{
  "schema": "ferrofinder.endpoint_parent_recovery.v4_variable_cell",
  "status": "complete",
  "input_atom_count": 56,
  "input_formula": "Bi8Nb8O36Pb4",
  "input_spacegroup": "Cmc2_1",
  "input_pointgroup": "mm2",
  "input_is_polar_point_group": true,
  "input_energy_eV": -401.90094163095335,
  "input_cartesian_polarization_e_A2": [
    -3.405486127141831e-17,
    6.456117451022237e-18,
    0.03208854693438608
  ],
  "input_reduced_polarization": [
    -1.0978200179255214e-15,
    9.329306297152686e-16,
    4.602101340975776
  ],
  "input_formal_targets": [
    {
      "orbit_id": 0,
      "representative_formal_class": [
        0.0,
        0.0,
        0.5
      ],
      "target_reduced_polarization": [
        0.0,
        0.0,
        4.5
      ]
    },
    {
      "orbit_id": 1,
      "representative_formal_class": [
        0.0,
        0.0,
        0.0
      ],
      "target_reduced_polarization": [
        0.0,
        0.0,
        5.0
      ]
    },
    {
      "orbit_id": 2,
      "representative_formal_class": [
        0.5,
        0.0,
        0.5
      ],
      "target_reduced_polarization": [
        -0.5,
        0.0,
        4.5
      ]
    },
    {
      "orbit_id": 3,
      "representative_formal_class": [
        0.0,
        0.5,
        0.5
      ],
      "target_reduced_polarization": [
        0.0,
        0.5,
        4.5
      ]
    },
    {
      "orbit_id": 4,
      "representative_formal_class": [
        0.5,
        0.0,
        0.0
      ],
      "target_reduced_polarization": [
        -0.5,
        0.0,
        5.0
      ]
    },
    {
      "orbit_id": 5,
      "representative_formal_class": [
        0.0,
        0.5,
        0.0
      ],
      "target_reduced_polarization": [
        0.0,
        0.5,
        5.0
      ]
    },
    {
      "orbit_id": 6,
      "representative_formal_class": [
        0.5,
        0.5,
        0.5
      ],
      "target_reduced_polarization": [
        -0.5,
        0.5,
        4.5
      ]
    },
    {
      "orbit_id": 7,
      "representative_formal_class": [
        0.5,
        0.5,
        0.0
      ],
      "target_reduced_polarization": [
        -0.5,
        0.5,
        5.0
      ]
    }
  ],
  "parent_candidates": [
    {
      "candidate_id": "inversion_parent_endpoint_00",
      "source": "same_species_inversion_center_projection_from_endpoint",
      "spacegroup": "Cmcm",
      "spacegroup_number": 63,
      "pointgroup": "mmm",
      "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": 6.563172810160064e-15,
      "parent_symmetrization_rmsd_A": 0.2753173206359,
      "parent_cell_rmsd_A": 0.0,
      "energy_eV": -400.22389112167923,
      "reduced_polarization": [
        7.829886668995433e-16,
        -5.320342065844996e-15,
        -3.762462808577837e-15
      ],
      "cartesian_polarization_e_A2": [
        2.42886538712812e-17,
        -3.681812147939966e-17,
        -2.623409513975053e-17
      ],
      "ranking_score": 0.2753173206359131
    },
    {
      "candidate_id": "inversion_parent_endpoint_01",
      "source": "same_species_inversion_center_projection_from_endpoint",
      "spacegroup": "Cmce",
      "spacegroup_number": 64,
      "pointgroup": "mmm",
      "has_inversion": true,
      "is_polar_point_group": false,
      "nonpolar_parent_hypothesis": true,
      "symmetry_tolerance_A": null,
      "target_reduced_polarization": [
        0.0,
        0.0,
        0.0
      ],
      "formal_class": [
        0.0,
        0.0,
        0.0
      ],
      "target_residual": 5.712977935255646e-15,
      "parent_symmetrization_rmsd_A": 0.3335132149150412,
      "parent_cell_rmsd_A": 0.0,
      "energy_eV": -400.6812972685365,
      "reduced_polarization": [
        5.134141493810612e-15,
        -2.577855278319759e-16,
        2.492439494128268e-15
      ],
      "cartesian_polarization_e_A2": [
        1.5926333412096198e-16,
        -1.783941476297056e-18,
        1.7378748480904737e-17
      ],
      "ranking_score": 0.33351321491505265
    },
    {
      "candidate_id": "bec_projection_00",
      "source": "MACEField_BEC_backprojection",
      "spacegroup": "Cmc2_1",
      "spacegroup_number": 36,
      "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,
        4.5
      ],
      "formal_class": [
        0.0,
        0.0,
        0.5
      ],
      "target_residual": 0.00040105046719318693,
      "parent_symmetrization_rmsd_A": 0.004761388667064093,
      "parent_cell_rmsd_A": 0.0030084576933443025,
      "energy_eV": -401.8753469795109,
      "reduced_polarization": [
        8.210519187111363e-16,
        -1.1387170869171034e-14,
        4.499598949532807
      ],
      "cartesian_polarization_e_A2": [
        7.228516235643174e-19,
        -7.691516995116475e-17,
        0.0313644453506942
      ],
      "ranking_score": 0.5063156040247866
    },
    {
      "candidate_id": "inversion_parent_bec_00_00",
      "source": "same_species_inversion_center_projection_after_BEC",
      "spacegroup": "Cmcm",
      "spacegroup_number": 63,
      "pointgroup": "mmm",
      "has_inversion": true,
      "is_polar_point_group": false,
      "nonpolar_parent_hypothesis": true,
      "symmetry_tolerance_A": null,
      "target_reduced_polarization": [
        0.0,
        0.0,
        4.5
      ],
      "formal_class": [
        0.0,
        0.0,
        0.5
      ],
      "target_residual": 0.49999999999999023,
      "parent_symmetrization_rmsd_A": 0.27531758935512773,
      "parent_cell_rmsd_A": 0.0030084576933443025,
      "energy_eV": -400.19669650022814,
      "reduced_polarization": [
        4.275270878623132e-15,
        -3.193773943807025e-15,
        -9.550865716990896e-15
      ],
      "cartesian_polarization_e_A2": [
        1.3248761346289666e-16,
        -2.2081762085150132e-17,
        -6.657429010722907e-17
      ],
      "ranking_score": 1.2760697037784443
    },
    {
      "candidate_id": "bec_projection_01",
      "source": "MACEField_BEC_backprojection",
      "spacegroup": "Cmc2_1",
      "spacegroup_number": 36,
      "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,
        5.0
      ],
      "formal_class": [
        0.0,
        0.0,
        0.0
      ],
      "target_residual": 7.3343992914587375e-06,
      "parent_symmetrization_rmsd_A": 0.018918233733081977,
      "parent_cell_rmsd_A": 0.011903994183633927,
      "energy_eV": -401.92516111696466,
      "reduced_polarization": [
        -2.9644544589820195e-16,
        1.3288591514718924e-15,
        5.0000073343992915
      ],
      "cartesian_polarization_e_A2": [
        9.461295890224275e-17,
        9.745799198716276e-18,
        0.034904360586176575
      ],
      "ranking_score": 0.5219089010775734
    },
    {
      "candidate_id": "bec_projection_02",
      "source": "MACEField_BEC_backprojection",
      "spacegroup": "Cc",
      "spacegroup_number": 9,
      "pointgroup": "m",
      "has_inversion": false,
      "is_polar_point_group": true,
      "nonpolar_parent_hypothesis": false,
      "symmetry_tolerance_A": null,
      "target_reduced_polarization": [
        -0.5,
        0.0,
        4.5
      ],
      "formal_class": [
        0.5,
        0.0,
        0.5
      ],
      "target_residual": 0.0003533431786664643,
      "parent_symmetrization_rmsd_A": 0.10616099627114428,
      "parent_cell_rmsd_A": 0.11521969972680118,
      "energy_eV": -400.83487645430233,
      "reduced_polarization": [
        -0.49993177015591456,
        -3.871786769176751e-15,
        4.500346693077932
      ],
      "cartesian_polarization_e_A2": [
        -0.01508332744485867,
        -5.438490085331425e-16,
        0.031168811143851262
      ],
      "ranking_score": 0.6356726075601775
    },
    {
      "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": [
        0.0,
        0.5,
        4.5
      ],
      "formal_class": [
        0.0,
        0.5,
        0.5
      ],
      "target_residual": 3.2944687600414967e-06,
      "parent_symmetrization_rmsd_A": 0.020144902292046525,
      "parent_cell_rmsd_A": 0.00863859872109705,
      "energy_eV": -401.80285358785943,
      "reduced_polarization": [
        5.26450557358593e-16,
        0.4999967137952474,
        4.500000233201061
      ],
      "cartesian_polarization_e_A2": [
        -6.505092825555296e-17,
        0.00332851601479557,
        0.03135358263523917
      ],
      "ranking_score": 0.5223111409098409
    },
    {
      "candidate_id": "bec_projection_04",
      "source": "MACEField_BEC_backprojection",
      "spacegroup": "Cc",
      "spacegroup_number": 9,
      "pointgroup": "m",
      "has_inversion": false,
      "is_polar_point_group": true,
      "nonpolar_parent_hypothesis": false,
      "symmetry_tolerance_A": null,
      "target_reduced_polarization": [
        -0.5,
        0.0,
        5.0
      ],
      "formal_class": [
        0.5,
        0.0,
        0.0
      ],
      "target_residual": 0.00042494063499011285,
      "parent_symmetrization_rmsd_A": 0.10827174784903285,
      "parent_cell_rmsd_A": 0.11491628683672693,
      "energy_eV": -400.8753207181789,
      "reduced_polarization": [
        -0.499954272459406,
        2.6556139595861327e-15,
        5.0004224731178395
      ],
      "cartesian_polarization_e_A2": [
        -0.01511358596311743,
        -4.292451670846363e-16,
        0.03470512687636229
      ],
      "ranking_score": 0.6378507008281948
    },
    {
      "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": [
        0.0,
        0.5,
        5.0
      ],
      "formal_class": [
        0.0,
        0.5,
        0.0
      ],
      "target_residual": 8.473769069894415e-06,
      "parent_symmetrization_rmsd_A": 0.027599365096425327,
      "parent_cell_rmsd_A": 0.014483264417053826,
      "energy_eV": -401.8291069802779,
      "reduced_polarization": [
        -2.772932347842983e-16,
        0.4999929787209009,
        4.999995255908721
      ],
      "cartesian_polarization_e_A2": [
        2.662320619941296e-17,
        0.003328022488571209,
        0.03489049125779726
      ],
      "ranking_score": 0.5312371287388286
    },
    {
      "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,
        4.5
      ],
      "formal_class": [
        0.5,
        0.5,
        0.5
      ],
      "target_residual": 0.0003664286967503297,
      "parent_symmetrization_rmsd_A": 0.10810486305480167,
      "parent_cell_rmsd_A": 0.11564584173365439,
      "energy_eV": -400.75724839334583,
      "reduced_polarization": [
        -0.49993010485598244,
        0.49999684947342177,
        4.500359686992852
      ],
      "cartesian_polarization_e_A2": [
        -0.015083214467178146,
        0.003326443554871085,
        0.03115479978979006
      ],
      "ranking_score": 0.637749180881716
    },
    {
      "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,
        5.0
      ],
      "formal_class": [
        0.5,
        0.5,
        0.0
      ],
      "target_residual": 0.000427480732259731,
      "parent_symmetrization_rmsd_A": 0.11025979032267728,
      "parent_cell_rmsd_A": 0.1153447024565832,
      "energy_eV": -400.77459687023486,
      "reduced_polarization": [
        -0.4999508193953067,
        0.5000085113127802,
        5.000424556948041
      ],
      "cartesian_polarization_e_A2": [
        -0.015113414515667096,
        0.003325991164460368,
        0.03469096518336803
      ],
      "ranking_score": 0.6399509274013425
    }
  ],
  "formal_branches": [
    {
      "orbit_id": 0,
      "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,
        4.5
      ],
      "bec_backprojection": {
        "converged_to_target": true,
        "history": [
          {
            "iteration": 0,
            "reduced_polarization": [
              -1.0978200179255214e-15,
              9.329306297152686e-16,
              4.602101340975776
            ],
            "branch_aligned_reduced_polarization": [
              -1.0978200179255214e-15,
              9.329306297152686e-16,
              4.602101340975776
            ],
            "target_residual": 0.10210134097577583,
            "energy_eV": -401.90094163095335,
            "max_atomic_step_A": 0.004165830574152928,
            "max_log_strain_component": 0.0008044986694903259,
            "step_scale": 1.0,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 11.389706069423637,
            "cell_principal_stretches": [
              1.0008048223653434,
              1.0002002068852975,
              1.0000993115780505
            ],
            "cell_volume_ratio": 1.0011046017867133,
            "cell_rmsd_from_input_A": 0.0030084576933443025
          },
          {
            "iteration": 1,
            "reduced_polarization": [
              8.210519187111363e-16,
              -1.1387170869171034e-14,
              4.499598949532807
            ],
            "branch_aligned_reduced_polarization": [
              8.210519187111363e-16,
              -1.1387170869171034e-14,
              4.499598949532807
            ],
            "target_residual": 0.00040105046719318693,
            "energy_eV": -401.8753469795109
          }
        ],
        "iterations": 1
      },
      "parent": {
        "candidate_id": "bec_projection_00",
        "source": "MACEField_BEC_backprojection",
        "spacegroup": "Cmc2_1",
        "spacegroup_number": 36,
        "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,
          4.5
        ],
        "formal_class": [
          0.0,
          0.0,
          0.5
        ],
        "target_residual": 0.00040105046719318693,
        "parent_symmetrization_rmsd_A": 0.004761388667064093,
        "parent_cell_rmsd_A": 0.0030084576933443025,
        "energy_eV": -401.8753469795109,
        "reduced_polarization": [
          8.210519187111363e-16,
          -1.1387170869171034e-14,
          4.499598949532807
        ],
        "cartesian_polarization_e_A2": [
          7.228516235643174e-19,
          -7.691516995116475e-17,
          0.0313644453506942
        ],
        "ranking_score": 0.5063156040247866
      },
      "branch_status": "awaiting_branch_sampling"
    },
    {
      "orbit_id": 1,
      "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,
        5.0
      ],
      "bec_backprojection": {
        "converged_to_target": true,
        "history": [
          {
            "iteration": 0,
            "reduced_polarization": [
              -1.0978200179255214e-15,
              9.329306297152686e-16,
              4.602101340975776
            ],
            "branch_aligned_reduced_polarization": [
              -1.0978200179255214e-15,
              9.329306297152686e-16,
              4.602101340975776
            ],
            "target_residual": 0.39789865902422417,
            "energy_eV": -401.90094163095335,
            "max_atomic_step_A": 0.016234638872870816,
            "max_log_strain_component": 0.0031352080072378384,
            "step_scale": 1.0,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 11.389706069423637,
            "cell_principal_stretches": [
              0.9996130674076159,
              0.9992201570109711,
              0.99686970162514
            ],
            "cell_volume_ratio": 0.9957068792015457,
            "cell_rmsd_from_input_A": 0.011712753839028272
          },
          {
            "iteration": 1,
            "reduced_polarization": [
              -5.188432311876001e-16,
              2.4590819769897368e-14,
              4.99393326805936
            ],
            "branch_aligned_reduced_polarization": [
              -5.188432311876001e-16,
              2.4590819769897368e-14,
              4.99393326805936
            ],
            "target_residual": 0.006066731940640224,
            "energy_eV": -401.92577949593027,
            "max_atomic_step_A": 0.0002529701913948669,
            "max_log_strain_component": 5.123076289948995e-05,
            "step_scale": 1.0,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 11.389706069423637,
            "cell_principal_stretches": [
              0.9996067459917362,
              0.9992074190636165,
              0.9968186325379798
            ],
            "cell_volume_ratio": 0.9956368808640842,
            "cell_rmsd_from_input_A": 0.011903994183633927
          },
          {
            "iteration": 2,
            "reduced_polarization": [
              -2.9644544589820195e-16,
              1.3288591514718924e-15,
              5.0000073343992915
            ],
            "branch_aligned_reduced_polarization": [
              -2.9644544589820195e-16,
              1.3288591514718924e-15,
              5.0000073343992915
            ],
            "target_residual": 7.3343992914587375e-06,
            "energy_eV": -401.92516111696466
          }
        ],
        "iterations": 2
      },
      "parent": {
        "candidate_id": "inversion_parent_endpoint_00",
        "source": "same_species_inversion_center_projection_from_endpoint",
        "spacegroup": "Cmcm",
        "spacegroup_number": 63,
        "pointgroup": "mmm",
        "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": 6.563172810160064e-15,
        "parent_symmetrization_rmsd_A": 0.2753173206359,
        "parent_cell_rmsd_A": 0.0,
        "energy_eV": -400.22389112167923,
        "reduced_polarization": [
          7.829886668995433e-16,
          -5.320342065844996e-15,
          -3.762462808577837e-15
        ],
        "cartesian_polarization_e_A2": [
          2.42886538712812e-17,
          -3.681812147939966e-17,
          -2.623409513975053e-17
        ],
        "ranking_score": 0.2753173206359131
      },
      "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": [
          -401.90094163095324,
          -401.6589517027703,
          -401.35949834226005,
          -401.05989277496474,
          -400.78862225988246,
          -400.5584853981307,
          -400.379288779623,
          -400.26387755706446,
          -400.22389112167923
        ],
        "cartesian_polarizations_e_A2": [
          [
            -1.622859106564292e-17,
            3.350304736418048e-17,
            0.03208854693438612
          ],
          [
            -2.799531808631428e-17,
            -1.5104598257371882e-17,
            0.02896437347189079
          ],
          [
            3.7811538973280265e-18,
            3.818914444894613e-17,
            0.025799806660787333
          ],
          [
            1.659164097653283e-17,
            3.5884297784971725e-17,
            0.022344089223431982
          ],
          [
            2.853389795209791e-17,
            2.4780285127592255e-17,
            0.018447255710826695
          ],
          [
            4.464537897863176e-17,
            2.208068572006422e-17,
            0.0141413031036398
          ],
          [
            1.7353614347821218e-17,
            -9.67780919679862e-19,
            0.009557257348833023
          ],
          [
            2.3060057420070096e-17,
            -1.3132956866181987e-17,
            0.004815021429879948
          ],
          [
            1.7199060063134298e-17,
            -2.080728977311703e-17,
            -2.3967860956621604e-17
          ]
        ],
        "raw_reduced_polarization": [
          [
            -5.231579712686366e-16,
            4.8413027352679905e-15,
            4.602101340975781
          ],
          [
            -9.024796888291132e-16,
            -2.182665118896636e-15,
            4.154036088579343
          ],
          [
            1.2189233150180817e-16,
            5.518459484252644e-15,
            3.7001776700362377
          ],
          [
            5.348615414727392e-16,
            5.185401409344432e-15,
            3.204562774011009
          ],
          [
            9.198417844546546e-16,
            3.580834330228625e-15,
            2.6456835336829756
          ],
          [
            1.439224501899489e-15,
            3.1907331596179005e-15,
            2.028128918067843
          ],
          [
            5.594251306020439e-16,
            -1.3984758946422173e-16,
            1.370690513068461
          ],
          [
            7.4338263922138e-16,
            -1.897756323694307e-15,
            0.6905646623572037
          ],
          [
            5.544427938298232e-16,
            -3.006723173480767e-15,
            -3.4374421900229165e-15
          ]
        ],
        "unwrapped_reduced_polarization": [
          [
            -5.231579712686366e-16,
            4.8413027352679905e-15,
            4.602101340975781
          ],
          [
            -9.024796888291132e-16,
            -2.1826651188966365e-15,
            4.154036088579343
          ],
          [
            1.2189233150180822e-16,
            5.518459484252644e-15,
            3.7001776700362377
          ],
          [
            5.348615414727392e-16,
            5.185401409344432e-15,
            3.204562774011009
          ],
          [
            9.198417844546546e-16,
            3.580834330228625e-15,
            3.6456835336829756
          ],
          [
            1.439224501899489e-15,
            3.1907331596179005e-15,
            4.028128918067843
          ],
          [
            5.594251306020439e-16,
            -1.3984758946422158e-16,
            4.370690513068461
          ],
          [
            7.4338263922138e-16,
            -1.897756323694307e-15,
            4.690564662357204
          ],
          [
            5.544427938298232e-16,
            -3.006723173480767e-15,
            4.9999999999999964
          ]
        ],
        "berry_integer_shifts": [
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            1
          ],
          [
            0,
            0,
            2
          ],
          [
            0,
            0,
            3
          ],
          [
            0,
            0,
            4
          ],
          [
            0,
            0,
            5
          ]
        ],
        "folded_reduced_polarization": [
          [
            -4.996003610813204e-16,
            4.884981308350689e-15,
            -0.39789865902421884
          ],
          [
            -8.881784197001252e-16,
            -2.1649348980190553e-15,
            0.1540360885793426
          ],
          [
            1.1102230246251565e-16,
            5.551115123125783e-15,
            -0.2998223299637619
          ],
          [
            5.551115123125783e-16,
            5.218048215738236e-15,
            0.2045627740110092
          ],
          [
            8.881784197001252e-16,
            3.552713678800501e-15,
            -0.35431646631702485
          ],
          [
            1.4432899320127035e-15,
            3.219646771412954e-15,
            0.02812891806784279
          ],
          [
            5.551115123125783e-16,
            -1.6653345369377348e-16,
            0.37069051306846124
          ],
          [
            7.771561172376096e-16,
            -1.887379141862766e-15,
            -0.30943533764279607
          ],
          [
            5.551115123125783e-16,
            -2.9976021664879227e-15,
            -3.552713678800501e-15
          ]
        ]
      },
      "reflected": {
        "reached": true,
        "construction": "reflect_displacements_about_reconstructed_parent",
        "energies_eV": [
          -400.22389112167923,
          -400.2638775570644,
          -400.379288779623,
          -400.55848539813076,
          -400.78862225988246,
          -401.05989277496474,
          -401.35949834226005,
          -401.6589517027703,
          -401.9009416309532
        ],
        "cartesian_polarizations_e_A2": [
          [
            1.796144468590401e-17,
            -1.970367995242947e-17,
            -2.3811846052815677e-17
          ],
          [
            2.0437975812119218e-17,
            -1.935561839359724e-18,
            -0.004815021429880029
          ],
          [
            9.277211694250836e-18,
            5.641144044976038e-17,
            -0.009557257348833085
          ],
          [
            4.426628128259975e-17,
            3.5281557036750056e-17,
            -0.014141303103639829
          ],
          [
            2.5446246096469685e-17,
            2.8235432796975624e-17,
            -0.018447255710826765
          ],
          [
            3.835323772820402e-17,
            5.625014362981374e-17,
            -0.022344089223432135
          ],
          [
            2.6112839184102765e-17,
            8.420542931846097e-17,
            -0.025799806660787416
          ],
          [
            5.316037071765187e-17,
            4.499969043853534e-17,
            -0.028964373471890816
          ],
          [
            2.656363240359586e-17,
            3.2936386167788986e-17,
            -0.03208854693438613
          ]
        ],
        "raw_reduced_polarization": [
          [
            5.790196403940943e-16,
            -2.8472478521619177e-15,
            -3.415066717568972e-15
          ],
          [
            6.588550983542923e-16,
            -2.7969517892844346e-16,
            -0.6905646623572154
          ],
          [
            2.990676904336465e-16,
            8.15164238587503e-15,
            -1.37069051306847
          ],
          [
            1.4270036023299264e-15,
            5.098303349239522e-15,
            -2.028128918067847
          ],
          [
            8.203057449894621e-16,
            4.080114759280715e-15,
            -2.645683533682986
          ],
          [
            1.236385953673425e-15,
            8.12833445429766e-15,
            -3.204562774011031
          ],
          [
            8.417945782453638e-16,
            1.2167967016628204e-14,
            -3.70017767003625
          ],
          [
            1.7137206541246715e-15,
            6.502606226776082e-15,
            -4.154036088579346
          ],
          [
            8.563267126258368e-16,
            4.759418291436967e-15,
            -4.602101340975783
          ]
        ],
        "unwrapped_reduced_polarization": [
          [
            5.790196403940943e-16,
            -2.8472478521619177e-15,
            4.9999999999999964
          ],
          [
            6.588550983542923e-16,
            -2.7969517892844356e-16,
            5.3094353376427845
          ],
          [
            2.990676904336465e-16,
            8.15164238587503e-15,
            5.62930948693153
          ],
          [
            1.4270036023299264e-15,
            5.098303349239522e-15,
            5.971871081932154
          ],
          [
            8.203057449894621e-16,
            4.080114759280715e-15,
            6.354316466317014
          ],
          [
            1.236385953673425e-15,
            8.12833445429766e-15,
            6.7954372259889695
          ],
          [
            8.417945782453638e-16,
            1.2167967016628204e-14,
            6.2998223299637495
          ],
          [
            1.7137206541246715e-15,
            6.502606226776082e-15,
            5.845963911420654
          ],
          [
            8.563267126258368e-16,
            4.759418291436967e-15,
            5.397898659024217
          ]
        ],
        "gauge_integer_shift": [
          0,
          0,
          5
        ],
        "expected_opposite_endpoint_reduced_polarization": [
          1.6320435589282833e-15,
          -1.0854749082229524e-14,
          -4.602101340975788
        ],
        "actual_opposite_endpoint_branch_residual": 1.6516747621322576e-14
      },
      "pnp_branch": {
        "construction": "incoming_path_concatenated_with_parent_reflection",
        "reduced_polarization": [
          [
            -5.231579712686366e-16,
            4.8413027352679905e-15,
            4.602101340975781
          ],
          [
            -9.024796888291132e-16,
            -2.182665118896636e-15,
            4.154036088579343
          ],
          [
            1.2189233150180817e-16,
            5.518459484252644e-15,
            3.7001776700362377
          ],
          [
            5.348615414727392e-16,
            5.185401409344432e-15,
            3.204562774011009
          ],
          [
            9.198417844546546e-16,
            3.580834330228625e-15,
            2.6456835336829756
          ],
          [
            1.439224501899489e-15,
            3.1907331596179005e-15,
            2.028128918067843
          ],
          [
            5.594251306020439e-16,
            -1.3984758946422173e-16,
            1.370690513068461
          ],
          [
            7.4338263922138e-16,
            -1.897756323694307e-15,
            0.6905646623572037
          ],
          [
            5.544427938298232e-16,
            -3.006723173480767e-15,
            -3.4374421900229165e-15
          ],
          [
            6.588550983542923e-16,
            -2.7969517892844346e-16,
            -0.6905646623572154
          ],
          [
            2.990676904336465e-16,
            8.15164238587503e-15,
            -1.37069051306847
          ],
          [
            1.4270036023299264e-15,
            5.098303349239522e-15,
            -2.028128918067847
          ],
          [
            8.203057449894621e-16,
            4.080114759280715e-15,
            -2.645683533682986
          ],
          [
            1.236385953673425e-15,
            8.12833445429766e-15,
            -3.204562774011031
          ],
          [
            8.417945782453638e-16,
            1.2167967016628204e-14,
            -3.70017767003625
          ],
          [
            1.7137206541246715e-15,
            6.502606226776082e-15,
            -4.154036088579346
          ],
          [
            8.563267126258368e-16,
            4.759418291436967e-15,
            -4.602101340975783
          ]
        ],
        "unwrapped_reduced_polarization": [
          [
            -5.231579712686366e-16,
            4.8413027352679905e-15,
            4.602101340975781
          ],
          [
            -9.024796888291132e-16,
            -2.1826651188966365e-15,
            4.154036088579343
          ],
          [
            1.2189233150180822e-16,
            5.518459484252644e-15,
            3.7001776700362377
          ],
          [
            5.348615414727392e-16,
            5.185401409344432e-15,
            3.204562774011009
          ],
          [
            9.198417844546546e-16,
            3.580834330228625e-15,
            3.6456835336829756
          ],
          [
            1.439224501899489e-15,
            3.1907331596179005e-15,
            4.028128918067843
          ],
          [
            5.594251306020439e-16,
            -1.3984758946422158e-16,
            4.370690513068461
          ],
          [
            7.4338263922138e-16,
            -1.897756323694307e-15,
            4.690564662357204
          ],
          [
            5.544427938298232e-16,
            -3.006723173480767e-15,
            4.9999999999999964
          ],
          [
            6.588550983542923e-16,
            -2.7969517892844356e-16,
            5.3094353376427845
          ],
          [
            2.990676904336465e-16,
            8.15164238587503e-15,
            5.62930948693153
          ],
          [
            1.4270036023299264e-15,
            5.098303349239522e-15,
            5.971871081932153
          ],
          [
            8.203057449894621e-16,
            4.080114759280715e-15,
            6.354316466317015
          ],
          [
            1.236385953673425e-15,
            8.12833445429766e-15,
            6.795437225988969
          ],
          [
            8.417945782453638e-16,
            1.2167967016628204e-14,
            6.29982232996375
          ],
          [
            1.7137206541246715e-15,
            6.502606226776082e-15,
            5.845963911420655
          ],
          [
            8.563267126258368e-16,
            4.759418291436967e-15,
            5.397898659024217
          ]
        ],
        "berry_integer_shifts": [
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            1
          ],
          [
            0,
            0,
            2
          ],
          [
            0,
            0,
            3
          ],
          [
            0,
            0,
            4
          ],
          [
            0,
            0,
            5
          ],
          [
            0,
            0,
            6
          ],
          [
            0,
            0,
            7
          ],
          [
            0,
            0,
            8
          ],
          [
            0,
            0,
            9
          ],
          [
            0,
            0,
            10
          ],
          [
            0,
            0,
            10
          ],
          [
            0,
            0,
            10
          ],
          [
            0,
            0,
            10
          ]
        ],
        "folded_reduced_polarization": [
          [
            -4.996003610813204e-16,
            4.884981308350689e-15,
            -0.39789865902421884
          ],
          [
            -8.881784197001252e-16,
            -2.1649348980190553e-15,
            0.1540360885793426
          ],
          [
            1.1102230246251565e-16,
            5.551115123125783e-15,
            -0.2998223299637619
          ],
          [
            5.551115123125783e-16,
            5.218048215738236e-15,
            0.2045627740110092
          ],
          [
            8.881784197001252e-16,
            3.552713678800501e-15,
            -0.35431646631702485
          ],
          [
            1.4432899320127035e-15,
            3.219646771412954e-15,
            0.02812891806784279
          ],
          [
            5.551115123125783e-16,
            -1.6653345369377348e-16,
            0.37069051306846124
          ],
          [
            7.771561172376096e-16,
            -1.887379141862766e-15,
            -0.30943533764279607
          ],
          [
            5.551115123125783e-16,
            -2.9976021664879227e-15,
            -3.552713678800501e-15
          ],
          [
            6.661338147750939e-16,
            -2.7755575615628914e-16,
            0.3094353376427845
          ],
          [
            3.3306690738754696e-16,
            8.104628079763643e-15,
            -0.3706905130684701
          ],
          [
            1.4432899320127035e-15,
            5.10702591327572e-15,
            -0.02812891806784723
          ],
          [
            7.771561172376096e-16,
            4.107825191113079e-15,
            0.3543164663170151
          ],
          [
            1.2212453270876722e-15,
            8.104628079763643e-15,
            -0.2045627740110314
          ],
          [
            8.881784197001252e-16,
            1.2212453270876722e-14,
            0.29982232996375036
          ],
          [
            1.6653345369377348e-15,
            6.5503158452884236e-15,
            -0.15403608857934525
          ],
          [
            8.881784197001252e-16,
            4.773959005888173e-15,
            0.39789865902421706
          ]
        ]
      },
      "incoming_structure_ids": [
        "incoming_01_000",
        "incoming_01_001",
        "incoming_01_002",
        "incoming_01_003",
        "incoming_01_004",
        "incoming_01_005",
        "incoming_01_006",
        "incoming_01_007",
        "incoming_01_008"
      ],
      "reflected_structure_ids": [
        "reflected_01_001",
        "reflected_01_002",
        "reflected_01_003",
        "reflected_01_004",
        "reflected_01_005",
        "reflected_01_006",
        "reflected_01_007",
        "reflected_01_008"
      ]
    },
    {
      "orbit_id": 2,
      "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,
        4.5
      ],
      "bec_backprojection": {
        "converged_to_target": true,
        "history": [
          {
            "iteration": 0,
            "reduced_polarization": [
              -1.0978200179255214e-15,
              9.329306297152686e-16,
              4.602101340975776
            ],
            "branch_aligned_reduced_polarization": [
              -1.1102230246251565e-15,
              9.329306297152686e-16,
              4.602101340975776
            ],
            "target_residual": 0.5103182182021827,
            "energy_eV": -401.90094163095335,
            "max_atomic_step_A": 0.09328986575290736,
            "max_log_strain_component": 0.012681919029237359,
            "step_scale": 1.0,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 11.389706069423637,
            "cell_principal_stretches": [
              1.0132254146344295,
              1.0002002068852838,
              0.9878396252355057
            ],
            "cell_volume_ratio": 1.0011046017866911,
            "cell_rmsd_from_input_A": 0.11287582128116598
          },
          {
            "iteration": 1,
            "reduced_polarization": [
              -0.4909225380940667,
              1.4651608595144451e-13,
              4.533621376521419
            ],
            "branch_aligned_reduced_polarization": [
              -0.4909225380940667,
              1.4651608595144451e-13,
              4.533621376521419
            ],
            "target_residual": 0.03482523903505429,
            "energy_eV": -400.88484208443316,
            "max_atomic_step_A": 0.0024031221598919137,
            "max_log_strain_component": 0.00026019516878274067,
            "step_scale": 1.0,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 11.389706069423637,
            "cell_principal_stretches": [
              1.0136322616371254,
              1.0002649674215136,
              0.9877318158548781
            ],
            "cell_volume_ratio": 1.0014621189395625,
            "cell_rmsd_from_input_A": 0.11521969972680118
          },
          {
            "iteration": 2,
            "reduced_polarization": [
              -0.49993177015591456,
              -3.871786769176751e-15,
              4.500346693077932
            ],
            "branch_aligned_reduced_polarization": [
              -0.49993177015591456,
              -3.871786769176751e-15,
              4.500346693077932
            ],
            "target_residual": 0.0003533431786664643,
            "energy_eV": -400.83487645430233
          }
        ],
        "iterations": 2
      },
      "parent": {
        "candidate_id": "bec_projection_02",
        "source": "MACEField_BEC_backprojection",
        "spacegroup": "Cc",
        "spacegroup_number": 9,
        "pointgroup": "m",
        "has_inversion": false,
        "is_polar_point_group": true,
        "nonpolar_parent_hypothesis": false,
        "symmetry_tolerance_A": null,
        "target_reduced_polarization": [
          -0.5,
          0.0,
          4.5
        ],
        "formal_class": [
          0.5,
          0.0,
          0.5
        ],
        "target_residual": 0.0003533431786664643,
        "parent_symmetrization_rmsd_A": 0.10616099627114428,
        "parent_cell_rmsd_A": 0.11521969972680118,
        "energy_eV": -400.83487645430233,
        "reduced_polarization": [
          -0.49993177015591456,
          -3.871786769176751e-15,
          4.500346693077932
        ],
        "cartesian_polarization_e_A2": [
          -0.01508332744485867,
          -5.438490085331425e-16,
          0.031168811143851262
        ],
        "ranking_score": 0.6356726075601775
      },
      "branch_status": "awaiting_branch_sampling"
    },
    {
      "orbit_id": 3,
      "formal_class": [
        0.0,
        0.5,
        0.5
      ],
      "formal_classes_in_orbit": [
        [
          0.0,
          0.5,
          0.5
        ]
      ],
      "target_reduced_polarization": [
        0.0,
        0.5,
        4.5
      ],
      "bec_backprojection": {
        "converged_to_target": true,
        "history": [
          {
            "iteration": 0,
            "reduced_polarization": [
              -1.0978200179255214e-15,
              9.329306297152686e-16,
              4.602101340975776
            ],
            "branch_aligned_reduced_polarization": [
              -1.0978200179255214e-15,
              9.43689570931383e-16,
              4.602101340975776
            ],
            "target_residual": 0.5103182182021828,
            "energy_eV": -401.90094163095335,
            "max_atomic_step_A": 0.01769198059300559,
            "max_log_strain_component": 0.004102902671054662,
            "step_scale": 1.0,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 11.389706069423637,
            "cell_principal_stretches": [
              1.004627028222265,
              1.0000993115780525,
              0.9963948433210613
            ],
            "cell_volume_ratio": 1.0011046017867222,
            "cell_rmsd_from_input_A": 0.00867197693537875
          },
          {
            "iteration": 1,
            "reduced_polarization": [
              -3.2911594309276343e-15,
              0.5003889534022022,
              4.497171288372824
            ],
            "branch_aligned_reduced_polarization": [
              -3.2911594309276343e-15,
              0.5003889534022022,
              4.497171288372824
            ],
            "target_residual": 0.0028553273400443702,
            "energy_eV": -401.8020596175644,
            "max_atomic_step_A": 0.00011555440329779764,
            "max_log_strain_component": 2.1860504447373376e-05,
            "step_scale": 1.0,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 11.389706069423637,
            "cell_principal_stretches": [
              1.0046100104877649,
              1.0000966128712108,
              0.9963845200780798
            ],
            "cell_volume_ratio": 1.001074570510865,
            "cell_rmsd_from_input_A": 0.00863859872109705
          },
          {
            "iteration": 2,
            "reduced_polarization": [
              5.26450557358593e-16,
              0.4999967137952474,
              4.500000233201061
            ],
            "branch_aligned_reduced_polarization": [
              5.26450557358593e-16,
              0.4999967137952474,
              4.500000233201061
            ],
            "target_residual": 3.2944687600414967e-06,
            "energy_eV": -401.80285358785943
          }
        ],
        "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": [
          0.0,
          0.5,
          4.5
        ],
        "formal_class": [
          0.0,
          0.5,
          0.5
        ],
        "target_residual": 3.2944687600414967e-06,
        "parent_symmetrization_rmsd_A": 0.020144902292046525,
        "parent_cell_rmsd_A": 0.00863859872109705,
        "energy_eV": -401.80285358785943,
        "reduced_polarization": [
          5.26450557358593e-16,
          0.4999967137952474,
          4.500000233201061
        ],
        "cartesian_polarization_e_A2": [
          -6.505092825555296e-17,
          0.00332851601479557,
          0.03135358263523917
        ],
        "ranking_score": 0.5223111409098409
      },
      "branch_status": "awaiting_branch_sampling"
    },
    {
      "orbit_id": 4,
      "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,
        5.0
      ],
      "bec_backprojection": {
        "converged_to_target": true,
        "history": [
          {
            "iteration": 0,
            "reduced_polarization": [
              -1.0978200179255214e-15,
              9.329306297152686e-16,
              4.602101340975776
            ],
            "branch_aligned_reduced_polarization": [
              -1.1102230246251565e-15,
              9.329306297152686e-16,
              4.602101340975776
            ],
            "target_residual": 0.6390018332158952,
            "energy_eV": -401.90094163095335,
            "max_atomic_step_A": 0.09671442245823814,
            "max_log_strain_component": 0.012681919029241083,
            "step_scale": 1.0,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 11.389706069423637,
            "cell_principal_stretches": [
              1.0110557042940373,
              0.9992201570109577,
              0.9855876150196888
            ],
            "cell_volume_ratio": 0.9957068792015236,
            "cell_rmsd_from_input_A": 0.11239695396258031
          },
          {
            "iteration": 1,
            "reduced_polarization": [
              -0.4895892691100609,
              1.591577342217747e-13,
              5.025447397999515
            ],
            "branch_aligned_reduced_polarization": [
              -0.4895892691100609,
              1.591577342217747e-13,
              5.025447397999515
            ],
            "target_residual": 0.027494606427596796,
            "energy_eV": -400.9198139147141,
            "max_atomic_step_A": 0.0024385016749850713,
            "max_log_strain_component": 0.00028911054727239247,
            "step_scale": 1.0,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 11.389706069423637,
            "cell_principal_stretches": [
              1.0114563567970922,
              0.9992724403743002,
              0.9854299675940313
            ],
            "cell_volume_ratio": 0.9959942321041781,
            "cell_rmsd_from_input_A": 0.11491628683672693
          },
          {
            "iteration": 2,
            "reduced_polarization": [
              -0.499954272459406,
              2.6556139595861327e-15,
              5.0004224731178395
            ],
            "branch_aligned_reduced_polarization": [
              -0.499954272459406,
              2.6556139595861327e-15,
              5.0004224731178395
            ],
            "target_residual": 0.00042494063499011285,
            "energy_eV": -400.8753207181789
          }
        ],
        "iterations": 2
      },
      "parent": {
        "candidate_id": "bec_projection_04",
        "source": "MACEField_BEC_backprojection",
        "spacegroup": "Cc",
        "spacegroup_number": 9,
        "pointgroup": "m",
        "has_inversion": false,
        "is_polar_point_group": true,
        "nonpolar_parent_hypothesis": false,
        "symmetry_tolerance_A": null,
        "target_reduced_polarization": [
          -0.5,
          0.0,
          5.0
        ],
        "formal_class": [
          0.5,
          0.0,
          0.0
        ],
        "target_residual": 0.00042494063499011285,
        "parent_symmetrization_rmsd_A": 0.10827174784903285,
        "parent_cell_rmsd_A": 0.11491628683672693,
        "energy_eV": -400.8753207181789,
        "reduced_polarization": [
          -0.499954272459406,
          2.6556139595861327e-15,
          5.0004224731178395
        ],
        "cartesian_polarization_e_A2": [
          -0.01511358596311743,
          -4.292451670846363e-16,
          0.03470512687636229
        ],
        "ranking_score": 0.6378507008281948
      },
      "branch_status": "awaiting_branch_sampling"
    },
    {
      "orbit_id": 5,
      "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,
        5.0
      ],
      "bec_backprojection": {
        "converged_to_target": true,
        "history": [
          {
            "iteration": 0,
            "reduced_polarization": [
              -1.0978200179255214e-15,
              9.329306297152686e-16,
              4.602101340975776
            ],
            "branch_aligned_reduced_polarization": [
              -1.0978200179255214e-15,
              9.43689570931383e-16,
              4.602101340975776
            ],
            "target_residual": 0.6390018332158953,
            "energy_eV": -401.90094163095335,
            "max_atomic_step_A": 0.023689498019680098,
            "max_log_strain_component": 0.004102902671054908,
            "step_scale": 1.0,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 11.389706069423637,
            "cell_principal_stretches": [
              1.0023135291328231,
              0.9996130674076181,
              0.9937931304181372
            ],
            "cell_volume_ratio": 0.9957068792015545,
            "cell_rmsd_from_input_A": 0.014225619234694576
          },
          {
            "iteration": 1,
            "reduced_polarization": [
              2.268102217182296e-15,
              0.49614569950449017,
              4.991575004285482
            ],
            "branch_aligned_reduced_polarization": [
              2.268102217182296e-15,
              0.49614569950449017,
              4.991575004285482
            ],
            "target_residual": 0.009264781977970619,
            "energy_eV": -401.83185092883633,
            "max_atomic_step_A": 0.0003776797919459132,
            "max_log_strain_component": 7.156823504801788e-05,
            "step_scale": 1.0,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 11.389706069423637,
            "cell_principal_stretches": [
              1.0023089605730557,
              0.9996042365414735,
              0.9937088416121286
            ],
            "cell_volume_ratio": 0.9956090944472359,
            "cell_rmsd_from_input_A": 0.014483264417053826
          },
          {
            "iteration": 2,
            "reduced_polarization": [
              -2.772932347842983e-16,
              0.4999929787209009,
              4.999995255908721
            ],
            "branch_aligned_reduced_polarization": [
              -2.772932347842983e-16,
              0.4999929787209009,
              4.999995255908721
            ],
            "target_residual": 8.473769069894415e-06,
            "energy_eV": -401.8291069802779
          }
        ],
        "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": [
          0.0,
          0.5,
          5.0
        ],
        "formal_class": [
          0.0,
          0.5,
          0.0
        ],
        "target_residual": 8.473769069894415e-06,
        "parent_symmetrization_rmsd_A": 0.027599365096425327,
        "parent_cell_rmsd_A": 0.014483264417053826,
        "energy_eV": -401.8291069802779,
        "reduced_polarization": [
          -2.772932347842983e-16,
          0.4999929787209009,
          4.999995255908721
        ],
        "cartesian_polarization_e_A2": [
          2.662320619941296e-17,
          0.003328022488571209,
          0.03489049125779726
        ],
        "ranking_score": 0.5312371287388286
      },
      "branch_status": "awaiting_branch_sampling"
    },
    {
      "orbit_id": 6,
      "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,
        4.5
      ],
      "bec_backprojection": {
        "converged_to_target": true,
        "history": [
          {
            "iteration": 0,
            "reduced_polarization": [
              -1.0978200179255214e-15,
              9.329306297152686e-16,
              4.602101340975776
            ],
            "branch_aligned_reduced_polarization": [
              -1.1102230246251565e-15,
              9.43689570931383e-16,
              4.602101340975776
            ],
            "target_residual": 0.7144401191345917,
            "energy_eV": -401.90094163095335,
            "max_atomic_step_A": 0.0962175073280859,
            "max_log_strain_component": 0.012681919029235919,
            "step_scale": 1.0,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 11.389706069423637,
            "cell_principal_stretches": [
              1.0138858749093316,
              1.0001906495984596,
              0.9872055649915669
            ],
            "cell_volume_ratio": 1.0011046017867,
            "cell_rmsd_from_input_A": 0.1131707725417324
          },
          {
            "iteration": 1,
            "reduced_polarization": [
              -0.49040124310243516,
              0.4946466586917749,
              4.5314465684683904
            ],
            "branch_aligned_reduced_polarization": [
              -0.49040124310243516,
              0.4946466586917749,
              4.5314465684683904
            ],
            "target_residual": 0.03331187574391551,
            "energy_eV": -400.80957675272856,
            "max_atomic_step_A": 0.0024412203945969,
            "max_log_strain_component": 0.00026724623625645755,
            "step_scale": 1.0,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 11.389706069423637,
            "cell_principal_stretches": [
              1.014300382038325,
              1.0002484049490827,
              0.9870738790934072
            ],
            "cell_volume_ratio": 1.001438113069569,
            "cell_rmsd_from_input_A": 0.11564584173365439
          },
          {
            "iteration": 2,
            "reduced_polarization": [
              -0.49993010485598244,
              0.49999684947342177,
              4.500359686992852
            ],
            "branch_aligned_reduced_polarization": [
              -0.49993010485598244,
              0.49999684947342177,
              4.500359686992852
            ],
            "target_residual": 0.0003664286967503297,
            "energy_eV": -400.75724839334583
          }
        ],
        "iterations": 2
      },
      "parent": {
        "candidate_id": "bec_projection_06",
        "source": "MACEField_BEC_backprojection",
        "spacegroup": "P1",
        "spacegroup_number": 1,
        "pointgroup": "1",
        "has_inversion": false,
        "is_polar_point_group": true,
        "nonpolar_parent_hypothesis": false,
        "symmetry_tolerance_A": null,
        "target_reduced_polarization": [
          -0.5,
          0.5,
          4.5
        ],
        "formal_class": [
          0.5,
          0.5,
          0.5
        ],
        "target_residual": 0.0003664286967503297,
        "parent_symmetrization_rmsd_A": 0.10810486305480167,
        "parent_cell_rmsd_A": 0.11564584173365439,
        "energy_eV": -400.75724839334583,
        "reduced_polarization": [
          -0.49993010485598244,
          0.49999684947342177,
          4.500359686992852
        ],
        "cartesian_polarization_e_A2": [
          -0.015083214467178146,
          0.003326443554871085,
          0.03115479978979006
        ],
        "ranking_score": 0.637749180881716
      },
      "branch_status": "awaiting_branch_sampling"
    },
    {
      "orbit_id": 7,
      "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,
        5.0
      ],
      "bec_backprojection": {
        "converged_to_target": true,
        "history": [
          {
            "iteration": 0,
            "reduced_polarization": [
              -1.0978200179255214e-15,
              9.329306297152686e-16,
              4.602101340975776
            ],
            "branch_aligned_reduced_polarization": [
              -1.1102230246251565e-15,
              9.43689570931383e-16,
              4.602101340975776
            ],
            "target_residual": 0.8113712731254871,
            "energy_eV": -401.90094163095335,
            "max_atomic_step_A": 0.09953146432914765,
            "max_log_strain_component": 0.012681919029239644,
            "step_scale": 1.0,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 11.389706069423637,
            "cell_principal_stretches": [
              1.0116864598139723,
              0.9992572011855078,
              0.9849366166904542
            ],
            "cell_volume_ratio": 0.9957068792015327,
            "cell_rmsd_from_input_A": 0.11268882020525364
          },
          {
            "iteration": 1,
            "reduced_polarization": [
              -0.48910390795600556,
              0.4910097338915056,
              5.023349191623582
            ],
            "branch_aligned_reduced_polarization": [
              -0.48910390795600556,
              0.4910097338915056,
              5.023349191623582
            ],
            "target_residual": 0.02728982330480563,
            "energy_eV": -400.8242158146609,
            "max_atomic_step_A": 0.002502899781434333,
            "max_log_strain_component": 0.00030392550242928554,
            "step_scale": 1.0,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 11.389706069423637,
            "cell_principal_stretches": [
              1.0121039707343857,
              0.9993022545537588,
              0.9847444801785984
            ],
            "cell_volume_ratio": 0.9959683809206581,
            "cell_rmsd_from_input_A": 0.1153447024565832
          },
          {
            "iteration": 2,
            "reduced_polarization": [
              -0.4999508193953067,
              0.5000085113127802,
              5.000424556948041
            ],
            "branch_aligned_reduced_polarization": [
              -0.4999508193953067,
              0.5000085113127802,
              5.000424556948041
            ],
            "target_residual": 0.000427480732259731,
            "energy_eV": -400.77459687023486
          }
        ],
        "iterations": 2
      },
      "parent": {
        "candidate_id": "bec_projection_07",
        "source": "MACEField_BEC_backprojection",
        "spacegroup": "P1",
        "spacegroup_number": 1,
        "pointgroup": "1",
        "has_inversion": false,
        "is_polar_point_group": true,
        "nonpolar_parent_hypothesis": false,
        "symmetry_tolerance_A": null,
        "target_reduced_polarization": [
          -0.5,
          0.5,
          5.0
        ],
        "formal_class": [
          0.5,
          0.5,
          0.0
        ],
        "target_residual": 0.000427480732259731,
        "parent_symmetrization_rmsd_A": 0.11025979032267728,
        "parent_cell_rmsd_A": 0.1153447024565832,
        "energy_eV": -400.77459687023486,
        "reduced_polarization": [
          -0.4999508193953067,
          0.5000085113127802,
          5.000424556948041
        ],
        "cartesian_polarization_e_A2": [
          -0.015113414515667096,
          0.003325991164460368,
          0.03469096518336803
        ],
        "ranking_score": 0.6399509274013425
      },
      "branch_status": "awaiting_branch_sampling"
    }
  ],
  "sampled_polarization_branches": [
    {
      "orbit_id": 1,
      "candidate_id": "inversion_parent_endpoint_00",
      "formal_class": [
        0.0,
        0.0,
        0.0
      ],
      "construction": "MACEField-BEC-parent plus variable-cell P-N-P path and symmetric log-strain continuation beyond both polar endpoints",
      "geometry_diagnostics": {
        "collision_aware": false,
        "permutations_tested": 1,
        "selected_order": [
          0,
          1,
          2,
          3,
          4,
          5,
          6,
          7,
          8,
          9,
          10,
          11,
          12,
          13,
          14,
          15,
          16,
          17,
          18,
          19,
          20,
          21,
          22,
          23,
          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
        ],
        "endpoint_rmsd_A": 0.2753173206359,
        "minimum_distance_A_by_image": [
          1.9001953115365182,
          1.8970626126222152,
          1.8943434163854405,
          1.8920395056570247,
          1.8901523990147129,
          1.8886833458273116,
          1.8876333221470747,
          1.8870030274816025,
          1.886792882470051
        ],
        "minimum_distance_A": 1.886792882470051,
        "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": [
          817.3687752669215,
          817.3687752669215,
          817.3687752669215,
          817.3687752669215,
          817.3687752669215,
          817.3687752669215,
          817.3687752669215,
          817.3687752669215,
          817.3687752669215
        ],
        "cell_deformation_log_strain_norm": 0.0
      },
      "parent_reduced_polarization": [
        5.544427938298232e-16,
        -3.006723173480767e-15,
        -3.4374421900229165e-15
      ],
      "incoming": {
        "reached": true,
        "construction": "variable_cell_linear_interpolation",
        "continuation_fractions": [
          0.0,
          0.125,
          0.25,
          0.375,
          0.5,
          0.625,
          0.75,
          0.875,
          1.0
        ],
        "energies_eV": [
          -401.90094163095324,
          -401.6589517027703,
          -401.35949834226005,
          -401.05989277496474,
          -400.78862225988246,
          -400.5584853981307,
          -400.379288779623,
          -400.26387755706446,
          -400.22389112167923
        ],
        "cartesian_polarizations_e_A2": [
          [
            -1.622859106564292e-17,
            3.350304736418048e-17,
            0.03208854693438612
          ],
          [
            -2.799531808631428e-17,
            -1.5104598257371882e-17,
            0.02896437347189079
          ],
          [
            3.7811538973280265e-18,
            3.818914444894613e-17,
            0.025799806660787333
          ],
          [
            1.659164097653283e-17,
            3.5884297784971725e-17,
            0.022344089223431982
          ],
          [
            2.853389795209791e-17,
            2.4780285127592255e-17,
            0.018447255710826695
          ],
          [
            4.464537897863176e-17,
            2.208068572006422e-17,
            0.0141413031036398
          ],
          [
            1.7353614347821218e-17,
            -9.67780919679862e-19,
            0.009557257348833023
          ],
          [
            2.3060057420070096e-17,
            -1.3132956866181987e-17,
            0.004815021429879948
          ],
          [
            1.7199060063134298e-17,
            -2.080728977311703e-17,
            -2.3967860956621604e-17
          ]
        ],
        "raw_reduced_polarization": [
          [
            -5.231579712686366e-16,
            4.8413027352679905e-15,
            4.602101340975781
          ],
          [
            -9.024796888291132e-16,
            -2.182665118896636e-15,
            4.154036088579343
          ],
          [
            1.2189233150180817e-16,
            5.518459484252644e-15,
            3.7001776700362377
          ],
          [
            5.348615414727392e-16,
            5.185401409344432e-15,
            3.204562774011009
          ],
          [
            9.198417844546546e-16,
            3.580834330228625e-15,
            2.6456835336829756
          ],
          [
            1.439224501899489e-15,
            3.1907331596179005e-15,
            2.028128918067843
          ],
          [
            5.594251306020439e-16,
            -1.3984758946422173e-16,
            1.370690513068461
          ],
          [
            7.4338263922138e-16,
            -1.897756323694307e-15,
            0.6905646623572037
          ],
          [
            5.544427938298232e-16,
            -3.006723173480767e-15,
            -3.4374421900229165e-15
          ]
        ],
        "unwrapped_reduced_polarization": [
          [
            -5.231579712686366e-16,
            4.8413027352679905e-15,
            4.602101340975781
          ],
          [
            -9.024796888291132e-16,
            -2.1826651188966365e-15,
            4.154036088579343
          ],
          [
            1.2189233150180822e-16,
            5.518459484252644e-15,
            3.7001776700362377
          ],
          [
            5.348615414727392e-16,
            5.185401409344432e-15,
            3.204562774011009
          ],
          [
            9.198417844546546e-16,
            3.580834330228625e-15,
            3.6456835336829756
          ],
          [
            1.439224501899489e-15,
            3.1907331596179005e-15,
            4.028128918067843
          ],
          [
            5.594251306020439e-16,
            -1.3984758946422158e-16,
            4.370690513068461
          ],
          [
            7.4338263922138e-16,
            -1.897756323694307e-15,
            4.690564662357204
          ],
          [
            5.544427938298232e-16,
            -3.006723173480767e-15,
            4.9999999999999964
          ]
        ],
        "berry_integer_shifts": [
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            1
          ],
          [
            0,
            0,
            2
          ],
          [
            0,
            0,
            3
          ],
          [
            0,
            0,
            4
          ],
          [
            0,
            0,
            5
          ]
        ],
        "folded_reduced_polarization": [
          [
            -4.996003610813204e-16,
            4.884981308350689e-15,
            -0.39789865902421884
          ],
          [
            -8.881784197001252e-16,
            -2.1649348980190553e-15,
            0.1540360885793426
          ],
          [
            1.1102230246251565e-16,
            5.551115123125783e-15,
            -0.2998223299637619
          ],
          [
            5.551115123125783e-16,
            5.218048215738236e-15,
            0.2045627740110092
          ],
          [
            8.881784197001252e-16,
            3.552713678800501e-15,
            -0.35431646631702485
          ],
          [
            1.4432899320127035e-15,
            3.219646771412954e-15,
            0.02812891806784279
          ],
          [
            5.551115123125783e-16,
            -1.6653345369377348e-16,
            0.37069051306846124
          ],
          [
            7.771561172376096e-16,
            -1.887379141862766e-15,
            -0.30943533764279607
          ],
          [
            5.551115123125783e-16,
            -2.9976021664879227e-15,
            -3.552713678800501e-15
          ]
        ]
      },
      "reflected": {
        "reached": true,
        "construction": "reflect_displacements_about_reconstructed_parent",
        "energies_eV": [
          -400.22389112167923,
          -400.2638775570644,
          -400.379288779623,
          -400.55848539813076,
          -400.78862225988246,
          -401.05989277496474,
          -401.35949834226005,
          -401.6589517027703,
          -401.9009416309532
        ],
        "cartesian_polarizations_e_A2": [
          [
            1.796144468590401e-17,
            -1.970367995242947e-17,
            -2.3811846052815677e-17
          ],
          [
            2.0437975812119218e-17,
            -1.935561839359724e-18,
            -0.004815021429880029
          ],
          [
            9.277211694250836e-18,
            5.641144044976038e-17,
            -0.009557257348833085
          ],
          [
            4.426628128259975e-17,
            3.5281557036750056e-17,
            -0.014141303103639829
          ],
          [
            2.5446246096469685e-17,
            2.8235432796975624e-17,
            -0.018447255710826765
          ],
          [
            3.835323772820402e-17,
            5.625014362981374e-17,
            -0.022344089223432135
          ],
          [
            2.6112839184102765e-17,
            8.420542931846097e-17,
            -0.025799806660787416
          ],
          [
            5.316037071765187e-17,
            4.499969043853534e-17,
            -0.028964373471890816
          ],
          [
            2.656363240359586e-17,
            3.2936386167788986e-17,
            -0.03208854693438613
          ]
        ],
        "raw_reduced_polarization": [
          [
            5.790196403940943e-16,
            -2.8472478521619177e-15,
            -3.415066717568972e-15
          ],
          [
            6.588550983542923e-16,
            -2.7969517892844346e-16,
            -0.6905646623572154
          ],
          [
            2.990676904336465e-16,
            8.15164238587503e-15,
            -1.37069051306847
          ],
          [
            1.4270036023299264e-15,
            5.098303349239522e-15,
            -2.028128918067847
          ],
          [
            8.203057449894621e-16,
            4.080114759280715e-15,
            -2.645683533682986
          ],
          [
            1.236385953673425e-15,
            8.12833445429766e-15,
            -3.204562774011031
          ],
          [
            8.417945782453638e-16,
            1.2167967016628204e-14,
            -3.70017767003625
          ],
          [
            1.7137206541246715e-15,
            6.502606226776082e-15,
            -4.154036088579346
          ],
          [
            8.563267126258368e-16,
            4.759418291436967e-15,
            -4.602101340975783
          ]
        ],
        "unwrapped_reduced_polarization": [
          [
            5.790196403940943e-16,
            -2.8472478521619177e-15,
            4.9999999999999964
          ],
          [
            6.588550983542923e-16,
            -2.7969517892844356e-16,
            5.3094353376427845
          ],
          [
            2.990676904336465e-16,
            8.15164238587503e-15,
            5.62930948693153
          ],
          [
            1.4270036023299264e-15,
            5.098303349239522e-15,
            5.971871081932154
          ],
          [
            8.203057449894621e-16,
            4.080114759280715e-15,
            6.354316466317014
          ],
          [
            1.236385953673425e-15,
            8.12833445429766e-15,
            6.7954372259889695
          ],
          [
            8.417945782453638e-16,
            1.2167967016628204e-14,
            6.2998223299637495
          ],
          [
            1.7137206541246715e-15,
            6.502606226776082e-15,
            5.845963911420654
          ],
          [
            8.563267126258368e-16,
            4.759418291436967e-15,
            5.397898659024217
          ]
        ],
        "gauge_integer_shift": [
          0,
          0,
          5
        ],
        "expected_opposite_endpoint_reduced_polarization": [
          1.6320435589282833e-15,
          -1.0854749082229524e-14,
          -4.602101340975788
        ],
        "actual_opposite_endpoint_branch_residual": 1.6516747621322576e-14
      },
      "pnp_branch": {
        "construction": "incoming_path_concatenated_with_parent_reflection",
        "reduced_polarization": [
          [
            -5.231579712686366e-16,
            4.8413027352679905e-15,
            4.602101340975781
          ],
          [
            -9.024796888291132e-16,
            -2.182665118896636e-15,
            4.154036088579343
          ],
          [
            1.2189233150180817e-16,
            5.518459484252644e-15,
            3.7001776700362377
          ],
          [
            5.348615414727392e-16,
            5.185401409344432e-15,
            3.204562774011009
          ],
          [
            9.198417844546546e-16,
            3.580834330228625e-15,
            2.6456835336829756
          ],
          [
            1.439224501899489e-15,
            3.1907331596179005e-15,
            2.028128918067843
          ],
          [
            5.594251306020439e-16,
            -1.3984758946422173e-16,
            1.370690513068461
          ],
          [
            7.4338263922138e-16,
            -1.897756323694307e-15,
            0.6905646623572037
          ],
          [
            5.544427938298232e-16,
            -3.006723173480767e-15,
            -3.4374421900229165e-15
          ],
          [
            6.588550983542923e-16,
            -2.7969517892844346e-16,
            -0.6905646623572154
          ],
          [
            2.990676904336465e-16,
            8.15164238587503e-15,
            -1.37069051306847
          ],
          [
            1.4270036023299264e-15,
            5.098303349239522e-15,
            -2.028128918067847
          ],
          [
            8.203057449894621e-16,
            4.080114759280715e-15,
            -2.645683533682986
          ],
          [
            1.236385953673425e-15,
            8.12833445429766e-15,
            -3.204562774011031
          ],
          [
            8.417945782453638e-16,
            1.2167967016628204e-14,
            -3.70017767003625
          ],
          [
            1.7137206541246715e-15,
            6.502606226776082e-15,
            -4.154036088579346
          ],
          [
            8.563267126258368e-16,
            4.759418291436967e-15,
            -4.602101340975783
          ]
        ],
        "unwrapped_reduced_polarization": [
          [
            -5.231579712686366e-16,
            4.8413027352679905e-15,
            4.602101340975781
          ],
          [
            -9.024796888291132e-16,
            -2.1826651188966365e-15,
            4.154036088579343
          ],
          [
            1.2189233150180822e-16,
            5.518459484252644e-15,
            3.7001776700362377
          ],
          [
            5.348615414727392e-16,
            5.185401409344432e-15,
            3.204562774011009
          ],
          [
            9.198417844546546e-16,
            3.580834330228625e-15,
            3.6456835336829756
          ],
          [
            1.439224501899489e-15,
            3.1907331596179005e-15,
            4.028128918067843
          ],
          [
            5.594251306020439e-16,
            -1.3984758946422158e-16,
            4.370690513068461
          ],
          [
            7.4338263922138e-16,
            -1.897756323694307e-15,
            4.690564662357204
          ],
          [
            5.544427938298232e-16,
            -3.006723173480767e-15,
            4.9999999999999964
          ],
          [
            6.588550983542923e-16,
            -2.7969517892844356e-16,
            5.3094353376427845
          ],
          [
            2.990676904336465e-16,
            8.15164238587503e-15,
            5.62930948693153
          ],
          [
            1.4270036023299264e-15,
            5.098303349239522e-15,
            5.971871081932153
          ],
          [
            8.203057449894621e-16,
            4.080114759280715e-15,
            6.354316466317015
          ],
          [
            1.236385953673425e-15,
            8.12833445429766e-15,
            6.795437225988969
          ],
          [
            8.417945782453638e-16,
            1.2167967016628204e-14,
            6.29982232996375
          ],
          [
            1.7137206541246715e-15,
            6.502606226776082e-15,
            5.845963911420655
          ],
          [
            8.563267126258368e-16,
            4.759418291436967e-15,
            5.397898659024217
          ]
        ],
        "berry_integer_shifts": [
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            1
          ],
          [
            0,
            0,
            2
          ],
          [
            0,
            0,
            3
          ],
          [
            0,
            0,
            4
          ],
          [
            0,
            0,
            5
          ],
          [
            0,
            0,
            6
          ],
          [
            0,
            0,
            7
          ],
          [
            0,
            0,
            8
          ],
          [
            0,
            0,
            9
          ],
          [
            0,
            0,
            10
          ],
          [
            0,
            0,
            10
          ],
          [
            0,
            0,
            10
          ],
          [
            0,
            0,
            10
          ]
        ],
        "folded_reduced_polarization": [
          [
            -4.996003610813204e-16,
            4.884981308350689e-15,
            -0.39789865902421884
          ],
          [
            -8.881784197001252e-16,
            -2.1649348980190553e-15,
            0.1540360885793426
          ],
          [
            1.1102230246251565e-16,
            5.551115123125783e-15,
            -0.2998223299637619
          ],
          [
            5.551115123125783e-16,
            5.218048215738236e-15,
            0.2045627740110092
          ],
          [
            8.881784197001252e-16,
            3.552713678800501e-15,
            -0.35431646631702485
          ],
          [
            1.4432899320127035e-15,
            3.219646771412954e-15,
            0.02812891806784279
          ],
          [
            5.551115123125783e-16,
            -1.6653345369377348e-16,
            0.37069051306846124
          ],
          [
            7.771561172376096e-16,
            -1.887379141862766e-15,
            -0.30943533764279607
          ],
          [
            5.551115123125783e-16,
            -2.9976021664879227e-15,
            -3.552713678800501e-15
          ],
          [
            6.661338147750939e-16,
            -2.7755575615628914e-16,
            0.3094353376427845
          ],
          [
            3.3306690738754696e-16,
            8.104628079763643e-15,
            -0.3706905130684701
          ],
          [
            1.4432899320127035e-15,
            5.10702591327572e-15,
            -0.02812891806784723
          ],
          [
            7.771561172376096e-16,
            4.107825191113079e-15,
            0.3543164663170151
          ],
          [
            1.2212453270876722e-15,
            8.104628079763643e-15,
            -0.2045627740110314
          ],
          [
            8.881784197001252e-16,
            1.2212453270876722e-14,
            0.29982232996375036
          ],
          [
            1.6653345369377348e-15,
            6.5503158452884236e-15,
            -0.15403608857934525
          ],
          [
            8.881784197001252e-16,
            4.773959005888173e-15,
            0.39789865902421706
          ]
        ]
      },
      "incoming_structure_ids": [
        "incoming_01_000",
        "incoming_01_001",
        "incoming_01_002",
        "incoming_01_003",
        "incoming_01_004",
        "incoming_01_005",
        "incoming_01_006",
        "incoming_01_007",
        "incoming_01_008"
      ],
      "reflected_structure_ids": [
        "reflected_01_001",
        "reflected_01_002",
        "reflected_01_003",
        "reflected_01_004",
        "reflected_01_005",
        "reflected_01_006",
        "reflected_01_007",
        "reflected_01_008"
      ],
      "positive_extension_structure_ids": [
        "extension_plus_01_000",
        "extension_plus_01_001",
        "extension_plus_01_002",
        "extension_plus_01_003"
      ],
      "negative_extension_structure_ids": [
        "extension_minus_01_000",
        "extension_minus_01_001",
        "extension_minus_01_002",
        "extension_minus_01_003"
      ],
      "extension": {
        "enabled": true,
        "fraction_beyond_polar_endpoint": 0.35,
        "images_per_side": 4,
        "construction": "continue fractional atomic displacements and symmetric log strain beyond +P; reflect these structures about N for the -P side",
        "positive_path_coordinates": [
          1.35,
          1.2625,
          1.175,
          1.0875
        ],
        "negative_path_coordinates": [
          -1.0875,
          -1.175,
          -1.2625,
          -1.35
        ]
      },
      "branch_coordinates": [
        1.35,
        1.2625,
        1.175,
        1.0875,
        1.0,
        0.875,
        0.75,
        0.625,
        0.5,
        0.375,
        0.25,
        0.125,
        0.0,
        -0.125,
        -0.25,
        -0.375,
        -0.5,
        -0.625,
        -0.75,
        -0.875,
        -1.0,
        -1.0875,
        -1.175,
        -1.2625,
        -1.35
      ],
      "parent": {
        "candidate_id": "inversion_parent_endpoint_00",
        "source": "same_species_inversion_center_projection_from_endpoint",
        "spacegroup": "Cmcm",
        "spacegroup_number": 63,
        "pointgroup": "mmm",
        "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": 6.563172810160064e-15,
        "parent_symmetrization_rmsd_A": 0.2753173206359,
        "parent_cell_rmsd_A": 0.0,
        "energy_eV": -400.22389112167923,
        "reduced_polarization": [
          7.829886668995433e-16,
          -5.320342065844996e-15,
          -3.762462808577837e-15
        ],
        "cartesian_polarization_e_A2": [
          2.42886538712812e-17,
          -3.681812147939966e-17,
          -2.623409513975053e-17
        ],
        "ranking_score": 0.2753173206359131
      }
    }
  ],
  "path_sampling": {
    "num_images": 17,
    "images_per_leg_including_parent": 9,
    "extension_fraction_beyond_polar_endpoint": 0.35,
    "extension_images_per_side": 4,
    "total_images_per_sampled_branch": 25,
    "construction": "linear polar-to-parent interpolation plus parent-reflected second leg and symmetric log-strain continuation beyond both polar endpoints"
  },
  "branch_folding": "componentwise integer unwrap with per-image shifts, then reduced-coordinate fold [-0.5, 0.5)",
  "bec_backprojection_settings": {
    "variable_cell": true,
    "max_strain_step_log_component": 0.02,
    "strain_response_refresh_iterations": 4,
    "cell_principal_stretch_bounds": [
      0.85,
      1.15
    ],
    "cell_volume_ratio_bounds": [
      0.7,
      1.3
    ],
    "strain_jacobian": "branch-matched finite differences of reduced polarization in six symmetric log-strain coordinates at fixed fractional positions"
  },
  "model_input_contract": "one polar endpoint structure; no reference parent or path frame",
  "run": {
    "model_file": "MACEField-MH-0-omat-dielectric.model",
    "model_sha256": "f92e043aaf2cd8879919db8452503553fe7b608cb749d8d169dd96d4aa094aa2",
    "model_head": "mp-ferroelectric",
    "device": "cpu",
    "dtype": "float64",
    "num_images": 17,
    "compute_becs_for_every_image": true,
    "compute_polarizability_for_every_image": true,
    "initial_structure_relaxation": {
      "enabled": false
    },
    "model_evaluations_for_recovery": {
      "total": 49,
      "full_response": 16,
      "energy_polarization": 33
    },
    "model_evaluations_for_recovery_and_path_properties": {
      "total": 74,
      "full_response": 41,
      "energy_polarization": 33
    },
    "elapsed_seconds": 807.229559281026
  }
}
