": 0.0028727314909126438,
            "energy_eV": -525.4825238927025,
            "max_atomic_step_A": 0.0002227556598219617,
            "max_log_strain_component": 4.412831322907224e-05,
            "step_scale": 1.0,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 4.362664515679049,
            "cell_principal_stretches": [
              1.0258425131003615,
              0.9997477672296238,
              0.9750510949082116
            ],
            "cell_volume_ratio": 0.9999965700594624,
            "cell_rmsd_from_input_A": 0.3141667477423024
          },
          {
            "iteration": 3,
            "reduced_polarization": [
              -2.4885871376136794e-15,
              0.4999923755658896,
              6.994449262548315e-06
            ],
            "branch_aligned_reduced_polarization": [
              -2.4885871376136794e-15,
              0.4999923755658896,
              6.994449262548315e-06
            ],
            "target_residual": 1.0346705562166417e-05,
            "energy_eV": -525.4784216430337
          }
        ],
        "iterations": 3
      },
      "parent": {
        "candidate_id": "bec_projection_02",
        "source": "MACEField_BEC_backprojection",
        "spacegroup": "Pm",
        "spacegroup_number": 6,
        "pointgroup": "m",
        "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": 1.0346705562166417e-05,
        "parent_symmetrization_rmsd_A": 0.039164920992552775,
        "parent_cell_rmsd_A": 0.3141667477423024,
        "energy_eV": -525.4784216430337,
        "reduced_polarization": [
          -2.4885871376136794e-15,
          0.4999923755658896,
          6.994449262548315e-06
        ],
        "cartesian_polarization_e_A2": [
          2.5963475528985604e-17,
          0.0064490171479085956,
          -0.00016347531831747313
        ],
        "ranking_score": 0.6177273013392527
      },
      "branch_status": "awaiting_branch_sampling"
    },
    {
      "orbit_id": 3,
      "formal_class": [
        0.5,
        0.0,
        0.0
      ],
      "formal_classes_in_orbit": [
        [
          0.5,
          0.0,
          0.0
        ]
      ],
      "target_reduced_polarization": [
        0.5,
        0.0,
        0.0
      ],
      "bec_backprojection": {
        "converged_to_target": true,
        "history": [
          {
            "iteration": 0,
            "reduced_polarization": [
              1.0076417930981045e-15,
              4.519596387496164e-09,
              0.009561000517746545
            ],
            "branch_aligned_reduced_polarization": [
              9.992007221626409e-16,
              4.519596387496164e-09,
              0.009561000517746545
            ],
            "target_residual": 0.5000914043761394,
            "energy_eV": -530.008915134207,
            "max_atomic_step_A": 0.03050363879190309,
            "max_log_strain_component": 0.00521202131679635,
            "step_scale": 1.0,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 4.362664515679049,
            "cell_principal_stretches": [
              1.005152741785681,
              1.000144330622304,
              0.9947293523223409
            ],
            "cell_volume_ratio": 0.999999245506596,
            "cell_rmsd_from_input_A": 0.03187439926186918
          },
          {
            "iteration": 1,
            "reduced_polarization": [
              0.5001062538333132,
              -7.090157329439822e-13,
              -0.0032744132746565556
            ],
            "branch_aligned_reduced_polarization": [
              0.5001062538333132,
              -7.090157329439822e-13,
              -0.0032744132746565556
            ],
            "target_residual": 0.0032761367752798137,
            "energy_eV": -529.1776923883364,
            "max_atomic_step_A": 0.00023390945659240923,
            "max_log_strain_component": 4.942382180079638e-05,
            "step_scale": 1.0,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 4.362664515679049,
            "cell_principal_stretches": [
              1.0051774724526157,
              1.0000949008886455,
              0.994754299073132
            ],
            "cell_volume_ratio": 0.9999995038899488,
            "cell_rmsd_from_input_A": 0.03183008575264966
          },
          {
            "iteration": 2,
            "reduced_polarization": [
              0.49999310021355436,
              -6.123815689582648e-14,
              4.95354993048566e-07
            ],
            "branch_aligned_reduced_polarization": [
              0.49999310021355436,
              -6.123815689582648e-14,
              4.95354993048566e-07
            ],
            "target_residual": 6.917545053305645e-06,
            "energy_eV": -529.1788431746174
          }
        ],
        "iterations": 2
      },
      "parent": {
        "candidate_id": "bec_projection_03",
        "source": "MACEField_BEC_backprojection",
        "spacegroup": "Cm",
        "spacegroup_number": 8,
        "pointgroup": "m",
        "has_inversion": false,
        "is_polar_point_group": true,
        "nonpolar_parent_hypothesis": false,
        "symmetry_tolerance_A": null,
        "target_reduced_polarization": [
          0.5,
          0.0,
          0.0
        ],
        "formal_class": [
          0.5,
          0.0,
          0.0
        ],
        "target_residual": 6.917545053305645e-06,
        "parent_symmetrization_rmsd_A": 0.02106107558206401,
        "parent_cell_rmsd_A": 0.03183008575264966,
        "energy_eV": -529.1788431746174,
        "reduced_polarization": [
          0.49999310021355436,
          -6.123815689582648e-14,
          4.95354993048566e-07
        ],
        "cartesian_polarization_e_A2": [
          0.0031846348215341736,
          -1.78380057870211e-14,
          1.6601088697817424e-05
        ],
        "ranking_score": 0.529032432110333
      },
      "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": [
              1.0076417930981045e-15,
              4.519596387496164e-09,
              0.009561000517746545
            ],
            "branch_aligned_reduced_polarization": [
              1.0076417930981045e-15,
              4.519596363827816e-09,
              0.009561000517746554
            ],
            "target_residual": 0.7003787601673522,
            "energy_eV": -530.008915134207,
            "max_atomic_step_A": 0.05336205387254795,
            "max_log_strain_component": 0.02,
            "step_scale": 0.7916568804741957,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 4.362664515679049,
            "cell_principal_stretches": [
              1.019635027405245,
              1.0022559876576445,
              0.9785655004032306
            ],
            "cell_volume_ratio": 1.000030639421337,
            "cell_rmsd_from_input_A": 0.26086549742574594
          },
          {
            "iteration": 1,
            "reduced_polarization": [
              -3.464012677391476e-14,
              0.4066614766597576,
              0.4142764537336384
            ],
            "branch_aligned_reduced_polarization": [
              -3.464012677391476e-14,
              0.4066614766597576,
              0.4142764537336384
            ],
            "target_residual": 0.1267304475010564,
            "energy_eV": -525.9685950461283,
            "max_atomic_step_A": 0.01199275624204185,
            "max_log_strain_component": 0.004427754818807145,
            "step_scale": 1.0,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 4.362664515679049,
            "cell_principal_stretches": [
              1.024034413567359,
              1.0027037027839698,
              0.9739323085515886
            ],
            "cell_volume_ratio": 1.0000367119184301,
            "cell_rmsd_from_input_A": 0.3173433293070294
          },
          {
            "iteration": 2,
            "reduced_polarization": [
              -4.565548378330599e-15,
              0.5007708330818648,
              0.5018031487543405
            ],
            "branch_aligned_reduced_polarization": [
              -4.565548378330599e-15,
              0.5007708330818648,
              0.5018031487543405
            ],
            "target_residual": 0.001961002057718672,
            "energy_eV": -523.7901292123636,
            "max_atomic_step_A": 0.00015828870462429058,
            "max_log_strain_component": 3.3396888459434824e-05,
            "step_scale": 1.0,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 4.362664515679049,
            "cell_principal_stretches": [
              1.0240012661799576,
              1.0026935375858017,
              0.973973574871992
            ],
            "cell_volume_ratio": 1.0000365740743307,
            "cell_rmsd_from_input_A": 0.3168334619558985
          },
          {
            "iteration": 3,
            "reduced_polarization": [
              2.6246535534396177e-15,
              0.4999947280660967,
              0.4999918804597061
            ],
            "branch_aligned_reduced_polarization": [
              2.6246535534396177e-15,
              0.4999947280660967,
              0.4999918804597061
            ],
            "target_residual": 9.680920496786864e-06,
            "energy_eV": -523.8167202373735
          }
        ],
        "iterations": 3
      },
      "parent": {
        "candidate_id": "bec_projection_04",
        "source": "MACEField_BEC_backprojection",
        "spacegroup": "Pm",
        "spacegroup_number": 6,
        "pointgroup": "m",
        "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": 9.680920496786864e-06,
        "parent_symmetrization_rmsd_A": 0.04539888665590686,
        "parent_cell_rmsd_A": 0.3168334619558985,
        "energy_eV": -523.8167202373735,
        "reduced_polarization": [
          2.6246535534396177e-15,
          0.4999947280660967,
          0.4999918804597061
        ],
        "cartesian_polarization_e_A2": [
          1.0909373627051875e-16,
          0.006309719047137636,
          0.003544031374428587
        ],
        "ranking_score": 0.624626613985875
      },
      "branch_status": "awaiting_branch_sampling"
    },
    {
      "orbit_id": 5,
      "formal_class": [
        0.5,
        0.0,
        0.5
      ],
      "formal_classes_in_orbit": [
        [
          0.5,
          0.0,
          0.5
        ]
      ],
      "target_reduced_polarization": [
        0.5,
        0.0,
        0.5
      ],
      "bec_backprojection": {
        "converged_to_target": true,
        "history": [
          {
            "iteration": 0,
            "reduced_polarization": [
              1.0076417930981045e-15,
              4.519596387496164e-09,
              0.009561000517746545
            ],
            "branch_aligned_reduced_polarization": [
              9.992007221626409e-16,
              4.519596387496164e-09,
              0.009561000517746554
            ],
            "target_residual": 0.7003787633938888,
            "energy_eV": -530.008915134207,
            "max_atomic_step_A": 0.04670913187699147,
            "max_log_strain_component": 0.007403017927705297,
            "step_scale": 1.0,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 4.362664515679049,
            "cell_principal_stretches": [
              1.009046387598097,
              0.9984372285252244,
              0.9926243169144788
            ],
            "cell_volume_ratio": 1.000038703093704,
            "cell_rmsd_from_input_A": 0.11941575852365995
          },
          {
            "iteration": 1,
            "reduced_polarization": [
              0.49037460033018254,
              -1.706794189000923e-10,
              0.49329635164634555
            ],
            "branch_aligned_reduced_polarization": [
              0.49037460033018254,
              -1.706794189000923e-10,
              0.49329635164634555
            ],
            "target_residual": 0.011729757885530972,
            "energy_eV": -528.1147143783708,
            "max_atomic_step_A": 0.0007765053983859773,
            "max_log_strain_component": 0.00010621504723699021,
            "step_scale": 1.0,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 4.362664515679049,
            "cell_principal_stretches": [
              1.009206909428988,
              0.9983850118988836,
              0.9925188908747842
            ],
            "cell_volume_ratio": 1.0000392583985351,
            "cell_rmsd_from_input_A": 0.12117005890368908
          },
          {
            "iteration": 2,
            "reduced_polarization": [
              0.4999748369000347,
              2.4995553919888466e-13,
              0.49998213145869697
            ],
            "branch_aligned_reduced_polarization": [
              0.4999748369000347,
              2.4995553919888466e-13,
              0.49998213145869697
            ],
            "target_residual": 3.0862053855217666e-05,
            "energy_eV": -528.0541685607567
          }
        ],
        "iterations": 2
      },
      "parent": {
        "candidate_id": "bec_projection_05",
        "source": "MACEField_BEC_backprojection",
        "spacegroup": "Cm",
        "spacegroup_number": 8,
        "pointgroup": "m",
        "has_inversion": false,
        "is_polar_point_group": true,
        "nonpolar_parent_hypothesis": false,
        "symmetry_tolerance_A": null,
        "target_reduced_polarization": [
          0.5,
          0.0,
          0.5
        ],
        "formal_class": [
          0.5,
          0.0,
          0.5
        ],
        "target_residual": 3.0862053855217666e-05,
        "parent_symmetrization_rmsd_A": 0.032312116183036185,
        "parent_cell_rmsd_A": 0.12117005890368908,
        "energy_eV": -528.0541685607567,
        "reduced_polarization": [
          0.4999748369000347,
          2.4995553919888466e-13,
          0.49998213145869697
        ],
        "cartesian_polarization_e_A2": [
          0.0032133790628668256,
          8.220724773604733e-13,
          0.003718032308722053
        ],
        "ranking_score": 0.5626663550166688
      },
      "branch_status": "awaiting_branch_sampling"
    },
    {
      "orbit_id": 6,
      "formal_class": [
        0.5,
        0.5,
        0.0
      ],
      "formal_classes_in_orbit": [
        [
          0.5,
          0.5,
          0.0
        ]
      ],
      "target_reduced_polarization": [
        0.5,
        0.5,
        0.0
      ],
      "bec_backprojection": {
        "converged_to_target": true,
        "history": [
          {
            "iteration": 0,
            "reduced_polarization": [
              1.0076417930981045e-15,
              4.519596387496164e-09,
              0.009561000517746545
            ],
            "branch_aligned_reduced_polarization": [
              9.992007221626409e-16,
              4.519596363827816e-09,
              0.009561000517746545
            ],
            "target_residual": 0.7071714135987843,
            "energy_eV": -530.008915134207,
            "max_atomic_step_A": 0.05231968910273041,
            "max_log_strain_component": 0.02,
            "step_scale": 0.7916568802359503,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 4.362664515679049,
            "cell_principal_stretches": [
              1.0206501706558435,
              0.999962527935211,
              0.9798037612422373
            ],
            "cell_volume_ratio": 0.9999994026745131,
            "cell_rmsd_from_input_A": 0.2483546311658399
          },
          {
            "iteration": 1,
            "reduced_polarization": [
              0.3938070130041502,
              0.39518671061948135,
              0.018845373349588575
            ],
            "branch_aligned_reduced_polarization": [
              0.3938070130041502,
              0.39518671061948135,
              0.018845373349588575
            ],
            "target_residual": 0.1503925670189536,
            "energy_eV": -526.6668280093113,
            "max_atomic_step_A": 0.014342458905781471,
            "max_log_strain_component": 0.005399409521940481,
            "step_scale": 1.0,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 4.362664515679049,
            "cell_principal_stretches": [
              1.0263728380944508,
              0.9998172765103875,
              0.9744800368787143
            ],
            "cell_volume_ratio": 0.9999970847667825,
            "cell_rmsd_from_input_A": 0.3158916832414546
          },
          {
            "iteration": 2,
            "reduced_polarization": [
              0.49939452396334366,
              0.4995793384567189,
              0.0026321962307153716
            ],
            "branch_aligned_reduced_polarization": [
              0.49939452396334366,
              0.4995793384567189,
              0.0026321962307153716
            ],
            "target_residual": 0.0027334985571521512,
            "energy_eV": -524.6183032416304,
            "max_atomic_step_A": 0.00021460947662896207,
            "max_log_strain_component": 4.081906093537877e-05,
            "step_scale": 1.0,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 4.362664515679049,
            "cell_principal_stretches": [
              1.0264104742456548,
              0.9998038985947998,
              0.9744571355419596
            ],
            "cell_volume_ratio": 0.9999968713688303,
            "cell_rmsd_from_input_A": 0.3162924913310569
          },
          {
            "iteration": 3,
            "reduced_polarization": [
              0.5000034674880731,
              0.4999926438400197,
              7.338523771993432e-06
            ],
            "branch_aligned_reduced_polarization": [
              0.5000034674880731,
              0.4999926438400197,
              7.338523771993432e-06
            ],
            "target_residual": 1.0954017269723053e-05,
            "energy_eV": -524.6099819918131
          }
        ],
        "iterations": 3
      },
      "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,
          0.5,
          0.0
        ],
        "formal_class": [
          0.5,
          0.5,
          0.0
        ],
        "target_residual": 1.0954017269723053e-05,
        "parent_symmetrization_rmsd_A": 0.044592683335285495,
        "parent_cell_rmsd_A": 0.3162924913310569,
        "energy_eV": -524.6099819918131,
        "reduced_polarization": [
          0.5000034674880731,
          0.4999926438400197,
          7.338523771993432e-06
        ],
        "cartesian_polarization_e_A2": [
          0.003183662137926056,
          0.006448441552649926,
          -0.00014701588497370558
        ],
        "ranking_score": 0.6236877142025892
      },
      "branch_status": "awaiting_branch_sampling"
    },
    {
      "orbit_id": 7,
      "formal_class": [
        0.5,
        0.5,
        0.5
      ],
      "formal_classes_in_orbit": [
        [
          0.5,
          0.5,
          0.5
        ]
      ],
      "target_reduced_polarization": [
        0.5,
        0.5,
        0.5
      ],
      "bec_backprojection": {
        "converged_to_target": true,
        "history": [
          {
            "iteration": 0,
            "reduced_polarization": [
              1.0076417930981045e-15,
              4.519596387496164e-09,
              0.009561000517746545
            ],
            "branch_aligned_reduced_polarization": [
              9.992007221626409e-16,
              4.519596363827816e-09,
              0.009561000517746554
            ],
            "target_residual": 0.860540764690178,
            "energy_eV": -530.008915134207,
            "max_atomic_step_A": 0.059063391932348684,
            "max_log_strain_component": 0.02,
            "step_scale": 0.7916568804741725,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 4.362664515679049,
            "cell_principal_stretches": [
              1.0202413155467034,
              1.0019342895099623,
              0.9782979867642743
            ],
            "cell_volume_ratio": 1.0000306394213507,
            "cell_rmsd_from_input_A": 0.2621052450937029
          },
          {
            "iteration": 1,
            "reduced_polarization": [
              0.3876139634992378,
              0.4063328037501256,
              0.4122015695924171
            ],
            "branch_aligned_reduced_polarization": [
              0.3876139634992378,
              0.4063328037501256,
              0.4122015695924171
            ],
            "target_residual": 0.17062452706366193,
            "energy_eV": -525.5090423531449,
            "max_atomic_step_A": 0.014643580562328886,
            "max_log_strain_component": 0.0044645439884330495,
            "step_scale": 1.0,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 4.362664515679049,
            "cell_principal_stretches": [
              1.0249073259865664,
              1.0022889791006686,
              0.9735057584154102
            ],
            "cell_volume_ratio": 1.000037019875155,
            "cell_rmsd_from_input_A": 0.3197791379134606
          },
          {
            "iteration": 2,
            "reduced_polarization": [
              0.4987185529170867,
              0.5007184072849102,
              0.5015594026040581
            ],
            "branch_aligned_reduced_polarization": [
              0.4987185529170867,
              0.5007184072849102,
              0.5015594026040581
            ],
            "target_residual": 0.0021424173577671876,
            "energy_eV": -523.0036643377148,
            "max_atomic_step_A": 0.00016220275681109737,
            "max_log_strain_component": 3.117460028083041e-05,
            "step_scale": 1.0,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 4.362664515679049,
            "cell_principal_stretches": [
              1.02488092659732,
              1.002278590608726,
              0.9735408114591619
            ],
            "cell_volume_ratio": 1.000036903261888,
            "cell_rmsd_from_input_A": 0.31932483023135577
          },
          {
            "iteration": 3,
            "reduced_polarization": [
              0.5000036197722607,
              0.4999953011649954,
              0.4999910386996462
            ],
            "branch_aligned_reduced_polarization": [
              0.5000036197722607,
              0.4999953011649954,
              0.4999910386996462
            ],
            "target_residual": 1.0746474103224336e-05,
            "energy_eV": -523.0235273440912
          }
        ],
        "iterations": 3
      },
      "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": 1.0746474103224336e-05,
        "parent_symmetrization_rmsd_A": 0.05027857293999296,
        "parent_cell_rmsd_A": 0.31932483023135577,
        "energy_eV": -523.0235273440912,
        "reduced_polarization": [
          0.5000036197722607,
          0.4999953011649954,
          0.4999910386996462
        ],
        "cartesian_polarization_e_A2": [
          0.003212803792911518,
          0.0063089895266538135,
          0.0035611644615956483
        ],
        "ranking_score": 0.6301312734460384
      },
      "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,
          32,
          33,
          34,
          35,
          36,
          37,
          38,
          39,
          40,
          41,
          42,
          43,
          44,
          45,
          46,
          47,
          48,
          49,
          50,
          51,
          52,
          53,
          54,
          55,
          56,
          57,
          58,
          59,
          60,
          61,
          62,
          63,
          64,
          65,
          66,
          67,
          68,
          69,
          70,
          71,
          72,
          73,
          74,
          75,
          76,
          77
        ],
        "endpoint_rmsd_A": 0.000471389707033928,
        "minimum_distance_A_by_image": [
          1.5830821199409881,
          1.5829533276634522,
          1.5828245385720967,
          1.5826957526669636,
          1.5825669699480958,
          1.5824381904155398,
          1.5823094140693388,
          1.5821806409095385,
          1.5820518709361837
        ],
        "minimum_distance_A": 1.5820518709361837,
        "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": [
          1285.9308716832525,
          1285.9307504049134,
          1285.9306291265862,
          1285.9305078482723,
          1285.9303865699678,
          1285.9302652916758,
          1285.9301440133952,
          1285.930022735125,
          1285.9299014568696
        ],
        "cell_deformation_log_strain_norm": 0.00017869739729747778
      },
      "parent_reduced_polarization": [
        3.7138180110567695e-15,
        3.0409739126167407e-12,
        -1.0431427738261615e-06
      ],
      "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": [
          -530.0089151342067,
          -530.0089485729909,
          -530.0089680333314,
          -530.0089735144835,
          -530.0089650156979,
          -530.0089425362188,
          -530.0089060752849,
          -530.0088556321302,
          -530.0087912059823
        ],
        "cartesian_polarizations_e_A2": [
          [
            2.752559580054663e-18,
            5.8237626749629e-11,
            7.044639857895299e-05
          ],
          [
            -9.840340734291479e-18,
            5.096355215786202e-11,
            6.163917981594125e-05
          ],
          [
            1.9502152207228053e-17,
            4.368930070919169e-11,
            5.2832091191813295e-05
          ],
          [
            2.869471922963185e-17,
            3.641482843499598e-11,
            4.4025133105765186e-05
          ],
          [
            3.0970591733172965e-17,
            2.914014556088046e-11,
            3.52183059565358e-05
          ],
          [
            1.6039777491848544e-17,
            2.1865173599154635e-11,
            2.641161014300293e-05
          ],
          [
            1.8105168223930785e-18,
            1.4590047407769698e-11,
            1.7605046063937355e-05
          ],
          [
            2.7258094961962097e-17,
            7.31475961697792e-12,
            8.798614117899094e-06
          ],
          [
            2.3653871066050646e-17,
            3.9188640986319486e-14,
            -7.685296550117599e-09
          ]
        ],
        "raw_reduced_polarization": [
          [
            4.3214686787523274e-16,
            4.519597153676033e-09,
            0.009561000517746514
          ],
          [
            -1.5447491266148405e-15,
            3.9548761522066514e-09,
            0.008365775763418992
          ],
          [
            3.0621480855435684e-15,
            3.3902008973308743e-09,
            0.00717054212815114
          ],
          [
            4.505490924071416e-15,
            2.8255679759109798e-09,
            0.005975299666270017
          ],
          [
            4.862864672121758e-15,
            2.2609781805527237e-09,
            0.004780048432043001
          ],
          [
            2.518681630838705e-15,
            1.6964254197289443e-09,
            0.0035847884797587707
          ],
          [
            2.84563062029961e-16,
            1.131920157480124e-09,
            0.002389519863693878
          ],
          [
            4.279853485205878e-15,
            5.674618207431195e-10,
            0.0011942426380986784
          ],
          [
            3.7138180110567695e-15,
            3.0409739126167407e-12,
            -1.0431427738261615e-06
          ]
        ],
        "unwrapped_reduced_polarization": [
          [
            4.3214686787523274e-16,
            4.519597153676033e-09,
            0.009561000517746514
          ],
          [
            -1.5447491266148407e-15,
            3.9548761522066514e-09,
            0.008365775763418992
          ],
          [
            3.0621480855435684e-15,
            3.3902008973308743e-09,
            0.00717054212815114
          ],
          [
            4.505490924071416e-15,
            2.8255679759109798e-09,
            0.005975299666270017
          ],
          [
            4.862864672121758e-15,
            2.2609781805527237e-09,
            0.004780048432043001
          ],
          [
            2.518681630838705e-15,
            1.6964254197289443e-09,
            0.0035847884797587707
          ],
          [
            2.8456306202996105e-16,
            1.131920157480124e-09,
            0.002389519863693878
          ],
          [
            4.279853485205878e-15,
            5.674618207431195e-10,
            0.0011942426380986784
          ],
          [
            3.7138180110567695e-15,
            3.040973912616721e-12,
            -1.0431427738262326e-06
          ]
        ],
        "berry_integer_shifts": [
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ]
        ],
        "folded_reduced_polarization": [
          [
            4.440892098500626e-16,
            4.519597140983933e-09,
            0.009561000517746554
          ],
          [
            -1.5543122344752192e-15,
            3.954876204304014e-09,
            0.008365775763419014
          ],
          [
            3.1086244689504383e-15,
            3.3902008977904075e-09,
            0.007170542128151158
          ],
          [
            4.551914400963142e-15,
            2.8255680017963414e-09,
            0.005975299666269973
          ],
          [
            4.884981308350689e-15,
            2.2609781824556308e-09,
            0.004780048432043049
          ],
          [
            2.55351295663786e-15,
            1.6964254445639426e-09,
            0.003584788479758738
          ],
          [
            3.3306690738754696e-16,
            1.131920113195406e-09,
            0.0023895198636938453
          ],
          [
            4.3298697960381105e-15,
            5.674618552831134e-10,
            0.0011942426380986415
          ],
          [
            3.6637359812630166e-15,
            3.0410118867507663e-12,
            -1.0431427738266663e-06
          ]
        ]
      },
      "reflected": {
        "reached": true,
        "construction": "reflect_displacements_about_reconstructed_parent",
        "energies_eV": [
          -530.0087912059822,
          -530.0087648766214,
          -530.0087278159003,
          -530.0086800242486,
          -530.0086215020924,
          -530.0085522498539,
          -530.0084722679517,
          -530.0083815568003,
          -530.0082801168104
        ],
        "cartesian_polarizations_e_A2": [
          [
            1.727885466739744e-17,
            3.9210527865496727e-14,
            -7.685296514503916e-09
          ],
          [
            4.687632690763198e-17,
            -5.275744934174847e-12,
            -7.911870773406911e-06
          ],
          [
            1.8237119214525882e-18,
            -1.0589654422690336e-11,
            -1.5816285531468843e-05
          ],
          [
            7.966545085891722e-18,
            -1.5902504799581863e-11,
            -2.372092931175711e-05
          ],
          [
            9.068393259257302e-18,
            -2.12143880609697e-11,
            -3.162580185540195e-05
          ],
          [
            1.4737818253215546e-17,
            -2.6525317046080325e-11,
            -3.953090290348439e-05
          ],
          [
            3.3816139705960306e-17,
            -3.183517195574668e-11,
            -4.743623219711572e-05
          ],
          [
            2.3721263556700732e-17,
            -3.714406811349013e-11,
            -5.534178947740192e-05
          ],
          [
            6.924648793266873e-17,
            -4.245192990601275e-11,
            -6.324757448520135e-05
          ]
        ],
        "raw_reduced_polarization": [
          [
            2.7128971984628734e-15,
            3.0426722223279195e-12,
            -1.0431427689922355e-06
          ],
          [
            7.359691755631243e-15,
            -4.0925559833881716e-10,
            -0.001073884284288334
          ],
          [
            2.860585316701662e-16,
            -8.215226549210059e-10,
            -0.002146732721405128
          ],
          [
            1.2504351263181494e-15,
            -1.2337574759053296e-09,
            -0.003219588418333773
          ],
          [
            1.4233967768594793e-15,
            -1.6459671980652723e-09,
            -0.004292451339300211
          ],
          [
            2.313517493578547e-15,
            -2.0581528159633256e-09,
            -0.00536532144852529
          ],
          [
            5.308872719736929e-15,
            -2.470305031052037e-09,
            -0.0064381987102355214
          ],
          [
            3.724061870705479e-15,
            -2.8824327907395323e-09,
            -0.0075110830886583125
          ],
          [
            1.0871573167135084e-14,
            -3.2945302252120348e-09,
            -0.008583974547989008
          ]
        ],
        "unwrapped_reduced_polarization": [
          [
            2.7128971984628734e-15,
            3.0426722223279195e-12,
            -1.0431427689922355e-06
          ],
          [
            7.359691755631243e-15,
            -4.0925559833881716e-10,
            -0.001073884284288334
          ],
          [
            2.860585316701661e-16,
            -8.215226549210059e-10,
            -0.002146732721405128
          ],
          [
            1.2504351263181494e-15,
            -1.2337574759053296e-09,
            -0.003219588418333773
          ],
          [
            1.4233967768594793e-15,
            -1.6459671980652723e-09,
            -0.004292451339300211
          ],
          [
            2.313517493578547e-15,
            -2.0581528159633256e-09,
            -0.00536532144852529
          ],
          [
            5.308872719736929e-15,
            -2.470305031052037e-09,
            -0.0064381987102355214
          ],
          [
            3.724061870705479e-15,
            -2.8824327907395323e-09,
            -0.0075110830886583125
          ],
          [
            1.0871573167135085e-14,
            -3.2945302252120348e-09,
            -0.008583974547989008
          ]
        ],
        "gauge_integer_shift": [
          0,
          0,
          0
        ],
        "expected_opposite_endpoint_reduced_polarization": [
          6.995082950064171e-15,
          -4.51351459570987e-09,
          -0.009563086617980932
        ],
        "actual_opposite_endpoint_branch_residual": 0.0009791120699926832
      },
      "pnp_branch": {
        "construction": "incoming_path_concatenated_with_parent_reflection",
        "reduced_polarization": [
          [
            4.3214686787523274e-16,
            4.519597153676033e-09,
            0.009561000517746514
          ],
          [
            -1.5447491266148405e-15,
            3.9548761522066514e-09,
            0.008365775763418992
          ],
          [
            3.0621480855435684e-15,
            3.3902008973308743e-09,
            0.00717054212815114
          ],
          [
            4.505490924071416e-15,
            2.8255679759109798e-09,
            0.005975299666270017
          ],
          [
            4.862864672121758e-15,
            2.2609781805527237e-09,
            0.004780048432043001
          ],
          [
            2.518681630838705e-15,
            1.6964254197289443e-09,
            0.0035847884797587707
          ],
          [
            2.84563062029961e-16,
            1.131920157480124e-09,
            0.002389519863693878
          ],
          [
            4.279853485205878e-15,
            5.674618207431195e-10,
            0.0011942426380986784
          ],
          [
            3.7138180110567695e-15,
            3.0409739126167407e-12,
            -1.0431427738261615e-06
          ],
          [
            7.359691755631243e-15,
            -4.0925559833881716e-10,
            -0.001073884284288334
          ],
          [
            2.860585316701662e-16,
            -8.215226549210059e-10,
            -0.002146732721405128
          ],
          [
            1.2504351263181494e-15,
            -1.2337574759053296e-09,
            -0.003219588418333773
          ],
          [
            1.4233967768594793e-15,
            -1.6459671980652723e-09,
            -0.004292451339300211
          ],
          [
            2.313517493578547e-15,
            -2.0581528159633256e-09,
            -0.00536532144852529
          ],
          [
            5.308872719736929e-15,
            -2.470305031052037e-09,
            -0.0064381987102355214
          ],
          [
            3.724061870705479e-15,
            -2.8824327907395323e-09,
            -0.0075110830886583125
          ],
          [
            1.0871573167135084e-14,
            -3.2945302252120348e-09,
            -0.008583974547989008
          ]
        ],
        "unwrapped_reduced_polarization": [
          [
            4.3214686787523274e-16,
            4.519597153676033e-09,
            0.009561000517746514
          ],
          [
            -1.5447491266148407e-15,
            3.9548761522066514e-09,
            0.008365775763418992
          ],
          [
            3.0621480855435684e-15,
            3.3902008973308743e-09,
            0.00717054212815114
          ],
          [
            4.505490924071416e-15,
            2.8255679759109798e-09,
            0.005975299666270017
          ],
          [
            4.862864672121758e-15,
            2.2609781805527237e-09,
            0.004780048432043001
          ],
          [
            2.518681630838705e-15,
            1.6964254197289443e-09,
            0.0035847884797587707
          ],
          [
            2.8456306202996105e-16,
            1.131920157480124e-09,
            0.002389519863693878
          ],
          [
            4.279853485205878e-15,
            5.674618207431195e-10,
            0.0011942426380986784
          ],
          [
            3.7138180110567695e-15,
            3.040973912616721e-12,
            -1.0431427738262326e-06
          ],
          [
            7.359691755631243e-15,
            -4.0925559833881716e-10,
            -0.001073884284288334
          ],
          [
            2.860585316701661e-16,
            -8.215226549210059e-10,
            -0.002146732721405128
          ],
          [
            1.2504351263181494e-15,
            -1.2337574759053296e-09,
            -0.003219588418333773
          ],
          [
            1.4233967768594793e-15,
            -1.6459671980652723e-09,
            -0.004292451339300211
          ],
          [
            2.313517493578547e-15,
            -2.0581528159633256e-09,
            -0.00536532144852529
          ],
          [
            5.308872719736929e-15,
            -2.470305031052037e-09,
            -0.0064381987102355214
          ],
          [
            3.724061870705479e-15,
            -2.8824327907395323e-09,
            -0.0075110830886583125
          ],
          [
            1.0871573167135085e-14,
            -3.2945302252120348e-09,
            -0.008583974547989008
          ]
        ],
        "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": [
          [
            4.440892098500626e-16,
            4.519597140983933e-09,
            0.009561000517746554
          ],
          [
            -1.5543122344752192e-15,
            3.954876204304014e-09,
            0.008365775763419014
          ],
          [
            3.1086244689504383e-15,
            3.3902008977904075e-09,
            0.007170542128151158
          ],
          [
            4.551914400963142e-15,
            2.8255680017963414e-09,
            0.005975299666269973
          ],
          [
            4.884981308350689e-15,
            2.2609781824556308e-09,
            0.004780048432043049
          ],
          [
            2.55351295663786e-15,
            1.6964254445639426e-09,
            0.003584788479758738
          ],
          [
            3.3306690738754696e-16,
            1.131920113195406e-09,
            0.0023895198636938453
          ],
          [
            4.3298697960381105e-15,
            5.674618552831134e-10,
            0.0011942426380986415
          ],
          [
            3.6637359812630166e-15,
            3.0410118867507663e-12,
            -1.0431427738266663e-06
          ],
          [
            7.327471962526033e-15,
            -4.092555738743897e-10,
            -0.00107388428428834
          ],
          [
            3.3306690738754696e-16,
            -8.215226277030752e-10,
            -0.0021467327214051424
          ],
          [
            1.2212453270876722e-15,
            -1.2337574850640465e-09,
            -0.003219588418333752
          ],
          [
            1.4432899320127035e-15,
            -1.64596719587351e-09,
            -0.0042924513393002295
          ],
          [
            2.3314683517128287e-15,
            -2.0581528148433392e-09,
            -0.0053653214485253065
          ],
          [
            5.329070518200751e-15,
            -2.470305016100127e-09,
            -0.006438198710235543
          ],
          [
            3.774758283725532e-15,
            -2.8824327924503734e-09,
            -0.007511083088658332
          ],
          [
            1.0880185641326534e-14,
            -3.294530204200896e-09,
            -0.008583974547988982
          ]
        ]
      },
      "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": "Amm2",
        "spacegroup_number": 38,
        "pointgroup": "mm2",
        "has_inversion": false,
        "is_polar_point_group": true,
        "nonpolar_parent_hypothesis": false,
        "symmetry_tolerance_A": null,
        "target_reduced_polarization": [
          0.0,
          0.0,
          0.0
        ],
        "formal_class": [
          0.0,
          0.0,
          0.0
        ],
        "target_residual": 1.0431427701187283e-06,
        "parent_symmetrization_rmsd_A": 0.000471389707033928,
        "parent_cell_rmsd_A": 0.0022575809039229,
        "energy_eV": -530.0087912059823,
        "reduced_polarization": [
          -5.675115823208565e-16,
          3.0422306102394555e-12,
          -1.0431427701142922e-06
        ],
        "cartesian_polarization_e_A2": [
          -3.614566179339567e-18,
          3.920483661238817e-14,
          -7.685296522770607e-09
        ],
        "ranking_score": 0.5010378712185549
      }
    }
  ],
  "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": 55,
      "full_response": 20,
      "energy_polarization": 35
    },
    "model_evaluations_for_recovery_and_path_properties": {
      "total": 80,
      "full_response": 45,
      "energy_polarization": 35
    },
    "elapsed_seconds": 1903.687826784968
  }
}