{
  "schema": "ferrofinder.endpoint_parent_recovery.v4_variable_cell",
  "status": "complete",
  "input_atom_count": 28,
  "input_formula": "Li4Mn4O16P4",
  "input_spacegroup": "Pna2_1",
  "input_pointgroup": "mm2",
  "input_is_polar_point_group": true,
  "input_energy_eV": -191.10179407364316,
  "input_cartesian_polarization_e_A2": [
    1.6743558669750566e-17,
    -8.214519391568233e-18,
    -0.0018636773725774394
  ],
  "input_reduced_polarization": [
    7.758177125247622e-16,
    -3.358252123070092e-16,
    -0.1383916181422002
  ],
  "input_formal_targets": [
    {
      "orbit_id": 0,
      "representative_formal_class": [
        0.0,
        0.0,
        0.0
      ],
      "target_reduced_polarization": [
        0.0,
        0.0,
        0.0
      ]
    },
    {
      "orbit_id": 1,
      "representative_formal_class": [
        0.0,
        0.0,
        0.5
      ],
      "target_reduced_polarization": [
        0.0,
        0.0,
        -0.5
      ]
    },
    {
      "orbit_id": 2,
      "representative_formal_class": [
        0.5,
        0.0,
        0.0
      ],
      "target_reduced_polarization": [
        0.5,
        0.0,
        0.0
      ]
    },
    {
      "orbit_id": 3,
      "representative_formal_class": [
        0.0,
        0.5,
        0.0
      ],
      "target_reduced_polarization": [
        0.0,
        -0.5,
        0.0
      ]
    },
    {
      "orbit_id": 4,
      "representative_formal_class": [
        0.5,
        0.0,
        0.5
      ],
      "target_reduced_polarization": [
        0.5,
        0.0,
        -0.5
      ]
    },
    {
      "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,
        0.5,
        0.0
      ],
      "target_reduced_polarization": [
        0.5,
        -0.5,
        0.0
      ]
    },
    {
      "orbit_id": 7,
      "representative_formal_class": [
        0.5,
        0.5,
        0.5
      ],
      "target_reduced_polarization": [
        0.5,
        -0.5,
        -0.5
      ]
    }
  ],
  "parent_candidates": [
    {
      "candidate_id": "inversion_parent_endpoint_00",
      "source": "same_species_inversion_center_projection_from_endpoint",
      "spacegroup": "Pnma",
      "spacegroup_number": 62,
      "pointgroup": "mmm",
      "has_inversion": true,
      "is_polar_point_group": false,
      "nonpolar_parent_hypothesis": true,
      "symmetry_tolerance_A": null,
      "target_reduced_polarization": [
        0.0,
        0.0,
        0.0
      ],
      "formal_class": [
        0.0,
        0.0,
        0.0
      ],
      "target_residual": 4.226856218944112e-15,
      "parent_symmetrization_rmsd_A": 0.6097940543705473,
      "parent_cell_rmsd_A": 0.0,
      "energy_eV": -173.2634713782113,
      "reduced_polarization": [
        2.510048908588402e-15,
        -2.042936708200973e-15,
        -2.7188927118232632e-15
      ],
      "cartesian_polarization_e_A2": [
        5.417142517682835e-17,
        -4.997165963204009e-17,
        -3.6614492217903984e-17
      ],
      "ranking_score": 0.6097940543705558
    },
    {
      "candidate_id": "inversion_parent_endpoint_01",
      "source": "same_species_inversion_center_projection_from_endpoint",
      "spacegroup": "Pnma",
      "spacegroup_number": 62,
      "pointgroup": "mmm",
      "has_inversion": true,
      "is_polar_point_group": false,
      "nonpolar_parent_hypothesis": true,
      "symmetry_tolerance_A": null,
      "target_reduced_polarization": [
        0.0,
        0.0,
        0.0
      ],
      "formal_class": [
        0.0,
        0.0,
        0.0
      ],
      "target_residual": 9.938080379921019e-15,
      "parent_symmetrization_rmsd_A": 0.7024835353932642,
      "parent_cell_rmsd_A": 0.0,
      "energy_eV": -148.94198791124808,
      "reduced_polarization": [
        9.933092070310998e-15,
        3.146470457651258e-16,
        1.0990772819093147e-17
      ],
      "cartesian_polarization_e_A2": [
        2.143742108053223e-16,
        7.696486637145011e-18,
        1.4800935840663482e-19
      ],
      "ranking_score": 0.7024835353932841
    },
    {
      "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": 4.349292083182255e-15,
      "parent_symmetrization_rmsd_A": 0.7424536074098663,
      "parent_cell_rmsd_A": 0.0,
      "energy_eV": -157.48897394579123,
      "reduced_polarization": [
        -2.486045708642884e-15,
        -1.2631263616051926e-16,
        -3.5665057797957265e-15
      ],
      "cartesian_polarization_e_A2": [
        -5.3653392422405127e-17,
        -3.089695356738502e-18,
        -4.8029036802953e-17
      ],
      "ranking_score": 0.742453607409875
    },
    {
      "candidate_id": "bec_projection_00",
      "source": "MACEField_BEC_backprojection",
      "spacegroup": "Pna2_1",
      "spacegroup_number": 33,
      "pointgroup": "mm2",
      "has_inversion": false,
      "is_polar_point_group": true,
      "nonpolar_parent_hypothesis": false,
      "symmetry_tolerance_A": null,
      "target_reduced_polarization": [
        0.0,
        0.0,
        0.0
      ],
      "formal_class": [
        0.0,
        0.0,
        0.0
      ],
      "target_residual": 0.0007830758391394628,
      "parent_symmetrization_rmsd_A": 0.012092884885228599,
      "parent_cell_rmsd_A": 0.01150298702586981,
      "energy_eV": -190.96373931894806,
      "reduced_polarization": [
        -1.023936048955266e-15,
        -6.631418008511183e-17,
        0.0007830758391394628
      ],
      "cartesian_polarization_e_A2": [
        -2.2059503851648343e-17,
        -1.6436130956858123e-18,
        1.0554608786143168e-05
      ],
      "ranking_score": 0.5165347833199749
    },
    {
      "candidate_id": "inversion_parent_bec_00_00",
      "source": "same_species_inversion_center_projection_after_BEC",
      "spacegroup": "Pnma",
      "spacegroup_number": 62,
      "pointgroup": "mmm",
      "has_inversion": true,
      "is_polar_point_group": false,
      "nonpolar_parent_hypothesis": true,
      "symmetry_tolerance_A": null,
      "target_reduced_polarization": [
        0.0,
        0.0,
        0.0
      ],
      "formal_class": [
        0.0,
        0.0,
        0.0
      ],
      "target_residual": 2.689687563149299e-15,
      "parent_symmetrization_rmsd_A": 0.6097976959340783,
      "parent_cell_rmsd_A": 0.01150298702586981,
      "energy_eV": -173.19240121780805,
      "reduced_polarization": [
        2.5363963323658924e-16,
        1.373065354007798e-15,
        -2.298864427806708e-15
      ],
      "cartesian_polarization_e_A2": [
        5.466398610370791e-18,
        3.3481691488521094e-17,
        -3.098501253026078e-17
      ],
      "ranking_score": 0.612673442690551
    },
    {
      "candidate_id": "inversion_parent_bec_00_01",
      "source": "same_species_inversion_center_projection_after_BEC",
      "spacegroup": "Pnma",
      "spacegroup_number": 62,
      "pointgroup": "mmm",
      "has_inversion": true,
      "is_polar_point_group": false,
      "nonpolar_parent_hypothesis": true,
      "symmetry_tolerance_A": null,
      "target_reduced_polarization": [
        0.0,
        0.0,
        0.0
      ],
      "formal_class": [
        0.0,
        0.0,
        0.0
      ],
      "target_residual": 1.0703893268519432e-14,
      "parent_symmetrization_rmsd_A": 0.8143962040042972,
      "parent_cell_rmsd_A": 0.01150298702586981,
      "energy_eV": -157.72234487944945,
      "reduced_polarization": [
        9.768553442219934e-15,
        4.604653807152552e-16,
        4.351628015296278e-15
      ],
      "cartesian_polarization_e_A2": [
        2.1053021675076696e-16,
        1.1228278226707571e-17,
        5.865297968424875e-17
      ],
      "ranking_score": 0.8172719507607861
    },
    {
      "candidate_id": "bec_projection_01",
      "source": "MACEField_BEC_backprojection",
      "spacegroup": "Pna2_1",
      "spacegroup_number": 33,
      "pointgroup": "mm2",
      "has_inversion": false,
      "is_polar_point_group": true,
      "nonpolar_parent_hypothesis": false,
      "symmetry_tolerance_A": null,
      "target_reduced_polarization": [
        0.0,
        0.0,
        -0.5
      ],
      "formal_class": [
        0.0,
        0.0,
        0.5
      ],
      "target_residual": 3.554557040635897e-05,
      "parent_symmetrization_rmsd_A": 0.03262340420440152,
      "parent_cell_rmsd_A": 0.030793328153789545,
      "energy_eV": -190.31183459130818,
      "reduced_polarization": [
        6.163737038963531e-16,
        2.961083956335434e-15,
        -0.49996445442959364
      ],
      "cartesian_polarization_e_A2": [
        2.7394408733108166e-17,
        2.7998628810356906e-17,
        -0.0067172329292050055
      ],
      "ranking_score": 0.5403928273836616
    },
    {
      "candidate_id": "bec_projection_02",
      "source": "MACEField_BEC_backprojection",
      "spacegroup": "Pc",
      "spacegroup_number": 7,
      "pointgroup": "m",
      "has_inversion": false,
      "is_polar_point_group": true,
      "nonpolar_parent_hypothesis": false,
      "symmetry_tolerance_A": null,
      "target_reduced_polarization": [
        0.5,
        0.0,
        0.0
      ],
      "formal_class": [
        0.5,
        0.0,
        0.0
      ],
      "target_residual": 0.0008486373581105927,
      "parent_symmetrization_rmsd_A": 0.08186591345440038,
      "parent_cell_rmsd_A": 0.06693075543466934,
      "energy_eV": -186.39669450481998,
      "reduced_polarization": [
        0.49968868056672855,
        1.2804183916113258e-15,
        0.0007894717069334841
      ],
      "cartesian_polarization_e_A2": [
        0.010775216671136227,
        -1.2972443669945168e-17,
        -0.00013107010961989967
      ],
      "ranking_score": 0.6002958770292889
    },
    {
      "candidate_id": "bec_projection_03",
      "source": "MACEField_BEC_backprojection",
      "spacegroup": "Pc",
      "spacegroup_number": 7,
      "pointgroup": "m",
      "has_inversion": false,
      "is_polar_point_group": true,
      "nonpolar_parent_hypothesis": false,
      "symmetry_tolerance_A": null,
      "target_reduced_polarization": [
        0.0,
        -0.5,
        0.0
      ],
      "formal_class": [
        0.0,
        0.5,
        0.0
      ],
      "target_residual": 0.0006522847421521644,
      "parent_symmetrization_rmsd_A": 0.07738770797562089,
      "parent_cell_rmsd_A": 0.11084323940260046,
      "energy_eV": -185.97651269767036,
      "reduced_polarization": [
        -3.166794499540811e-16,
        -0.49977743429644905,
        0.0006131393744063313
      ],
      "cartesian_polarization_e_A2": [
        -2.281362139005183e-17,
        -0.012203133273689782,
        -0.00022783986835421332
      ],
      "ranking_score": 0.6064030873105754
    },
    {
      "candidate_id": "bec_projection_04",
      "source": "MACEField_BEC_backprojection",
      "spacegroup": "Pc",
      "spacegroup_number": 7,
      "pointgroup": "m",
      "has_inversion": false,
      "is_polar_point_group": true,
      "nonpolar_parent_hypothesis": false,
      "symmetry_tolerance_A": null,
      "target_reduced_polarization": [
        0.5,
        0.0,
        -0.5
      ],
      "formal_class": [
        0.5,
        0.0,
        0.5
      ],
      "target_residual": 7.127406107223118e-05,
      "parent_symmetrization_rmsd_A": 0.09119085511682927,
      "parent_cell_rmsd_A": 0.07733284575785092,
      "energy_eV": -186.4819848802464,
      "reduced_polarization": [
        0.499957484062324,
        -3.5628941334461205e-16,
        -0.49994279522025864
      ],
      "cartesian_polarization_e_A2": [
        0.010931205997878285,
        -4.3098780652486e-17,
        -0.006861959112431653
      ],
      "ranking_score": 0.6106666146784365
    },
    {
      "candidate_id": "bec_projection_05",
      "source": "MACEField_BEC_backprojection",
      "spacegroup": "Pc",
      "spacegroup_number": 7,
      "pointgroup": "m",
      "has_inversion": false,
      "is_polar_point_group": true,
      "nonpolar_parent_hypothesis": false,
      "symmetry_tolerance_A": null,
      "target_reduced_polarization": [
        0.0,
        -0.5,
        -0.5
      ],
      "formal_class": [
        0.0,
        0.5,
        0.5
      ],
      "target_residual": 0.00010538982313539257,
      "parent_symmetrization_rmsd_A": 0.08646460930271617,
      "parent_cell_rmsd_A": 0.12212973307852483,
      "energy_eV": -186.1860536081239,
      "reduced_polarization": [
        -1.1626122249185144e-15,
        -0.4999817327976177,
        -0.49989620537519874
      ],
      "cartesian_polarization_e_A2": [
        3.9017054763563624e-17,
        -0.012493866171565877,
        -0.006963485150127539
      ],
      "ranking_score": 0.6172078222186181
    },
    {
      "candidate_id": "bec_projection_06",
      "source": "MACEField_BEC_backprojection",
      "spacegroup": "P1",
      "spacegroup_number": 1,
      "pointgroup": "1",
      "has_inversion": false,
      "is_polar_point_group": true,
      "nonpolar_parent_hypothesis": false,
      "symmetry_tolerance_A": null,
      "target_reduced_polarization": [
        0.5,
        -0.5,
        0.0
      ],
      "formal_class": [
        0.5,
        0.5,
        0.0
      ],
      "target_residual": 0.0007907773634256206,
      "parent_symmetrization_rmsd_A": 0.11593625798137375,
      "parent_cell_rmsd_A": 0.13658359095719178,
      "energy_eV": -180.54167761467983,
      "reduced_polarization": [
        0.4995908965591897,
        -0.49967699920430914,
        0.0005946710848919922
      ],
      "cartesian_polarization_e_A2": [
        0.010782678536622379,
        -0.012221113015752355,
        -0.00039210436566518536
      ],
      "ranking_score": 0.6516637104475229
    },
    {
      "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": 0.00017063660636711496,
      "parent_symmetrization_rmsd_A": 0.1273257131453979,
      "parent_cell_rmsd_A": 0.15325577099346918,
      "energy_eV": -181.10491714267505,
      "reduced_polarization": [
        0.49990924984495866,
        -0.4999485105439246,
        -0.49986498112463246
      ],
      "cartesian_polarization_e_A2": [
        0.01095254874189006,
        -0.012535918993109223,
        -0.007141367341267068
      ],
      "ranking_score": 0.6659809291064994
    }
  ],
  "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": [
              7.758177125247622e-16,
              -3.358252123070092e-16,
              -0.1383916181422002
            ],
            "branch_aligned_reduced_polarization": [
              7.758177125247622e-16,
              -3.358252123070092e-16,
              -0.1383916181422002
            ],
            "target_residual": 0.1383916181422002,
            "energy_eV": -191.10179407364316,
            "max_atomic_step_A": 0.019226133395983894,
            "max_log_strain_component": 0.002687056382801487,
            "step_scale": 1.0,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 3.315984221629218,
            "cell_principal_stretches": [
              1.0026906697545233,
              1.0004276952768956,
              0.9987043075439539
            ],
            "cell_volume_ratio": 1.0018197814290062,
            "cell_rmsd_from_input_A": 0.01150298702586981
          },
          {
            "iteration": 1,
            "reduced_polarization": [
              -1.023936048955266e-15,
              -6.631418008511183e-17,
              0.0007830758391394628
            ],
            "branch_aligned_reduced_polarization": [
              -1.023936048955266e-15,
              -6.631418008511183e-17,
              0.0007830758391394628
            ],
            "target_residual": 0.0007830758391394628,
            "energy_eV": -190.96373931894806
          }
        ],
        "iterations": 1
      },
      "parent": {
        "candidate_id": "bec_projection_00",
        "source": "MACEField_BEC_backprojection",
        "spacegroup": "Pna2_1",
        "spacegroup_number": 33,
        "pointgroup": "mm2",
        "has_inversion": false,
        "is_polar_point_group": true,
        "nonpolar_parent_hypothesis": false,
        "symmetry_tolerance_A": null,
        "target_reduced_polarization": [
          0.0,
          0.0,
          0.0
        ],
        "formal_class": [
          0.0,
          0.0,
          0.0
        ],
        "target_residual": 0.0007830758391394628,
        "parent_symmetrization_rmsd_A": 0.012092884885228599,
        "parent_cell_rmsd_A": 0.01150298702586981,
        "energy_eV": -190.96373931894806,
        "reduced_polarization": [
          -1.023936048955266e-15,
          -6.631418008511183e-17,
          0.0007830758391394628
        ],
        "cartesian_polarization_e_A2": [
          -2.2059503851648343e-17,
          -1.6436130956858123e-18,
          1.0554608786143168e-05
        ],
        "ranking_score": 0.5165347833199749
      },
      "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": [
          -191.1017940736431,
          -191.09499541460028,
          -191.08505622850387,
          -191.07205512683157,
          -191.0560688159097,
          -191.03717209998922,
          -191.0154378905097,
          -190.99093723219792,
          -190.96373931894811
        ],
        "cartesian_polarizations_e_A2": [
          [
            1.5439226198792098e-17,
            -4.255269054190752e-18,
            -0.0018636773725774394
          ],
          [
            -1.9421813872206169e-19,
            -1.1616094392138547e-17,
            -0.001631200402099391
          ],
          [
            -5.9824086168897415e-18,
            -1.775305184610248e-17,
            -0.0013981685095343583
          ],
          [
            -8.819043140010437e-18,
            2.0836607167278325e-17,
            -0.0011646004517120489
          ],
          [
            2.5647047695059248e-17,
            -1.2569363915416424e-17,
            -0.0009305159703141253
          ],
          [
            1.6807703983896968e-17,
            6.8376585750872766e-18,
            -0.0006959358575292041
          ],
          [
            2.248524195385463e-17,
            -1.8937857849384547e-17,
            -0.00046088199021858455
          ],
          [
            -1.3161129283667499e-17,
            4.091494928185756e-17,
            -0.00022537722939421033
          ],
          [
            -3.065615436897133e-18,
            -1.647306608260387e-17,
            1.0554608786098182e-05
          ]
        ],
        "raw_reduced_polarization": [
          [
            7.153810840905128e-16,
            -1.7396351087975706e-16,
            -0.1383916181422002
          ],
          [
            -1.649860218477657e-18,
            -4.955540857549045e-16,
            -0.12111535415508028
          ],
          [
            -2.6469118710677907e-16,
            -7.614592272743698e-16,
            -0.10380164323631795
          ],
          [
            -3.9310056172591334e-16,
            8.08955849922753e-16,
            -0.08645189057590755
          ],
          [
            1.2059647938785886e-15,
            -5.614137275859858e-16,
            -0.0690675738567748
          ],
          [
            7.951499368901118e-16,
            2.3636639668987766e-16,
            -0.05165024808795794
          ],
          [
            1.055410984138223e-15,
            -8.107713365041173e-16,
            -0.0342015480978444
          ],
          [
            -6.034563362775028e-16,
            1.6574206573053293e-15,
            -0.016723181031820626
          ],
          [
            -1.4262401252340467e-16,
            -6.744617141547602e-16,
            0.0007830758391361251
          ]
        ],
        "unwrapped_reduced_polarization": [
          [
            7.153810840905128e-16,
            -1.7396351087975706e-16,
            -0.1383916181422002
          ],
          [
            -1.6498602184776534e-18,
            -4.955540857549045e-16,
            -0.12111535415508028
          ],
          [
            -2.6469118710677907e-16,
            -7.614592272743698e-16,
            -0.10380164323631795
          ],
          [
            -3.9310056172591334e-16,
            8.089558499227531e-16,
            -0.08645189057590755
          ],
          [
            1.2059647938785886e-15,
            -5.614137275859858e-16,
            -0.0690675738567748
          ],
          [
            7.951499368901118e-16,
            2.363663966898776e-16,
            -0.05165024808795794
          ],
          [
            1.055410984138223e-15,
            -8.107713365041172e-16,
            -0.0342015480978444
          ],
          [
            -6.034563362775029e-16,
            1.6574206573053291e-15,
            -0.016723181031820626
          ],
          [
            -1.4262401252340472e-16,
            -6.7446171415476e-16,
            0.0007830758391361263
          ]
        ],
        "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": [
          [
            6.661338147750939e-16,
            -1.6653345369377348e-16,
            -0.1383916181422002
          ],
          [
            0.0,
            -4.996003610813204e-16,
            -0.12111535415508029
          ],
          [
            -2.7755575615628914e-16,
            -7.771561172376096e-16,
            -0.10380164323631796
          ],
          [
            -3.885780586188048e-16,
            7.771561172376096e-16,
            -0.08645189057590752
          ],
          [
            1.2212453270876722e-15,
            -5.551115123125783e-16,
            -0.06906757385677481
          ],
          [
            7.771561172376096e-16,
            2.220446049250313e-16,
            -0.05165024808795793
          ],
          [
            1.1102230246251565e-15,
            -8.326672684688674e-16,
            -0.03420154809784437
          ],
          [
            -6.106226635438361e-16,
            1.6653345369377348e-15,
            -0.016723181031820633
          ],
          [
            -1.6653345369377348e-16,
            -6.661338147750939e-16,
            0.0007830758391361714
          ]
        ]
      },
      "reflected": {
        "reached": true,
        "construction": "reflect_displacements_about_reconstructed_parent",
        "energies_eV": [
          -190.96373931894811,
          -190.94254212543544,
          -190.91944710410138,
          -190.89449182532562,
          -190.8677130529178,
          -190.83914675977383,
          -190.8088281449352,
          -190.77679165040263,
          -190.74307097737017
        ],
        "cartesian_polarizations_e_A2": [
          [
            -1.0914329657868708e-17,
            -5.0785797900404305e-18,
            1.055460878612134e-05
          ],
          [
            -3.1475879718413214e-17,
            9.993222375388233e-18,
            0.0002186987464087633
          ],
          [
            -1.769996860459551e-17,
            -1.0826911902184728e-16,
            0.00042703331202120505
          ],
          [
            -8.445432348148339e-18,
            -1.2171032263655352e-16,
            0.0006355416593046776
          ],
          [
            3.3087002071463823e-18,
            -1.4223714018989614e-16,
            0.0008442067510929935
          ],
          [
            -1.4559741033036097e-17,
            -1.3875664311483925e-16,
            0.0010530112367442737
          ],
          [
            3.4119146516728204e-18,
            -1.1367501010207494e-16,
            0.001261937509610164
          ],
          [
            1.2772154741674629e-17,
            -1.8075234777066542e-16,
            0.001470967763272024
          ],
          [
            2.442154413709475e-17,
            -1.8369811495243465e-16,
            0.001680084050399448
          ]
        ],
        "raw_reduced_polarization": [
          [
            -5.068025399745872e-16,
            -2.0718023405392316e-16,
            0.0007830758391378434
          ],
          [
            -1.4671198947290897e-15,
            4.2889472665719165e-16,
            0.016227631946033372
          ],
          [
            -8.325372132227513e-16,
            -4.4044066156138126e-15,
            0.031689674733326345
          ],
          [
            -4.0598375352995736e-16,
            -4.945524363045823e-15,
            0.04716797391337397
          ],
          [
            1.3819736621364215e-16,
            -5.781571520780873e-15,
            0.06266126965216914
          ],
          [
            -6.892185868245886e-16,
            -5.639590148014405e-15,
            0.07816827829698084
          ],
          [
            1.4677304768586797e-16,
            -4.6191773774247974e-15,
            0.09368769663014848
          ],
          [
            5.8527563277250945e-16,
            -7.37390885992843e-15,
            0.10921820603409964
          ],
          [
            1.1315794260029683e-15,
            -7.509929128370035e-15,
            0.12475847685381508
          ]
        ],
        "unwrapped_reduced_polarization": [
          [
            -5.068025399745872e-16,
            -2.0718023405392316e-16,
            0.0007830758391378434
          ],
          [
            -1.4671198947290897e-15,
            4.2889472665719165e-16,
            0.016227631946033372
          ],
          [
            -8.325372132227513e-16,
            -4.4044066156138126e-15,
            0.031689674733326345
          ],
          [
            -4.0598375352995736e-16,
            -4.945524363045823e-15,
            0.04716797391337397
          ],
          [
            1.3819736621364213e-16,
            -5.781571520780873e-15,
            0.06266126965216914
          ],
          [
            -6.892185868245886e-16,
            -5.639590148014405e-15,
            0.07816827829698084
          ],
          [
            1.4677304768586792e-16,
            -4.6191773774247974e-15,
            0.09368769663014848
          ],
          [
            5.8527563277250945e-16,
            -7.37390885992843e-15,
            0.10921820603409964
          ],
          [
            1.1315794260029683e-15,
            -7.509929128370035e-15,
            0.12475847685381508
          ]
        ],
        "gauge_integer_shift": [
          0,
          0,
          0
        ],
        "expected_opposite_endpoint_reduced_polarization": [
          -9.994734688272116e-16,
          -1.1729371782138043e-15,
          0.13995913128611515
        ],
        "actual_opposite_endpoint_branch_residual": 0.015200654432300065
      },
      "pnp_branch": {
        "construction": "incoming_path_concatenated_with_parent_reflection",
        "reduced_polarization": [
          [
            7.153810840905128e-16,
            -1.7396351087975706e-16,
            -0.1383916181422002
          ],
          [
            -1.649860218477657e-18,
            -4.955540857549045e-16,
            -0.12111535415508028
          ],
          [
            -2.6469118710677907e-16,
            -7.614592272743698e-16,
            -0.10380164323631795
          ],
          [
            -3.9310056172591334e-16,
            8.08955849922753e-16,
            -0.08645189057590755
          ],
          [
            1.2059647938785886e-15,
            -5.614137275859858e-16,
            -0.0690675738567748
          ],
          [
            7.951499368901118e-16,
            2.3636639668987766e-16,
            -0.05165024808795794
          ],
          [
            1.055410984138223e-15,
            -8.107713365041173e-16,
            -0.0342015480978444
          ],
          [
            -6.034563362775028e-16,
            1.6574206573053293e-15,
            -0.016723181031820626
          ],
          [
            -1.4262401252340467e-16,
            -6.744617141547602e-16,
            0.0007830758391361251
          ],
          [
            -1.4671198947290897e-15,
            4.2889472665719165e-16,
            0.016227631946033372
          ],
          [
            -8.325372132227513e-16,
            -4.4044066156138126e-15,
            0.031689674733326345
          ],
          [
            -4.0598375352995736e-16,
            -4.945524363045823e-15,
            0.04716797391337397
          ],
          [
            1.3819736621364215e-16,
            -5.781571520780873e-15,
            0.06266126965216914
          ],
          [
            -6.892185868245886e-16,
            -5.639590148014405e-15,
            0.07816827829698084
          ],
          [
            1.4677304768586797e-16,
            -4.6191773774247974e-15,
            0.09368769663014848
          ],
          [
            5.8527563277250945e-16,
            -7.37390885992843e-15,
            0.10921820603409964
          ],
          [
            1.1315794260029683e-15,
            -7.509929128370035e-15,
            0.12475847685381508
          ]
        ],
        "unwrapped_reduced_polarization": [
          [
            7.153810840905128e-16,
            -1.7396351087975706e-16,
            -0.1383916181422002
          ],
          [
            -1.6498602184776534e-18,
            -4.955540857549045e-16,
            -0.12111535415508028
          ],
          [
            -2.6469118710677907e-16,
            -7.614592272743698e-16,
            -0.10380164323631795
          ],
          [
            -3.9310056172591334e-16,
            8.089558499227531e-16,
            -0.08645189057590755
          ],
          [
            1.2059647938785886e-15,
            -5.614137275859858e-16,
            -0.0690675738567748
          ],
          [
            7.951499368901118e-16,
            2.363663966898776e-16,
            -0.05165024808795794
          ],
          [
            1.055410984138223e-15,
            -8.107713365041172e-16,
            -0.0342015480978444
          ],
          [
            -6.034563362775029e-16,
            1.6574206573053291e-15,
            -0.016723181031820626
          ],
          [
            -1.4262401252340472e-16,
            -6.7446171415476e-16,
            0.0007830758391361263
          ],
          [
            -1.4671198947290897e-15,
            4.2889472665719175e-16,
            0.016227631946033372
          ],
          [
            -8.325372132227513e-16,
            -4.4044066156138126e-15,
            0.031689674733326345
          ],
          [
            -4.0598375352995736e-16,
            -4.945524363045823e-15,
            0.04716797391337397
          ],
          [
            1.3819736621364213e-16,
            -5.781571520780873e-15,
            0.06266126965216914
          ],
          [
            -6.892185868245886e-16,
            -5.639590148014405e-15,
            0.07816827829698084
          ],
          [
            1.4677304768586792e-16,
            -4.6191773774247974e-15,
            0.09368769663014848
          ],
          [
            5.8527563277250945e-16,
            -7.37390885992843e-15,
            0.10921820603409964
          ],
          [
            1.1315794260029683e-15,
            -7.509929128370035e-15,
            0.12475847685381508
          ]
        ],
        "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": [
          [
            6.661338147750939e-16,
            -1.6653345369377348e-16,
            -0.1383916181422002
          ],
          [
            0.0,
            -4.996003610813204e-16,
            -0.12111535415508029
          ],
          [
            -2.7755575615628914e-16,
            -7.771561172376096e-16,
            -0.10380164323631796
          ],
          [
            -3.885780586188048e-16,
            7.771561172376096e-16,
            -0.08645189057590752
          ],
          [
            1.2212453270876722e-15,
            -5.551115123125783e-16,
            -0.06906757385677481
          ],
          [
            7.771561172376096e-16,
            2.220446049250313e-16,
            -0.05165024808795793
          ],
          [
            1.1102230246251565e-15,
            -8.326672684688674e-16,
            -0.03420154809784437
          ],
          [
            -6.106226635438361e-16,
            1.6653345369377348e-15,
            -0.016723181031820633
          ],
          [
            -1.6653345369377348e-16,
            -6.661338147750939e-16,
            0.0007830758391361714
          ],
          [
            -1.4432899320127035e-15,
            4.440892098500626e-16,
            0.016227631946033383
          ],
          [
            -8.326672684688674e-16,
            -4.385380947269368e-15,
            0.0316896747333264
          ],
          [
            -3.885780586188048e-16,
            -4.9404924595819466e-15,
            0.04716797391337402
          ],
          [
            1.1102230246251565e-16,
            -5.773159728050814e-15,
            0.06266126965216912
          ],
          [
            -6.661338147750939e-16,
            -5.662137425588298e-15,
            0.07816827829698081
          ],
          [
            1.1102230246251565e-16,
            -4.6074255521944e-15,
            0.09368769663014853
          ],
          [
            5.551115123125783e-16,
            -7.382983113757291e-15,
            0.1092182060340996
          ],
          [
            1.1102230246251565e-15,
            -7.494005416219807e-15,
            0.12475847685381503
          ]
        ]
      },
      "incoming_structure_ids": [
        "incoming_00_000",
        "incoming_00_001",
        "incoming_00_002",
        "incoming_00_003",
        "incoming_00_004",
        "incoming_00_005",
        "incoming_00_006",
        "incoming_00_007",
        "incoming_00_008"
      ],
      "reflected_structure_ids": [
        "reflected_00_001",
        "reflected_00_002",
        "reflected_00_003",
        "reflected_00_004",
        "reflected_00_005",
        "reflected_00_006",
        "reflected_00_007",
        "reflected_00_008"
      ]
    },
    {
      "orbit_id": 1,
      "formal_class": [
        0.0,
        0.0,
        0.5
      ],
      "formal_classes_in_orbit": [
        [
          0.0,
          0.0,
          0.5
        ]
      ],
      "target_reduced_polarization": [
        0.0,
        0.0,
        -0.5
      ],
      "bec_backprojection": {
        "converged_to_target": true,
        "history": [
          {
            "iteration": 0,
            "reduced_polarization": [
              7.758177125247622e-16,
              -3.358252123070092e-16,
              -0.1383916181422002
            ],
            "branch_aligned_reduced_polarization": [
              7.758177125247622e-16,
              -3.358252123070092e-16,
              -0.1383916181422002
            ],
            "target_residual": 0.3616083818577998,
            "energy_eV": -191.10179407364316,
            "max_atomic_step_A": 0.05023664785507668,
            "max_log_strain_component": 0.007021105205570441,
            "step_scale": 1.0,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 3.315984221629218,
            "cell_principal_stretches": [
              1.003393501059005,
              0.9988833226610818,
              0.9930034851693904
            ],
            "cell_volume_ratio": 0.9952606161257339,
            "cell_rmsd_from_input_A": 0.03007266569298193
          },
          {
            "iteration": 1,
            "reduced_polarization": [
              -2.993721322663943e-15,
              -8.846739464460283e-16,
              -0.49214463238353623
            ],
            "branch_aligned_reduced_polarization": [
              -2.993721322663943e-15,
              -8.846739464460283e-16,
              -0.49214463238353623
            ],
            "target_residual": 0.007855367616463771,
            "energy_eV": -190.3516379205546,
            "max_atomic_step_A": 0.0011333634115368466,
            "max_log_strain_component": 0.00016818138566570585,
            "step_scale": 1.0,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 3.315984221629218,
            "cell_principal_stretches": [
              1.0034749290069729,
              0.9988565894150325,
              0.9928364945100375
            ],
            "cell_volume_ratio": 0.9951473662789645,
            "cell_rmsd_from_input_A": 0.030793328153789545
          },
          {
            "iteration": 2,
            "reduced_polarization": [
              6.163737038963531e-16,
              2.961083956335434e-15,
              -0.49996445442959364
            ],
            "branch_aligned_reduced_polarization": [
              6.163737038963531e-16,
              2.961083956335434e-15,
              -0.49996445442959364
            ],
            "target_residual": 3.554557040635897e-05,
            "energy_eV": -190.31183459130818
          }
        ],
        "iterations": 2
      },
      "parent": {
        "candidate_id": "bec_projection_01",
        "source": "MACEField_BEC_backprojection",
        "spacegroup": "Pna2_1",
        "spacegroup_number": 33,
        "pointgroup": "mm2",
        "has_inversion": false,
        "is_polar_point_group": true,
        "nonpolar_parent_hypothesis": false,
        "symmetry_tolerance_A": null,
        "target_reduced_polarization": [
          0.0,
          0.0,
          -0.5
        ],
        "formal_class": [
          0.0,
          0.0,
          0.5
        ],
        "target_residual": 3.554557040635897e-05,
        "parent_symmetrization_rmsd_A": 0.03262340420440152,
        "parent_cell_rmsd_A": 0.030793328153789545,
        "energy_eV": -190.31183459130818,
        "reduced_polarization": [
          6.163737038963531e-16,
          2.961083956335434e-15,
          -0.49996445442959364
        ],
        "cartesian_polarization_e_A2": [
          2.7394408733108166e-17,
          2.7998628810356906e-17,
          -0.0067172329292050055
        ],
        "ranking_score": 0.5403928273836616
      },
      "branch_status": "awaiting_branch_sampling"
    },
    {
      "orbit_id": 2,
      "formal_class": [
        0.5,
        0.0,
        0.0
      ],
      "formal_classes_in_orbit": [
        [
          0.5,
          0.0,
          0.0
        ]
      ],
      "target_reduced_polarization": [
        0.5,
        0.0,
        0.0
      ],
      "bec_backprojection": {
        "converged_to_target": true,
        "history": [
          {
            "iteration": 0,
            "reduced_polarization": [
              7.758177125247622e-16,
              -3.358252123070092e-16,
              -0.1383916181422002
            ],
            "branch_aligned_reduced_polarization": [
              7.771561172376096e-16,
              -3.358252123070092e-16,
              -0.1383916181422002
            ],
            "target_residual": 0.518798843456706,
            "energy_eV": -191.10179407364316,
            "max_atomic_step_A": 0.12,
            "max_log_strain_component": 0.011811425688112354,
            "step_scale": 0.9206147292844394,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 3.315984221629218,
            "cell_principal_stretches": [
              1.0133795438985511,
              0.9988071050649593,
              0.9896307094875662
            ],
            "cell_volume_ratio": 1.0016751966553736,
            "cell_rmsd_from_input_A": 0.060746746494763595
          },
          {
            "iteration": 1,
            "reduced_polarization": [
              0.4534405001841348,
              9.09791493456269e-15,
              0.027419097053020737
            ],
            "branch_aligned_reduced_polarization": [
              0.4534405001841348,
              9.09791493456269e-15,
              0.027419097053020737
            ],
            "target_residual": 0.05403326666329294,
            "energy_eV": -187.12423178502883,
            "max_atomic_step_A": 0.013652357131515002,
            "max_log_strain_component": 0.0013358074516823851,
            "step_scale": 1.0,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 3.315984221629218,
            "cell_principal_stretches": [
              1.0142836380630986,
              0.9991555320933622,
              0.9879204845311929
            ],
            "cell_volume_ratio": 1.0011853996539348,
            "cell_rmsd_from_input_A": 0.06693075543466934
          },
          {
            "iteration": 2,
            "reduced_polarization": [
              0.49968868056672855,
              1.2804183916113258e-15,
              0.0007894717069334841
            ],
            "branch_aligned_reduced_polarization": [
              0.49968868056672855,
              1.2804183916113258e-15,
              0.0007894717069334841
            ],
            "target_residual": 0.0008486373581105927,
            "energy_eV": -186.39669450481998
          }
        ],
        "iterations": 2
      },
      "parent": {
        "candidate_id": "bec_projection_02",
        "source": "MACEField_BEC_backprojection",
        "spacegroup": "Pc",
        "spacegroup_number": 7,
        "pointgroup": "m",
        "has_inversion": false,
        "is_polar_point_group": true,
        "nonpolar_parent_hypothesis": false,
        "symmetry_tolerance_A": null,
        "target_reduced_polarization": [
          0.5,
          0.0,
          0.0
        ],
        "formal_class": [
          0.5,
          0.0,
          0.0
        ],
        "target_residual": 0.0008486373581105927,
        "parent_symmetrization_rmsd_A": 0.08186591345440038,
        "parent_cell_rmsd_A": 0.06693075543466934,
        "energy_eV": -186.39669450481998,
        "reduced_polarization": [
          0.49968868056672855,
          1.2804183916113258e-15,
          0.0007894717069334841
        ],
        "cartesian_polarization_e_A2": [
          0.010775216671136227,
          -1.2972443669945168e-17,
          -0.00013107010961989967
        ],
        "ranking_score": 0.6002958770292889
      },
      "branch_status": "awaiting_branch_sampling"
    },
    {
      "orbit_id": 3,
      "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": [
              7.758177125247622e-16,
              -3.358252123070092e-16,
              -0.1383916181422002
            ],
            "branch_aligned_reduced_polarization": [
              7.758177125247622e-16,
              -3.3306690738754696e-16,
              -0.1383916181422002
            ],
            "target_residual": 0.5187988434567065,
            "energy_eV": -191.10179407364316,
            "max_atomic_step_A": 0.12,
            "max_log_strain_component": 0.01834537578934306,
            "step_scale": 0.9938723945066048,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 3.315984221629218,
            "cell_principal_stretches": [
              1.0193272733797991,
              1.0004250739720393,
              0.982395924025929
            ],
            "cell_volume_ratio": 1.0018086204485301,
            "cell_rmsd_from_input_A": 0.10551609419745156
          },
          {
            "iteration": 1,
            "reduced_polarization": [
              1.4607720819940148e-14,
              -0.4808881337564982,
              0.045275736780693486
            ],
            "branch_aligned_reduced_polarization": [
              1.4607720819940148e-14,
              -0.4808881337564982,
              0.045275736780693486
            ],
            "target_residual": 0.04914423437539896,
            "energy_eV": -186.19756122333146,
            "max_atomic_step_A": 0.00842172559451642,
            "max_log_strain_component": 0.000995629204848638,
            "step_scale": 1.0,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 3.315984221629218,
            "cell_principal_stretches": [
              1.0200159194019853,
              1.0002686703719976,
              0.9812336589623086
            ],
            "cell_volume_ratio": 1.0011428579718333,
            "cell_rmsd_from_input_A": 0.11084323940260046
          },
          {
            "iteration": 2,
            "reduced_polarization": [
              -3.166794499540811e-16,
              -0.49977743429644905,
              0.0006131393744063313
            ],
            "branch_aligned_reduced_polarization": [
              -3.166794499540811e-16,
              -0.49977743429644905,
              0.0006131393744063313
            ],
            "target_residual": 0.0006522847421521644,
            "energy_eV": -185.97651269767036
          }
        ],
        "iterations": 2
      },
      "parent": {
        "candidate_id": "bec_projection_03",
        "source": "MACEField_BEC_backprojection",
        "spacegroup": "Pc",
        "spacegroup_number": 7,
        "pointgroup": "m",
        "has_inversion": false,
        "is_polar_point_group": true,
        "nonpolar_parent_hypothesis": false,
        "symmetry_tolerance_A": null,
        "target_reduced_polarization": [
          0.0,
          -0.5,
          0.0
        ],
        "formal_class": [
          0.0,
          0.5,
          0.0
        ],
        "target_residual": 0.0006522847421521644,
        "parent_symmetrization_rmsd_A": 0.07738770797562089,
        "parent_cell_rmsd_A": 0.11084323940260046,
        "energy_eV": -185.97651269767036,
        "reduced_polarization": [
          -3.166794499540811e-16,
          -0.49977743429644905,
          0.0006131393744063313
        ],
        "cartesian_polarization_e_A2": [
          -2.281362139005183e-17,
          -0.012203133273689782,
          -0.00022783986835421332
        ],
        "ranking_score": 0.6064030873105754
      },
      "branch_status": "awaiting_branch_sampling"
    },
    {
      "orbit_id": 4,
      "formal_class": [
        0.5,
        0.0,
        0.5
      ],
      "formal_classes_in_orbit": [
        [
          0.5,
          0.0,
          0.5
        ]
      ],
      "target_reduced_polarization": [
        0.5,
        0.0,
        -0.5
      ],
      "bec_backprojection": {
        "converged_to_target": true,
        "history": [
          {
            "iteration": 0,
            "reduced_polarization": [
              7.758177125247622e-16,
              -3.358252123070092e-16,
              -0.1383916181422002
            ],
            "branch_aligned_reduced_polarization": [
              7.771561172376096e-16,
              -3.358252123070092e-16,
              -0.1383916181422002
            ],
            "target_residual": 0.6170580376510914,
            "energy_eV": -191.10179407364316,
            "max_atomic_step_A": 0.12,
            "max_log_strain_component": 0.010892069316305665,
            "step_scale": 0.8489575864722289,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 3.315984221629218,
            "cell_principal_stretches": [
              1.0077519567308904,
              1.002880201097681,
              0.9854752896453741
            ],
            "cell_volume_ratio": 0.995975021359296,
            "cell_rmsd_from_input_A": 0.06012711890699981
          },
          {
            "iteration": 1,
            "reduced_polarization": [
              0.4117730457726779,
              9.034545630878407e-15,
              -0.4017430001541966
            ],
            "branch_aligned_reduced_polarization": [
              0.4117730457726779,
              9.034545630878407e-15,
              -0.4017430001541966
            ],
            "target_residual": 0.13205466092087847,
            "energy_eV": -188.11869717136483,
            "max_atomic_step_A": 0.029428333083634513,
            "max_log_strain_component": 0.0026900266759291363,
            "step_scale": 1.0,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 3.315984221629218,
            "cell_principal_stretches": [
              1.009161233248231,
              1.004108254547968,
              0.9812102049501613
            ],
            "cell_volume_ratio": 0.9942672912829417,
            "cell_rmsd_from_input_A": 0.07679432170610367
          },
          {
            "iteration": 2,
            "reduced_polarization": [
              0.4977592855408998,
              2.189844757192795e-15,
              -0.4960003189717541
            ],
            "branch_aligned_reduced_polarization": [
              0.4977592855408998,
              2.189844757192795e-15,
              -0.4960003189717541
            ],
            "target_residual": 0.004584566458775644,
            "energy_eV": -186.53423238186468,
            "max_atomic_step_A": 0.0009097847406510126,
            "max_log_strain_component": 0.00010342452727612045,
            "step_scale": 1.0,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 3.315984221629218,
            "cell_principal_stretches": [
              1.0091870885961771,
              1.004158364221945,
              0.9810674460539035
            ],
            "cell_volume_ratio": 0.9941977153418425,
            "cell_rmsd_from_input_A": 0.07733284575785092
          },
          {
            "iteration": 3,
            "reduced_polarization": [
              0.499957484062324,
              -3.5628941334461205e-16,
              -0.49994279522025864
            ],
            "branch_aligned_reduced_polarization": [
              0.499957484062324,
              -3.5628941334461205e-16,
              -0.49994279522025864
            ],
            "target_residual": 7.127406107223118e-05,
            "energy_eV": -186.4819848802464
          }
        ],
        "iterations": 3
      },
      "parent": {
        "candidate_id": "bec_projection_04",
        "source": "MACEField_BEC_backprojection",
        "spacegroup": "Pc",
        "spacegroup_number": 7,
        "pointgroup": "m",
        "has_inversion": false,
        "is_polar_point_group": true,
        "nonpolar_parent_hypothesis": false,
        "symmetry_tolerance_A": null,
        "target_reduced_polarization": [
          0.5,
          0.0,
          -0.5
        ],
        "formal_class": [
          0.5,
          0.0,
          0.5
        ],
        "target_residual": 7.127406107223118e-05,
        "parent_symmetrization_rmsd_A": 0.09119085511682927,
        "parent_cell_rmsd_A": 0.07733284575785092,
        "energy_eV": -186.4819848802464,
        "reduced_polarization": [
          0.499957484062324,
          -3.5628941334461205e-16,
          -0.49994279522025864
        ],
        "cartesian_polarization_e_A2": [
          0.010931205997878285,
          -4.3098780652486e-17,
          -0.006861959112431653
        ],
        "ranking_score": 0.6106666146784365
      },
      "branch_status": "awaiting_branch_sampling"
    },
    {
      "orbit_id": 5,
      "formal_class": [
        0.0,
        0.5,
        0.5
      ],
      "formal_classes_in_orbit": [
        [
          0.0,
          0.5,
          0.5
        ]
      ],
      "target_reduced_polarization": [
        0.0,
        -0.5,
        -0.5
      ],
      "bec_backprojection": {
        "converged_to_target": true,
        "history": [
          {
            "iteration": 0,
            "reduced_polarization": [
              7.758177125247622e-16,
              -3.358252123070092e-16,
              -0.1383916181422002
            ],
            "branch_aligned_reduced_polarization": [
              7.758177125247622e-16,
              -3.3306690738754696e-16,
              -0.1383916181422002
            ],
            "target_residual": 0.6170580376510917,
            "energy_eV": -191.10179407364316,
            "max_atomic_step_A": 0.12,
            "max_log_strain_component": 0.017098791731909393,
            "step_scale": 0.9263379108116229,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 3.315984221629218,
            "cell_principal_stretches": [
              1.0162126193436596,
              0.9989655368857474,
              0.9807395909912325
            ],
            "cell_volume_ratio": 0.9956089613901554,
            "cell_rmsd_from_input_A": 0.10176534284455971
          },
          {
            "iteration": 1,
            "reduced_polarization": [
              5.471213184152402e-15,
              -0.44006774523383363,
              -0.4195211850138727
            ],
            "branch_aligned_reduced_polarization": [
              5.471213184152402e-15,
              -0.44006774523383363,
              -0.4195211850138727
            ],
            "target_residual": 0.10034298591794037,
            "energy_eV": -187.49777469492727,
            "max_atomic_step_A": 0.021326191695261298,
            "max_log_strain_component": 0.0030919451535783285,
            "step_scale": 1.0,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 3.315984221629218,
            "cell_principal_stretches": [
              1.0191281380348425,
              0.9986301728922101,
              0.97686668857064
            ],
            "cell_volume_ratio": 0.9941885948631802,
            "cell_rmsd_from_input_A": 0.1213782997837833
          },
          {
            "iteration": 2,
            "reduced_polarization": [
              2.8288902106455766e-15,
              -0.4981213726118948,
              -0.4962245686105638
            ],
            "branch_aligned_reduced_polarization": [
              2.8288902106455766e-15,
              -0.4981213726118948,
              -0.4962245686105638
            ],
            "target_residual": 0.004217004036004597,
            "energy_eV": -186.2362852530905,
            "max_atomic_step_A": 0.00085393567445,
            "max_log_strain_component": 0.00011351630768463445,
            "step_scale": 1.0,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 3.315984221629218,
            "cell_principal_stretches": [
              1.0192349093398694,
              0.9986143794076141,
              0.9767141222512129
            ],
            "cell_volume_ratio": 0.9941217429784303,
            "cell_rmsd_from_input_A": 0.12212973307852483
          },
          {
            "iteration": 3,
            "reduced_polarization": [
              -1.1626122249185144e-15,
              -0.4999817327976177,
              -0.49989620537519874
            ],
            "branch_aligned_reduced_polarization": [
              -1.1626122249185144e-15,
              -0.4999817327976177,
              -0.49989620537519874
            ],
            "target_residual": 0.00010538982313539257,
            "energy_eV": -186.1860536081239
          }
        ],
        "iterations": 3
      },
      "parent": {
        "candidate_id": "bec_projection_05",
        "source": "MACEField_BEC_backprojection",
        "spacegroup": "Pc",
        "spacegroup_number": 7,
        "pointgroup": "m",
        "has_inversion": false,
        "is_polar_point_group": true,
        "nonpolar_parent_hypothesis": false,
        "symmetry_tolerance_A": null,
        "target_reduced_polarization": [
          0.0,
          -0.5,
          -0.5
        ],
        "formal_class": [
          0.0,
          0.5,
          0.5
        ],
        "target_residual": 0.00010538982313539257,
        "parent_symmetrization_rmsd_A": 0.08646460930271617,
        "parent_cell_rmsd_A": 0.12212973307852483,
        "energy_eV": -186.1860536081239,
        "reduced_polarization": [
          -1.1626122249185144e-15,
          -0.4999817327976177,
          -0.49989620537519874
        ],
        "cartesian_polarization_e_A2": [
          3.9017054763563624e-17,
          -0.012493866171565877,
          -0.006963485150127539
        ],
        "ranking_score": 0.6172078222186181
      },
      "branch_status": "awaiting_branch_sampling"
    },
    {
      "orbit_id": 6,
      "formal_class": [
        0.5,
        0.5,
        0.0
      ],
      "formal_classes_in_orbit": [
        [
          0.5,
          0.5,
          0.0
        ]
      ],
      "target_reduced_polarization": [
        0.5,
        -0.5,
        0.0
      ],
      "bec_backprojection": {
        "converged_to_target": true,
        "history": [
          {
            "iteration": 0,
            "reduced_polarization": [
              7.758177125247622e-16,
              -3.358252123070092e-16,
              -0.1383916181422002
            ],
            "branch_aligned_reduced_polarization": [
              7.771561172376096e-16,
              -3.3306690738754696e-16,
              -0.1383916181422002
            ],
            "target_residual": 0.7205221994997901,
            "energy_eV": -191.10179407364316,
            "max_atomic_step_A": 0.12,
            "max_log_strain_component": 0.011989443336227217,
            "step_scale": 0.6495357137521772,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 3.315984221629218,
            "cell_principal_stretches": [
              1.015403099083896,
              0.9999153042805675,
              0.9860777855585584
            ],
            "cell_volume_ratio": 1.001181636412518,
            "cell_rmsd_from_input_A": 0.08082085908951817
          },
          {
            "iteration": 1,
            "reduced_polarization": [
              0.31741000899876637,
              -0.31668099650793047,
              -0.009524801267567811
            ],
            "branch_aligned_reduced_polarization": [
              0.31741000899876637,
              -0.31668099650793047,
              -0.009524801267567811
            ],
            "target_residual": 0.2589125020047171,
            "energy_eV": -187.23344905987426,
            "max_atomic_step_A": 0.07432397850483499,
            "max_log_strain_component": 0.007802196620581243,
            "step_scale": 1.0,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 3.315984221629218,
            "cell_principal_stretches": [
              1.0246387301173856,
              0.9999593975114248,
              0.9765679693602218
            ],
            "cell_volume_ratio": 1.0005887359562513,
            "cell_rmsd_from_input_A": 0.13253512004011286
          },
          {
            "iteration": 2,
            "reduced_polarization": [
              0.49014932659074334,
              -0.4893085444399239,
              0.017961219458463712
            ],
            "branch_aligned_reduced_polarization": [
              0.49014932659074334,
              -0.4893085444399239,
              0.017961219458463712
            ],
            "target_residual": 0.023107323363903795,
            "energy_eV": -180.91352133054482,
            "max_atomic_step_A": 0.0054937671391908326,
            "max_log_strain_component": 0.0006280703352781011,
            "step_scale": 1.0,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 3.315984221629218,
            "cell_principal_stretches": [
              1.0252071525450612,
              0.9999828512941613,
              0.9756752360306161
            ],
            "cell_volume_ratio": 1.0002520772168846,
            "cell_rmsd_from_input_A": 0.13658359095719178
          },
          {
            "iteration": 3,
            "reduced_polarization": [
              0.4995908965591897,
              -0.49967699920430914,
              0.0005946710848919922
            ],
            "branch_aligned_reduced_polarization": [
              0.4995908965591897,
              -0.49967699920430914,
              0.0005946710848919922
            ],
            "target_residual": 0.0007907773634256206,
            "energy_eV": -180.54167761467983
          }
        ],
        "iterations": 3
      },
      "parent": {
        "candidate_id": "bec_projection_06",
        "source": "MACEField_BEC_backprojection",
        "spacegroup": "P1",
        "spacegroup_number": 1,
        "pointgroup": "1",
        "has_inversion": false,
        "is_polar_point_group": true,
        "nonpolar_parent_hypothesis": false,
        "symmetry_tolerance_A": null,
        "target_reduced_polarization": [
          0.5,
          -0.5,
          0.0
        ],
        "formal_class": [
          0.5,
          0.5,
          0.0
        ],
        "target_residual": 0.0007907773634256206,
        "parent_symmetrization_rmsd_A": 0.11593625798137375,
        "parent_cell_rmsd_A": 0.13658359095719178,
        "energy_eV": -180.54167761467983,
        "reduced_polarization": [
          0.4995908965591897,
          -0.49967699920430914,
          0.0005946710848919922
        ],
        "cartesian_polarization_e_A2": [
          0.010782678536622379,
          -0.012221113015752355,
          -0.00039210436566518536
        ],
        "ranking_score": 0.6516637104475229
      },
      "branch_status": "awaiting_branch_sampling"
    },
    {
      "orbit_id": 7,
      "formal_class": [
        0.5,
        0.5,
        0.5
      ],
      "formal_classes_in_orbit": [
        [
          0.5,
          0.5,
          0.5
        ]
      ],
      "target_reduced_polarization": [
        0.5,
        -0.5,
        -0.5
      ],
      "bec_backprojection": {
        "converged_to_target": true,
        "history": [
          {
            "iteration": 0,
            "reduced_polarization": [
              7.758177125247622e-16,
              -3.358252123070092e-16,
              -0.1383916181422002
            ],
            "branch_aligned_reduced_polarization": [
              7.771561172376096e-16,
              -3.3306690738754696e-16,
              -0.1383916181422002
            ],
            "target_residual": 0.7942043954989265,
            "energy_eV": -191.10179407364316,
            "max_atomic_step_A": 0.11999999999999998,
            "max_log_strain_component": 0.011488986222047488,
            "step_scale": 0.6224231314788587,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 3.315984221629218,
            "cell_principal_stretches": [
              1.0128424609508773,
              1.0001787909979518,
              0.9842292951566873
            ],
            "cell_volume_ratio": 0.9970474526893756,
            "cell_rmsd_from_input_A": 0.07920102310406718
          },
          {
            "iteration": 1,
            "reduced_polarization": [
              0.30124198910603806,
              -0.2997778297198809,
              -0.31988426818881394
            ],
            "branch_aligned_reduced_polarization": [
              0.30124198910603806,
              -0.2997778297198809,
              -0.31988426818881394
            ],
            "target_residual": 0.3347168074837062,
            "energy_eV": -188.02418241179137,
            "max_atomic_step_A": 0.08493880422994866,
            "max_log_strain_component": 0.009159151202941798,
            "step_scale": 1.0,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 3.315984221629218,
            "cell_principal_stretches": [
              1.0227469964554823,
              1.0002949969390738,
              0.9711575081718826
            ],
            "cell_volume_ratio": 0.9935414298129709,
            "cell_rmsd_from_input_A": 0.14338151269380933
          },
          {
            "iteration": 2,
            "reduced_polarization": [
              0.48314876652952116,
              -0.48171201639795125,
              -0.46769164048172074
            ],
            "branch_aligned_reduced_polarization": [
              0.48314876652952116,
              -0.48171201639795125,
              -0.46769164048172074
            ],
            "target_residual": 0.040770632917184114,
            "energy_eV": -182.0192078367357,
            "max_atomic_step_A": 0.009835311215787994,
            "max_log_strain_component": 0.0012824881981060464,
            "step_scale": 1.0,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 3.315984221629218,
            "cell_principal_stretches": [
              1.0240613173954933,
              1.0002967312664963,
              0.9692034630029172
            ],
            "cell_volume_ratio": 0.9928182879838684,
            "cell_rmsd_from_input_A": 0.15263121140021169
          },
          {
            "iteration": 3,
            "reduced_polarization": [
              0.49862449710228307,
              -0.4990123390962603,
              -0.4977883587499087
            ],
            "branch_aligned_reduced_polarization": [
              0.49862449710228307,
              -0.4990123390962603,
              -0.4977883587499087
            ],
            "target_residual": 0.0027854693144080925,
            "energy_eV": -181.16469660893642,
            "max_atomic_step_A": 0.0006881006397443887,
            "max_log_strain_component": 8.069134456818497e-05,
            "step_scale": 1.0,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 3.315984221629218,
            "cell_principal_stretches": [
              1.0241486515772669,
              1.0002992471185614,
              0.969068289166033
            ],
            "cell_volume_ratio": 0.9927669754179448,
            "cell_rmsd_from_input_A": 0.15325577099346918
          },
          {
            "iteration": 4,
            "reduced_polarization": [
              0.49990924984495866,
              -0.4999485105439246,
              -0.49986498112463246
            ],
            "branch_aligned_reduced_polarization": [
              0.49990924984495866,
              -0.4999485105439246,
              -0.49986498112463246
            ],
            "target_residual": 0.00017063660636711496,
            "energy_eV": -181.10491714267505
          }
        ],
        "iterations": 4
      },
      "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": 0.00017063660636711496,
        "parent_symmetrization_rmsd_A": 0.1273257131453979,
        "parent_cell_rmsd_A": 0.15325577099346918,
        "energy_eV": -181.10491714267505,
        "reduced_polarization": [
          0.49990924984495866,
          -0.4999485105439246,
          -0.49986498112463246
        ],
        "cartesian_polarization_e_A2": [
          0.01095254874189006,
          -0.012535918993109223,
          -0.007141367341267068
        ],
        "ranking_score": 0.6659809291064994
      },
      "branch_status": "awaiting_branch_sampling"
    }
  ],
  "sampled_polarization_branches": [
    {
      "orbit_id": 0,
      "candidate_id": "bec_projection_00",
      "formal_class": [
        0.0,
        0.0,
        0.0
      ],
      "construction": "MACEField-BEC-parent plus variable-cell P-N-P path and symmetric log-strain continuation beyond both polar endpoints",
      "geometry_diagnostics": {
        "collision_aware": false,
        "permutations_tested": 1,
        "selected_order": [
          0,
          1,
          2,
          3,
          4,
          5,
          6,
          7,
          8,
          9,
          10,
          11,
          12,
          13,
          14,
          15,
          16,
          17,
          18,
          19,
          20,
          21,
          22,
          23,
          24,
          25,
          26,
          27
        ],
        "endpoint_rmsd_A": 0.012092884885228599,
        "minimum_distance_A_by_image": [
          1.5385592916930495,
          1.5430983691378775,
          1.5476403263483982,
          1.5504479906899136,
          1.5490419924978844,
          1.5476397658618637,
          1.546241332451244,
          1.5448467140021132,
          1.5434559323170367
        ],
        "minimum_distance_A": 1.5385592916930495,
        "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": [
          375.05163071343634,
          375.13687686653617,
          375.22214239538636,
          375.30742730439005,
          375.39273159795334,
          375.4780552804807,
          375.5633983563802,
          375.6487608300591,
          375.7341427059273
        ],
        "cell_deformation_log_strain_norm": 0.0030139863652290377
      },
      "parent_reduced_polarization": [
        -1.4262401252340467e-16,
        -6.744617141547602e-16,
        0.0007830758391361251
      ],
      "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": [
          -191.1017940736431,
          -191.09499541460028,
          -191.08505622850387,
          -191.07205512683157,
          -191.0560688159097,
          -191.03717209998922,
          -191.0154378905097,
          -190.99093723219792,
          -190.96373931894811
        ],
        "cartesian_polarizations_e_A2": [
          [
            1.5439226198792098e-17,
            -4.255269054190752e-18,
            -0.0018636773725774394
          ],
          [
            -1.9421813872206169e-19,
            -1.1616094392138547e-17,
            -0.001631200402099391
          ],
          [
            -5.9824086168897415e-18,
            -1.775305184610248e-17,
            -0.0013981685095343583
          ],
          [
            -8.819043140010437e-18,
            2.0836607167278325e-17,
            -0.0011646004517120489
          ],
          [
            2.5647047695059248e-17,
            -1.2569363915416424e-17,
            -0.0009305159703141253
          ],
          [
            1.6807703983896968e-17,
            6.8376585750872766e-18,
            -0.0006959358575292041
          ],
          [
            2.248524195385463e-17,
            -1.8937857849384547e-17,
            -0.00046088199021858455
          ],
          [
            -1.3161129283667499e-17,
            4.091494928185756e-17,
            -0.00022537722939421033
          ],
          [
            -3.065615436897133e-18,
            -1.647306608260387e-17,
            1.0554608786098182e-05
          ]
        ],
        "raw_reduced_polarization": [
          [
            7.153810840905128e-16,
            -1.7396351087975706e-16,
            -0.1383916181422002
          ],
          [
            -1.649860218477657e-18,
            -4.955540857549045e-16,
            -0.12111535415508028
          ],
          [
            -2.6469118710677907e-16,
            -7.614592272743698e-16,
            -0.10380164323631795
          ],
          [
            -3.9310056172591334e-16,
            8.08955849922753e-16,
            -0.08645189057590755
          ],
          [
            1.2059647938785886e-15,
            -5.614137275859858e-16,
            -0.0690675738567748
          ],
          [
            7.951499368901118e-16,
            2.3636639668987766e-16,
            -0.05165024808795794
          ],
          [
            1.055410984138223e-15,
            -8.107713365041173e-16,
            -0.0342015480978444
          ],
          [
            -6.034563362775028e-16,
            1.6574206573053293e-15,
            -0.016723181031820626
          ],
          [
            -1.4262401252340467e-16,
            -6.744617141547602e-16,
            0.0007830758391361251
          ]
        ],
        "unwrapped_reduced_polarization": [
          [
            7.153810840905128e-16,
            -1.7396351087975706e-16,
            -0.1383916181422002
          ],
          [
            -1.6498602184776534e-18,
            -4.955540857549045e-16,
            -0.12111535415508028
          ],
          [
            -2.6469118710677907e-16,
            -7.614592272743698e-16,
            -0.10380164323631795
          ],
          [
            -3.9310056172591334e-16,
            8.089558499227531e-16,
            -0.08645189057590755
          ],
          [
            1.2059647938785886e-15,
            -5.614137275859858e-16,
            -0.0690675738567748
          ],
          [
            7.951499368901118e-16,
            2.363663966898776e-16,
            -0.05165024808795794
          ],
          [
            1.055410984138223e-15,
            -8.107713365041172e-16,
            -0.0342015480978444
          ],
          [
            -6.034563362775029e-16,
            1.6574206573053291e-15,
            -0.016723181031820626
          ],
          [
            -1.4262401252340472e-16,
            -6.7446171415476e-16,
            0.0007830758391361263
          ]
        ],
        "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": [
          [
            6.661338147750939e-16,
            -1.6653345369377348e-16,
            -0.1383916181422002
          ],
          [
            0.0,
            -4.996003610813204e-16,
            -0.12111535415508029
          ],
          [
            -2.7755575615628914e-16,
            -7.771561172376096e-16,
            -0.10380164323631796
          ],
          [
            -3.885780586188048e-16,
            7.771561172376096e-16,
            -0.08645189057590752
          ],
          [
            1.2212453270876722e-15,
            -5.551115123125783e-16,
            -0.06906757385677481
          ],
          [
            7.771561172376096e-16,
            2.220446049250313e-16,
            -0.05165024808795793
          ],
          [
            1.1102230246251565e-15,
            -8.326672684688674e-16,
            -0.03420154809784437
          ],
          [
            -6.106226635438361e-16,
            1.6653345369377348e-15,
            -0.016723181031820633
          ],
          [
            -1.6653345369377348e-16,
            -6.661338147750939e-16,
            0.0007830758391361714
          ]
        ]
      },
      "reflected": {
        "reached": true,
        "construction": "reflect_displacements_about_reconstructed_parent",
        "energies_eV": [
          -190.96373931894811,
          -190.94254212543544,
          -190.91944710410138,
          -190.89449182532562,
          -190.8677130529178,
          -190.83914675977383,
          -190.8088281449352,
          -190.77679165040263,
          -190.74307097737017
        ],
        "cartesian_polarizations_e_A2": [
          [
            -1.0914329657868708e-17,
            -5.0785797900404305e-18,
            1.055460878612134e-05
          ],
          [
            -3.1475879718413214e-17,
            9.993222375388233e-18,
            0.0002186987464087633
          ],
          [
            -1.769996860459551e-17,
            -1.0826911902184728e-16,
            0.00042703331202120505
          ],
          [
            -8.445432348148339e-18,
            -1.2171032263655352e-16,
            0.0006355416593046776
          ],
          [
            3.3087002071463823e-18,
            -1.4223714018989614e-16,
            0.0008442067510929935
          ],
          [
            -1.4559741033036097e-17,
            -1.3875664311483925e-16,
            0.0010530112367442737
          ],
          [
            3.4119146516728204e-18,
            -1.1367501010207494e-16,
            0.001261937509610164
          ],
          [
            1.2772154741674629e-17,
            -1.8075234777066542e-16,
            0.001470967763272024
          ],
          [
            2.442154413709475e-17,
            -1.8369811495243465e-16,
            0.001680084050399448
          ]
        ],
        "raw_reduced_polarization": [
          [
            -5.068025399745872e-16,
            -2.0718023405392316e-16,
            0.0007830758391378434
          ],
          [
            -1.4671198947290897e-15,
            4.2889472665719165e-16,
            0.016227631946033372
          ],
          [
            -8.325372132227513e-16,
            -4.4044066156138126e-15,
            0.031689674733326345
          ],
          [
            -4.0598375352995736e-16,
            -4.945524363045823e-15,
            0.04716797391337397
          ],
          [
            1.3819736621364215e-16,
            -5.781571520780873e-15,
            0.06266126965216914
          ],
          [
            -6.892185868245886e-16,
            -5.639590148014405e-15,
            0.07816827829698084
          ],
          [
            1.4677304768586797e-16,
            -4.6191773774247974e-15,
            0.09368769663014848
          ],
          [
            5.8527563277250945e-16,
            -7.37390885992843e-15,
            0.10921820603409964
          ],
          [
            1.1315794260029683e-15,
            -7.509929128370035e-15,
            0.12475847685381508
          ]
        ],
        "unwrapped_reduced_polarization": [
          [
            -5.068025399745872e-16,
            -2.0718023405392316e-16,
            0.0007830758391378434
          ],
          [
            -1.4671198947290897e-15,
            4.2889472665719165e-16,
            0.016227631946033372
          ],
          [
            -8.325372132227513e-16,
            -4.4044066156138126e-15,
            0.031689674733326345
          ],
          [
            -4.0598375352995736e-16,
            -4.945524363045823e-15,
            0.04716797391337397
          ],
          [
            1.3819736621364213e-16,
            -5.781571520780873e-15,
            0.06266126965216914
          ],
          [
            -6.892185868245886e-16,
            -5.639590148014405e-15,
            0.07816827829698084
          ],
          [
            1.4677304768586792e-16,
            -4.6191773774247974e-15,
            0.09368769663014848
          ],
          [
            5.8527563277250945e-16,
            -7.37390885992843e-15,
            0.10921820603409964
          ],
          [
            1.1315794260029683e-15,
            -7.509929128370035e-15,
            0.12475847685381508
          ]
        ],
        "gauge_integer_shift": [
          0,
          0,
          0
        ],
        "expected_opposite_endpoint_reduced_polarization": [
          -9.994734688272116e-16,
          -1.1729371782138043e-15,
          0.13995913128611515
        ],
        "actual_opposite_endpoint_branch_residual": 0.015200654432300065
      },
      "pnp_branch": {
        "construction": "incoming_path_concatenated_with_parent_reflection",
        "reduced_polarization": [
          [
            7.153810840905128e-16,
            -1.7396351087975706e-16,
            -0.1383916181422002
          ],
          [
            -1.649860218477657e-18,
            -4.955540857549045e-16,
            -0.12111535415508028
          ],
          [
            -2.6469118710677907e-16,
            -7.614592272743698e-16,
            -0.10380164323631795
          ],
          [
            -3.9310056172591334e-16,
            8.08955849922753e-16,
            -0.08645189057590755
          ],
          [
            1.2059647938785886e-15,
            -5.614137275859858e-16,
            -0.0690675738567748
          ],
          [
            7.951499368901118e-16,
            2.3636639668987766e-16,
            -0.05165024808795794
          ],
          [
            1.055410984138223e-15,
            -8.107713365041173e-16,
            -0.0342015480978444
          ],
          [
            -6.034563362775028e-16,
            1.6574206573053293e-15,
            -0.016723181031820626
          ],
          [
            -1.4262401252340467e-16,
            -6.744617141547602e-16,
            0.0007830758391361251
          ],
          [
            -1.4671198947290897e-15,
            4.2889472665719165e-16,
            0.016227631946033372
          ],
          [
            -8.325372132227513e-16,
            -4.4044066156138126e-15,
            0.031689674733326345
          ],
          [
            -4.0598375352995736e-16,
            -4.945524363045823e-15,
            0.04716797391337397
          ],
          [
            1.3819736621364215e-16,
            -5.781571520780873e-15,
            0.06266126965216914
          ],
          [
            -6.892185868245886e-16,
            -5.639590148014405e-15,
            0.07816827829698084
          ],
          [
            1.4677304768586797e-16,
            -4.6191773774247974e-15,
            0.09368769663014848
          ],
          [
            5.8527563277250945e-16,
            -7.37390885992843e-15,
            0.10921820603409964
          ],
          [
            1.1315794260029683e-15,
            -7.509929128370035e-15,
            0.12475847685381508
          ]
        ],
        "unwrapped_reduced_polarization": [
          [
            7.153810840905128e-16,
            -1.7396351087975706e-16,
            -0.1383916181422002
          ],
          [
            -1.6498602184776534e-18,
            -4.955540857549045e-16,
            -0.12111535415508028
          ],
          [
            -2.6469118710677907e-16,
            -7.614592272743698e-16,
            -0.10380164323631795
          ],
          [
            -3.9310056172591334e-16,
            8.089558499227531e-16,
            -0.08645189057590755
          ],
          [
            1.2059647938785886e-15,
            -5.614137275859858e-16,
            -0.0690675738567748
          ],
          [
            7.951499368901118e-16,
            2.363663966898776e-16,
            -0.05165024808795794
          ],
          [
            1.055410984138223e-15,
            -8.107713365041172e-16,
            -0.0342015480978444
          ],
          [
            -6.034563362775029e-16,
            1.6574206573053291e-15,
            -0.016723181031820626
          ],
          [
            -1.4262401252340472e-16,
            -6.7446171415476e-16,
            0.0007830758391361263
          ],
          [
            -1.4671198947290897e-15,
            4.2889472665719175e-16,
            0.016227631946033372
          ],
          [
            -8.325372132227513e-16,
            -4.4044066156138126e-15,
            0.031689674733326345
          ],
          [
            -4.0598375352995736e-16,
            -4.945524363045823e-15,
            0.04716797391337397
          ],
          [
            1.3819736621364213e-16,
            -5.781571520780873e-15,
            0.06266126965216914
          ],
          [
            -6.892185868245886e-16,
            -5.639590148014405e-15,
            0.07816827829698084
          ],
          [
            1.4677304768586792e-16,
            -4.6191773774247974e-15,
            0.09368769663014848
          ],
          [
            5.8527563277250945e-16,
            -7.37390885992843e-15,
            0.10921820603409964
          ],
          [
            1.1315794260029683e-15,
            -7.509929128370035e-15,
            0.12475847685381508
          ]
        ],
        "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": [
          [
            6.661338147750939e-16,
            -1.6653345369377348e-16,
            -0.1383916181422002
          ],
          [
            0.0,
            -4.996003610813204e-16,
            -0.12111535415508029
          ],
          [
            -2.7755575615628914e-16,
            -7.771561172376096e-16,
            -0.10380164323631796
          ],
          [
            -3.885780586188048e-16,
            7.771561172376096e-16,
            -0.08645189057590752
          ],
          [
            1.2212453270876722e-15,
            -5.551115123125783e-16,
            -0.06906757385677481
          ],
          [
            7.771561172376096e-16,
            2.220446049250313e-16,
            -0.05165024808795793
          ],
          [
            1.1102230246251565e-15,
            -8.326672684688674e-16,
            -0.03420154809784437
          ],
          [
            -6.106226635438361e-16,
            1.6653345369377348e-15,
            -0.016723181031820633
          ],
          [
            -1.6653345369377348e-16,
            -6.661338147750939e-16,
            0.0007830758391361714
          ],
          [
            -1.4432899320127035e-15,
            4.440892098500626e-16,
            0.016227631946033383
          ],
          [
            -8.326672684688674e-16,
            -4.385380947269368e-15,
            0.0316896747333264
          ],
          [
            -3.885780586188048e-16,
            -4.9404924595819466e-15,
            0.04716797391337402
          ],
          [
            1.1102230246251565e-16,
            -5.773159728050814e-15,
            0.06266126965216912
          ],
          [
            -6.661338147750939e-16,
            -5.662137425588298e-15,
            0.07816827829698081
          ],
          [
            1.1102230246251565e-16,
            -4.6074255521944e-15,
            0.09368769663014853
          ],
          [
            5.551115123125783e-16,
            -7.382983113757291e-15,
            0.1092182060340996
          ],
          [
            1.1102230246251565e-15,
            -7.494005416219807e-15,
            0.12475847685381503
          ]
        ]
      },
      "incoming_structure_ids": [
        "incoming_00_000",
        "incoming_00_001",
        "incoming_00_002",
        "incoming_00_003",
        "incoming_00_004",
        "incoming_00_005",
        "incoming_00_006",
        "incoming_00_007",
        "incoming_00_008"
      ],
      "reflected_structure_ids": [
        "reflected_00_001",
        "reflected_00_002",
        "reflected_00_003",
        "reflected_00_004",
        "reflected_00_005",
        "reflected_00_006",
        "reflected_00_007",
        "reflected_00_008"
      ],
      "positive_extension_structure_ids": [
        "extension_plus_00_000",
        "extension_plus_00_001",
        "extension_plus_00_002",
        "extension_plus_00_003"
      ],
      "negative_extension_structure_ids": [
        "extension_minus_00_000",
        "extension_minus_00_001",
        "extension_minus_00_002",
        "extension_minus_00_003"
      ],
      "extension": {
        "enabled": true,
        "fraction_beyond_polar_endpoint": 0.35,
        "images_per_side": 4,
        "construction": "continue fractional atomic displacements and symmetric log strain beyond +P; reflect these structures about N for the -P side",
        "positive_path_coordinates": [
          1.35,
          1.2625,
          1.175,
          1.0875
        ],
        "negative_path_coordinates": [
          -1.0875,
          -1.175,
          -1.2625,
          -1.35
        ]
      },
      "branch_coordinates": [
        1.35,
        1.2625,
        1.175,
        1.0875,
        1.0,
        0.875,
        0.75,
        0.625,
        0.5,
        0.375,
        0.25,
        0.125,
        0.0,
        -0.125,
        -0.25,
        -0.375,
        -0.5,
        -0.625,
        -0.75,
        -0.875,
        -1.0,
        -1.0875,
        -1.175,
        -1.2625,
        -1.35
      ],
      "parent": {
        "candidate_id": "bec_projection_00",
        "source": "MACEField_BEC_backprojection",
        "spacegroup": "Pna2_1",
        "spacegroup_number": 33,
        "pointgroup": "mm2",
        "has_inversion": false,
        "is_polar_point_group": true,
        "nonpolar_parent_hypothesis": false,
        "symmetry_tolerance_A": null,
        "target_reduced_polarization": [
          0.0,
          0.0,
          0.0
        ],
        "formal_class": [
          0.0,
          0.0,
          0.0
        ],
        "target_residual": 0.0007830758391394628,
        "parent_symmetrization_rmsd_A": 0.012092884885228599,
        "parent_cell_rmsd_A": 0.01150298702586981,
        "energy_eV": -190.96373931894806,
        "reduced_polarization": [
          -1.023936048955266e-15,
          -6.631418008511183e-17,
          0.0007830758391394628
        ],
        "cartesian_polarization_e_A2": [
          -2.2059503851648343e-17,
          -1.6436130956858123e-18,
          1.0554608786143168e-05
        ],
        "ranking_score": 0.5165347833199749
      }
    }
  ],
  "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": 56,
      "full_response": 21,
      "energy_polarization": 35
    },
    "model_evaluations_for_recovery_and_path_properties": {
      "total": 81,
      "full_response": 46,
      "energy_polarization": 35
    },
    "elapsed_seconds": 421.97058148297947
  }
}
