{
  "schema": "ferrofinder.endpoint_parent_recovery.v4_variable_cell",
  "status": "complete",
  "input_atom_count": 6,
  "input_formula": "Ag4S2",
  "input_spacegroup": "P2_1",
  "input_pointgroup": "2",
  "input_is_polar_point_group": true,
  "input_energy_eV": -18.99747221400674,
  "input_cartesian_polarization_e_A2": [
    -1.5400453686657833e-16,
    0.012105075152355541,
    -9.914314731708195e-17
  ],
  "input_reduced_polarization": [
    -4.713130945575961e-15,
    0.23679769298653291,
    -3.642309135131839e-15
  ],
  "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/m",
      "spacegroup_number": 11,
      "pointgroup": "2/m",
      "has_inversion": true,
      "is_polar_point_group": false,
      "nonpolar_parent_hypothesis": true,
      "symmetry_tolerance_A": null,
      "target_reduced_polarization": [
        0.0,
        0.0,
        0.0
      ],
      "formal_class": [
        0.0,
        0.0,
        0.0
      ],
      "target_residual": 5.2896710220797375e-15,
      "parent_symmetrization_rmsd_A": 0.3798557983484948,
      "parent_cell_rmsd_A": 0.0,
      "energy_eV": -18.754138156938062,
      "reduced_polarization": [
        -2.2315415632089064e-15,
        -3.621418348508111e-15,
        3.1442281912402646e-15
      ],
      "cartesian_polarization_e_A2": [
        -7.296673878451905e-17,
        -1.8512655555855897e-16,
        1.3306341004052801e-16
      ],
      "ranking_score": 0.3798557983485054
    },
    {
      "candidate_id": "inversion_parent_endpoint_01",
      "source": "same_species_inversion_center_projection_from_endpoint",
      "spacegroup": "P2_1/c",
      "spacegroup_number": 14,
      "pointgroup": "2/m",
      "has_inversion": true,
      "is_polar_point_group": false,
      "nonpolar_parent_hypothesis": true,
      "symmetry_tolerance_A": null,
      "target_reduced_polarization": [
        0.0,
        0.0,
        0.0
      ],
      "formal_class": [
        0.0,
        0.0,
        0.0
      ],
      "target_residual": 2.4758358181913277e-15,
      "parent_symmetrization_rmsd_A": 0.4067551146382107,
      "parent_cell_rmsd_A": 0.0,
      "energy_eV": -18.978308358394397,
      "reduced_polarization": [
        -1.7604166529900137e-15,
        6.494696618727681e-16,
        -1.6152044343739995e-15
      ],
      "cartesian_polarization_e_A2": [
        -5.752012759913431e-17,
        3.320082627068464e-17,
        -4.6449882656442e-17
      ],
      "ranking_score": 0.4067551146382156
    },
    {
      "candidate_id": "inversion_parent_endpoint_02",
      "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": 1.0762098885646544e-15,
      "parent_symmetrization_rmsd_A": 0.7666521738112465,
      "parent_cell_rmsd_A": 0.0,
      "energy_eV": -16.945409807575636,
      "reduced_polarization": [
        -5.948981799593074e-16,
        -2.517169428640294e-16,
        -8.607917636691444e-16
      ],
      "cartesian_polarization_e_A2": [
        -1.9434580170946938e-17,
        -1.2867745762470552e-17,
        -2.7341529132869536e-17
      ],
      "ranking_score": 0.7666521738112486
    },
    {
      "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": 6.415464039825651e-06,
      "parent_symmetrization_rmsd_A": 0.1249724847177829,
      "parent_cell_rmsd_A": 0.0686763795629701,
      "energy_eV": -18.714394147368736,
      "reduced_polarization": [
        3.849892975345772e-15,
        6.415464039825651e-06,
        -7.484490264748843e-15
      ],
      "cartesian_polarization_e_A2": [
        1.2637249657316842e-16,
        3.2253693824325006e-07,
        -3.0709059038509854e-16
      ],
      "ranking_score": 0.642154410536605
    },
    {
      "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": 3.129463677665325e-15,
      "parent_symmetrization_rmsd_A": 0.4077347138122603,
      "parent_cell_rmsd_A": 0.0686763795629701,
      "energy_eV": -18.98104804241658,
      "reduced_polarization": [
        -1.8784696503755475e-15,
        -3.169168735160734e-16,
        -2.482832732530596e-15
      ],
      "cartesian_polarization_e_A2": [
        -6.140310200495484e-17,
        -1.5932970308456945e-17,
        -7.790723232088272e-17
      ],
      "ranking_score": 0.4249038087030091
    },
    {
      "candidate_id": "inversion_parent_bec_00_01",
      "source": "same_species_inversion_center_projection_after_BEC",
      "spacegroup": "P2_1/m",
      "spacegroup_number": 11,
      "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": 6.373840463422241e-15,
      "parent_symmetrization_rmsd_A": 0.3820280564493407,
      "parent_cell_rmsd_A": 0.0686763795629701,
      "energy_eV": -18.736464841486203,
      "reduced_polarization": [
        1.8229000655634748e-15,
        -5.179637489928791e-15,
        3.236391984456071e-15
      ],
      "cartesian_polarization_e_A2": [
        5.955236104606821e-17,
        -2.604058579146779e-16,
        1.0630476106584125e-16
      ],
      "ranking_score": 0.399197151340096
    },
    {
      "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": 6.195905394312806e-05,
      "parent_symmetrization_rmsd_A": 0.239685878996376,
      "parent_cell_rmsd_A": 0.3583502939256202,
      "energy_eV": -17.426749359770405,
      "reduced_polarization": [
        -1.436770537686837e-14,
        0.49993804094605687,
        -2.635481432898041e-15
      ],
      "cartesian_polarization_e_A2": [
        -2.3645648655239104e-15,
        0.027806552047724104,
        -2.068489487793817e-15
      ],
      "ranking_score": 0.8293973705856673
    },
    {
      "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": 0.01266240768814133,
      "parent_symmetrization_rmsd_A": 0.30891532811891087,
      "parent_cell_rmsd_A": 0.4295557551235941,
      "energy_eV": -17.718393592239025,
      "reduced_polarization": [
        -0.48863939731702305,
        -0.005014246671537236,
        0.0024760059485419883
      ],
      "cartesian_polarization_e_A2": [
        -0.015954807824526532,
        -0.0009842400145073282,
        0.0038357386493846346
      ],
      "ranking_score": 0.941629082276092
    },
    {
      "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": 0.005055468229232899,
      "parent_symmetrization_rmsd_A": 0.2817957869398434,
      "parent_cell_rmsd_A": 0.4605196957241978,
      "energy_eV": -15.993741941480664,
      "reduced_polarization": [
        0.0028203596532944374,
        -0.0005242316875878685,
        -0.4958372471151195
      ],
      "cartesian_polarization_e_A2": [
        0.00029666650802839806,
        -0.0015085321384022208,
        -0.018412626793930895
      ],
      "ranking_score": 0.9070366473293587
    },
    {
      "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": 0.08547465255969858,
      "parent_symmetrization_rmsd_A": 0.2881135550032468,
      "parent_cell_rmsd_A": 0.5173434687201702,
      "energy_eV": -16.566985654709516,
      "reduced_polarization": [
        -0.4463801407545038,
        0.43415348948097,
        -0.009750075751584118
      ],
      "cartesian_polarization_e_A2": [
        -0.013044963578802988,
        0.02323780514370754,
        0.0037405894104045622
      ],
      "ranking_score": 1.0883987273026865
    },
    {
      "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": 0.15353697983003378,
      "parent_symmetrization_rmsd_A": 0.2670241302290601,
      "parent_cell_rmsd_A": 0.5763725478462561,
      "energy_eV": -16.63839159903634,
      "reduced_polarization": [
        -0.005775496266739392,
        0.4056545443707114,
        -0.3790075092400234
      ],
      "cartesian_polarization_e_A2": [
        0.0008559685730964574,
        0.020918058422845096,
        -0.01206065411507787
      ],
      "ranking_score": 1.2181912268506916
    },
    {
      "candidate_id": "bec_projection_06",
      "source": "MACEField_BEC_backprojection",
      "spacegroup": "P1",
      "spacegroup_number": 1,
      "pointgroup": "1",
      "has_inversion": false,
      "is_polar_point_group": true,
      "nonpolar_parent_hypothesis": false,
      "symmetry_tolerance_A": null,
      "target_reduced_polarization": [
        -0.5,
        0.0,
        -0.5
      ],
      "formal_class": [
        0.5,
        0.0,
        0.5
      ],
      "target_residual": 0.23553313306102092,
      "parent_symmetrization_rmsd_A": 0.25115266653644164,
      "parent_cell_rmsd_A": 0.5470175153856808,
      "energy_eV": -17.847594845926977,
      "reduced_polarization": [
        -0.3292629267382977,
        0.015568586480918047,
        -0.3384997594473777
      ],
      "cartesian_polarization_e_A2": [
        -0.010535436352585137,
        -0.0008163650698659112,
        -0.009674447134535602
      ],
      "ranking_score": 1.3589733115049036
    },
    {
      "candidate_id": "bec_projection_07",
      "source": "MACEField_BEC_backprojection",
      "spacegroup": "P1",
      "spacegroup_number": 1,
      "pointgroup": "1",
      "has_inversion": false,
      "is_polar_point_group": true,
      "nonpolar_parent_hypothesis": false,
      "symmetry_tolerance_A": null,
      "target_reduced_polarization": [
        -0.5,
        0.5,
        -0.5
      ],
      "formal_class": [
        0.5,
        0.5,
        0.5
      ],
      "target_residual": 0.2682250066224924,
      "parent_symmetrization_rmsd_A": 0.23055265422382437,
      "parent_cell_rmsd_A": 0.6126066074353149,
      "energy_eV": -17.12141223053661,
      "reduced_polarization": [
        -0.347335369569506,
        0.3754499390135527,
        -0.317996024490043
      ],
      "cartesian_polarization_e_A2": [
        -0.009784089423988781,
        0.01870643819913293,
        -0.007290843792702864
      ],
      "ranking_score": 1.4201543193276378
    }
  ],
  "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": [
              -4.713130945575961e-15,
              0.23679769298653291,
              -3.642309135131839e-15
            ],
            "branch_aligned_reduced_polarization": [
              -4.713130945575961e-15,
              0.23679769298653291,
              -3.642309135131839e-15
            ],
            "target_residual": 0.23679769298653291,
            "energy_eV": -18.99747221400674,
            "max_atomic_step_A": 0.12,
            "max_log_strain_component": 0.009768874667392789,
            "step_scale": 0.6364156172543186,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 3.058474547756647,
            "cell_principal_stretches": [
              1.0086233298904197,
              1.0059620984678572,
              0.9902786857920246
            ],
            "cell_volume_ratio": 1.0047732379569934,
            "cell_rmsd_from_input_A": 0.05991852510575849
          },
          {
            "iteration": 1,
            "reduced_polarization": [
              1.0323951858611963e-13,
              0.04777625053738559,
              8.20926066489499e-14
            ],
            "branch_aligned_reduced_polarization": [
              1.0323951858611963e-13,
              0.04777625053738559,
              8.20926066489499e-14
            ],
            "target_residual": 0.04777625053738559,
            "energy_eV": -18.80137644984835,
            "max_atomic_step_A": 0.02716640933234458,
            "max_log_strain_component": 0.0014726213018677109,
            "step_scale": 1.0,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 3.058474547756647,
            "cell_principal_stretches": [
              1.0099296987194033,
              1.0068639404611113,
              0.9888214535435148
            ],
            "cell_volume_ratio": 1.0054947592144485,
            "cell_rmsd_from_input_A": 0.0688960174453537
          },
          {
            "iteration": 2,
            "reduced_polarization": [
              5.419750787958998e-16,
              -0.0012593727733096324,
              2.377729956012977e-15
            ],
            "branch_aligned_reduced_polarization": [
              5.419750787958998e-16,
              -0.0012593727733096324,
              2.377729956012977e-15
            ],
            "target_residual": 0.0012593727733096324,
            "energy_eV": -18.71188806835834,
            "max_atomic_step_A": 0.0006894729366464017,
            "max_log_strain_component": 3.605594495198208e-05,
            "step_scale": 1.0,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 3.058474547756647,
            "cell_principal_stretches": [
              1.0098976931345278,
              1.006841849934788,
              0.9888571070781682
            ],
            "cell_volume_ratio": 1.0054770871622885,
            "cell_rmsd_from_input_A": 0.0686763795629701
          },
          {
            "iteration": 3,
            "reduced_polarization": [
              3.849892975345772e-15,
              6.415464039825651e-06,
              -7.484490264748843e-15
            ],
            "branch_aligned_reduced_polarization": [
              3.849892975345772e-15,
              6.415464039825651e-06,
              -7.484490264748843e-15
            ],
            "target_residual": 6.415464039825651e-06,
            "energy_eV": -18.714394147368736
          }
        ],
        "iterations": 3
      },
      "parent": {
        "candidate_id": "inversion_parent_endpoint_00",
        "source": "same_species_inversion_center_projection_from_endpoint",
        "spacegroup": "P2_1/m",
        "spacegroup_number": 11,
        "pointgroup": "2/m",
        "has_inversion": true,
        "is_polar_point_group": false,
        "nonpolar_parent_hypothesis": true,
        "symmetry_tolerance_A": null,
        "target_reduced_polarization": [
          0.0,
          0.0,
          0.0
        ],
        "formal_class": [
          0.0,
          0.0,
          0.0
        ],
        "target_residual": 5.2896710220797375e-15,
        "parent_symmetrization_rmsd_A": 0.3798557983484948,
        "parent_cell_rmsd_A": 0.0,
        "energy_eV": -18.754138156938062,
        "reduced_polarization": [
          -2.2315415632089064e-15,
          -3.621418348508111e-15,
          3.1442281912402646e-15
        ],
        "cartesian_polarization_e_A2": [
          -7.296673878451905e-17,
          -1.8512655555855897e-16,
          1.3306341004052801e-16
        ],
        "ranking_score": 0.3798557983485054
      },
      "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": [
          -18.997472214006734,
          -19.026888943137703,
          -19.037327146766835,
          -19.024644601042404,
          -18.984937912788485,
          -18.920621293957417,
          -18.844348257586276,
          -18.779796540495724,
          -18.754138156938048
        ],
        "cartesian_polarizations_e_A2": [
          [
            -2.2489897664226947e-16,
            0.0121050751523554,
            -2.461673085749768e-16
          ],
          [
            -6.129642331375143e-17,
            0.013274416611650854,
            -3.99190230121584e-17
          ],
          [
            -2.048303967673046e-16,
            0.013678280610451475,
            -2.5951455021736177e-16
          ],
          [
            -6.76223887091208e-17,
            0.013303784642615484,
            -3.765585435778057e-17
          ],
          [
            2.3373351452200947e-16,
            0.012143027285106266,
            -1.7047386056831582e-16
          ],
          [
            -2.792150243473375e-16,
            0.010170959309406537,
            4.122784343878655e-17
          ],
          [
            5.724998682809275e-16,
            0.007392894726119755,
            -1.6632926255066002e-17
          ],
          [
            -1.0754141172127921e-16,
            0.003906604119045956,
            3.5578101930508395e-16
          ],
          [
            -3.3265852510132004e-17,
            2.501886615769754e-16,
            1.0677793313907945e-16
          ]
        ],
        "raw_reduced_polarization": [
          [
            -6.883630006758619e-15,
            0.2367976929865302,
            -8.061428247244527e-15
          ],
          [
            -1.875910099077802e-15,
            0.2596721779764716,
            -1.4620995659667316e-15
          ],
          [
            -6.269676238345938e-15,
            0.2675725058961783,
            -8.297299458818012e-15
          ],
          [
            -2.069455430736073e-15,
            0.26024667106242555,
            -1.440336471892133e-15
          ],
          [
            7.150432453342821e-15,
            0.23754010700430475,
            -3.153470901728153e-15
          ],
          [
            -8.543186168154617e-15,
            0.19896280441172667,
            -6.262559413469641e-16
          ],
          [
            1.7517442536284898e-14,
            0.1446187151755773,
            3.1207478463022595e-15
          ],
          [
            -3.2875896156829476e-15,
            0.07642041302170338,
            8.953021583900741e-15
          ],
          [
            -1.0169798432458124e-15,
            4.894153660936821e-15,
            2.6808282263887977e-15
          ]
        ],
        "unwrapped_reduced_polarization": [
          [
            -6.883630006758619e-15,
            0.2367976929865302,
            -8.061428247244527e-15
          ],
          [
            -1.875910099077802e-15,
            0.2596721779764716,
            -1.4620995659667316e-15
          ],
          [
            -6.269676238345938e-15,
            0.2675725058961783,
            -8.297299458818012e-15
          ],
          [
            -2.069455430736073e-15,
            0.26024667106242555,
            -1.4403364718921333e-15
          ],
          [
            7.150432453342821e-15,
            0.23754010700430475,
            -3.153470901728153e-15
          ],
          [
            -8.543186168154616e-15,
            0.19896280441172667,
            -6.262559413469642e-16
          ],
          [
            1.75174425362849e-14,
            0.1446187151755773,
            3.12074784630226e-15
          ],
          [
            -3.2875896156829487e-15,
            0.07642041302170338,
            8.953021583900741e-15
          ],
          [
            -1.0169798432458126e-15,
            4.898859096158503e-15,
            2.6808282263887977e-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": [
          [
            -6.8833827526759706e-15,
            0.2367976929865302,
            -8.049116928532385e-15
          ],
          [
            -1.887379141862766e-15,
            0.2596721779764716,
            -1.4432899320127035e-15
          ],
          [
            -6.2727600891321345e-15,
            0.2675725058961783,
            -8.271161533457416e-15
          ],
          [
            -2.0539125955565396e-15,
            0.2602466710624256,
            -1.4432899320127035e-15
          ],
          [
            7.105427357601002e-15,
            0.23754010700430472,
            -3.164135620181696e-15
          ],
          [
            -8.548717289613705e-15,
            0.19896280441172665,
            -6.106226635438361e-16
          ],
          [
            1.7541523789077473e-14,
            0.14461871517557734,
            3.1086244689504383e-15
          ],
          [
            -3.2751579226442118e-15,
            0.07642041302170344,
            8.992806499463768e-15
          ],
          [
            -9.992007221626409e-16,
            4.884981308350689e-15,
            2.6645352591003757e-15
          ]
        ]
      },
      "reflected": {
        "reached": true,
        "construction": "reflect_displacements_about_reconstructed_parent",
        "energies_eV": [
          -18.754138156938044,
          -18.77979654049573,
          -18.84434825758626,
          -18.9206212939574,
          -18.98493791278848,
          -19.024644601042432,
          -19.037327146766824,
          -19.02688894313773,
          -18.997472214006734
        ],
        "cartesian_polarizations_e_A2": [
          [
            2.366783604819228e-16,
            -4.562913219895322e-16,
            3.089906890531278e-16
          ],
          [
            1.0514190760579427e-16,
            -0.003906604119046053,
            5.250551278156573e-16
          ],
          [
            1.1561247101881942e-16,
            -0.007392894726120179,
            5.953496915624772e-16
          ],
          [
            -2.5958271794791533e-17,
            -0.010170959309406157,
            3.5261803660739926e-16
          ],
          [
            1.5149596438220773e-16,
            -0.012143027285106026,
            -2.6277296773782143e-16
          ],
          [
            2.3995041154849314e-16,
            -0.01330378464261533,
            2.308704698387604e-16
          ],
          [
            -4.569964656309938e-17,
            -0.013678280610451616,
            -2.289481398371503e-16
          ],
          [
            3.4029331092331756e-17,
            -0.013274416611650965,
            -2.1494648798145131e-16
          ],
          [
            -1.644751002796035e-16,
            -0.012105075152355305,
            1.5847633999089115e-16
          ]
        ],
        "raw_reduced_polarization": [
          [
            7.244591182515333e-15,
            -8.925903475772403e-15,
            9.834246640763546e-15
          ],
          [
            3.2216110625495343e-15,
            -0.07642041302170526,
            1.4858326649136512e-14
          ],
          [
            3.54258754651933e-15,
            -0.14461871517558564,
            1.6825074902502153e-14
          ],
          [
            -7.913023497188623e-16,
            -0.19896280441171926,
            9.376295341409098e-15
          ],
          [
            4.633314690769209e-15,
            -0.2375401070043001,
            -6.163042787325854e-15
          ],
          [
            7.344050666638752e-15,
            -0.2602466710624225,
            7.741529339561609e-15
          ],
          [
            -1.4002707640410816e-15,
            -0.26757250589618103,
            -6.477995373289205e-15
          ],
          [
            1.0394271221406132e-15,
            -0.25967217797647374,
            -5.601988522321094e-15
          ],
          [
            -5.031336786194623e-15,
            -0.2367976929865283,
            3.2609045509363288e-15
          ]
        ],
        "unwrapped_reduced_polarization": [
          [
            7.244591182515333e-15,
            -8.925903475772403e-15,
            9.834246640763546e-15
          ],
          [
            3.2216110625495343e-15,
            -0.07642041302170526,
            1.4858326649136512e-14
          ],
          [
            3.54258754651933e-15,
            -0.14461871517558564,
            1.6825074902502153e-14
          ],
          [
            -7.913023497188622e-16,
            -0.19896280441171926,
            9.376295341409098e-15
          ],
          [
            4.633314690769209e-15,
            -0.2375401070043001,
            -6.163042787325853e-15
          ],
          [
            7.344050666638752e-15,
            -0.2602466710624225,
            7.741529339561609e-15
          ],
          [
            -1.4002707640410812e-15,
            -0.26757250589618103,
            -6.477995373289205e-15
          ],
          [
            1.0394271221406132e-15,
            -0.25967217797647374,
            -5.601988522321094e-15
          ],
          [
            -5.0313367861946226e-15,
            -0.2367976929865283,
            3.260904550936328e-15
          ]
        ],
        "gauge_integer_shift": [
          0,
          0,
          0
        ],
        "expected_opposite_endpoint_reduced_polarization": [
          4.849670320266994e-15,
          -0.2367976929865204,
          1.3423084700022122e-14
        ],
        "actual_opposite_endpoint_branch_residual": 1.6231995278263223e-14
      },
      "pnp_branch": {
        "construction": "incoming_path_concatenated_with_parent_reflection",
        "reduced_polarization": [
          [
            -6.883630006758619e-15,
            0.2367976929865302,
            -8.061428247244527e-15
          ],
          [
            -1.875910099077802e-15,
            0.2596721779764716,
            -1.4620995659667316e-15
          ],
          [
            -6.269676238345938e-15,
            0.2675725058961783,
            -8.297299458818012e-15
          ],
          [
            -2.069455430736073e-15,
            0.26024667106242555,
            -1.440336471892133e-15
          ],
          [
            7.150432453342821e-15,
            0.23754010700430475,
            -3.153470901728153e-15
          ],
          [
            -8.543186168154617e-15,
            0.19896280441172667,
            -6.262559413469641e-16
          ],
          [
            1.7517442536284898e-14,
            0.1446187151755773,
            3.1207478463022595e-15
          ],
          [
            -3.2875896156829476e-15,
            0.07642041302170338,
            8.953021583900741e-15
          ],
          [
            -1.0169798432458124e-15,
            4.894153660936821e-15,
            2.6808282263887977e-15
          ],
          [
            3.2216110625495343e-15,
            -0.07642041302170526,
            1.4858326649136512e-14
          ],
          [
            3.54258754651933e-15,
            -0.14461871517558564,
            1.6825074902502153e-14
          ],
          [
            -7.913023497188623e-16,
            -0.19896280441171926,
            9.376295341409098e-15
          ],
          [
            4.633314690769209e-15,
            -0.2375401070043001,
            -6.163042787325854e-15
          ],
          [
            7.344050666638752e-15,
            -0.2602466710624225,
            7.741529339561609e-15
          ],
          [
            -1.4002707640410816e-15,
            -0.26757250589618103,
            -6.477995373289205e-15
          ],
          [
            1.0394271221406132e-15,
            -0.25967217797647374,
            -5.601988522321094e-15
          ],
          [
            -5.031336786194623e-15,
            -0.2367976929865283,
            3.2609045509363288e-15
          ]
        ],
        "unwrapped_reduced_polarization": [
          [
            -6.883630006758619e-15,
            0.2367976929865302,
            -8.061428247244527e-15
          ],
          [
            -1.875910099077802e-15,
            0.2596721779764716,
            -1.4620995659667316e-15
          ],
          [
            -6.269676238345938e-15,
            0.2675725058961783,
            -8.297299458818012e-15
          ],
          [
            -2.069455430736073e-15,
            0.26024667106242555,
            -1.4403364718921333e-15
          ],
          [
            7.150432453342821e-15,
            0.23754010700430475,
            -3.153470901728153e-15
          ],
          [
            -8.543186168154616e-15,
            0.19896280441172667,
            -6.262559413469642e-16
          ],
          [
            1.75174425362849e-14,
            0.1446187151755773,
            3.12074784630226e-15
          ],
          [
            -3.2875896156829487e-15,
            0.07642041302170338,
            8.953021583900741e-15
          ],
          [
            -1.0169798432458126e-15,
            4.898859096158503e-15,
            2.6808282263887977e-15
          ],
          [
            3.2216110625495343e-15,
            -0.07642041302170526,
            1.4858326649136512e-14
          ],
          [
            3.54258754651933e-15,
            -0.14461871517558564,
            1.6825074902502153e-14
          ],
          [
            -7.913023497188622e-16,
            -0.19896280441171926,
            9.376295341409098e-15
          ],
          [
            4.633314690769209e-15,
            -0.2375401070043001,
            -6.163042787325853e-15
          ],
          [
            7.344050666638752e-15,
            -0.2602466710624225,
            7.741529339561609e-15
          ],
          [
            -1.4002707640410812e-15,
            -0.26757250589618103,
            -6.477995373289205e-15
          ],
          [
            1.0394271221406132e-15,
            -0.25967217797647374,
            -5.601988522321094e-15
          ],
          [
            -5.0313367861946226e-15,
            -0.2367976929865283,
            3.260904550936328e-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": [
          [
            -6.8833827526759706e-15,
            0.2367976929865302,
            -8.049116928532385e-15
          ],
          [
            -1.887379141862766e-15,
            0.2596721779764716,
            -1.4432899320127035e-15
          ],
          [
            -6.2727600891321345e-15,
            0.2675725058961783,
            -8.271161533457416e-15
          ],
          [
            -2.0539125955565396e-15,
            0.2602466710624256,
            -1.4432899320127035e-15
          ],
          [
            7.105427357601002e-15,
            0.23754010700430472,
            -3.164135620181696e-15
          ],
          [
            -8.548717289613705e-15,
            0.19896280441172665,
            -6.106226635438361e-16
          ],
          [
            1.7541523789077473e-14,
            0.14461871517557734,
            3.1086244689504383e-15
          ],
          [
            -3.2751579226442118e-15,
            0.07642041302170344,
            8.992806499463768e-15
          ],
          [
            -9.992007221626409e-16,
            4.884981308350689e-15,
            2.6645352591003757e-15
          ],
          [
            3.219646771412954e-15,
            -0.07642041302170527,
            1.4876988529977098e-14
          ],
          [
            3.552713678800501e-15,
            -0.14461871517558567,
            1.687538997430238e-14
          ],
          [
            -7.771561172376096e-16,
            -0.19896280441171926,
            9.325873406851315e-15
          ],
          [
            4.6629367034256575e-15,
            -0.23754010700430006,
            -6.161737786669619e-15
          ],
          [
            7.327471962526033e-15,
            -0.2602466710624225,
            7.771561172376096e-15
          ],
          [
            -1.3877787807814457e-15,
            -0.26757250589618103,
            -6.494804694057166e-15
          ],
          [
            9.992007221626409e-16,
            -0.25967217797647374,
            -5.6066262743570405e-15
          ],
          [
            -5.051514762044462e-15,
            -0.2367976929865283,
            3.219646771412954e-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": [
              -4.713130945575961e-15,
              0.23679769298653291,
              -3.642309135131839e-15
            ],
            "branch_aligned_reduced_polarization": [
              -4.713130945575961e-15,
              0.23679769298653291,
              -3.642309135131839e-15
            ],
            "target_residual": 0.2632023070134671,
            "energy_eV": -18.99747221400674,
            "max_atomic_step_A": 0.12000000000000001,
            "max_log_strain_component": 0.009768874667392914,
            "step_scale": 0.5725700190717327,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 3.058474547756647,
            "cell_principal_stretches": [
              1.0098167458791671,
              0.9940732374739187,
              0.9914503961638911
            ],
            "cell_volume_ratio": 0.9952494376077342,
            "cell_rmsd_from_input_A": 0.060575593143127916
          },
          {
            "iteration": 1,
            "reduced_polarization": [
              -7.788067634994084e-14,
              0.33725850162948834,
              -5.990200486728594e-14
            ],
            "branch_aligned_reduced_polarization": [
              -7.788067634994084e-14,
              0.33725850162948834,
              -5.990200486728594e-14
            ],
            "target_residual": 0.16274149837051166,
            "energy_eV": -18.786232636747062,
            "max_atomic_step_A": 0.09578045233130282,
            "max_log_strain_component": 0.02,
            "step_scale": 0.46293580367054094,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 3.058474547756647,
            "cell_principal_stretches": [
              1.0302163973273841,
              0.9820486131139988,
              0.9741739676700534
            ],
            "cell_volume_ratio": 0.9855938040341026,
            "cell_rmsd_from_input_A": 0.18677806355418444
          },
          {
            "iteration": 2,
            "reduced_polarization": [
              -2.195492667154958e-13,
              0.40331015587318225,
              -1.5827244502171707e-13
            ],
            "branch_aligned_reduced_polarization": [
              -2.195492667154958e-13,
              0.40331015587318225,
              -1.5827244502171707e-13
            ],
            "target_residual": 0.09668984412681775,
            "energy_eV": -18.259997689149117,
            "max_atomic_step_A": 0.10812381832609542,
            "max_log_strain_component": 0.02,
            "step_scale": 0.8162685224090539,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 3.058474547756647,
            "cell_principal_stretches": [
              1.051028149070934,
              0.9701694424143786,
              0.9571985880059478
            ],
            "cell_volume_ratio": 0.9760318467351664,
            "cell_rmsd_from_input_A": 0.3161466967932603
          },
          {
            "iteration": 3,
            "reduced_polarization": [
              -2.309049928158468e-13,
              0.4717481196560702,
              -1.2329030922275386e-13
            ],
            "branch_aligned_reduced_polarization": [
              -2.309049928158468e-13,
              0.4717481196560702,
              -1.2329030922275386e-13
            ],
            "target_residual": 0.02825188034392978,
            "energy_eV": -17.76677849447193,
            "max_atomic_step_A": 0.031547454908712004,
            "max_log_strain_component": 0.006146335022386634,
            "step_scale": 1.0,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 3.058474547756647,
            "cell_principal_stretches": [
              1.0575080135025556,
              0.9665477206208352,
              0.9520414312767158
            ],
            "cell_volume_ratio": 0.973111974141757,
            "cell_rmsd_from_input_A": 0.35658305483686115
          },
          {
            "iteration": 4,
            "reduced_polarization": [
              -4.653941957283717e-14,
              0.4937059286640312,
              -1.378837241342186e-14
            ],
            "branch_aligned_reduced_polarization": [
              -4.653941957283717e-14,
              0.4937059286640312,
              -1.378837241342186e-14
            ],
            "target_residual": 0.0062940713359688205,
            "energy_eV": -17.48662972905074,
            "max_atomic_step_A": 0.007199341183864566,
            "max_log_strain_component": 0.001876401921545761,
            "step_scale": 1.0,
            "strain_jacobian_refreshed": true,
            "strain_jacobian_frobenius_norm": 3.33873580096748,
            "cell_principal_stretches": [
              1.0579353431017762,
              0.9649652063031441,
              0.9524614613861374
            ],
            "cell_volume_ratio": 0.9723400908271079,
            "cell_rmsd_from_input_A": 0.3583502939256202
          },
          {
            "iteration": 5,
            "reduced_polarization": [
              -1.436770537686837e-14,
              0.49993804094605687,
              -2.635481432898041e-15
            ],
            "branch_aligned_reduced_polarization": [
              -1.436770537686837e-14,
              0.49993804094605687,
              -2.635481432898041e-15
            ],
            "target_residual": 6.195905394312806e-05,
            "energy_eV": -17.426749359770405
          }
        ],
        "iterations": 5
      },
      "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": 6.195905394312806e-05,
        "parent_symmetrization_rmsd_A": 0.239685878996376,
        "parent_cell_rmsd_A": 0.3583502939256202,
        "energy_eV": -17.426749359770405,
        "reduced_polarization": [
          -1.436770537686837e-14,
          0.49993804094605687,
          -2.635481432898041e-15
        ],
        "cartesian_polarization_e_A2": [
          -2.3645648655239104e-15,
          0.027806552047724104,
          -2.068489487793817e-15
        ],
        "ranking_score": 0.8293973705856673
      },
      "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": false,
        "history": [
          {
            "iteration": 0,
            "reduced_polarization": [
              -4.713130945575961e-15,
              0.23679769298653291,
              -3.642309135131839e-15
            ],
            "branch_aligned_reduced_polarization": [
              -4.718447854656915e-15,
              0.23679769298653291,
              -3.642309135131839e-15
            ],
            "target_residual": 0.553238779735965,
            "energy_eV": -18.99747221400674,
            "max_atomic_step_A": 0.12,
            "max_log_strain_component": 0.00939178600398811,
            "step_scale": 0.2939468257573745,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 3.058474547756647,
            "cell_principal_stretches": [
              1.0103253166171366,
              1.0039341221987192,
              0.9880723388842072
            ],
            "cell_volume_ratio": 1.0022018324892725,
            "cell_rmsd_from_input_A": 0.055137771225814695
          },
          {
            "iteration": 1,
            "reduced_polarization": [
              -0.14089863216556225,
              0.15547838792582683,
              0.004741283518216966
            ],
            "branch_aligned_reduced_polarization": [
              -0.14089863216556225,
              0.15547838792582683,
              0.004741283518216966
            ],
            "target_residual": 0.3913435846695052,
            "energy_eV": -18.84850459777834,
            "max_atomic_step_A": 0.12,
            "max_log_strain_component": 0.012084241079878157,
            "step_scale": 0.4246983461851568,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 3.058474547756647,
            "cell_principal_stretches": [
              1.0246566857193617,
              1.0060116308191438,
              0.9733963873388738
            ],
            "cell_volume_ratio": 1.0033930993841738,
            "cell_rmsd_from_input_A": 0.12094317726419555
          },
          {
            "iteration": 2,
            "reduced_polarization": [
              -0.27156602059450996,
              0.08376154043106963,
              0.01870953399995202
            ],
            "branch_aligned_reduced_polarization": [
              -0.27156602059450996,
              0.08376154043106963,
              0.01870953399995202
            ],
            "target_residual": 0.24402484558935578,
            "energy_eV": -18.446449449062545,
            "max_atomic_step_A": 0.12,
            "max_log_strain_component": 0.018662767333845476,
            "step_scale": 0.6099776211022243,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 3.058474547756647,
            "cell_principal_stretches": [
              1.049234818424783,
              1.007206814765879,
              0.9501518585088994
            ],
            "cell_volume_ratio": 1.0041171199712629,
            "cell_rmsd_from_input_A": 0.22916731708245344
          },
          {
            "iteration": 3,
            "reduced_polarization": [
              -0.3751411342017829,
              0.025798643327930162,
              0.03660213972885574
            ],
            "branch_aligned_reduced_polarization": [
              -0.3751411342017829,
              0.025798643327930162,
              0.03660213972885574
            ],
            "target_residual": 0.13264623250853988,
            "energy_eV": -17.870608833002755,
            "max_atomic_step_A": 0.08153867485238529,
            "max_log_strain_component": 0.02,
            "step_scale": 0.8031309000215925,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 3.058474547756647,
            "cell_principal_stretches": [
              1.0774692204591625,
              1.0080731708971342,
              0.9249489630771943
            ],
            "cell_volume_ratio": 1.0046497929285492,
            "cell_rmsd_from_input_A": 0.35257940037868046
          },
          {
            "iteration": 4,
            "reduced_polarization": [
              -0.43485652796377794,
              -0.005350143696313971,
              0.04125461976898866
            ],
            "branch_aligned_reduced_polarization": [
              -0.43485652796377794,
              -0.005350143696313971,
              0.04125461976898866
            ],
            "target_residual": 0.0772932056444102,
            "energy_eV": -17.53394067880089,
            "max_atomic_step_A": 0.08124417695804581,
            "max_log_strain_component": 0.019040836637079922,
            "step_scale": 1.0,
            "strain_jacobian_refreshed": true,
            "strain_jacobian_frobenius_norm": 2.268707978969109,
            "cell_principal_stretches": [
              1.0921431372856523,
              1.0111061879506025,
              0.913313061135717
            ],
            "cell_volume_ratio": 1.00854666556933,
            "cell_rmsd_from_input_A": 0.4295557551235941
          },
          {
            "iteration": 5,
            "reduced_polarization": [
              -0.48863939731702305,
              -0.005014246671537236,
              0.0024760059485419883
            ],
            "branch_aligned_reduced_polarization": [
              -0.48863939731702305,
              -0.005014246671537236,
              0.0024760059485419883
            ],
            "target_residual": 0.01266240768814133,
            "energy_eV": -17.718393592239025
          }
        ],
        "iterations": 5
      },
      "parent": {
        "candidate_id": "bec_projection_02",
        "source": "MACEField_BEC_backprojection",
        "spacegroup": "P1",
        "spacegroup_number": 1,
        "pointgroup": "1",
        "has_inversion": false,
        "is_polar_point_group": true,
        "nonpolar_parent_hypothesis": false,
        "symmetry_tolerance_A": null,
        "target_reduced_polarization": [
          -0.5,
          0.0,
          0.0
        ],
        "formal_class": [
          0.5,
          0.0,
          0.0
        ],
        "target_residual": 0.01266240768814133,
        "parent_symmetrization_rmsd_A": 0.30891532811891087,
        "parent_cell_rmsd_A": 0.4295557551235941,
        "energy_eV": -17.718393592239025,
        "reduced_polarization": [
          -0.48863939731702305,
          -0.005014246671537236,
          0.0024760059485419883
        ],
        "cartesian_polarization_e_A2": [
          -0.015954807824526532,
          -0.0009842400145073282,
          0.0038357386493846346
        ],
        "ranking_score": 0.941629082276092
      },
      "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": false,
        "history": [
          {
            "iteration": 0,
            "reduced_polarization": [
              -4.713130945575961e-15,
              0.23679769298653291,
              -3.642309135131839e-15
            ],
            "branch_aligned_reduced_polarization": [
              -4.713130945575961e-15,
              0.23679769298653291,
              -3.6637359812630166e-15
            ],
            "target_residual": 0.5532387797359659,
            "energy_eV": -18.99747221400674,
            "max_atomic_step_A": 0.10623498780159633,
            "max_log_strain_component": 0.02,
            "step_scale": 0.25055750140177196,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 3.058474547756647,
            "cell_principal_stretches": [
              1.0216135581426888,
              1.0027472362315617,
              0.9779937412049253
            ],
            "cell_volume_ratio": 1.0018765165060124,
            "cell_rmsd_from_input_A": 0.11325498269894367
          },
          {
            "iteration": 1,
            "reduced_polarization": [
              0.002934064550251514,
              0.16184884384309203,
              -0.1299054591809876
            ],
            "branch_aligned_reduced_polarization": [
              0.002934064550251514,
              0.16184884384309203,
              -0.12990545918098761
            ],
            "target_residual": 0.40394755369003815,
            "energy_eV": -18.810138189877023,
            "max_atomic_step_A": 0.11150398831816151,
            "max_log_strain_component": 0.02,
            "step_scale": 0.4209444091526639,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 3.058474547756647,
            "cell_principal_stretches": [
              1.0439423799060061,
              1.0040355925541404,
              0.9566697623373657
            ],
            "cell_volume_ratio": 1.0027384874849186,
            "cell_rmsd_from_input_A": 0.22470594546319014
          },
          {
            "iteration": 2,
            "reduced_polarization": [
              0.017516102470356117,
              0.07511253340839932,
              -0.28456306829441774
            ],
            "branch_aligned_reduced_polarization": [
              0.017516102470356117,
              0.07511253340839932,
              -0.28456306829441774
            ],
            "target_residual": 0.22882696096285426,
            "energy_eV": -18.208942932066122,
            "max_atomic_step_A": 0.08995665595451786,
            "max_log_strain_component": 0.02,
            "step_scale": 0.7152634356279421,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 3.058474547756647,
            "cell_principal_stretches": [
              1.0674699239337928,
              1.0046469875856496,
              0.9353715388491
            ],
            "cell_volume_ratio": 1.003120914168861,
            "cell_rmsd_from_input_A": 0.3377677094476369
          },
          {
            "iteration": 3,
            "reduced_polarization": [
              0.032353849221864496,
              0.011538966749220225,
              -0.40102460809695895
            ],
            "branch_aligned_reduced_polarization": [
              0.032353849221864496,
              0.011538966749220225,
              -0.40102460809695895
            ],
            "target_residual": 0.10476663359806555,
            "energy_eV": -17.22911876975386,
            "max_atomic_step_A": 0.06368431676852654,
            "max_log_strain_component": 0.02,
            "step_scale": 0.9864422818585864,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 3.058474547756647,
            "cell_principal_stretches": [
              1.0920096102865986,
              1.004866998083738,
              0.9142617971096938
            ],
            "cell_volume_ratio": 1.003241795297382,
            "cell_rmsd_from_input_A": 0.45316384278473953
          },
          {
            "iteration": 4,
            "reduced_polarization": [
              0.03341280482206392,
              -0.009422974747792218,
              -0.45299697408540335
            ],
            "branch_aligned_reduced_polarization": [
              0.03341280482206392,
              -0.009422974747792218,
              -0.45299697408540335
            ],
            "target_residual": 0.05843365831695901,
            "energy_eV": -16.4020218398962,
            "max_atomic_step_A": 0.055758933882473986,
            "max_log_strain_component": 0.012485951090961164,
            "step_scale": 1.0,
            "strain_jacobian_refreshed": true,
            "strain_jacobian_frobenius_norm": 2.2696749036297974,
            "cell_principal_stretches": [
              1.0899740580776618,
              1.0119440957929977,
              0.90673232674198
            ],
            "cell_volume_ratio": 1.000119239384044,
            "cell_rmsd_from_input_A": 0.4605196957241978
          },
          {
            "iteration": 5,
            "reduced_polarization": [
              0.0028203596532944374,
              -0.0005242316875878685,
              -0.4958372471151195
            ],
            "branch_aligned_reduced_polarization": [
              0.0028203596532944374,
              -0.0005242316875878685,
              -0.4958372471151195
            ],
            "target_residual": 0.005055468229232899,
            "energy_eV": -15.993741941480664
          }
        ],
        "iterations": 5
      },
      "parent": {
        "candidate_id": "bec_projection_03",
        "source": "MACEField_BEC_backprojection",
        "spacegroup": "P1",
        "spacegroup_number": 1,
        "pointgroup": "1",
        "has_inversion": false,
        "is_polar_point_group": true,
        "nonpolar_parent_hypothesis": false,
        "symmetry_tolerance_A": null,
        "target_reduced_polarization": [
          0.0,
          0.0,
          -0.5
        ],
        "formal_class": [
          0.0,
          0.0,
          0.5
        ],
        "target_residual": 0.005055468229232899,
        "parent_symmetrization_rmsd_A": 0.2817957869398434,
        "parent_cell_rmsd_A": 0.4605196957241978,
        "energy_eV": -15.993741941480664,
        "reduced_polarization": [
          0.0028203596532944374,
          -0.0005242316875878685,
          -0.4958372471151195
        ],
        "cartesian_polarization_e_A2": [
          0.00029666650802839806,
          -0.0015085321384022208,
          -0.018412626793930895
        ],
        "ranking_score": 0.9070366473293587
      },
      "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": false,
        "history": [
          {
            "iteration": 0,
            "reduced_polarization": [
              -4.713130945575961e-15,
              0.23679769298653291,
              -3.642309135131839e-15
            ],
            "branch_aligned_reduced_polarization": [
              -4.718447854656915e-15,
              0.23679769298653291,
              -3.642309135131839e-15
            ],
            "target_residual": 0.565044648162609,
            "energy_eV": -18.99747221400674,
            "max_atomic_step_A": 0.12,
            "max_log_strain_component": 0.009033179572934367,
            "step_scale": 0.2827230583016941,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 3.058474547756647,
            "cell_principal_stretches": [
              1.0118380385619479,
              0.9958122083718763,
              0.9901258233842207
            ],
            "cell_volume_ratio": 0.997651444704546,
            "cell_rmsd_from_input_A": 0.05527652465896864
          },
          {
            "iteration": 1,
            "reduced_polarization": [
              -0.13793357011073384,
              0.29682481368428987,
              0.004544988428844902
            ],
            "branch_aligned_reduced_polarization": [
              -0.13793357011073382,
              0.29682481368428987,
              0.004544988428844902
            ],
            "target_residual": 0.41520225542137984,
            "energy_eV": -18.822342272842683,
            "max_atomic_step_A": 0.12,
            "max_log_strain_component": 0.01163904083442095,
            "step_scale": 0.38933011212615354,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 3.058474547756647,
            "cell_principal_stretches": [
              1.0304081828694092,
              0.9871469150157425,
              0.9759298261193581
            ],
            "cell_volume_ratio": 0.9926809383489792,
            "cell_rmsd_from_input_A": 0.14719853445998793
          },
          {
            "iteration": 2,
            "reduced_polarization": [
              -0.2703593761676469,
              0.3508570106555571,
              0.011975969843914434
            ],
            "branch_aligned_reduced_polarization": [
              -0.2703593761676469,
              0.3508570106555571,
              0.011975969843914434
            ],
            "target_residual": 0.27408369385720716,
            "energy_eV": -18.027736912224185,
            "max_atomic_step_A": 0.119119301621267,
            "max_log_strain_component": 0.02,
            "step_scale": 0.5375831992101886,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 3.058474547756647,
            "cell_principal_stretches": [
              1.0606522003911063,
              0.9708033046785702,
              0.9547099812521865
            ],
            "cell_volume_ratio": 0.9830502236417404,
            "cell_rmsd_from_input_A": 0.3073625308181965
          },
          {
            "iteration": 3,
            "reduced_polarization": [
              -0.3732959824732771,
              0.4049041991512093,
              0.0054294715650119105
            ],
            "branch_aligned_reduced_polarization": [
              -0.3732959824732771,
              0.4049041991512093,
              0.0054294715650119105
            ],
            "target_residual": 0.15851371725488062,
            "energy_eV": -16.74416664594207,
            "max_atomic_step_A": 0.10835189866237577,
            "max_log_strain_component": 0.02,
            "step_scale": 0.5470995233757289,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 3.058474547756647,
            "cell_principal_stretches": [
              1.0932758876054172,
              0.9555735086568143,
              0.9326678273033011
            ],
            "cell_volume_ratio": 0.9743631863319492,
            "cell_rmsd_from_input_A": 0.475515739376209
          },
          {
            "iteration": 4,
            "reduced_polarization": [
              -0.42409235791283056,
              0.41399832270348824,
              -0.0012668619022555225
            ],
            "branch_aligned_reduced_polarization": [
              -0.42409235791283056,
              0.41399832270348824,
              -0.0012668619022555225
            ],
            "target_residual": 0.11471644853344505,
            "energy_eV": -15.470290036212687,
            "max_atomic_step_A": 0.07334734405435014,
            "max_log_strain_component": 0.02,
            "step_scale": 0.45952126215813216,
            "strain_jacobian_refreshed": true,
            "strain_jacobian_frobenius_norm": 2.624287808005531,
            "cell_principal_stretches": [
              1.1009099519836287,
              0.969954016519824,
              0.9179962098213228
            ],
            "cell_volume_ratio": 0.9802657560392176,
            "cell_rmsd_from_input_A": 0.5173434687201702
          },
          {
            "iteration": 5,
            "reduced_polarization": [
              -0.4463801407545038,
              0.43415348948097,
              -0.009750075751584118
            ],
            "branch_aligned_reduced_polarization": [
              -0.4463801407545038,
              0.43415348948097,
              -0.009750075751584118
            ],
            "target_residual": 0.08547465255969858,
            "energy_eV": -16.566985654709516
          }
        ],
        "iterations": 5
      },
      "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": 0.08547465255969858,
        "parent_symmetrization_rmsd_A": 0.2881135550032468,
        "parent_cell_rmsd_A": 0.5173434687201702,
        "energy_eV": -16.566985654709516,
        "reduced_polarization": [
          -0.4463801407545038,
          0.43415348948097,
          -0.009750075751584118
        ],
        "cartesian_polarization_e_A2": [
          -0.013044963578802988,
          0.02323780514370754,
          0.0037405894104045622
        ],
        "ranking_score": 1.0883987273026865
      },
      "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": false,
        "history": [
          {
            "iteration": 0,
            "reduced_polarization": [
              -4.713130945575961e-15,
              0.23679769298653291,
              -3.642309135131839e-15
            ],
            "branch_aligned_reduced_polarization": [
              -4.713130945575961e-15,
              0.23679769298653291,
              -3.6637359812630166e-15
            ],
            "target_residual": 0.56504464816261,
            "energy_eV": -18.99747221400674,
            "max_atomic_step_A": 0.10916260765233696,
            "max_log_strain_component": 0.02,
            "step_scale": 0.25055750140181227,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 3.058474547756647,
            "cell_principal_stretches": [
              1.0226160918891678,
              0.9969562057188222,
              0.9788278344001146
            ],
            "cell_volume_ratio": 0.9979183628158385,
            "cell_rmsd_from_input_A": 0.11480828941228996
          },
          {
            "iteration": 1,
            "reduced_polarization": [
              0.003055130991366688,
              0.28849766952295125,
              -0.1301059246562103
            ],
            "branch_aligned_reduced_polarization": [
              0.003055130991366688,
              0.28849766952295125,
              -0.1301059246562103
            ],
            "target_residual": 0.4261035045584985,
            "energy_eV": -18.782009233737163,
            "max_atomic_step_A": 0.12,
            "max_log_strain_component": 0.0166993865362034,
            "step_scale": 0.3055866783464286,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 3.058474547756647,
            "cell_principal_stretches": [
              1.0433751454342064,
              0.9919866242748894,
              0.9609095596991919
            ],
            "cell_volume_ratio": 0.9945550280305709,
            "cell_rmsd_from_input_A": 0.21908144126268936
          },
          {
            "iteration": 2,
            "reduced_polarization": [
              0.003985861502665395,
              0.3342255213428115,
              -0.24481996748732665
            ],
            "branch_aligned_reduced_polarization": [
              0.003985861502665395,
              0.3342255213428115,
              -0.24481996748732665
            ],
            "target_residual": 0.3043253421244279,
            "energy_eV": -17.98557800283906,
            "max_atomic_step_A": 0.12000000000000001,
            "max_log_strain_component": 0.016145219717454275,
            "step_scale": 0.36527007336883105,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 3.058474547756647,
            "cell_principal_stretches": [
              1.0657337756357805,
              0.9844717647320222,
              0.9430954349272858
            ],
            "cell_volume_ratio": 0.9894814054932333,
            "cell_rmsd_from_input_A": 0.3334214073398715
          },
          {
            "iteration": 3,
            "reduced_polarization": [
              -0.007800694305151806,
              0.3741998314149202,
              -0.3157930725787325
            ],
            "branch_aligned_reduced_polarization": [
              -0.007800694305151806,
              0.3741998314149202,
              -0.3157930725787325
            ],
            "target_residual": 0.22320108726809784,
            "energy_eV": -16.57609845304494,
            "max_atomic_step_A": 0.09252807258919372,
            "max_log_strain_component": 0.02,
            "step_scale": 0.36087910360979664,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 3.058474547756647,
            "cell_principal_stretches": [
              1.093188324493547,
              0.9756199485815497,
              0.9219876513351402
            ],
            "cell_volume_ratio": 0.9833333323518357,
            "cell_rmsd_from_input_A": 0.47852859544442133
          },
          {
            "iteration": 4,
            "reduced_polarization": [
              -0.010037396615020662,
              0.39199270570461126,
              -0.35483923061526035
            ],
            "branch_aligned_reduced_polarization": [
              -0.010037396615020662,
              0.39199270570461126,
              -0.35483923061526035
            ],
            "target_residual": 0.1812125103854243,
            "energy_eV": -15.344465471224485,
            "max_atomic_step_A": 0.12,
            "max_log_strain_component": 0.01688612139109898,
            "step_scale": 0.2492370704540843,
            "strain_jacobian_refreshed": true,
            "strain_jacobian_frobenius_norm": 2.3996508726127663,
            "cell_principal_stretches": [
              1.1125355794081655,
              0.9830477684188481,
              0.9077934276302809
            ],
            "cell_volume_ratio": 0.992831538546138,
            "cell_rmsd_from_input_A": 0.5763725478462561
          },
          {
            "iteration": 5,
            "reduced_polarization": [
              -0.005775496266739392,
              0.4056545443707114,
              -0.3790075092400234
            ],
            "branch_aligned_reduced_polarization": [
              -0.005775496266739392,
              0.4056545443707114,
              -0.3790075092400234
            ],
            "target_residual": 0.15353697983003378,
            "energy_eV": -16.63839159903634
          }
        ],
        "iterations": 5
      },
      "parent": {
        "candidate_id": "bec_projection_05",
        "source": "MACEField_BEC_backprojection",
        "spacegroup": "P1",
        "spacegroup_number": 1,
        "pointgroup": "1",
        "has_inversion": false,
        "is_polar_point_group": true,
        "nonpolar_parent_hypothesis": false,
        "symmetry_tolerance_A": null,
        "target_reduced_polarization": [
          0.0,
          0.5,
          -0.5
        ],
        "formal_class": [
          0.0,
          0.5,
          0.5
        ],
        "target_residual": 0.15353697983003378,
        "parent_symmetrization_rmsd_A": 0.2670241302290601,
        "parent_cell_rmsd_A": 0.5763725478462561,
        "energy_eV": -16.63839159903634,
        "reduced_polarization": [
          -0.005775496266739392,
          0.4056545443707114,
          -0.3790075092400234
        ],
        "cartesian_polarization_e_A2": [
          0.0008559685730964574,
          0.020918058422845096,
          -0.01206065411507787
        ],
        "ranking_score": 1.2181912268506916
      },
      "branch_status": "awaiting_branch_sampling"
    },
    {
      "orbit_id": 6,
      "formal_class": [
        0.5,
        0.0,
        0.5
      ],
      "formal_classes_in_orbit": [
        [
          0.5,
          0.0,
          0.5
        ]
      ],
      "target_reduced_polarization": [
        -0.5,
        0.0,
        -0.5
      ],
      "bec_backprojection": {
        "converged_to_target": false,
        "history": [
          {
            "iteration": 0,
            "reduced_polarization": [
              -4.713130945575961e-15,
              0.23679769298653291,
              -3.642309135131839e-15
            ],
            "branch_aligned_reduced_polarization": [
              -4.718447854656915e-15,
              0.23679769298653291,
              -3.6637359812630166e-15
            ],
            "target_residual": 0.7457031228335683,
            "energy_eV": -18.99747221400674,
            "max_atomic_step_A": 0.08151369294242676,
            "max_log_strain_component": 0.02,
            "step_scale": 0.20846639139631648,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 3.058474547756647,
            "cell_principal_stretches": [
              1.0240247171378098,
              1.002464586080635,
              0.975658744881843
            ],
            "cell_volume_ratio": 1.0015610349265403,
            "cell_rmsd_from_input_A": 0.11902523258451357
          },
          {
            "iteration": 1,
            "reduced_polarization": [
              -0.10041491488850365,
              0.17921578084710613,
              -0.10254086868897072
            ],
            "branch_aligned_reduced_polarization": [
              -0.10041491488850363,
              0.17921578084710613,
              -0.10254086868897072
            ],
            "target_residual": 0.5914053579489433,
            "energy_eV": -18.91162219212667,
            "max_atomic_step_A": 0.07365427519075969,
            "max_log_strain_component": 0.02,
            "step_scale": 0.265752076498532,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 3.058474547756647,
            "cell_principal_stretches": [
              1.049147413692631,
              1.0040140991285813,
              0.9517451648195602
            ],
            "cell_volume_ratio": 1.0025291403532304,
            "cell_rmsd_from_input_A": 0.23829534502796823
          },
          {
            "iteration": 2,
            "reduced_polarization": [
              -0.18838069254807993,
              0.11836192779800693,
              -0.19490389383507908
            ],
            "branch_aligned_reduced_polarization": [
              -0.18838069254807993,
              0.11836192779800693,
              -0.1949038938350791
            ],
            "target_residual": 0.45188468963428224,
            "energy_eV": -18.68608711290909,
            "max_atomic_step_A": 0.0633683400629329,
            "max_log_strain_component": 0.02,
            "step_scale": 0.29999919506124206,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 3.058474547756647,
            "cell_principal_stretches": [
              1.075830316233808,
              1.0048311369148297,
              0.927841288653895
            ],
            "cell_volume_ratio": 1.0030222268265936,
            "cell_rmsd_from_input_A": 0.36062471815230546
          },
          {
            "iteration": 3,
            "reduced_polarization": [
              -0.24784114880347605,
              0.0641945087095994,
              -0.2577405316068622
            ],
            "branch_aligned_reduced_polarization": [
              -0.24784114880347607,
              0.0641945087095994,
              -0.2577405316068622
            ],
            "target_residual": 0.35552028241908123,
            "energy_eV": -18.351983122943167,
            "max_atomic_step_A": 0.04707762239002905,
            "max_log_strain_component": 0.02,
            "step_scale": 0.28405221409920195,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 3.058474547756647,
            "cell_principal_stretches": [
              1.1038838204461727,
              1.00522482931374,
              0.9041119260570039
            ],
            "cell_volume_ratio": 1.0032490870997917,
            "cell_rmsd_from_input_A": 0.4866916456594224
          },
          {
            "iteration": 4,
            "reduced_polarization": [
              -0.2776607055840649,
              0.026419502267230093,
              -0.28498132831501294
            ],
            "branch_aligned_reduced_polarization": [
              -0.2776607055840649,
              0.026419502267230093,
              -0.28498132831501294
            ],
            "target_residual": 0.31042838322969163,
            "energy_eV": -18.034488982601033,
            "max_atomic_step_A": 0.06878809883090456,
            "max_log_strain_component": 0.02,
            "step_scale": 0.2847448485945802,
            "strain_jacobian_refreshed": true,
            "strain_jacobian_frobenius_norm": 2.3357692983453946,
            "cell_principal_stretches": [
              1.1113623741297551,
              1.0162781307541948,
              0.8890545901162147
            ],
            "cell_volume_ratio": 1.0041456195017413,
            "cell_rmsd_from_input_A": 0.5470175153856808
          },
          {
            "iteration": 5,
            "reduced_polarization": [
              -0.3292629267382977,
              0.015568586480918047,
              -0.3384997594473777
            ],
            "branch_aligned_reduced_polarization": [
              -0.3292629267382977,
              0.015568586480918047,
              -0.3384997594473777
            ],
            "target_residual": 0.23553313306102092,
            "energy_eV": -17.847594845926977
          }
        ],
        "iterations": 5
      },
      "parent": {
        "candidate_id": "bec_projection_06",
        "source": "MACEField_BEC_backprojection",
        "spacegroup": "P1",
        "spacegroup_number": 1,
        "pointgroup": "1",
        "has_inversion": false,
        "is_polar_point_group": true,
        "nonpolar_parent_hypothesis": false,
        "symmetry_tolerance_A": null,
        "target_reduced_polarization": [
          -0.5,
          0.0,
          -0.5
        ],
        "formal_class": [
          0.5,
          0.0,
          0.5
        ],
        "target_residual": 0.23553313306102092,
        "parent_symmetrization_rmsd_A": 0.25115266653644164,
        "parent_cell_rmsd_A": 0.5470175153856808,
        "energy_eV": -17.847594845926977,
        "reduced_polarization": [
          -0.3292629267382977,
          0.015568586480918047,
          -0.3384997594473777
        ],
        "cartesian_polarization_e_A2": [
          -0.010535436352585137,
          -0.0008163650698659112,
          -0.009674447134535602
        ],
        "ranking_score": 1.3589733115049036
      },
      "branch_status": "awaiting_branch_sampling"
    },
    {
      "orbit_id": 7,
      "formal_class": [
        0.5,
        0.5,
        0.5
      ],
      "formal_classes_in_orbit": [
        [
          0.5,
          0.5,
          0.5
        ]
      ],
      "target_reduced_polarization": [
        -0.5,
        0.5,
        -0.5
      ],
      "bec_backprojection": {
        "converged_to_target": false,
        "history": [
          {
            "iteration": 0,
            "reduced_polarization": [
              -4.713130945575961e-15,
              0.23679769298653291,
              -3.642309135131839e-15
            ],
            "branch_aligned_reduced_polarization": [
              -4.718447854656915e-15,
              0.23679769298653291,
              -3.6637359812630166e-15
            ],
            "target_residual": 0.7545034489100781,
            "energy_eV": -18.99747221400674,
            "max_atomic_step_A": 0.08519532940561686,
            "max_log_strain_component": 0.02,
            "step_scale": 0.20846639139634435,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 3.058474547756647,
            "cell_principal_stretches": [
              1.0250384254242937,
              0.9972681676420342,
              0.9765510241530007
            ],
            "cell_volume_ratio": 0.9982677536047767,
            "cell_rmsd_from_input_A": 0.12042664492488778
          },
          {
            "iteration": 1,
            "reduced_polarization": [
              -0.10143298808257516,
              0.2799735782932472,
              -0.1019283675010007
            ],
            "branch_aligned_reduced_polarization": [
              -0.10143298808257517,
              0.2799735782932472,
              -0.1019283675010007
            ],
            "target_residual": 0.604754755118371,
            "energy_eV": -18.8834270365671,
            "max_atomic_step_A": 0.0865109207849345,
            "max_log_strain_component": 0.02,
            "step_scale": 0.23351660728060777,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 3.058474547756647,
            "cell_principal_stretches": [
              1.051938074146067,
              0.9924606332794413,
              0.9532821807751501
            ],
            "cell_volume_ratio": 0.9952333909980126,
            "cell_rmsd_from_input_A": 0.24830611296528388
          },
          {
            "iteration": 2,
            "reduced_polarization": [
              -0.18783954887487728,
              0.3112725084262664,
              -0.1884734122198028
            ],
            "branch_aligned_reduced_polarization": [
              -0.1878395488748773,
              0.3112725084262664,
              -0.1884734122198028
            ],
            "target_residual": 0.479698893282366,
            "energy_eV": -18.413728958421792,
            "max_atomic_step_A": 0.08164971041316577,
            "max_log_strain_component": 0.02,
            "step_scale": 0.23772181719997496,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 3.058474547756647,
            "cell_principal_stretches": [
              1.0812628159060116,
              0.9856559111335899,
              0.929829553720692
            ],
            "cell_volume_ratio": 0.9909687163194735,
            "cell_rmsd_from_input_A": 0.38794804787765014
          },
          {
            "iteration": 3,
            "reduced_polarization": [
              -0.25761704345914316,
              0.33628816490299507,
              -0.2435116014519651
            ],
            "branch_aligned_reduced_polarization": [
              -0.25761704345914316,
              0.33628816490299507,
              -0.2435116014519651
            ],
            "target_residual": 0.3890210292028587,
            "energy_eV": -17.701696320069217,
            "max_atomic_step_A": 0.06589046769792262,
            "max_log_strain_component": 0.02,
            "step_scale": 0.23657031310192553,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 3.058474547756647,
            "cell_principal_stretches": [
              1.1115499513394813,
              0.9789366859922618,
              0.9068344851408413
            ],
            "cell_volume_ratio": 0.9867601794444218,
            "cell_rmsd_from_input_A": 0.5332784352316292
          },
          {
            "iteration": 4,
            "reduced_polarization": [
              -0.3114519712513869,
              0.35135359368263835,
              -0.27479216912978444
            ],
            "branch_aligned_reduced_polarization": [
              -0.3114519712513869,
              0.35135359368263835,
              -0.27479216912978444
            ],
            "target_residual": 0.32918791038147444,
            "energy_eV": -17.15045722106079,
            "max_atomic_step_A": 0.051795793799744354,
            "max_log_strain_component": 0.02,
            "step_scale": 0.21240082521975726,
            "strain_jacobian_refreshed": true,
            "strain_jacobian_frobenius_norm": 2.689889506147933,
            "cell_principal_stretches": [
              1.1259200844344035,
              0.9886051864666567,
              0.8975774658630417
            ],
            "cell_volume_ratio": 0.9990848919405902,
            "cell_rmsd_from_input_A": 0.6126066074353149
          },
          {
            "iteration": 5,
            "reduced_polarization": [
              -0.347335369569506,
              0.3754499390135527,
              -0.317996024490043
            ],
            "branch_aligned_reduced_polarization": [
              -0.347335369569506,
              0.3754499390135527,
              -0.317996024490043
            ],
            "target_residual": 0.2682250066224924,
            "energy_eV": -17.12141223053661
          }
        ],
        "iterations": 5
      },
      "parent": {
        "candidate_id": "bec_projection_07",
        "source": "MACEField_BEC_backprojection",
        "spacegroup": "P1",
        "spacegroup_number": 1,
        "pointgroup": "1",
        "has_inversion": false,
        "is_polar_point_group": true,
        "nonpolar_parent_hypothesis": false,
        "symmetry_tolerance_A": null,
        "target_reduced_polarization": [
          -0.5,
          0.5,
          -0.5
        ],
        "formal_class": [
          0.5,
          0.5,
          0.5
        ],
        "target_residual": 0.2682250066224924,
        "parent_symmetrization_rmsd_A": 0.23055265422382437,
        "parent_cell_rmsd_A": 0.6126066074353149,
        "energy_eV": -17.12141223053661,
        "reduced_polarization": [
          -0.347335369569506,
          0.3754499390135527,
          -0.317996024490043
        ],
        "cartesian_polarization_e_A2": [
          -0.009784089423988781,
          0.01870643819913293,
          -0.007290843792702864
        ],
        "ranking_score": 1.4201543193276378
      },
      "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
        ],
        "endpoint_rmsd_A": 0.3798557983484948,
        "minimum_distance_A_by_image": [
          2.429230303565214,
          2.429047708284677,
          2.4290076084004624,
          2.4291100109695347,
          2.429354897971533,
          2.4297422263246222,
          2.4302719279233713,
          2.4309439096985805,
          2.4317580536989376
        ],
        "minimum_distance_A": 2.4290076084004624,
        "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": [
          127.23934491365347,
          127.23934491365347,
          127.23934491365347,
          127.23934491365347,
          127.23934491365347,
          127.23934491365347,
          127.23934491365347,
          127.23934491365347,
          127.23934491365347
        ],
        "cell_deformation_log_strain_norm": 0.0
      },
      "parent_reduced_polarization": [
        -1.0169798432458124e-15,
        4.894153660936821e-15,
        2.6808282263887977e-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": [
          -18.997472214006734,
          -19.026888943137703,
          -19.037327146766835,
          -19.024644601042404,
          -18.984937912788485,
          -18.920621293957417,
          -18.844348257586276,
          -18.779796540495724,
          -18.754138156938048
        ],
        "cartesian_polarizations_e_A2": [
          [
            -2.2489897664226947e-16,
            0.0121050751523554,
            -2.461673085749768e-16
          ],
          [
            -6.129642331375143e-17,
            0.013274416611650854,
            -3.99190230121584e-17
          ],
          [
            -2.048303967673046e-16,
            0.013678280610451475,
            -2.5951455021736177e-16
          ],
          [
            -6.76223887091208e-17,
            0.013303784642615484,
            -3.765585435778057e-17
          ],
          [
            2.3373351452200947e-16,
            0.012143027285106266,
            -1.7047386056831582e-16
          ],
          [
            -2.792150243473375e-16,
            0.010170959309406537,
            4.122784343878655e-17
          ],
          [
            5.724998682809275e-16,
            0.007392894726119755,
            -1.6632926255066002e-17
          ],
          [
            -1.0754141172127921e-16,
            0.003906604119045956,
            3.5578101930508395e-16
          ],
          [
            -3.3265852510132004e-17,
            2.501886615769754e-16,
            1.0677793313907945e-16
          ]
        ],
        "raw_reduced_polarization": [
          [
            -6.883630006758619e-15,
            0.2367976929865302,
            -8.061428247244527e-15
          ],
          [
            -1.875910099077802e-15,
            0.2596721779764716,
            -1.4620995659667316e-15
          ],
          [
            -6.269676238345938e-15,
            0.2675725058961783,
            -8.297299458818012e-15
          ],
          [
            -2.069455430736073e-15,
            0.26024667106242555,
            -1.440336471892133e-15
          ],
          [
            7.150432453342821e-15,
            0.23754010700430475,
            -3.153470901728153e-15
          ],
          [
            -8.543186168154617e-15,
            0.19896280441172667,
            -6.262559413469641e-16
          ],
          [
            1.7517442536284898e-14,
            0.1446187151755773,
            3.1207478463022595e-15
          ],
          [
            -3.2875896156829476e-15,
            0.07642041302170338,
            8.953021583900741e-15
          ],
          [
            -1.0169798432458124e-15,
            4.894153660936821e-15,
            2.6808282263887977e-15
          ]
        ],
        "unwrapped_reduced_polarization": [
          [
            -6.883630006758619e-15,
            0.2367976929865302,
            -8.061428247244527e-15
          ],
          [
            -1.875910099077802e-15,
            0.2596721779764716,
            -1.4620995659667316e-15
          ],
          [
            -6.269676238345938e-15,
            0.2675725058961783,
            -8.297299458818012e-15
          ],
          [
            -2.069455430736073e-15,
            0.26024667106242555,
            -1.4403364718921333e-15
          ],
          [
            7.150432453342821e-15,
            0.23754010700430475,
            -3.153470901728153e-15
          ],
          [
            -8.543186168154616e-15,
            0.19896280441172667,
            -6.262559413469642e-16
          ],
          [
            1.75174425362849e-14,
            0.1446187151755773,
            3.12074784630226e-15
          ],
          [
            -3.2875896156829487e-15,
            0.07642041302170338,
            8.953021583900741e-15
          ],
          [
            -1.0169798432458126e-15,
            4.898859096158503e-15,
            2.6808282263887977e-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": [
          [
            -6.8833827526759706e-15,
            0.2367976929865302,
            -8.049116928532385e-15
          ],
          [
            -1.887379141862766e-15,
            0.2596721779764716,
            -1.4432899320127035e-15
          ],
          [
            -6.2727600891321345e-15,
            0.2675725058961783,
            -8.271161533457416e-15
          ],
          [
            -2.0539125955565396e-15,
            0.2602466710624256,
            -1.4432899320127035e-15
          ],
          [
            7.105427357601002e-15,
            0.23754010700430472,
            -3.164135620181696e-15
          ],
          [
            -8.548717289613705e-15,
            0.19896280441172665,
            -6.106226635438361e-16
          ],
          [
            1.7541523789077473e-14,
            0.14461871517557734,
            3.1086244689504383e-15
          ],
          [
            -3.2751579226442118e-15,
            0.07642041302170344,
            8.992806499463768e-15
          ],
          [
            -9.992007221626409e-16,
            4.884981308350689e-15,
            2.6645352591003757e-15
          ]
        ]
      },
      "reflected": {
        "reached": true,
        "construction": "reflect_displacements_about_reconstructed_parent",
        "energies_eV": [
          -18.754138156938044,
          -18.77979654049573,
          -18.84434825758626,
          -18.9206212939574,
          -18.98493791278848,
          -19.024644601042432,
          -19.037327146766824,
          -19.02688894313773,
          -18.997472214006734
        ],
        "cartesian_polarizations_e_A2": [
          [
            2.366783604819228e-16,
            -4.562913219895322e-16,
            3.089906890531278e-16
          ],
          [
            1.0514190760579427e-16,
            -0.003906604119046053,
            5.250551278156573e-16
          ],
          [
            1.1561247101881942e-16,
            -0.007392894726120179,
            5.953496915624772e-16
          ],
          [
            -2.5958271794791533e-17,
            -0.010170959309406157,
            3.5261803660739926e-16
          ],
          [
            1.5149596438220773e-16,
            -0.012143027285106026,
            -2.6277296773782143e-16
          ],
          [
            2.3995041154849314e-16,
            -0.01330378464261533,
            2.308704698387604e-16
          ],
          [
            -4.569964656309938e-17,
            -0.013678280610451616,
            -2.289481398371503e-16
          ],
          [
            3.4029331092331756e-17,
            -0.013274416611650965,
            -2.1494648798145131e-16
          ],
          [
            -1.644751002796035e-16,
            -0.012105075152355305,
            1.5847633999089115e-16
          ]
        ],
        "raw_reduced_polarization": [
          [
            7.244591182515333e-15,
            -8.925903475772403e-15,
            9.834246640763546e-15
          ],
          [
            3.2216110625495343e-15,
            -0.07642041302170526,
            1.4858326649136512e-14
          ],
          [
            3.54258754651933e-15,
            -0.14461871517558564,
            1.6825074902502153e-14
          ],
          [
            -7.913023497188623e-16,
            -0.19896280441171926,
            9.376295341409098e-15
          ],
          [
            4.633314690769209e-15,
            -0.2375401070043001,
            -6.163042787325854e-15
          ],
          [
            7.344050666638752e-15,
            -0.2602466710624225,
            7.741529339561609e-15
          ],
          [
            -1.4002707640410816e-15,
            -0.26757250589618103,
            -6.477995373289205e-15
          ],
          [
            1.0394271221406132e-15,
            -0.25967217797647374,
            -5.601988522321094e-15
          ],
          [
            -5.031336786194623e-15,
            -0.2367976929865283,
            3.2609045509363288e-15
          ]
        ],
        "unwrapped_reduced_polarization": [
          [
            7.244591182515333e-15,
            -8.925903475772403e-15,
            9.834246640763546e-15
          ],
          [
            3.2216110625495343e-15,
            -0.07642041302170526,
            1.4858326649136512e-14
          ],
          [
            3.54258754651933e-15,
            -0.14461871517558564,
            1.6825074902502153e-14
          ],
          [
            -7.913023497188622e-16,
            -0.19896280441171926,
            9.376295341409098e-15
          ],
          [
            4.633314690769209e-15,
            -0.2375401070043001,
            -6.163042787325853e-15
          ],
          [
            7.344050666638752e-15,
            -0.2602466710624225,
            7.741529339561609e-15
          ],
          [
            -1.4002707640410812e-15,
            -0.26757250589618103,
            -6.477995373289205e-15
          ],
          [
            1.0394271221406132e-15,
            -0.25967217797647374,
            -5.601988522321094e-15
          ],
          [
            -5.0313367861946226e-15,
            -0.2367976929865283,
            3.260904550936328e-15
          ]
        ],
        "gauge_integer_shift": [
          0,
          0,
          0
        ],
        "expected_opposite_endpoint_reduced_polarization": [
          4.849670320266994e-15,
          -0.2367976929865204,
          1.3423084700022122e-14
        ],
        "actual_opposite_endpoint_branch_residual": 1.6231995278263223e-14
      },
      "pnp_branch": {
        "construction": "incoming_path_concatenated_with_parent_reflection",
        "reduced_polarization": [
          [
            -6.883630006758619e-15,
            0.2367976929865302,
            -8.061428247244527e-15
          ],
          [
            -1.875910099077802e-15,
            0.2596721779764716,
            -1.4620995659667316e-15
          ],
          [
            -6.269676238345938e-15,
            0.2675725058961783,
            -8.297299458818012e-15
          ],
          [
            -2.069455430736073e-15,
            0.26024667106242555,
            -1.440336471892133e-15
          ],
          [
            7.150432453342821e-15,
            0.23754010700430475,
            -3.153470901728153e-15
          ],
          [
            -8.543186168154617e-15,
            0.19896280441172667,
            -6.262559413469641e-16
          ],
          [
            1.7517442536284898e-14,
            0.1446187151755773,
            3.1207478463022595e-15
          ],
          [
            -3.2875896156829476e-15,
            0.07642041302170338,
            8.953021583900741e-15
          ],
          [
            -1.0169798432458124e-15,
            4.894153660936821e-15,
            2.6808282263887977e-15
          ],
          [
            3.2216110625495343e-15,
            -0.07642041302170526,
            1.4858326649136512e-14
          ],
          [
            3.54258754651933e-15,
            -0.14461871517558564,
            1.6825074902502153e-14
          ],
          [
            -7.913023497188623e-16,
            -0.19896280441171926,
            9.376295341409098e-15
          ],
          [
            4.633314690769209e-15,
            -0.2375401070043001,
            -6.163042787325854e-15
          ],
          [
            7.344050666638752e-15,
            -0.2602466710624225,
            7.741529339561609e-15
          ],
          [
            -1.4002707640410816e-15,
            -0.26757250589618103,
            -6.477995373289205e-15
          ],
          [
            1.0394271221406132e-15,
            -0.25967217797647374,
            -5.601988522321094e-15
          ],
          [
            -5.031336786194623e-15,
            -0.2367976929865283,
            3.2609045509363288e-15
          ]
        ],
        "unwrapped_reduced_polarization": [
          [
            -6.883630006758619e-15,
            0.2367976929865302,
            -8.061428247244527e-15
          ],
          [
            -1.875910099077802e-15,
            0.2596721779764716,
            -1.4620995659667316e-15
          ],
          [
            -6.269676238345938e-15,
            0.2675725058961783,
            -8.297299458818012e-15
          ],
          [
            -2.069455430736073e-15,
            0.26024667106242555,
            -1.4403364718921333e-15
          ],
          [
            7.150432453342821e-15,
            0.23754010700430475,
            -3.153470901728153e-15
          ],
          [
            -8.543186168154616e-15,
            0.19896280441172667,
            -6.262559413469642e-16
          ],
          [
            1.75174425362849e-14,
            0.1446187151755773,
            3.12074784630226e-15
          ],
          [
            -3.2875896156829487e-15,
            0.07642041302170338,
            8.953021583900741e-15
          ],
          [
            -1.0169798432458126e-15,
            4.898859096158503e-15,
            2.6808282263887977e-15
          ],
          [
            3.2216110625495343e-15,
            -0.07642041302170526,
            1.4858326649136512e-14
          ],
          [
            3.54258754651933e-15,
            -0.14461871517558564,
            1.6825074902502153e-14
          ],
          [
            -7.913023497188622e-16,
            -0.19896280441171926,
            9.376295341409098e-15
          ],
          [
            4.633314690769209e-15,
            -0.2375401070043001,
            -6.163042787325853e-15
          ],
          [
            7.344050666638752e-15,
            -0.2602466710624225,
            7.741529339561609e-15
          ],
          [
            -1.4002707640410812e-15,
            -0.26757250589618103,
            -6.477995373289205e-15
          ],
          [
            1.0394271221406132e-15,
            -0.25967217797647374,
            -5.601988522321094e-15
          ],
          [
            -5.0313367861946226e-15,
            -0.2367976929865283,
            3.260904550936328e-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": [
          [
            -6.8833827526759706e-15,
            0.2367976929865302,
            -8.049116928532385e-15
          ],
          [
            -1.887379141862766e-15,
            0.2596721779764716,
            -1.4432899320127035e-15
          ],
          [
            -6.2727600891321345e-15,
            0.2675725058961783,
            -8.271161533457416e-15
          ],
          [
            -2.0539125955565396e-15,
            0.2602466710624256,
            -1.4432899320127035e-15
          ],
          [
            7.105427357601002e-15,
            0.23754010700430472,
            -3.164135620181696e-15
          ],
          [
            -8.548717289613705e-15,
            0.19896280441172665,
            -6.106226635438361e-16
          ],
          [
            1.7541523789077473e-14,
            0.14461871517557734,
            3.1086244689504383e-15
          ],
          [
            -3.2751579226442118e-15,
            0.07642041302170344,
            8.992806499463768e-15
          ],
          [
            -9.992007221626409e-16,
            4.884981308350689e-15,
            2.6645352591003757e-15
          ],
          [
            3.219646771412954e-15,
            -0.07642041302170527,
            1.4876988529977098e-14
          ],
          [
            3.552713678800501e-15,
            -0.14461871517558567,
            1.687538997430238e-14
          ],
          [
            -7.771561172376096e-16,
            -0.19896280441171926,
            9.325873406851315e-15
          ],
          [
            4.6629367034256575e-15,
            -0.23754010700430006,
            -6.161737786669619e-15
          ],
          [
            7.327471962526033e-15,
            -0.2602466710624225,
            7.771561172376096e-15
          ],
          [
            -1.3877787807814457e-15,
            -0.26757250589618103,
            -6.494804694057166e-15
          ],
          [
            9.992007221626409e-16,
            -0.25967217797647374,
            -5.6066262743570405e-15
          ],
          [
            -5.051514762044462e-15,
            -0.2367976929865283,
            3.219646771412954e-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/m",
        "spacegroup_number": 11,
        "pointgroup": "2/m",
        "has_inversion": true,
        "is_polar_point_group": false,
        "nonpolar_parent_hypothesis": true,
        "symmetry_tolerance_A": null,
        "target_reduced_polarization": [
          0.0,
          0.0,
          0.0
        ],
        "formal_class": [
          0.0,
          0.0,
          0.0
        ],
        "target_residual": 5.2896710220797375e-15,
        "parent_symmetrization_rmsd_A": 0.3798557983484948,
        "parent_cell_rmsd_A": 0.0,
        "energy_eV": -18.754138156938062,
        "reduced_polarization": [
          -2.2315415632089064e-15,
          -3.621418348508111e-15,
          3.1442281912402646e-15
        ],
        "cartesian_polarization_e_A2": [
          -7.296673878451905e-17,
          -1.8512655555855897e-16,
          1.3306341004052801e-16
        ],
        "ranking_score": 0.3798557983485054
      }
    }
  ],
  "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": 158,
      "full_response": 39,
      "energy_polarization": 119
    },
    "model_evaluations_for_recovery_and_path_properties": {
      "total": 183,
      "full_response": 64,
      "energy_polarization": 119
    },
    "elapsed_seconds": 161.23458304203814
  }
}