{
  "schema": "ferrofinder.endpoint_parent_recovery.v4_variable_cell",
  "status": "complete",
  "input_atom_count": 44,
  "input_formula": "C8Co4Li8O24",
  "input_spacegroup": "P2_1",
  "input_pointgroup": "2",
  "input_is_polar_point_group": true,
  "input_energy_eV": -287.00197366041743,
  "input_cartesian_polarization_e_A2": [
    1.7785370906245867e-17,
    -0.0007278769233131218,
    -7.755248941676977e-18
  ],
  "input_reduced_polarization": [
    1.3333947163716728e-15,
    -0.04081853091385199,
    -6.738711745001055e-17
  ],
  "input_formal_targets": [
    {
      "orbit_id": 0,
      "representative_formal_class": [
        0.0,
        0.0,
        0.0
      ],
      "target_reduced_polarization": [
        0.0,
        0.0,
        0.0
      ]
    },
    {
      "orbit_id": 1,
      "representative_formal_class": [
        0.0,
        0.5,
        0.0
      ],
      "target_reduced_polarization": [
        0.0,
        -0.5,
        0.0
      ]
    },
    {
      "orbit_id": 2,
      "representative_formal_class": [
        0.5,
        0.0,
        0.0
      ],
      "target_reduced_polarization": [
        0.5,
        0.0,
        0.0
      ]
    },
    {
      "orbit_id": 3,
      "representative_formal_class": [
        0.0,
        0.0,
        0.5
      ],
      "target_reduced_polarization": [
        0.0,
        0.0,
        -0.5
      ]
    },
    {
      "orbit_id": 4,
      "representative_formal_class": [
        0.5,
        0.5,
        0.0
      ],
      "target_reduced_polarization": [
        0.5,
        -0.5,
        0.0
      ]
    },
    {
      "orbit_id": 5,
      "representative_formal_class": [
        0.0,
        0.5,
        0.5
      ],
      "target_reduced_polarization": [
        0.0,
        -0.5,
        -0.5
      ]
    },
    {
      "orbit_id": 6,
      "representative_formal_class": [
        0.5,
        0.0,
        0.5
      ],
      "target_reduced_polarization": [
        0.5,
        0.0,
        -0.5
      ]
    },
    {
      "orbit_id": 7,
      "representative_formal_class": [
        0.5,
        0.5,
        0.5
      ],
      "target_reduced_polarization": [
        0.5,
        -0.5,
        -0.5
      ]
    }
  ],
  "parent_candidates": [
    {
      "candidate_id": "inversion_parent_endpoint_00",
      "source": "same_species_inversion_center_projection_from_endpoint",
      "spacegroup": "P2_1/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": 2.532078477257827e-15,
      "parent_symmetrization_rmsd_A": 0.1289775037027087,
      "parent_cell_rmsd_A": 0.0,
      "energy_eV": -286.8897117633994,
      "reduced_polarization": [
        1.7002729874093697e-15,
        9.687525869811251e-16,
        1.606863904783386e-15
      ],
      "cartesian_polarization_e_A2": [
        2.272287939911354e-17,
        1.7274817017585465e-17,
        1.4786674648797436e-17
      ],
      "ranking_score": 0.12897750370271374
    },
    {
      "candidate_id": "bec_projection_00",
      "source": "MACEField_BEC_backprojection",
      "spacegroup": "P2_1",
      "spacegroup_number": 4,
      "pointgroup": "2",
      "has_inversion": false,
      "is_polar_point_group": true,
      "nonpolar_parent_hypothesis": false,
      "symmetry_tolerance_A": null,
      "target_reduced_polarization": [
        0.0,
        0.0,
        0.0
      ],
      "formal_class": [
        0.0,
        0.0,
        0.0
      ],
      "target_residual": 2.1832724955982325e-06,
      "parent_symmetrization_rmsd_A": 0.006136148718732546,
      "parent_cell_rmsd_A": 0.005973469158023786,
      "energy_eV": -286.96780479919323,
      "reduced_polarization": [
        -2.8573506317881407e-15,
        -2.1832724955982325e-06,
        3.677558749538425e-16
      ],
      "cartesian_polarization_e_A2": [
        -3.8080157674636447e-17,
        -3.8933218840057464e-08,
        1.9840950538752232e-17
      ],
      "ranking_score": 0.5076338825532297
    },
    {
      "candidate_id": "inversion_parent_bec_00_00",
      "source": "same_species_inversion_center_projection_after_BEC",
      "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": 1.5537404626720015e-15,
      "parent_symmetrization_rmsd_A": 0.12897884160801912,
      "parent_cell_rmsd_A": 0.005973469158023786,
      "energy_eV": -286.88561712204915,
      "reduced_polarization": [
        7.9212011620554e-16,
        -1.1959305629997783e-15,
        -5.969968470015232e-16
      ],
      "cartesian_polarization_e_A2": [
        1.0540504973712123e-17,
        -2.1326438372057252e-17,
        -1.271060893888815e-17
      ],
      "ranking_score": 0.13047220889752817
    },
    {
      "candidate_id": "bec_projection_01",
      "source": "MACEField_BEC_backprojection",
      "spacegroup": "P2_1",
      "spacegroup_number": 4,
      "pointgroup": "2",
      "has_inversion": false,
      "is_polar_point_group": true,
      "nonpolar_parent_hypothesis": false,
      "symmetry_tolerance_A": null,
      "target_reduced_polarization": [
        0.0,
        -0.5,
        0.0
      ],
      "formal_class": [
        0.0,
        0.5,
        0.0
      ],
      "target_residual": 1.609329069812704e-05,
      "parent_symmetrization_rmsd_A": 0.0700328806405346,
      "parent_cell_rmsd_A": 0.06742965308524575,
      "energy_eV": -282.7065813639473,
      "reduced_polarization": [
        -1.0091123523227629e-16,
        -0.4999839067093019,
        3.5447988447104243e-15
      ],
      "cartesian_polarization_e_A2": [
        2.098480872405678e-17,
        -0.008912982918239097,
        -4.663522256393362e-16
      ],
      "ranking_score": 0.5869224804932422
    },
    {
      "candidate_id": "bec_projection_02",
      "source": "MACEField_BEC_backprojection",
      "spacegroup": "P1",
      "spacegroup_number": 1,
      "pointgroup": "1",
      "has_inversion": false,
      "is_polar_point_group": true,
      "nonpolar_parent_hypothesis": false,
      "symmetry_tolerance_A": null,
      "target_reduced_polarization": [
        0.5,
        0.0,
        0.0
      ],
      "formal_class": [
        0.5,
        0.0,
        0.0
      ],
      "target_residual": 4.544746344488303e-05,
      "parent_symmetrization_rmsd_A": 0.06812562342136219,
      "parent_cell_rmsd_A": 0.033780590963579236,
      "energy_eV": -282.4430895970466,
      "reduced_polarization": [
        0.4999790658923318,
        2.097034598337338e-05,
        3.445982674141929e-05
      ],
      "cartesian_polarization_e_A2": [
        0.0066655873383346925,
        -2.073448017344548e-06,
        -0.002534257938838368
      ],
      "ranking_score": 0.5766616660891468
    },
    {
      "candidate_id": "bec_projection_03",
      "source": "MACEField_BEC_backprojection",
      "spacegroup": "P1",
      "spacegroup_number": 1,
      "pointgroup": "1",
      "has_inversion": false,
      "is_polar_point_group": true,
      "nonpolar_parent_hypothesis": false,
      "symmetry_tolerance_A": null,
      "target_reduced_polarization": [
        0.0,
        0.0,
        -0.5
      ],
      "formal_class": [
        0.0,
        0.0,
        0.5
      ],
      "target_residual": 4.1177702198155256e-05,
      "parent_symmetrization_rmsd_A": 0.05914853277159431,
      "parent_cell_rmsd_A": 0.030585426724203127,
      "energy_eV": -283.60954373813536,
      "reduced_polarization": [
        -1.804568580718602e-05,
        4.156450810272701e-06,
        -0.49996322119769854
      ],
      "cartesian_polarization_e_A2": [
        -1.634519199480972e-05,
        -1.5712438949341818e-05,
        -0.007282183289977803
      ],
      "ranking_score": 0.5668772448570414
    },
    {
      "candidate_id": "bec_projection_04",
      "source": "MACEField_BEC_backprojection",
      "spacegroup": "P1",
      "spacegroup_number": 1,
      "pointgroup": "1",
      "has_inversion": false,
      "is_polar_point_group": true,
      "nonpolar_parent_hypothesis": false,
      "symmetry_tolerance_A": null,
      "target_reduced_polarization": [
        0.5,
        -0.5,
        0.0
      ],
      "formal_class": [
        0.5,
        0.5,
        0.0
      ],
      "target_residual": 6.33670051426966e-05,
      "parent_symmetrization_rmsd_A": 0.09900572425973898,
      "parent_cell_rmsd_A": 0.07635802922354974,
      "energy_eV": -277.62222633655267,
      "reduced_polarization": [
        0.4999872002942967,
        -0.4999379748265342,
        -2.1030290533095307e-06
      ],
      "cartesian_polarization_e_A2": [
        0.006708359535291934,
        -0.008914514387954944,
        -0.002635261103086562
      ],
      "ranking_score": 0.6182219655759118
    },
    {
      "candidate_id": "bec_projection_05",
      "source": "MACEField_BEC_backprojection",
      "spacegroup": "P1",
      "spacegroup_number": 1,
      "pointgroup": "1",
      "has_inversion": false,
      "is_polar_point_group": true,
      "nonpolar_parent_hypothesis": false,
      "symmetry_tolerance_A": null,
      "target_reduced_polarization": [
        0.0,
        -0.5,
        -0.5
      ],
      "formal_class": [
        0.0,
        0.5,
        0.5
      ],
      "target_residual": 0.00010627284629613578,
      "parent_symmetrization_rmsd_A": 0.09311937696351595,
      "parent_cell_rmsd_A": 0.07536700392840434,
      "energy_eV": -278.8644516758512,
      "reduced_polarization": [
        -2.2020491542118273e-05,
        -0.4999411695157452,
        -0.4999142795827444
      ],
      "cartesian_polarization_e_A2": [
        4.6383144633321676e-05,
        -0.00892861073964228,
        -0.007377238615780962
      ],
      "ranking_score": 0.6121736736382093
    },
    {
      "candidate_id": "bec_projection_06",
      "source": "MACEField_BEC_backprojection",
      "spacegroup": "P1",
      "spacegroup_number": 1,
      "pointgroup": "1",
      "has_inversion": false,
      "is_polar_point_group": true,
      "nonpolar_parent_hypothesis": false,
      "symmetry_tolerance_A": null,
      "target_reduced_polarization": [
        0.5,
        0.0,
        -0.5
      ],
      "formal_class": [
        0.5,
        0.0,
        0.5
      ],
      "target_residual": 1.8168303325206094e-05,
      "parent_symmetrization_rmsd_A": 0.10816461601091837,
      "parent_cell_rmsd_A": 0.06461088261276758,
      "energy_eV": -273.1947726859802,
      "reduced_polarization": [
        0.5000006298442637,
        3.8005869219539276e-06,
        -0.4999822448294582
      ],
      "cartesian_polarization_e_A2": [
        0.006651837648688066,
        -7.529581819085333e-05,
        -0.0098206645156119
      ],
      "ranking_score": 0.6243536732707606
    },
    {
      "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": 3.519612844116622e-05,
      "parent_symmetrization_rmsd_A": 0.12899144663505432,
      "parent_cell_rmsd_A": 0.09476320215524346,
      "energy_eV": -268.97973855803997,
      "reduced_polarization": [
        0.5000043763862132,
        -0.49996740484974117,
        -0.4999874632188914
      ],
      "cartesian_polarization_e_A2": [
        0.006756570710303103,
        -0.008990002123720146,
        -0.010020170546159222
      ],
      "ranking_score": 0.6527526394307475
    }
  ],
  "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": [
              1.3333947163716728e-15,
              -0.04081853091385199,
              -6.738711745001055e-17
            ],
            "branch_aligned_reduced_polarization": [
              1.3333947163716728e-15,
              -0.04081853091385199,
              -6.738711745001055e-17
            ],
            "target_residual": 0.04081853091385199,
            "energy_eV": -287.00197366041743,
            "max_atomic_step_A": 0.008028846115486564,
            "max_log_strain_component": 0.0006562843046071314,
            "step_scale": 1.0,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 0.8949175130845075,
            "cell_principal_stretches": [
              1.0006564997062704,
              1.0004800868099217,
              0.9994930171223793
            ],
            "cell_volume_ratio": 1.000629342425729,
            "cell_rmsd_from_input_A": 0.005973469158023786
          },
          {
            "iteration": 1,
            "reduced_polarization": [
              -2.8573506317881407e-15,
              -2.1832724955982325e-06,
              3.677558749538425e-16
            ],
            "branch_aligned_reduced_polarization": [
              -2.8573506317881407e-15,
              -2.1832724955982325e-06,
              3.677558749538425e-16
            ],
            "target_residual": 2.1832724955982325e-06,
            "energy_eV": -286.96780479919323
          }
        ],
        "iterations": 1
      },
      "parent": {
        "candidate_id": "inversion_parent_endpoint_00",
        "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": 2.532078477257827e-15,
        "parent_symmetrization_rmsd_A": 0.1289775037027087,
        "parent_cell_rmsd_A": 0.0,
        "energy_eV": -286.8897117633994,
        "reduced_polarization": [
          1.7002729874093697e-15,
          9.687525869811251e-16,
          1.606863904783386e-15
        ],
        "cartesian_polarization_e_A2": [
          2.272287939911354e-17,
          1.7274817017585465e-17,
          1.4786674648797436e-17
        ],
        "ranking_score": 0.12897750370271374
      },
      "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": [
          -287.00197366041743,
          -286.9962692651054,
          -286.98232171420835,
          -286.9634528840513,
          -286.94248269280257,
          -286.9221220983991,
          -286.9050627742812,
          -286.8936994806504,
          -286.88971176339936
        ],
        "cartesian_polarizations_e_A2": [
          [
            5.9069146105772974e-18,
            -0.0007278769233131369,
            1.33390281796844e-17
          ],
          [
            -1.4140403903657687e-17,
            -0.0006457149521292147,
            4.5859372075116524e-17
          ],
          [
            2.7789642041009165e-17,
            -0.000559649080074024,
            3.210673061854268e-17
          ],
          [
            -5.764735046646553e-18,
            -0.00047074716626271067,
            1.2692757434544652e-17
          ],
          [
            -3.471766442890727e-17,
            -0.0003796642948605932,
            1.3778492286379429e-17
          ],
          [
            -2.1818100355917893e-17,
            -0.0002867455189746879,
            -2.1559592057861996e-17
          ],
          [
            1.3752641456573838e-17,
            -0.00019222604404736817,
            -3.675987998354887e-17
          ],
          [
            -2.585082980558992e-18,
            -9.64664127138447e-05,
            -1.680303937363345e-17
          ],
          [
            -1.4011149754629738e-17,
            -9.677904408467727e-18,
            -2.388616674036509e-17
          ]
        ],
        "raw_reduced_polarization": [
          [
            4.407271377160515e-16,
            -0.04081853091385284,
            1.06865235820373e-15
          ],
          [
            -1.0654206444221404e-15,
            -0.03621097865701172,
            2.7747635465547532e-15
          ],
          [
            2.077530602733219e-15,
            -0.031384499967288024,
            2.9265039940640885e-15
          ],
          [
            -4.3354812306772836e-16,
            -0.026398979199999426,
            7.196676026627325e-16
          ],
          [
            -2.6026515999934066e-15,
            -0.021291152748891613,
            3.830557731810339e-17
          ],
          [
            -1.6315896569739408e-15,
            -0.016080370809670137,
            -2.0475625236756264e-15
          ],
          [
            1.035158399940575e-15,
            -0.010779823442787696,
            -2.1610703219946405e-15
          ],
          [
            -1.914158326221565e-16,
            -0.0054097294795188485,
            -1.2194136380228025e-15
          ],
          [
            -1.0464351277394315e-15,
            -5.427261500202898e-16,
            -2.0032661952472797e-15
          ]
        ],
        "unwrapped_reduced_polarization": [
          [
            4.407271377160515e-16,
            -0.04081853091385284,
            1.06865235820373e-15
          ],
          [
            -1.0654206444221404e-15,
            -0.03621097865701172,
            2.7747635465547532e-15
          ],
          [
            2.0775306027332196e-15,
            -0.031384499967288024,
            2.9265039940640885e-15
          ],
          [
            -4.3354812306772826e-16,
            -0.026398979199999426,
            7.196676026627323e-16
          ],
          [
            -2.6026515999934066e-15,
            -0.021291152748891613,
            3.83055773181034e-17
          ],
          [
            -1.6315896569739408e-15,
            -0.016080370809670137,
            -2.0475625236756264e-15
          ],
          [
            1.035158399940575e-15,
            -0.010779823442787696,
            -2.1610703219946405e-15
          ],
          [
            -1.9141583262215651e-16,
            -0.0054097294795188485,
            -1.2194136380228025e-15
          ],
          [
            -1.0464351277394315e-15,
            -5.429684479807406e-16,
            -2.0032661952472797e-15
          ]
        ],
        "berry_integer_shifts": [
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ]
        ],
        "folded_reduced_polarization": [
          [
            4.440892098500626e-16,
            -0.040818530913852846,
            1.1102230246251565e-15
          ],
          [
            -1.0547118733938987e-15,
            -0.03621097865701173,
            2.7755575615628914e-15
          ],
          [
            2.1094237467877974e-15,
            -0.03138449996728804,
            2.886579864025407e-15
          ],
          [
            -4.440892098500626e-16,
            -0.02639897919999945,
            6.661338147750939e-16
          ],
          [
            -2.609024107869118e-15,
            -0.021291152748891595,
            0.0
          ],
          [
            -1.609823385706477e-15,
            -0.01608037080967012,
            -2.0539125955565396e-15
          ],
          [
            9.992007221626409e-16,
            -0.010779823442787717,
            -2.1649348980190553e-15
          ],
          [
            -1.6653345369377348e-16,
            -0.005409729479518843,
            -1.2212453270876722e-15
          ],
          [
            -1.0547118733938987e-15,
            -5.551115123125783e-16,
            -1.9984014443252818e-15
          ]
        ]
      },
      "reflected": {
        "reached": true,
        "construction": "reflect_displacements_about_reconstructed_parent",
        "energies_eV": [
          -286.8897117633994,
          -286.8936994806504,
          -286.9050627742812,
          -286.922122098399,
          -286.9424826928026,
          -286.9634528840512,
          -286.9823217142084,
          -286.9962692651054,
          -287.00197366041743
        ],
        "cartesian_polarizations_e_A2": [
          [
            -1.5122735436270104e-17,
            3.6827738411788545e-17,
            -3.469181359910168e-17
          ],
          [
            -3.2572045555043303e-18,
            9.646641271378999e-05,
            2.4299780017254527e-18
          ],
          [
            -9.409702049234731e-18,
            0.00019222604404732502,
            -2.7712089551592397e-17
          ],
          [
            -3.02713217023458e-17,
            0.00028674551897468677,
            -6.348963800252885e-17
          ],
          [
            2.1456188738639635e-18,
            0.0003796642948605996,
            -4.6376388671228323e-17
          ],
          [
            -1.636357526693842e-17,
            0.000470747166262764,
            -5.0977836376623324e-17
          ],
          [
            -4.4592681414642616e-17,
            0.0005596490800740155,
            -3.443330530104578e-17
          ],
          [
            -2.0835768823305477e-17,
            0.0006457149521291456,
            -1.2010295527677077e-16
          ],
          [
            -2.049970803583281e-17,
            0.000727876923313119,
            -8.773771636017219e-17
          ]
        ],
        "raw_reduced_polarization": [
          [
            -1.1282663897425507e-15,
            2.065258741830132e-15,
            -2.7730641818028676e-15
          ],
          [
            -2.443319600807023e-16,
            0.00540972947951578,
            8.156019929617502e-17
          ],
          [
            -7.012153242867743e-16,
            0.010779823442785276,
            -2.145434897751141e-15
          ],
          [
            -2.2592554904663674e-15,
            0.016080370809670074,
            -5.142740885132129e-15
          ],
          [
            1.669210157908785e-16,
            0.021291152748891966,
            -3.1233224939226175e-15
          ],
          [
            -1.2190495299372014e-15,
            0.026398979200002417,
            -3.921943297450483e-15
          ],
          [
            -3.3359909357947685e-15,
            0.031384499967287545,
            -3.5246330360071715e-15
          ],
          [
            -1.5448562664759107e-15,
            0.03621097865700785,
            -8.777557514752388e-15
          ],
          [
            -1.5239977315815763e-15,
            0.04081853091385184,
            -6.549986682782339e-15
          ]
        ],
        "unwrapped_reduced_polarization": [
          [
            -1.1282663897425507e-15,
            2.065258741830132e-15,
            -2.7730641818028676e-15
          ],
          [
            -2.4433196008070226e-16,
            0.00540972947951578,
            8.15601992961752e-17
          ],
          [
            -7.012153242867743e-16,
            0.010779823442785276,
            -2.145434897751141e-15
          ],
          [
            -2.2592554904663674e-15,
            0.016080370809670074,
            -5.142740885132129e-15
          ],
          [
            1.669210157908786e-16,
            0.021291152748891966,
            -3.1233224939226175e-15
          ],
          [
            -1.2190495299372014e-15,
            0.026398979200002417,
            -3.921943297450483e-15
          ],
          [
            -3.3359909357947685e-15,
            0.031384499967287545,
            -3.5246330360071715e-15
          ],
          [
            -1.544856266475911e-15,
            0.03621097865700785,
            -8.777557514752388e-15
          ],
          [
            -1.5239977315815763e-15,
            0.04081853091385184,
            -6.549986682782339e-15
          ]
        ],
        "gauge_integer_shift": [
          0,
          0,
          0
        ],
        "expected_opposite_endpoint_reduced_polarization": [
          -2.5335973931949147e-15,
          0.04081853091385176,
          -5.075184748698289e-15
        ],
        "actual_opposite_endpoint_branch_residual": 1.7892080844070694e-15
      },
      "pnp_branch": {
        "construction": "incoming_path_concatenated_with_parent_reflection",
        "reduced_polarization": [
          [
            4.407271377160515e-16,
            -0.04081853091385284,
            1.06865235820373e-15
          ],
          [
            -1.0654206444221404e-15,
            -0.03621097865701172,
            2.7747635465547532e-15
          ],
          [
            2.077530602733219e-15,
            -0.031384499967288024,
            2.9265039940640885e-15
          ],
          [
            -4.3354812306772836e-16,
            -0.026398979199999426,
            7.196676026627325e-16
          ],
          [
            -2.6026515999934066e-15,
            -0.021291152748891613,
            3.830557731810339e-17
          ],
          [
            -1.6315896569739408e-15,
            -0.016080370809670137,
            -2.0475625236756264e-15
          ],
          [
            1.035158399940575e-15,
            -0.010779823442787696,
            -2.1610703219946405e-15
          ],
          [
            -1.914158326221565e-16,
            -0.0054097294795188485,
            -1.2194136380228025e-15
          ],
          [
            -1.0464351277394315e-15,
            -5.427261500202898e-16,
            -2.0032661952472797e-15
          ],
          [
            -2.443319600807023e-16,
            0.00540972947951578,
            8.156019929617502e-17
          ],
          [
            -7.012153242867743e-16,
            0.010779823442785276,
            -2.145434897751141e-15
          ],
          [
            -2.2592554904663674e-15,
            0.016080370809670074,
            -5.142740885132129e-15
          ],
          [
            1.669210157908785e-16,
            0.021291152748891966,
            -3.1233224939226175e-15
          ],
          [
            -1.2190495299372014e-15,
            0.026398979200002417,
            -3.921943297450483e-15
          ],
          [
            -3.3359909357947685e-15,
            0.031384499967287545,
            -3.5246330360071715e-15
          ],
          [
            -1.5448562664759107e-15,
            0.03621097865700785,
            -8.777557514752388e-15
          ],
          [
            -1.5239977315815763e-15,
            0.04081853091385184,
            -6.549986682782339e-15
          ]
        ],
        "unwrapped_reduced_polarization": [
          [
            4.407271377160515e-16,
            -0.04081853091385284,
            1.06865235820373e-15
          ],
          [
            -1.0654206444221404e-15,
            -0.03621097865701172,
            2.7747635465547532e-15
          ],
          [
            2.0775306027332196e-15,
            -0.031384499967288024,
            2.9265039940640885e-15
          ],
          [
            -4.3354812306772826e-16,
            -0.026398979199999426,
            7.196676026627323e-16
          ],
          [
            -2.6026515999934066e-15,
            -0.021291152748891613,
            3.83055773181034e-17
          ],
          [
            -1.6315896569739408e-15,
            -0.016080370809670137,
            -2.0475625236756264e-15
          ],
          [
            1.035158399940575e-15,
            -0.010779823442787696,
            -2.1610703219946405e-15
          ],
          [
            -1.9141583262215651e-16,
            -0.0054097294795188485,
            -1.2194136380228025e-15
          ],
          [
            -1.0464351277394315e-15,
            -5.429684479807406e-16,
            -2.0032661952472797e-15
          ],
          [
            -2.4433196008070226e-16,
            0.00540972947951578,
            8.15601992961752e-17
          ],
          [
            -7.012153242867743e-16,
            0.010779823442785276,
            -2.145434897751141e-15
          ],
          [
            -2.2592554904663674e-15,
            0.016080370809670074,
            -5.142740885132129e-15
          ],
          [
            1.669210157908786e-16,
            0.021291152748891966,
            -3.1233224939226175e-15
          ],
          [
            -1.2190495299372014e-15,
            0.026398979200002417,
            -3.921943297450483e-15
          ],
          [
            -3.3359909357947685e-15,
            0.031384499967287545,
            -3.5246330360071715e-15
          ],
          [
            -1.544856266475911e-15,
            0.03621097865700785,
            -8.777557514752388e-15
          ],
          [
            -1.5239977315815763e-15,
            0.04081853091385184,
            -6.549986682782339e-15
          ]
        ],
        "berry_integer_shifts": [
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            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,
            -0.040818530913852846,
            1.1102230246251565e-15
          ],
          [
            -1.0547118733938987e-15,
            -0.03621097865701173,
            2.7755575615628914e-15
          ],
          [
            2.1094237467877974e-15,
            -0.03138449996728804,
            2.886579864025407e-15
          ],
          [
            -4.440892098500626e-16,
            -0.02639897919999945,
            6.661338147750939e-16
          ],
          [
            -2.609024107869118e-15,
            -0.021291152748891595,
            0.0
          ],
          [
            -1.609823385706477e-15,
            -0.01608037080967012,
            -2.0539125955565396e-15
          ],
          [
            9.992007221626409e-16,
            -0.010779823442787717,
            -2.1649348980190553e-15
          ],
          [
            -1.6653345369377348e-16,
            -0.005409729479518843,
            -1.2212453270876722e-15
          ],
          [
            -1.0547118733938987e-15,
            -5.551115123125783e-16,
            -1.9984014443252818e-15
          ],
          [
            -2.220446049250313e-16,
            0.00540972947951579,
            1.1102230246251565e-16
          ],
          [
            -7.216449660063518e-16,
            0.010779823442785275,
            -2.1649348980190553e-15
          ],
          [
            -2.275957200481571e-15,
            0.016080370809670064,
            -5.162537064506978e-15
          ],
          [
            2.220446049250313e-16,
            0.02129115274889193,
            -3.1086244689504383e-15
          ],
          [
            -1.2212453270876722e-15,
            0.026398979200002448,
            -3.941291737419306e-15
          ],
          [
            -3.3306690738754696e-15,
            0.03138449996728754,
            -3.497202527569243e-15
          ],
          [
            -1.5543122344752192e-15,
            0.03621097865700784,
            -8.770761894538737e-15
          ],
          [
            -1.4988010832439613e-15,
            0.04081853091385179,
            -6.5503158452884236e-15
          ]
        ]
      },
      "incoming_structure_ids": [
        "incoming_00_000",
        "incoming_00_001",
        "incoming_00_002",
        "incoming_00_003",
        "incoming_00_004",
        "incoming_00_005",
        "incoming_00_006",
        "incoming_00_007",
        "incoming_00_008"
      ],
      "reflected_structure_ids": [
        "reflected_00_001",
        "reflected_00_002",
        "reflected_00_003",
        "reflected_00_004",
        "reflected_00_005",
        "reflected_00_006",
        "reflected_00_007",
        "reflected_00_008"
      ]
    },
    {
      "orbit_id": 1,
      "formal_class": [
        0.0,
        0.5,
        0.0
      ],
      "formal_classes_in_orbit": [
        [
          0.0,
          0.5,
          0.0
        ]
      ],
      "target_reduced_polarization": [
        0.0,
        -0.5,
        0.0
      ],
      "bec_backprojection": {
        "converged_to_target": true,
        "history": [
          {
            "iteration": 0,
            "reduced_polarization": [
              1.3333947163716728e-15,
              -0.04081853091385199,
              -6.738711745001055e-17
            ],
            "branch_aligned_reduced_polarization": [
              1.3333947163716728e-15,
              -0.040818530913852014,
              -6.738711745001055e-17
            ],
            "target_residual": 0.459181469086148,
            "energy_eV": -287.00197366041743,
            "max_atomic_step_A": 0.09031920727761025,
            "max_log_strain_component": 0.007382764258804269,
            "step_scale": 1.0,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 0.8949175130845075,
            "cell_principal_stretches": [
              1.0057209707881627,
              0.9946151873311428,
              0.9926444214023306
            ],
            "cell_volume_ratio": 0.9929475271267627,
            "cell_rmsd_from_input_A": 0.06695668420830939
          },
          {
            "iteration": 1,
            "reduced_polarization": [
              1.6526835345548518e-14,
              -0.4967834802953265,
              -7.076351027230826e-15
            ],
            "branch_aligned_reduced_polarization": [
              1.6526835345548518e-14,
              -0.4967834802953265,
              -7.076351027230826e-15
            ],
            "target_residual": 0.003216519704673515,
            "energy_eV": -282.7693737895451,
            "max_atomic_step_A": 0.0006453030265605334,
            "max_log_strain_component": 5.232168825415579e-05,
            "step_scale": 1.0,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 0.8949175130845075,
            "cell_principal_stretches": [
              1.0057616319160414,
              0.9945771287973032,
              0.9925924859290544
            ],
            "cell_volume_ratio": 0.9928977241245741,
            "cell_rmsd_from_input_A": 0.06742965308524575
          },
          {
            "iteration": 2,
            "reduced_polarization": [
              -1.0091123523227629e-16,
              -0.4999839067093019,
              3.5447988447104243e-15
            ],
            "branch_aligned_reduced_polarization": [
              -1.0091123523227629e-16,
              -0.4999839067093019,
              3.5447988447104243e-15
            ],
            "target_residual": 1.609329069812704e-05,
            "energy_eV": -282.7065813639473
          }
        ],
        "iterations": 2
      },
      "parent": {
        "candidate_id": "bec_projection_01",
        "source": "MACEField_BEC_backprojection",
        "spacegroup": "P2_1",
        "spacegroup_number": 4,
        "pointgroup": "2",
        "has_inversion": false,
        "is_polar_point_group": true,
        "nonpolar_parent_hypothesis": false,
        "symmetry_tolerance_A": null,
        "target_reduced_polarization": [
          0.0,
          -0.5,
          0.0
        ],
        "formal_class": [
          0.0,
          0.5,
          0.0
        ],
        "target_residual": 1.609329069812704e-05,
        "parent_symmetrization_rmsd_A": 0.0700328806405346,
        "parent_cell_rmsd_A": 0.06742965308524575,
        "energy_eV": -282.7065813639473,
        "reduced_polarization": [
          -1.0091123523227629e-16,
          -0.4999839067093019,
          3.5447988447104243e-15
        ],
        "cartesian_polarization_e_A2": [
          2.098480872405678e-17,
          -0.008912982918239097,
          -4.663522256393362e-16
        ],
        "ranking_score": 0.5869224804932422
      },
      "branch_status": "awaiting_branch_sampling"
    },
    {
      "orbit_id": 2,
      "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": [
              1.3333947163716728e-15,
              -0.04081853091385199,
              -6.738711745001055e-17
            ],
            "branch_aligned_reduced_polarization": [
              1.3322676295501878e-15,
              -0.04081853091385199,
              -6.738711745001055e-17
            ],
            "target_residual": 0.501663385614262,
            "energy_eV": -287.00197366041743,
            "max_atomic_step_A": 0.08244874719521253,
            "max_log_strain_component": 0.0037998855623978074,
            "step_scale": 1.0,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 0.8949175130845075,
            "cell_principal_stretches": [
              1.0043864466322916,
              0.999896420093939,
              0.9963625072910841
            ],
            "cell_volume_ratio": 1.0006293424257815,
            "cell_rmsd_from_input_A": 0.03263859555741829
          },
          {
            "iteration": 1,
            "reduced_polarization": [
              0.48895150194466297,
              0.0018568829489158042,
              0.008415968984527214
            ],
            "branch_aligned_reduced_polarization": [
              0.48895150194466297,
              0.0018568829489158042,
              0.008415968984527214
            ],
            "target_residual": 0.014012346609803956,
            "energy_eV": -282.69322203198067,
            "max_atomic_step_A": 0.003550301415653068,
            "max_log_strain_component": 0.00014008527064769452,
            "step_scale": 1.0,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 0.8949175130845075,
            "cell_principal_stretches": [
              1.0044857686547244,
              0.9999134248456105,
              0.9962135530309877
            ],
            "cell_volume_ratio": 1.0005957023328034,
            "cell_rmsd_from_input_A": 0.033780590963579236
          },
          {
            "iteration": 2,
            "reduced_polarization": [
              0.4999790658923318,
              2.097034598337338e-05,
              3.445982674141929e-05
            ],
            "branch_aligned_reduced_polarization": [
              0.4999790658923318,
              2.097034598337338e-05,
              3.445982674141929e-05
            ],
            "target_residual": 4.544746344488303e-05,
            "energy_eV": -282.4430895970466
          }
        ],
        "iterations": 2
      },
      "parent": {
        "candidate_id": "bec_projection_02",
        "source": "MACEField_BEC_backprojection",
        "spacegroup": "P1",
        "spacegroup_number": 1,
        "pointgroup": "1",
        "has_inversion": false,
        "is_polar_point_group": true,
        "nonpolar_parent_hypothesis": false,
        "symmetry_tolerance_A": null,
        "target_reduced_polarization": [
          0.5,
          0.0,
          0.0
        ],
        "formal_class": [
          0.5,
          0.0,
          0.0
        ],
        "target_residual": 4.544746344488303e-05,
        "parent_symmetrization_rmsd_A": 0.06812562342136219,
        "parent_cell_rmsd_A": 0.033780590963579236,
        "energy_eV": -282.4430895970466,
        "reduced_polarization": [
          0.4999790658923318,
          2.097034598337338e-05,
          3.445982674141929e-05
        ],
        "cartesian_polarization_e_A2": [
          0.0066655873383346925,
          -2.073448017344548e-06,
          -0.002534257938838368
        ],
        "ranking_score": 0.5766616660891468
      },
      "branch_status": "awaiting_branch_sampling"
    },
    {
      "orbit_id": 3,
      "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": [
              1.3333947163716728e-15,
              -0.04081853091385199,
              -6.738711745001055e-17
            ],
            "branch_aligned_reduced_polarization": [
              1.3333947163716728e-15,
              -0.04081853091385199,
              -5.551115123125783e-17
            ],
            "target_residual": 0.5016633856142633,
            "energy_eV": -287.00197366041743,
            "max_atomic_step_A": 0.06902635221052587,
            "max_log_strain_component": 0.002244917191068987,
            "step_scale": 1.0,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 0.8949175130845075,
            "cell_principal_stretches": [
              1.003217229480957,
              1.0004294643835616,
              0.9969922394136138
            ],
            "cell_volume_ratio": 1.0006293424257526,
            "cell_rmsd_from_input_A": 0.029723312154002327
          },
          {
            "iteration": 1,
            "reduced_polarization": [
              -0.00610130588247509,
              0.002070523445688274,
              -0.490417957898223
            ],
            "branch_aligned_reduced_polarization": [
              -0.00610130588247509,
              0.002070523445688274,
              -0.490417957898223
            ],
            "target_residual": 0.011546797462972005,
            "energy_eV": -283.77170129364464,
            "max_atomic_step_A": 0.0027612313166572957,
            "max_log_strain_component": 0.0001007126102892281,
            "step_scale": 1.0,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 0.8949175130845075,
            "cell_principal_stretches": [
              1.003293271746499,
              1.0004120250922537,
              0.996899328896353
            ],
            "cell_volume_ratio": 1.0005944895315289,
            "cell_rmsd_from_input_A": 0.030585426724203127
          },
          {
            "iteration": 2,
            "reduced_polarization": [
              -1.804568580718602e-05,
              4.156450810272701e-06,
              -0.49996322119769854
            ],
            "branch_aligned_reduced_polarization": [
              -1.804568580718602e-05,
              4.156450810272701e-06,
              -0.49996322119769854
            ],
            "target_residual": 4.1177702198155256e-05,
            "energy_eV": -283.60954373813536
          }
        ],
        "iterations": 2
      },
      "parent": {
        "candidate_id": "bec_projection_03",
        "source": "MACEField_BEC_backprojection",
        "spacegroup": "P1",
        "spacegroup_number": 1,
        "pointgroup": "1",
        "has_inversion": false,
        "is_polar_point_group": true,
        "nonpolar_parent_hypothesis": false,
        "symmetry_tolerance_A": null,
        "target_reduced_polarization": [
          0.0,
          0.0,
          -0.5
        ],
        "formal_class": [
          0.0,
          0.0,
          0.5
        ],
        "target_residual": 4.1177702198155256e-05,
        "parent_symmetrization_rmsd_A": 0.05914853277159431,
        "parent_cell_rmsd_A": 0.030585426724203127,
        "energy_eV": -283.60954373813536,
        "reduced_polarization": [
          -1.804568580718602e-05,
          4.156450810272701e-06,
          -0.49996322119769854
        ],
        "cartesian_polarization_e_A2": [
          -1.634519199480972e-05,
          -1.5712438949341818e-05,
          -0.007282183289977803
        ],
        "ranking_score": 0.5668772448570414
      },
      "branch_status": "awaiting_branch_sampling"
    },
    {
      "orbit_id": 4,
      "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": [
              1.3333947163716728e-15,
              -0.04081853091385199,
              -6.738711745001055e-17
            ],
            "branch_aligned_reduced_polarization": [
              1.3322676295501878e-15,
              -0.040818530913852014,
              -6.738711745001055e-17
            ],
            "target_residual": 0.6788575856187451,
            "energy_eV": -287.00197366041743,
            "max_atomic_step_A": 0.11943971087363216,
            "max_log_strain_component": 0.007382764258803861,
            "step_scale": 1.0,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 0.8949175130845075,
            "cell_principal_stretches": [
              1.0062148007419296,
              0.9966294591709355,
              0.9901520183848947
            ],
            "cell_volume_ratio": 0.9929475271268151,
            "cell_rmsd_from_input_A": 0.07407988550474373
          },
          {
            "iteration": 1,
            "reduced_polarization": [
              0.48175692119309343,
              -0.48822011511465346,
              0.0032211605092415897
            ],
            "branch_aligned_reduced_polarization": [
              0.48175692119309343,
              -0.48822011511465346,
              0.0032211605092415897
            ],
            "target_residual": 0.02195339352567882,
            "energy_eV": -278.23672382385985,
            "max_atomic_step_A": 0.004535196023651281,
            "max_log_strain_component": 0.00020151462750087545,
            "step_scale": 1.0,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 0.8949175130845075,
            "cell_principal_stretches": [
              1.0064094212943007,
              0.9965602844557921,
              0.9898380217059102
            ],
            "cell_volume_ratio": 0.9927557268215046,
            "cell_rmsd_from_input_A": 0.07635802922354974
          },
          {
            "iteration": 2,
            "reduced_polarization": [
              0.4999872002942967,
              -0.4999379748265342,
              -2.1030290533095307e-06
            ],
            "branch_aligned_reduced_polarization": [
              0.4999872002942967,
              -0.4999379748265342,
              -2.1030290533095307e-06
            ],
            "target_residual": 6.33670051426966e-05,
            "energy_eV": -277.62222633655267
          }
        ],
        "iterations": 2
      },
      "parent": {
        "candidate_id": "bec_projection_04",
        "source": "MACEField_BEC_backprojection",
        "spacegroup": "P1",
        "spacegroup_number": 1,
        "pointgroup": "1",
        "has_inversion": false,
        "is_polar_point_group": true,
        "nonpolar_parent_hypothesis": false,
        "symmetry_tolerance_A": null,
        "target_reduced_polarization": [
          0.5,
          -0.5,
          0.0
        ],
        "formal_class": [
          0.5,
          0.5,
          0.0
        ],
        "target_residual": 6.33670051426966e-05,
        "parent_symmetrization_rmsd_A": 0.09900572425973898,
        "parent_cell_rmsd_A": 0.07635802922354974,
        "energy_eV": -277.62222633655267,
        "reduced_polarization": [
          0.4999872002942967,
          -0.4999379748265342,
          -2.1030290533095307e-06
        ],
        "cartesian_polarization_e_A2": [
          0.006708359535291934,
          -0.008914514387954944,
          -0.002635261103086562
        ],
        "ranking_score": 0.6182219655759118
      },
      "branch_status": "awaiting_branch_sampling"
    },
    {
      "orbit_id": 5,
      "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": [
              1.3333947163716728e-15,
              -0.04081853091385199,
              -6.738711745001055e-17
            ],
            "branch_aligned_reduced_polarization": [
              1.3333947163716728e-15,
              -0.040818530913852014,
              -5.551115123125783e-17
            ],
            "target_residual": 0.678857585618746,
            "energy_eV": -287.00197366041743,
            "max_atomic_step_A": 0.11093915762651581,
            "max_log_strain_component": 0.007382764258802977,
            "step_scale": 1.0,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 0.8949175130845075,
            "cell_principal_stretches": [
              1.0063705038080146,
              0.9947797177932151,
              0.9918396761556693
            ],
            "cell_volume_ratio": 0.9929475271267861,
            "cell_rmsd_from_input_A": 0.07296691036369111
          },
          {
            "iteration": 1,
            "reduced_polarization": [
              -0.008196764471569197,
              -0.4880430094730939,
              -0.48099920138657976
            ],
            "branch_aligned_reduced_polarization": [
              -0.008196764471569197,
              -0.4880430094730939,
              -0.48099920138657976
            ],
            "target_residual": 0.023899517112499435,
            "energy_eV": -279.412774297257,
            "max_atomic_step_A": 0.005003886763117299,
            "max_log_strain_component": 0.00020694597082003465,
            "step_scale": 1.0,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 0.8949175130845075,
            "cell_principal_stretches": [
              1.0065910972996905,
              0.9946105053736327,
              0.9915942795697211
            ],
            "cell_volume_ratio": 0.9927505578171721,
            "cell_rmsd_from_input_A": 0.07536700392840434
          },
          {
            "iteration": 2,
            "reduced_polarization": [
              -2.2020491542118273e-05,
              -0.4999411695157452,
              -0.4999142795827444
            ],
            "branch_aligned_reduced_polarization": [
              -2.2020491542118273e-05,
              -0.4999411695157452,
              -0.4999142795827444
            ],
            "target_residual": 0.00010627284629613578,
            "energy_eV": -278.8644516758512
          }
        ],
        "iterations": 2
      },
      "parent": {
        "candidate_id": "bec_projection_05",
        "source": "MACEField_BEC_backprojection",
        "spacegroup": "P1",
        "spacegroup_number": 1,
        "pointgroup": "1",
        "has_inversion": false,
        "is_polar_point_group": true,
        "nonpolar_parent_hypothesis": false,
        "symmetry_tolerance_A": null,
        "target_reduced_polarization": [
          0.0,
          -0.5,
          -0.5
        ],
        "formal_class": [
          0.0,
          0.5,
          0.5
        ],
        "target_residual": 0.00010627284629613578,
        "parent_symmetrization_rmsd_A": 0.09311937696351595,
        "parent_cell_rmsd_A": 0.07536700392840434,
        "energy_eV": -278.8644516758512,
        "reduced_polarization": [
          -2.2020491542118273e-05,
          -0.4999411695157452,
          -0.4999142795827444
        ],
        "cartesian_polarization_e_A2": [
          4.6383144633321676e-05,
          -0.00892861073964228,
          -0.007377238615780962
        ],
        "ranking_score": 0.6121736736382093
      },
      "branch_status": "awaiting_branch_sampling"
    },
    {
      "orbit_id": 6,
      "formal_class": [
        0.5,
        0.0,
        0.5
      ],
      "formal_classes_in_orbit": [
        [
          0.5,
          0.0,
          0.5
        ]
      ],
      "target_reduced_polarization": [
        0.5,
        0.0,
        -0.5
      ],
      "bec_backprojection": {
        "converged_to_target": true,
        "history": [
          {
            "iteration": 0,
            "reduced_polarization": [
              1.3333947163716728e-15,
              -0.04081853091385199,
              -6.738711745001055e-17
            ],
            "branch_aligned_reduced_polarization": [
              1.3322676295501878e-15,
              -0.04081853091385199,
              -5.551115123125783e-17
            ],
            "target_residual": 0.7082839490387762,
            "energy_eV": -287.00197366041743,
            "max_atomic_step_A": 0.12,
            "max_log_strain_component": 0.0048065570343329604,
            "step_scale": 0.8187107248503982,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 0.8949175130845075,
            "cell_principal_stretches": [
              1.0050530907444533,
              1.0002652984255518,
              0.9952209137081952
            ],
            "cell_volume_ratio": 1.0005152200077088,
            "cell_rmsd_from_input_A": 0.04580823731075361
          },
          {
            "iteration": 1,
            "reduced_polarization": [
              0.3788789722376871,
              -0.0024651456781876902,
              -0.37399703312525745
            ],
            "branch_aligned_reduced_polarization": [
              0.3788789722376871,
              -0.0024651456781876902,
              -0.37399703312525745
            ],
            "target_residual": 0.1747945307229352,
            "energy_eV": -280.01468532710777,
            "max_atomic_step_A": 0.0484161348083868,
            "max_log_strain_component": 0.0019640618611999764,
            "step_scale": 1.0,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 0.8949175130845075,
            "cell_principal_stretches": [
              1.0070424500789155,
              1.0002358551869999,
              0.9932225536686065
            ],
            "cell_volume_ratio": 1.0004531803522518,
            "cell_rmsd_from_input_A": 0.0644464572864671
          },
          {
            "iteration": 2,
            "reduced_polarization": [
              0.49786183481891744,
              0.0017583026611029656,
              -0.5000457220763694
            ],
            "branch_aligned_reduced_polarization": [
              0.49786183481891744,
              0.0017583026611029656,
              -0.5000457220763694
            ],
            "target_residual": 0.002768658357021164,
            "energy_eV": -273.2639237566096,
            "max_atomic_step_A": 0.0005510029993898884,
            "max_log_strain_component": 2.8954340593428726e-05,
            "step_scale": 1.0,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 0.8949175130845075,
            "cell_principal_stretches": [
              1.0070555384063786,
              1.0002208405125914,
              0.9931969860292141
            ],
            "cell_volume_ratio": 1.0004254111893525,
            "cell_rmsd_from_input_A": 0.06461088261276758
          },
          {
            "iteration": 3,
            "reduced_polarization": [
              0.5000006298442637,
              3.8005869219539276e-06,
              -0.4999822448294582
            ],
            "branch_aligned_reduced_polarization": [
              0.5000006298442637,
              3.8005869219539276e-06,
              -0.4999822448294582
            ],
            "target_residual": 1.8168303325206094e-05,
            "energy_eV": -273.1947726859802
          }
        ],
        "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,
          0.0,
          -0.5
        ],
        "formal_class": [
          0.5,
          0.0,
          0.5
        ],
        "target_residual": 1.8168303325206094e-05,
        "parent_symmetrization_rmsd_A": 0.10816461601091837,
        "parent_cell_rmsd_A": 0.06461088261276758,
        "energy_eV": -273.1947726859802,
        "reduced_polarization": [
          0.5000006298442637,
          3.8005869219539276e-06,
          -0.4999822448294582
        ],
        "cartesian_polarization_e_A2": [
          0.006651837648688066,
          -7.529581819085333e-05,
          -0.0098206645156119
        ],
        "ranking_score": 0.6243536732707606
      },
      "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": [
              1.3333947163716728e-15,
              -0.04081853091385199,
              -6.738711745001055e-17
            ],
            "branch_aligned_reduced_polarization": [
              1.3322676295501878e-15,
              -0.040818530913852014,
              -5.551115123125783e-17
            ],
            "target_residual": 0.8431177981469208,
            "energy_eV": -287.00197366041743,
            "max_atomic_step_A": 0.12,
            "max_log_strain_component": 0.005479492075628621,
            "step_scale": 0.742200601772615,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 0.8949175130845075,
            "cell_principal_stretches": [
              1.0057649147431131,
              0.9967121354686507,
              0.9923216560701876
            ],
            "cell_volume_ratio": 0.9947608779171013,
            "cell_rmsd_from_input_A": 0.064538359823715
          },
          {
            "iteration": 1,
            "reduced_polarization": [
              0.3419169882395991,
              -0.37500419098840254,
              -0.3414537472250215
            ],
            "branch_aligned_reduced_polarization": [
              0.3419169882395991,
              -0.37500419098840254,
              -0.3414537472250215
            ],
            "target_residual": 0.25641978306419766,
            "energy_eV": -279.2833233599023,
            "max_atomic_step_A": 0.059317984972410864,
            "max_log_strain_component": 0.0024810824612139233,
            "step_scale": 1.0,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 0.8949175130845075,
            "cell_principal_stretches": [
              1.0084962034885223,
              0.9955793040793562,
              0.9888176692543692
            ],
            "cell_volume_ratio": 0.9928104640152022,
            "cell_rmsd_from_input_A": 0.09393864431567106
          },
          {
            "iteration": 2,
            "reduced_polarization": [
              0.49364290315679316,
              -0.49691434762411657,
              -0.49820327435997136
            ],
            "branch_aligned_reduced_polarization": [
              0.49364290315679316,
              -0.49691434762411657,
              -0.49820327435997136
            ],
            "target_residual": 0.007291238158518881,
            "energy_eV": -269.3118007099465,
            "max_atomic_step_A": 0.0018211895440283518,
            "max_log_strain_component": 7.927092802851652e-05,
            "step_scale": 1.0,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 0.8949175130845075,
            "cell_principal_stretches": [
              1.0085722977939875,
              0.9955613338765472,
              0.9887101478371949
            ],
            "cell_volume_ratio": 0.9927594914234512,
            "cell_rmsd_from_input_A": 0.09476320215524346
          },
          {
            "iteration": 3,
            "reduced_polarization": [
              0.5000043763862132,
              -0.49996740484974117,
              -0.4999874632188914
            ],
            "branch_aligned_reduced_polarization": [
              0.5000043763862132,
              -0.49996740484974117,
              -0.4999874632188914
            ],
            "target_residual": 3.519612844116622e-05,
            "energy_eV": -268.97973855803997
          }
        ],
        "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": 3.519612844116622e-05,
        "parent_symmetrization_rmsd_A": 0.12899144663505432,
        "parent_cell_rmsd_A": 0.09476320215524346,
        "energy_eV": -268.97973855803997,
        "reduced_polarization": [
          0.5000043763862132,
          -0.49996740484974117,
          -0.4999874632188914
        ],
        "cartesian_polarization_e_A2": [
          0.006756570710303103,
          -0.008990002123720146,
          -0.010020170546159222
        ],
        "ranking_score": 0.6527526394307475
      },
      "branch_status": "awaiting_branch_sampling"
    }
  ],
  "sampled_polarization_branches": [
    {
      "orbit_id": 0,
      "candidate_id": "inversion_parent_endpoint_00",
      "formal_class": [
        0.0,
        0.0,
        0.0
      ],
      "construction": "MACEField-BEC-parent plus variable-cell P-N-P path and symmetric log-strain continuation beyond both polar endpoints",
      "geometry_diagnostics": {
        "collision_aware": false,
        "permutations_tested": 1,
        "selected_order": [
          0,
          1,
          2,
          3,
          4,
          5,
          6,
          7,
          8,
          9,
          10,
          11,
          12,
          13,
          14,
          15,
          16,
          17,
          18,
          19,
          20,
          21,
          22,
          23,
          24,
          25,
          26,
          27,
          28,
          29,
          30,
          31,
          32,
          33,
          34,
          35,
          36,
          37,
          38,
          39,
          40,
          41,
          42,
          43
        ],
        "endpoint_rmsd_A": 0.1289775037027087,
        "minimum_distance_A_by_image": [
          1.285168264762201,
          1.2836698465141825,
          1.2823321267459298,
          1.281215493765174,
          1.2803205260353159,
          1.2796476886451857,
          1.2791973321058752,
          1.2789696914402724,
          1.2789648855707747
        ],
        "minimum_distance_A": 1.2789648855707747,
        "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": [
          536.841096095629,
          536.841096095629,
          536.841096095629,
          536.841096095629,
          536.841096095629,
          536.841096095629,
          536.841096095629,
          536.841096095629,
          536.841096095629
        ],
        "cell_deformation_log_strain_norm": 0.0
      },
      "parent_reduced_polarization": [
        -1.0464351277394315e-15,
        -5.427261500202898e-16,
        -2.0032661952472797e-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": [
          -287.00197366041743,
          -286.9962692651054,
          -286.98232171420835,
          -286.9634528840513,
          -286.94248269280257,
          -286.9221220983991,
          -286.9050627742812,
          -286.8936994806504,
          -286.88971176339936
        ],
        "cartesian_polarizations_e_A2": [
          [
            5.9069146105772974e-18,
            -0.0007278769233131369,
            1.33390281796844e-17
          ],
          [
            -1.4140403903657687e-17,
            -0.0006457149521292147,
            4.5859372075116524e-17
          ],
          [
            2.7789642041009165e-17,
            -0.000559649080074024,
            3.210673061854268e-17
          ],
          [
            -5.764735046646553e-18,
            -0.00047074716626271067,
            1.2692757434544652e-17
          ],
          [
            -3.471766442890727e-17,
            -0.0003796642948605932,
            1.3778492286379429e-17
          ],
          [
            -2.1818100355917893e-17,
            -0.0002867455189746879,
            -2.1559592057861996e-17
          ],
          [
            1.3752641456573838e-17,
            -0.00019222604404736817,
            -3.675987998354887e-17
          ],
          [
            -2.585082980558992e-18,
            -9.64664127138447e-05,
            -1.680303937363345e-17
          ],
          [
            -1.4011149754629738e-17,
            -9.677904408467727e-18,
            -2.388616674036509e-17
          ]
        ],
        "raw_reduced_polarization": [
          [
            4.407271377160515e-16,
            -0.04081853091385284,
            1.06865235820373e-15
          ],
          [
            -1.0654206444221404e-15,
            -0.03621097865701172,
            2.7747635465547532e-15
          ],
          [
            2.077530602733219e-15,
            -0.031384499967288024,
            2.9265039940640885e-15
          ],
          [
            -4.3354812306772836e-16,
            -0.026398979199999426,
            7.196676026627325e-16
          ],
          [
            -2.6026515999934066e-15,
            -0.021291152748891613,
            3.830557731810339e-17
          ],
          [
            -1.6315896569739408e-15,
            -0.016080370809670137,
            -2.0475625236756264e-15
          ],
          [
            1.035158399940575e-15,
            -0.010779823442787696,
            -2.1610703219946405e-15
          ],
          [
            -1.914158326221565e-16,
            -0.0054097294795188485,
            -1.2194136380228025e-15
          ],
          [
            -1.0464351277394315e-15,
            -5.427261500202898e-16,
            -2.0032661952472797e-15
          ]
        ],
        "unwrapped_reduced_polarization": [
          [
            4.407271377160515e-16,
            -0.04081853091385284,
            1.06865235820373e-15
          ],
          [
            -1.0654206444221404e-15,
            -0.03621097865701172,
            2.7747635465547532e-15
          ],
          [
            2.0775306027332196e-15,
            -0.031384499967288024,
            2.9265039940640885e-15
          ],
          [
            -4.3354812306772826e-16,
            -0.026398979199999426,
            7.196676026627323e-16
          ],
          [
            -2.6026515999934066e-15,
            -0.021291152748891613,
            3.83055773181034e-17
          ],
          [
            -1.6315896569739408e-15,
            -0.016080370809670137,
            -2.0475625236756264e-15
          ],
          [
            1.035158399940575e-15,
            -0.010779823442787696,
            -2.1610703219946405e-15
          ],
          [
            -1.9141583262215651e-16,
            -0.0054097294795188485,
            -1.2194136380228025e-15
          ],
          [
            -1.0464351277394315e-15,
            -5.429684479807406e-16,
            -2.0032661952472797e-15
          ]
        ],
        "berry_integer_shifts": [
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ]
        ],
        "folded_reduced_polarization": [
          [
            4.440892098500626e-16,
            -0.040818530913852846,
            1.1102230246251565e-15
          ],
          [
            -1.0547118733938987e-15,
            -0.03621097865701173,
            2.7755575615628914e-15
          ],
          [
            2.1094237467877974e-15,
            -0.03138449996728804,
            2.886579864025407e-15
          ],
          [
            -4.440892098500626e-16,
            -0.02639897919999945,
            6.661338147750939e-16
          ],
          [
            -2.609024107869118e-15,
            -0.021291152748891595,
            0.0
          ],
          [
            -1.609823385706477e-15,
            -0.01608037080967012,
            -2.0539125955565396e-15
          ],
          [
            9.992007221626409e-16,
            -0.010779823442787717,
            -2.1649348980190553e-15
          ],
          [
            -1.6653345369377348e-16,
            -0.005409729479518843,
            -1.2212453270876722e-15
          ],
          [
            -1.0547118733938987e-15,
            -5.551115123125783e-16,
            -1.9984014443252818e-15
          ]
        ]
      },
      "reflected": {
        "reached": true,
        "construction": "reflect_displacements_about_reconstructed_parent",
        "energies_eV": [
          -286.8897117633994,
          -286.8936994806504,
          -286.9050627742812,
          -286.922122098399,
          -286.9424826928026,
          -286.9634528840512,
          -286.9823217142084,
          -286.9962692651054,
          -287.00197366041743
        ],
        "cartesian_polarizations_e_A2": [
          [
            -1.5122735436270104e-17,
            3.6827738411788545e-17,
            -3.469181359910168e-17
          ],
          [
            -3.2572045555043303e-18,
            9.646641271378999e-05,
            2.4299780017254527e-18
          ],
          [
            -9.409702049234731e-18,
            0.00019222604404732502,
            -2.7712089551592397e-17
          ],
          [
            -3.02713217023458e-17,
            0.00028674551897468677,
            -6.348963800252885e-17
          ],
          [
            2.1456188738639635e-18,
            0.0003796642948605996,
            -4.6376388671228323e-17
          ],
          [
            -1.636357526693842e-17,
            0.000470747166262764,
            -5.0977836376623324e-17
          ],
          [
            -4.4592681414642616e-17,
            0.0005596490800740155,
            -3.443330530104578e-17
          ],
          [
            -2.0835768823305477e-17,
            0.0006457149521291456,
            -1.2010295527677077e-16
          ],
          [
            -2.049970803583281e-17,
            0.000727876923313119,
            -8.773771636017219e-17
          ]
        ],
        "raw_reduced_polarization": [
          [
            -1.1282663897425507e-15,
            2.065258741830132e-15,
            -2.7730641818028676e-15
          ],
          [
            -2.443319600807023e-16,
            0.00540972947951578,
            8.156019929617502e-17
          ],
          [
            -7.012153242867743e-16,
            0.010779823442785276,
            -2.145434897751141e-15
          ],
          [
            -2.2592554904663674e-15,
            0.016080370809670074,
            -5.142740885132129e-15
          ],
          [
            1.669210157908785e-16,
            0.021291152748891966,
            -3.1233224939226175e-15
          ],
          [
            -1.2190495299372014e-15,
            0.026398979200002417,
            -3.921943297450483e-15
          ],
          [
            -3.3359909357947685e-15,
            0.031384499967287545,
            -3.5246330360071715e-15
          ],
          [
            -1.5448562664759107e-15,
            0.03621097865700785,
            -8.777557514752388e-15
          ],
          [
            -1.5239977315815763e-15,
            0.04081853091385184,
            -6.549986682782339e-15
          ]
        ],
        "unwrapped_reduced_polarization": [
          [
            -1.1282663897425507e-15,
            2.065258741830132e-15,
            -2.7730641818028676e-15
          ],
          [
            -2.4433196008070226e-16,
            0.00540972947951578,
            8.15601992961752e-17
          ],
          [
            -7.012153242867743e-16,
            0.010779823442785276,
            -2.145434897751141e-15
          ],
          [
            -2.2592554904663674e-15,
            0.016080370809670074,
            -5.142740885132129e-15
          ],
          [
            1.669210157908786e-16,
            0.021291152748891966,
            -3.1233224939226175e-15
          ],
          [
            -1.2190495299372014e-15,
            0.026398979200002417,
            -3.921943297450483e-15
          ],
          [
            -3.3359909357947685e-15,
            0.031384499967287545,
            -3.5246330360071715e-15
          ],
          [
            -1.544856266475911e-15,
            0.03621097865700785,
            -8.777557514752388e-15
          ],
          [
            -1.5239977315815763e-15,
            0.04081853091385184,
            -6.549986682782339e-15
          ]
        ],
        "gauge_integer_shift": [
          0,
          0,
          0
        ],
        "expected_opposite_endpoint_reduced_polarization": [
          -2.5335973931949147e-15,
          0.04081853091385176,
          -5.075184748698289e-15
        ],
        "actual_opposite_endpoint_branch_residual": 1.7892080844070694e-15
      },
      "pnp_branch": {
        "construction": "incoming_path_concatenated_with_parent_reflection",
        "reduced_polarization": [
          [
            4.407271377160515e-16,
            -0.04081853091385284,
            1.06865235820373e-15
          ],
          [
            -1.0654206444221404e-15,
            -0.03621097865701172,
            2.7747635465547532e-15
          ],
          [
            2.077530602733219e-15,
            -0.031384499967288024,
            2.9265039940640885e-15
          ],
          [
            -4.3354812306772836e-16,
            -0.026398979199999426,
            7.196676026627325e-16
          ],
          [
            -2.6026515999934066e-15,
            -0.021291152748891613,
            3.830557731810339e-17
          ],
          [
            -1.6315896569739408e-15,
            -0.016080370809670137,
            -2.0475625236756264e-15
          ],
          [
            1.035158399940575e-15,
            -0.010779823442787696,
            -2.1610703219946405e-15
          ],
          [
            -1.914158326221565e-16,
            -0.0054097294795188485,
            -1.2194136380228025e-15
          ],
          [
            -1.0464351277394315e-15,
            -5.427261500202898e-16,
            -2.0032661952472797e-15
          ],
          [
            -2.443319600807023e-16,
            0.00540972947951578,
            8.156019929617502e-17
          ],
          [
            -7.012153242867743e-16,
            0.010779823442785276,
            -2.145434897751141e-15
          ],
          [
            -2.2592554904663674e-15,
            0.016080370809670074,
            -5.142740885132129e-15
          ],
          [
            1.669210157908785e-16,
            0.021291152748891966,
            -3.1233224939226175e-15
          ],
          [
            -1.2190495299372014e-15,
            0.026398979200002417,
            -3.921943297450483e-15
          ],
          [
            -3.3359909357947685e-15,
            0.031384499967287545,
            -3.5246330360071715e-15
          ],
          [
            -1.5448562664759107e-15,
            0.03621097865700785,
            -8.777557514752388e-15
          ],
          [
            -1.5239977315815763e-15,
            0.04081853091385184,
            -6.549986682782339e-15
          ]
        ],
        "unwrapped_reduced_polarization": [
          [
            4.407271377160515e-16,
            -0.04081853091385284,
            1.06865235820373e-15
          ],
          [
            -1.0654206444221404e-15,
            -0.03621097865701172,
            2.7747635465547532e-15
          ],
          [
            2.0775306027332196e-15,
            -0.031384499967288024,
            2.9265039940640885e-15
          ],
          [
            -4.3354812306772826e-16,
            -0.026398979199999426,
            7.196676026627323e-16
          ],
          [
            -2.6026515999934066e-15,
            -0.021291152748891613,
            3.83055773181034e-17
          ],
          [
            -1.6315896569739408e-15,
            -0.016080370809670137,
            -2.0475625236756264e-15
          ],
          [
            1.035158399940575e-15,
            -0.010779823442787696,
            -2.1610703219946405e-15
          ],
          [
            -1.9141583262215651e-16,
            -0.0054097294795188485,
            -1.2194136380228025e-15
          ],
          [
            -1.0464351277394315e-15,
            -5.429684479807406e-16,
            -2.0032661952472797e-15
          ],
          [
            -2.4433196008070226e-16,
            0.00540972947951578,
            8.15601992961752e-17
          ],
          [
            -7.012153242867743e-16,
            0.010779823442785276,
            -2.145434897751141e-15
          ],
          [
            -2.2592554904663674e-15,
            0.016080370809670074,
            -5.142740885132129e-15
          ],
          [
            1.669210157908786e-16,
            0.021291152748891966,
            -3.1233224939226175e-15
          ],
          [
            -1.2190495299372014e-15,
            0.026398979200002417,
            -3.921943297450483e-15
          ],
          [
            -3.3359909357947685e-15,
            0.031384499967287545,
            -3.5246330360071715e-15
          ],
          [
            -1.544856266475911e-15,
            0.03621097865700785,
            -8.777557514752388e-15
          ],
          [
            -1.5239977315815763e-15,
            0.04081853091385184,
            -6.549986682782339e-15
          ]
        ],
        "berry_integer_shifts": [
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            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,
            -0.040818530913852846,
            1.1102230246251565e-15
          ],
          [
            -1.0547118733938987e-15,
            -0.03621097865701173,
            2.7755575615628914e-15
          ],
          [
            2.1094237467877974e-15,
            -0.03138449996728804,
            2.886579864025407e-15
          ],
          [
            -4.440892098500626e-16,
            -0.02639897919999945,
            6.661338147750939e-16
          ],
          [
            -2.609024107869118e-15,
            -0.021291152748891595,
            0.0
          ],
          [
            -1.609823385706477e-15,
            -0.01608037080967012,
            -2.0539125955565396e-15
          ],
          [
            9.992007221626409e-16,
            -0.010779823442787717,
            -2.1649348980190553e-15
          ],
          [
            -1.6653345369377348e-16,
            -0.005409729479518843,
            -1.2212453270876722e-15
          ],
          [
            -1.0547118733938987e-15,
            -5.551115123125783e-16,
            -1.9984014443252818e-15
          ],
          [
            -2.220446049250313e-16,
            0.00540972947951579,
            1.1102230246251565e-16
          ],
          [
            -7.216449660063518e-16,
            0.010779823442785275,
            -2.1649348980190553e-15
          ],
          [
            -2.275957200481571e-15,
            0.016080370809670064,
            -5.162537064506978e-15
          ],
          [
            2.220446049250313e-16,
            0.02129115274889193,
            -3.1086244689504383e-15
          ],
          [
            -1.2212453270876722e-15,
            0.026398979200002448,
            -3.941291737419306e-15
          ],
          [
            -3.3306690738754696e-15,
            0.03138449996728754,
            -3.497202527569243e-15
          ],
          [
            -1.5543122344752192e-15,
            0.03621097865700784,
            -8.770761894538737e-15
          ],
          [
            -1.4988010832439613e-15,
            0.04081853091385179,
            -6.5503158452884236e-15
          ]
        ]
      },
      "incoming_structure_ids": [
        "incoming_00_000",
        "incoming_00_001",
        "incoming_00_002",
        "incoming_00_003",
        "incoming_00_004",
        "incoming_00_005",
        "incoming_00_006",
        "incoming_00_007",
        "incoming_00_008"
      ],
      "reflected_structure_ids": [
        "reflected_00_001",
        "reflected_00_002",
        "reflected_00_003",
        "reflected_00_004",
        "reflected_00_005",
        "reflected_00_006",
        "reflected_00_007",
        "reflected_00_008"
      ],
      "positive_extension_structure_ids": [
        "extension_plus_00_000",
        "extension_plus_00_001",
        "extension_plus_00_002",
        "extension_plus_00_003"
      ],
      "negative_extension_structure_ids": [
        "extension_minus_00_000",
        "extension_minus_00_001",
        "extension_minus_00_002",
        "extension_minus_00_003"
      ],
      "extension": {
        "enabled": true,
        "fraction_beyond_polar_endpoint": 0.35,
        "images_per_side": 4,
        "construction": "continue fractional atomic displacements and symmetric log strain beyond +P; reflect these structures about N for the -P side",
        "positive_path_coordinates": [
          1.35,
          1.2625,
          1.175,
          1.0875
        ],
        "negative_path_coordinates": [
          -1.0875,
          -1.175,
          -1.2625,
          -1.35
        ]
      },
      "branch_coordinates": [
        1.35,
        1.2625,
        1.175,
        1.0875,
        1.0,
        0.875,
        0.75,
        0.625,
        0.5,
        0.375,
        0.25,
        0.125,
        0.0,
        -0.125,
        -0.25,
        -0.375,
        -0.5,
        -0.625,
        -0.75,
        -0.875,
        -1.0,
        -1.0875,
        -1.175,
        -1.2625,
        -1.35
      ],
      "parent": {
        "candidate_id": "inversion_parent_endpoint_00",
        "source": "same_species_inversion_center_projection_from_endpoint",
        "spacegroup": "P2_1/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": 2.532078477257827e-15,
        "parent_symmetrization_rmsd_A": 0.1289775037027087,
        "parent_cell_rmsd_A": 0.0,
        "energy_eV": -286.8897117633994,
        "reduced_polarization": [
          1.7002729874093697e-15,
          9.687525869811251e-16,
          1.606863904783386e-15
        ],
        "cartesian_polarization_e_A2": [
          2.272287939911354e-17,
          1.7274817017585465e-17,
          1.4786674648797436e-17
        ],
        "ranking_score": 0.12897750370271374
      }
    }
  ],
  "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": 50,
      "full_response": 18,
      "energy_polarization": 32
    },
    "model_evaluations_for_recovery_and_path_properties": {
      "total": 75,
      "full_response": 43,
      "energy_polarization": 32
    },
    "elapsed_seconds": 1131.4540858819964
  }
}
