{
  "schema": "ferrofinder.endpoint_parent_recovery.v4_variable_cell",
  "status": "complete",
  "input_atom_count": 32,
  "input_formula": "Na16O12Sn4",
  "input_spacegroup": "Cc",
  "input_pointgroup": "m",
  "input_is_polar_point_group": true,
  "input_energy_eV": -136.11461798537022,
  "input_cartesian_polarization_e_A2": [
    0.001333421181857651,
    4.208643924744304e-12,
    -0.00048826818408777127
  ],
  "input_reduced_polarization": [
    0.10885109055045711,
    1.3824676480015927e-10,
    -0.048403891353765986
  ],
  "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": [
        0.5,
        0.0,
        0.0
      ],
      "target_reduced_polarization": [
        0.5,
        0.0,
        0.0
      ]
    },
    {
      "orbit_id": 2,
      "representative_formal_class": [
        0.0,
        0.0,
        0.5
      ],
      "target_reduced_polarization": [
        0.0,
        0.0,
        -0.5
      ]
    },
    {
      "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": [
        0.5,
        0.5,
        0.0
      ],
      "target_reduced_polarization": [
        0.5,
        0.5,
        0.0
      ]
    },
    {
      "orbit_id": 6,
      "representative_formal_class": [
        0.0,
        0.5,
        0.5
      ],
      "target_reduced_polarization": [
        0.0,
        0.5,
        -0.5
      ]
    },
    {
      "orbit_id": 7,
      "representative_formal_class": [
        0.5,
        0.5,
        0.5
      ],
      "target_reduced_polarization": [
        0.5,
        0.5,
        -0.5
      ]
    }
  ],
  "parent_candidates": [
    {
      "candidate_id": "inversion_parent_endpoint_00",
      "source": "same_species_inversion_center_projection_from_endpoint",
      "spacegroup": "C2/c",
      "spacegroup_number": 15,
      "pointgroup": "2/m",
      "has_inversion": true,
      "is_polar_point_group": false,
      "nonpolar_parent_hypothesis": true,
      "symmetry_tolerance_A": null,
      "target_reduced_polarization": [
        0.0,
        0.0,
        0.0
      ],
      "formal_class": [
        0.0,
        0.0,
        0.0
      ],
      "target_residual": 2.3338483797761127e-15,
      "parent_symmetrization_rmsd_A": 0.5559203511131643,
      "parent_cell_rmsd_A": 0.0,
      "energy_eV": -117.26563255394235,
      "reduced_polarization": [
        1.0664578556948111e-15,
        -1.4765120523550013e-15,
        -1.4592559957255048e-15
      ],
      "cartesian_polarization_e_A2": [
        1.6686912682485986e-17,
        -4.4949431460029815e-17,
        -1.472006186330408e-17
      ],
      "ranking_score": 0.555920351113169
    },
    {
      "candidate_id": "bec_projection_00",
      "source": "MACEField_BEC_backprojection",
      "spacegroup": "Cc",
      "spacegroup_number": 9,
      "pointgroup": "m",
      "has_inversion": false,
      "is_polar_point_group": true,
      "nonpolar_parent_hypothesis": false,
      "symmetry_tolerance_A": null,
      "target_reduced_polarization": [
        0.0,
        0.0,
        0.0
      ],
      "formal_class": [
        0.0,
        0.0,
        0.0
      ],
      "target_residual": 0.0008674402564783212,
      "parent_symmetrization_rmsd_A": 0.01718171949171929,
      "parent_cell_rmsd_A": 0.022533379012042918,
      "energy_eV": -135.95259462976534,
      "reduced_polarization": [
        0.0004990480529539278,
        -1.1871047811817705e-12,
        -0.0007095094357385739
      ],
      "cartesian_polarization_e_A2": [
        7.910996551343873e-06,
        -3.57641189430078e-14,
        -7.156198358873145e-06
      ],
      "ranking_score": 0.5245499447576867
    },
    {
      "candidate_id": "inversion_parent_bec_00_00",
      "source": "same_species_inversion_center_projection_after_BEC",
      "spacegroup": "C2/c",
      "spacegroup_number": 15,
      "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": 4.008110463257583e-15,
      "parent_symmetrization_rmsd_A": 0.5559226977363644,
      "parent_cell_rmsd_A": 0.022533379012042918,
      "energy_eV": -117.10124905458092,
      "reduced_polarization": [
        -3.815463677245684e-15,
        -5.501805397835167e-16,
        -1.097491588549671e-15
      ],
      "cartesian_polarization_e_A2": [
        -3.632616579864975e-17,
        -1.6662464805825628e-17,
        -1.0896604413376251e-17
      ],
      "ranking_score": 0.5615560424893831
    },
    {
      "candidate_id": "bec_projection_01",
      "source": "MACEField_BEC_backprojection",
      "spacegroup": "Cc",
      "spacegroup_number": 9,
      "pointgroup": "m",
      "has_inversion": false,
      "is_polar_point_group": true,
      "nonpolar_parent_hypothesis": false,
      "symmetry_tolerance_A": null,
      "target_reduced_polarization": [
        0.5,
        0.0,
        0.0
      ],
      "formal_class": [
        0.5,
        0.0,
        0.0
      ],
      "target_residual": 5.742995083898317e-05,
      "parent_symmetrization_rmsd_A": 0.05147464902746573,
      "parent_cell_rmsd_A": 0.055025250922220416,
      "energy_eV": -135.82665450660295,
      "reduced_polarization": [
        0.49996831714157586,
        1.1093375015754538e-14,
        4.789985110043424e-05
      ],
      "cartesian_polarization_e_A2": [
        0.005340867105407056,
        -1.5233938653799322e-13,
        3.1807114103521e-05
      ],
      "ranking_score": 0.5653458216596988
    },
    {
      "candidate_id": "bec_projection_02",
      "source": "MACEField_BEC_backprojection",
      "spacegroup": "Cc",
      "spacegroup_number": 9,
      "pointgroup": "m",
      "has_inversion": false,
      "is_polar_point_group": true,
      "nonpolar_parent_hypothesis": false,
      "symmetry_tolerance_A": null,
      "target_reduced_polarization": [
        0.0,
        0.0,
        -0.5
      ],
      "formal_class": [
        0.0,
        0.0,
        0.5
      ],
      "target_residual": 0.00013259239608386097,
      "parent_symmetrization_rmsd_A": 0.05764423660539236,
      "parent_cell_rmsd_A": 0.047613991018464155,
      "energy_eV": -135.66179260336574,
      "reduced_polarization": [
        -0.00011619824236101396,
        1.597827678944053e-13,
        -0.4999361352055396
      ],
      "cartesian_polarization_e_A2": [
        0.0017870145194516809,
        -1.236594133767149e-13,
        -0.00504995034847798
      ],
      "ranking_score": 0.5698129191521761
    },
    {
      "candidate_id": "bec_projection_03",
      "source": "MACEField_BEC_backprojection",
      "spacegroup": "P1",
      "spacegroup_number": 1,
      "pointgroup": "1",
      "has_inversion": false,
      "is_polar_point_group": true,
      "nonpolar_parent_hypothesis": false,
      "symmetry_tolerance_A": null,
      "target_reduced_polarization": [
        0.0,
        0.5,
        0.0
      ],
      "formal_class": [
        0.0,
        0.5,
        0.0
      ],
      "target_residual": 0.0004670454935148821,
      "parent_symmetrization_rmsd_A": 0.2284746259576941,
      "parent_cell_rmsd_A": 0.2753660038168413,
      "energy_eV": -129.3152243998772,
      "reduced_polarization": [
        8.221313830746546e-05,
        0.499834835658041,
        0.0004290608733588322
      ],
      "cartesian_polarization_e_A2": [
        -0.000451468463934174,
        0.015227853408950805,
        2.7317785319988072e-05
      ],
      "ranking_score": 0.7982502178989342
    },
    {
      "candidate_id": "bec_projection_04",
      "source": "MACEField_BEC_backprojection",
      "spacegroup": "Cc",
      "spacegroup_number": 9,
      "pointgroup": "m",
      "has_inversion": false,
      "is_polar_point_group": true,
      "nonpolar_parent_hypothesis": false,
      "symmetry_tolerance_A": null,
      "target_reduced_polarization": [
        0.5,
        0.0,
        -0.5
      ],
      "formal_class": [
        0.5,
        0.0,
        0.5
      ],
      "target_residual": 4.075074356528363e-05,
      "parent_symmetrization_rmsd_A": 0.08604352094870757,
      "parent_cell_rmsd_A": 0.10617575185736569,
      "energy_eV": -133.97609219605698,
      "reduced_polarization": [
        0.49997102379074104,
        1.8930219011326e-14,
        -0.499971346860589
      ],
      "cartesian_polarization_e_A2": [
        0.007135792342807811,
        -4.657619217124015e-13,
        -0.0049947246157864
      ],
      "ranking_score": 0.6126689604001796
    },
    {
      "candidate_id": "bec_projection_05",
      "source": "MACEField_BEC_backprojection",
      "spacegroup": "P1",
      "spacegroup_number": 1,
      "pointgroup": "1",
      "has_inversion": false,
      "is_polar_point_group": true,
      "nonpolar_parent_hypothesis": false,
      "symmetry_tolerance_A": null,
      "target_reduced_polarization": [
        0.5,
        0.5,
        0.0
      ],
      "formal_class": [
        0.5,
        0.5,
        0.0
      ],
      "target_residual": 0.0008796819126213241,
      "parent_symmetrization_rmsd_A": 0.24345141256117983,
      "parent_cell_rmsd_A": 0.2905950597332013,
      "energy_eV": -128.31239902812018,
      "reduced_polarization": [
        0.5003493249794255,
        0.4997817824469068,
        0.0007772988007609961
      ],
      "cartesian_polarization_e_A2": [
        0.004878508777489372,
        0.015316219975035086,
        8.891297671606612e-05
      ],
      "ranking_score": 0.8178595413197228
    },
    {
      "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": [
        0.0,
        0.5,
        -0.5
      ],
      "formal_class": [
        0.0,
        0.5,
        0.5
      ],
      "target_residual": 3.853337273481937e-06,
      "parent_symmetrization_rmsd_A": 0.2529732331196209,
      "parent_cell_rmsd_A": 0.3050967804552599,
      "energy_eV": -128.1204303928584,
      "reduced_polarization": [
        -2.5140623404783076e-06,
        0.5000001725878165,
        -0.5000029151178599
      ],
      "cartesian_polarization_e_A2": [
        0.0012688997336535895,
        0.01540106185139676,
        -0.005035286573705311
      ],
      "ranking_score": 0.8292551349079829
    },
    {
      "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": 4.867041127206118e-06,
      "parent_symmetrization_rmsd_A": 0.26760713842810346,
      "parent_cell_rmsd_A": 0.3268130564926751,
      "energy_eV": -125.31784877831413,
      "reduced_polarization": [
        0.499996966162749,
        0.5000001201432874,
        -0.5000038038778186
      ],
      "cartesian_polarization_e_A2": [
        0.006603630105753847,
        0.015431355454343414,
        -0.004957133719768818
      ],
      "ranking_score": 0.8493201366335266
    }
  ],
  "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": [
              0.10885109055045711,
              1.3824676480015927e-10,
              -0.048403891353765986
            ],
            "branch_aligned_reduced_polarization": [
              0.10885109055045711,
              1.3824676480015927e-10,
              -0.048403891353765986
            ],
            "target_residual": 0.11912806811247716,
            "energy_eV": -136.11461798537022,
            "max_atomic_step_A": 0.024863085285660308,
            "max_log_strain_component": 0.0035613358186357934,
            "step_scale": 1.0,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 2.3195488914165274,
            "cell_principal_stretches": [
              1.0062416861407333,
              1.000772701274623,
              0.9989664008889549
            ],
            "cell_volume_ratio": 1.0059783562135454,
            "cell_rmsd_from_input_A": 0.022533379012042918
          },
          {
            "iteration": 1,
            "reduced_polarization": [
              0.0004990480529539278,
              -1.1871047811817705e-12,
              -0.0007095094357385739
            ],
            "branch_aligned_reduced_polarization": [
              0.0004990480529539278,
              -1.1871047811817705e-12,
              -0.0007095094357385739
            ],
            "target_residual": 0.0008674402564783212,
            "energy_eV": -135.95259462976534
          }
        ],
        "iterations": 1
      },
      "parent": {
        "candidate_id": "bec_projection_00",
        "source": "MACEField_BEC_backprojection",
        "spacegroup": "Cc",
        "spacegroup_number": 9,
        "pointgroup": "m",
        "has_inversion": false,
        "is_polar_point_group": true,
        "nonpolar_parent_hypothesis": false,
        "symmetry_tolerance_A": null,
        "target_reduced_polarization": [
          0.0,
          0.0,
          0.0
        ],
        "formal_class": [
          0.0,
          0.0,
          0.0
        ],
        "target_residual": 0.0008674402564783212,
        "parent_symmetrization_rmsd_A": 0.01718171949171929,
        "parent_cell_rmsd_A": 0.022533379012042918,
        "energy_eV": -135.95259462976534,
        "reduced_polarization": [
          0.0004990480529539278,
          -1.1871047811817705e-12,
          -0.0007095094357385739
        ],
        "cartesian_polarization_e_A2": [
          7.910996551343873e-06,
          -3.57641189430078e-14,
          -7.156198358873145e-06
        ],
        "ranking_score": 0.5245499447576867
      },
      "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": [
          -136.1146179853702,
          -136.10081561655335,
          -136.08505608925202,
          -136.06739776775618,
          -136.04789796715616,
          -136.0266129739889,
          -136.00359806416566,
          -135.9789075178408,
          -135.95259462976534
        ],
        "cartesian_polarizations_e_A2": [
          [
            0.0013334211818576748,
            4.208650551904071e-12,
            -0.00048826818408783453
          ],
          [
            0.0011672411309668707,
            3.6854766693242666e-12,
            -0.0004281988669518816
          ],
          [
            0.001001193870793636,
            3.160134781160733e-12,
            -0.0003681000299374867
          ],
          [
            0.0008352816450527612,
            2.6328031531333457e-12,
            -0.0003079752310518325
          ],
          [
            0.0006695079588507994,
            2.1033207874487677e-12,
            -0.0002478290300922622
          ],
          [
            0.0005038775510526901,
            1.5716502311336715e-12,
            -0.00018766698911083695
          ],
          [
            0.00033839635440688066,
            1.0378720034092199e-12,
            -0.00012749566230752624
          ],
          [
            0.00017307144664603218,
            5.020797890084044e-13,
            -6.732257581483446e-05
          ],
          [
            7.910996551327186e-06,
            -3.5727213700517464e-14,
            -7.156198358879447e-06
          ]
        ],
        "raw_reduced_polarization": [
          [
            0.10885109055045719,
            1.3824698249103875e-10,
            -0.04840389135377225
          ],
          [
            0.09528764634232711,
            1.210398791845314e-10,
            -0.042419008908741625
          ],
          [
            0.08172934999078785,
            1.0376764345749899e-10,
            -0.03643979161081588
          ],
          [
            0.06817630250577647,
            8.643598368007922e-11,
            -0.030466580705636293
          ],
          [
            0.05462868892340489,
            6.903944855684656e-11,
            -0.024499817024509835
          ],
          [
            0.04108677567682448,
            5.157664215467489e-11,
            -0.018540041011050088
          ],
          [
            0.027550907169335677,
            3.405005274693965e-11,
            -0.012587891707358502
          ],
          [
            0.01402150183815107,
            1.646260649290383e-11,
            -0.0066441047448697246
          ],
          [
            0.00049904805295213,
            -1.1858862011894517e-12,
            -0.0007095094357392071
          ]
        ],
        "unwrapped_reduced_polarization": [
          [
            0.10885109055045719,
            1.3824698249103875e-10,
            -0.04840389135377225
          ],
          [
            0.09528764634232711,
            1.210398791845314e-10,
            -0.042419008908741625
          ],
          [
            0.08172934999078785,
            1.0376764345749899e-10,
            -0.03643979161081588
          ],
          [
            0.06817630250577647,
            8.643598368007922e-11,
            -0.030466580705636293
          ],
          [
            0.05462868892340489,
            6.903944855684656e-11,
            -0.024499817024509835
          ],
          [
            0.04108677567682448,
            5.157664215467489e-11,
            -0.018540041011050088
          ],
          [
            0.027550907169335677,
            3.405005274693965e-11,
            -0.012587891707358502
          ],
          [
            0.01402150183815107,
            1.646260649290383e-11,
            -0.0066441047448697246
          ],
          [
            0.0004990480529521307,
            -1.1858862011894515e-12,
            -0.0007095094357392074
          ]
        ],
        "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": [
          [
            0.10885109055045716,
            1.3824696942776882e-10,
            -0.048403891353772266
          ],
          [
            0.09528764634232711,
            1.2103984481370844e-10,
            -0.04241900890874162
          ],
          [
            0.08172934999078785,
            1.0376766113040503e-10,
            -0.0364397916108159
          ],
          [
            0.06817630250577644,
            8.643596949298171e-11,
            -0.030466580705636293
          ],
          [
            0.05462868892340489,
            6.903944083092028e-11,
            -0.024499817024509818
          ],
          [
            0.041086775676824505,
            5.1576631854288735e-11,
            -0.018540041011050112
          ],
          [
            0.027550907169335725,
            3.40500960760437e-11,
            -0.012587891707358523
          ],
          [
            0.014021501838151096,
            1.6462609053746746e-11,
            -0.0066441047448697055
          ],
          [
            0.0004990480529520891,
            -1.185884723753361e-12,
            -0.0007095094357392195
          ]
        ]
      },
      "reflected": {
        "reached": true,
        "construction": "reflect_displacements_about_reconstructed_parent",
        "energies_eV": [
          -135.95259462976537,
          -135.93939658611157,
          -135.92515984023214,
          -135.90988311437687,
          -135.89356466532024,
          -135.87620226344293,
          -135.85779317161297,
          -135.83833412505578,
          -135.8178213135909
        ],
        "cartesian_polarizations_e_A2": [
          [
            7.910996551344072e-06,
            -3.5785233449045374e-14,
            -7.156198358900393e-06
          ],
          [
            -0.0001329469839053867,
            -4.614255615893766e-13,
            3.0899171472154025e-05
          ],
          [
            -0.0002739896274171361,
            -8.859845633211295e-13,
            6.890603575781341e-05
          ],
          [
            -0.0004152193990727277,
            -1.3098430995573624e-12,
            0.0001068653380532347
          ],
          [
            -0.0005566393714132267,
            -1.7324967250747153e-12,
            0.00014477847499009213
          ],
          [
            -0.0006982532747704074,
            -2.154275745192504e-12,
            0.0001826472724731105
          ],
          [
            -0.000840065517109554,
            -2.5750322076830953e-12,
            0.0002204739466682243
          ],
          [
            -0.0009820811782852536,
            -2.9946880510989467e-12,
            0.0002582610555590398
          ],
          [
            -0.0011243059845508785,
            -3.4134054485397555e-12,
            0.00029601144688684274
          ]
        ],
        "raw_reduced_polarization": [
          [
            0.0004990480529529979,
            -1.1878019643695467e-12,
            -0.000709509435741286
          ],
          [
            -0.011494482329148315,
            -1.514865215381725e-11,
            0.0030328778559502887
          ],
          [
            -0.02349843631338219,
            -2.9079259707950563e-11,
            0.0067790420594900196
          ],
          [
            -0.03551299132355698,
            -4.2992274756548583e-11,
            0.010529097731544979
          ],
          [
            -0.04753836626472356,
            -5.6871158986950906e-11,
            0.014283204531909472
          ],
          [
            -0.059574827087474344,
            -7.072689147582618e-11,
            0.018041564873186484
          ],
          [
            -0.07162268997795257,
            -8.455469381245319e-11,
            0.021804420084495006
          ],
          [
            -0.08368232244121618,
            -9.835209885855863e-11,
            0.025572045657809184
          ],
          [
            -0.09575414263298367,
            -1.1212453907953913e-10,
            0.02934474614878077
          ]
        ],
        "unwrapped_reduced_polarization": [
          [
            0.0004990480529529979,
            -1.1878019643695467e-12,
            -0.000709509435741286
          ],
          [
            -0.011494482329148315,
            -1.514865215381725e-11,
            0.0030328778559502887
          ],
          [
            -0.02349843631338219,
            -2.9079259707950563e-11,
            0.0067790420594900196
          ],
          [
            -0.03551299132355698,
            -4.2992274756548583e-11,
            0.010529097731544979
          ],
          [
            -0.04753836626472356,
            -5.6871158986950906e-11,
            0.014283204531909472
          ],
          [
            -0.059574827087474344,
            -7.072689147582618e-11,
            0.018041564873186484
          ],
          [
            -0.07162268997795257,
            -8.455469381245319e-11,
            0.021804420084495006
          ],
          [
            -0.08368232244121618,
            -9.835209885855863e-11,
            0.025572045657809184
          ],
          [
            -0.09575414263298367,
            -1.1212453907953913e-10,
            0.02934474614878077
          ]
        ],
        "gauge_integer_shift": [
          0,
          0,
          0
        ],
        "expected_opposite_endpoint_reduced_polarization": [
          -0.10785211443123463,
          -1.4059413839100983e-10,
          0.04698504876210779
        ],
        "actual_opposite_endpoint_branch_residual": 0.021390212666568504
      },
      "pnp_branch": {
        "construction": "incoming_path_concatenated_with_parent_reflection",
        "reduced_polarization": [
          [
            0.10885109055045719,
            1.3824698249103875e-10,
            -0.04840389135377225
          ],
          [
            0.09528764634232711,
            1.210398791845314e-10,
            -0.042419008908741625
          ],
          [
            0.08172934999078785,
            1.0376764345749899e-10,
            -0.03643979161081588
          ],
          [
            0.06817630250577647,
            8.643598368007922e-11,
            -0.030466580705636293
          ],
          [
            0.05462868892340489,
            6.903944855684656e-11,
            -0.024499817024509835
          ],
          [
            0.04108677567682448,
            5.157664215467489e-11,
            -0.018540041011050088
          ],
          [
            0.027550907169335677,
            3.405005274693965e-11,
            -0.012587891707358502
          ],
          [
            0.01402150183815107,
            1.646260649290383e-11,
            -0.0066441047448697246
          ],
          [
            0.00049904805295213,
            -1.1858862011894517e-12,
            -0.0007095094357392071
          ],
          [
            -0.011494482329148315,
            -1.514865215381725e-11,
            0.0030328778559502887
          ],
          [
            -0.02349843631338219,
            -2.9079259707950563e-11,
            0.0067790420594900196
          ],
          [
            -0.03551299132355698,
            -4.2992274756548583e-11,
            0.010529097731544979
          ],
          [
            -0.04753836626472356,
            -5.6871158986950906e-11,
            0.014283204531909472
          ],
          [
            -0.059574827087474344,
            -7.072689147582618e-11,
            0.018041564873186484
          ],
          [
            -0.07162268997795257,
            -8.455469381245319e-11,
            0.021804420084495006
          ],
          [
            -0.08368232244121618,
            -9.835209885855863e-11,
            0.025572045657809184
          ],
          [
            -0.09575414263298367,
            -1.1212453907953913e-10,
            0.02934474614878077
          ]
        ],
        "unwrapped_reduced_polarization": [
          [
            0.10885109055045719,
            1.3824698249103875e-10,
            -0.04840389135377225
          ],
          [
            0.09528764634232711,
            1.210398791845314e-10,
            -0.042419008908741625
          ],
          [
            0.08172934999078785,
            1.0376764345749899e-10,
            -0.03643979161081588
          ],
          [
            0.06817630250577647,
            8.643598368007922e-11,
            -0.030466580705636293
          ],
          [
            0.05462868892340489,
            6.903944855684656e-11,
            -0.024499817024509835
          ],
          [
            0.04108677567682448,
            5.157664215467489e-11,
            -0.018540041011050088
          ],
          [
            0.027550907169335677,
            3.405005274693965e-11,
            -0.012587891707358502
          ],
          [
            0.01402150183815107,
            1.646260649290383e-11,
            -0.0066441047448697246
          ],
          [
            0.0004990480529521307,
            -1.1858862011894515e-12,
            -0.0007095094357392074
          ],
          [
            -0.011494482329148315,
            -1.514865215381725e-11,
            0.0030328778559502887
          ],
          [
            -0.02349843631338219,
            -2.9079259707950563e-11,
            0.0067790420594900196
          ],
          [
            -0.03551299132355698,
            -4.2992274756548583e-11,
            0.010529097731544979
          ],
          [
            -0.04753836626472356,
            -5.6871158986950906e-11,
            0.014283204531909472
          ],
          [
            -0.059574827087474344,
            -7.072689147582618e-11,
            0.018041564873186484
          ],
          [
            -0.07162268997795257,
            -8.455469381245319e-11,
            0.021804420084495006
          ],
          [
            -0.08368232244121618,
            -9.835209885855863e-11,
            0.025572045657809184
          ],
          [
            -0.09575414263298367,
            -1.1212453907953913e-10,
            0.02934474614878077
          ]
        ],
        "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": [
          [
            0.10885109055045716,
            1.3824696942776882e-10,
            -0.048403891353772266
          ],
          [
            0.09528764634232711,
            1.2103984481370844e-10,
            -0.04241900890874162
          ],
          [
            0.08172934999078785,
            1.0376766113040503e-10,
            -0.0364397916108159
          ],
          [
            0.06817630250577644,
            8.643596949298171e-11,
            -0.030466580705636293
          ],
          [
            0.05462868892340489,
            6.903944083092028e-11,
            -0.024499817024509818
          ],
          [
            0.041086775676824505,
            5.1576631854288735e-11,
            -0.018540041011050112
          ],
          [
            0.027550907169335725,
            3.40500960760437e-11,
            -0.012587891707358523
          ],
          [
            0.014021501838151096,
            1.6462609053746746e-11,
            -0.0066441047448697055
          ],
          [
            0.0004990480529520891,
            -1.185884723753361e-12,
            -0.0007095094357392195
          ],
          [
            -0.011494482329148292,
            -1.5148660104102873e-11,
            0.0030328778559503
          ],
          [
            -0.023498436313382165,
            -2.9079239016738256e-11,
            0.006779042059489981
          ],
          [
            -0.03551299132355701,
            -4.299227640558456e-11,
            0.010529097731544979
          ],
          [
            -0.047538366264723575,
            -5.6871174436423644e-11,
            0.014283204531909455
          ],
          [
            -0.05957482708747436,
            -7.072686880604806e-11,
            0.018041564873186533
          ],
          [
            -0.07162268997795257,
            -8.455469657775438e-11,
            0.021804420084495013
          ],
          [
            -0.0836823224412162,
            -9.835210423858598e-11,
            0.02557204565780924
          ],
          [
            -0.09575414263298365,
            -1.1212453188136351e-10,
            0.029344746148780798
          ]
        ]
      },
      "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": [
        0.5,
        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": [
              0.10885109055045711,
              1.3824676480015927e-10,
              -0.048403891353765986
            ],
            "branch_aligned_reduced_polarization": [
              0.10885109055045711,
              1.3824676480015927e-10,
              -0.048403891353765986
            ],
            "target_residual": 0.39413247273188984,
            "energy_eV": -136.11461798537022,
            "max_atomic_step_A": 0.05951546771441913,
            "max_log_strain_component": 0.007693335452708678,
            "step_scale": 1.0,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 2.3195488914165274,
            "cell_principal_stretches": [
              1.0004433400017056,
              0.9974817300216771,
              0.9879624896735495
            ],
            "cell_volume_ratio": 0.9859114336774123,
            "cell_rmsd_from_input_A": 0.055791428651813676
          },
          {
            "iteration": 1,
            "reduced_polarization": [
              0.5035654833360952,
              9.73657760217129e-12,
              -0.0024981107196918586
            ],
            "branch_aligned_reduced_polarization": [
              0.5035654833360952,
              9.73657760217129e-12,
              -0.0024981107196918586
            ],
            "target_residual": 0.004353530588822346,
            "energy_eV": -135.81654086398493,
            "max_atomic_step_A": 0.000926528783666643,
            "max_log_strain_component": 0.0001418445668632753,
            "step_scale": 1.0,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 2.3195488914165274,
            "cell_principal_stretches": [
              1.0003976941107153,
              0.9975072849493595,
              0.9881995364473114
            ],
            "cell_volume_ratio": 0.9861282580857841,
            "cell_rmsd_from_input_A": 0.055025250922220416
          },
          {
            "iteration": 2,
            "reduced_polarization": [
              0.49996831714157586,
              1.1093375015754538e-14,
              4.789985110043424e-05
            ],
            "branch_aligned_reduced_polarization": [
              0.49996831714157586,
              1.1093375015754538e-14,
              4.789985110043424e-05
            ],
            "target_residual": 5.742995083898317e-05,
            "energy_eV": -135.82665450660295
          }
        ],
        "iterations": 2
      },
      "parent": {
        "candidate_id": "bec_projection_01",
        "source": "MACEField_BEC_backprojection",
        "spacegroup": "Cc",
        "spacegroup_number": 9,
        "pointgroup": "m",
        "has_inversion": false,
        "is_polar_point_group": true,
        "nonpolar_parent_hypothesis": false,
        "symmetry_tolerance_A": null,
        "target_reduced_polarization": [
          0.5,
          0.0,
          0.0
        ],
        "formal_class": [
          0.5,
          0.0,
          0.0
        ],
        "target_residual": 5.742995083898317e-05,
        "parent_symmetrization_rmsd_A": 0.05147464902746573,
        "parent_cell_rmsd_A": 0.055025250922220416,
        "energy_eV": -135.82665450660295,
        "reduced_polarization": [
          0.49996831714157586,
          1.1093375015754538e-14,
          4.789985110043424e-05
        ],
        "cartesian_polarization_e_A2": [
          0.005340867105407056,
          -1.5233938653799322e-13,
          3.1807114103521e-05
        ],
        "ranking_score": 0.5653458216596988
      },
      "branch_status": "awaiting_branch_sampling"
    },
    {
      "orbit_id": 2,
      "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": [
              0.10885109055045711,
              1.3824676480015927e-10,
              -0.048403891353765986
            ],
            "branch_aligned_reduced_polarization": [
              0.10885109055045711,
              1.3824676480015927e-10,
              -0.04840389135376599
            ],
            "target_residual": 0.46452944498540133,
            "energy_eV": -136.11461798537022,
            "max_atomic_step_A": 0.06558370571781805,
            "max_log_strain_component": 0.011735813921213716,
            "step_scale": 1.0,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 2.3195488914165274,
            "cell_principal_stretches": [
              1.0065298569349128,
              1.0002009321189973,
              0.9831357277907788
            ],
            "cell_volume_ratio": 0.9897542969169888,
            "cell_rmsd_from_input_A": 0.0487267220910521
          },
          {
            "iteration": 1,
            "reduced_polarization": [
              0.0075702787570079595,
              -4.062839404153461e-12,
              -0.5036652952418106
            ],
            "branch_aligned_reduced_polarization": [
              0.0075702787570079595,
              -4.062839404153461e-12,
              -0.5036652952418106
            ],
            "target_residual": 0.008410916101617308,
            "energy_eV": -135.6477801971127,
            "max_atomic_step_A": 0.001723525013064517,
            "max_log_strain_component": 0.0002475032158779732,
            "step_scale": 1.0,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 2.3195488914165274,
            "cell_principal_stretches": [
              1.006459811013962,
              1.0002547009555607,
              0.9835589022457547
            ],
            "cell_volume_ratio": 0.990164638536785,
            "cell_rmsd_from_input_A": 0.047613991018464155
          },
          {
            "iteration": 2,
            "reduced_polarization": [
              -0.00011619824236101396,
              1.597827678944053e-13,
              -0.4999361352055396
            ],
            "branch_aligned_reduced_polarization": [
              -0.00011619824236101396,
              1.597827678944053e-13,
              -0.4999361352055396
            ],
            "target_residual": 0.00013259239608386097,
            "energy_eV": -135.66179260336574
          }
        ],
        "iterations": 2
      },
      "parent": {
        "candidate_id": "bec_projection_02",
        "source": "MACEField_BEC_backprojection",
        "spacegroup": "Cc",
        "spacegroup_number": 9,
        "pointgroup": "m",
        "has_inversion": false,
        "is_polar_point_group": true,
        "nonpolar_parent_hypothesis": false,
        "symmetry_tolerance_A": null,
        "target_reduced_polarization": [
          0.0,
          0.0,
          -0.5
        ],
        "formal_class": [
          0.0,
          0.0,
          0.5
        ],
        "target_residual": 0.00013259239608386097,
        "parent_symmetrization_rmsd_A": 0.05764423660539236,
        "parent_cell_rmsd_A": 0.047613991018464155,
        "energy_eV": -135.66179260336574,
        "reduced_polarization": [
          -0.00011619824236101396,
          1.597827678944053e-13,
          -0.4999361352055396
        ],
        "cartesian_polarization_e_A2": [
          0.0017870145194516809,
          -1.236594133767149e-13,
          -0.00504995034847798
        ],
        "ranking_score": 0.5698129191521761
      },
      "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": [
              0.10885109055045711,
              1.3824676480015927e-10,
              -0.048403891353765986
            ],
            "branch_aligned_reduced_polarization": [
              0.10885109055045711,
              1.382467473831639e-10,
              -0.048403891353765986
            ],
            "target_residual": 0.5139956191194281,
            "energy_eV": -136.11461798537022,
            "max_atomic_step_A": 0.12,
            "max_log_strain_component": 0.012184010437716506,
            "step_scale": 0.4664830173077921,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 2.3195488914165274,
            "cell_principal_stretches": [
              1.0134529062516893,
              1.000706842398853,
              0.9887741714964351
            ],
            "cell_volume_ratio": 1.0027843675741475,
            "cell_rmsd_from_input_A": 0.11372346111010365
          },
          {
            "iteration": 1,
            "reduced_polarization": [
              0.051026741823689804,
              0.22960590367472447,
              -0.005540792951291804
            ],
            "branch_aligned_reduced_polarization": [
              0.051026741823689804,
              0.22960590367472444,
              -0.005540792951291804
            ],
            "target_residual": 0.2752224483853615,
            "energy_eV": -134.55258889787575,
            "max_atomic_step_A": 0.12,
            "max_log_strain_component": 0.012730660388178095,
            "step_scale": 0.824166865038389,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 2.3195488914165274,
            "cell_principal_stretches": [
              1.026004230726494,
              1.000396502743731,
              0.9760524804137146
            ],
            "cell_volume_ratio": 1.0018310456340414,
            "cell_rmsd_from_input_A": 0.23176344333082888
          },
          {
            "iteration": 2,
            "reduced_polarization": [
              0.01136500446030265,
              0.4365537126413663,
              0.025537341445517874
            ],
            "branch_aligned_reduced_polarization": [
              0.01136500446030265,
              0.4365537126413663,
              0.025537341445517874
            ],
            "target_residual": 0.06933073282521965,
            "energy_eV": -130.4650761308661,
            "max_atomic_step_A": 0.04193251776486593,
            "max_log_strain_component": 0.004528270375231624,
            "step_scale": 1.0,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 2.3195488914165274,
            "cell_principal_stretches": [
              1.0301147766419858,
              0.9999179961036074,
              0.9710835023439135
            ],
            "cell_volume_ratio": 1.0002454343679092,
            "cell_rmsd_from_input_A": 0.27351018360403767
          },
          {
            "iteration": 3,
            "reduced_polarization": [
              0.003713173112617137,
              0.49758328035833294,
              0.007849489286729848
            ],
            "branch_aligned_reduced_polarization": [
              0.003713173112617137,
              0.49758328035833294,
              0.007849489286729848
            ],
            "target_residual": 0.00901347160938386,
            "energy_eV": -129.3509781795069,
            "max_atomic_step_A": 0.0022905306500323234,
            "max_log_strain_component": 0.00020961025393866322,
            "step_scale": 1.0,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 2.3195488914165274,
            "cell_principal_stretches": [
              1.0302760104410138,
              0.9998636585175055,
              0.9708260730883745
            ],
            "cell_volume_ratio": 1.0000824420977668,
            "cell_rmsd_from_input_A": 0.2753660038168413
          },
          {
            "iteration": 4,
            "reduced_polarization": [
              8.221313830746546e-05,
              0.499834835658041,
              0.0004290608733588322
            ],
            "branch_aligned_reduced_polarization": [
              8.221313830746546e-05,
              0.499834835658041,
              0.0004290608733588322
            ],
            "target_residual": 0.0004670454935148821,
            "energy_eV": -129.3152243998772
          }
        ],
        "iterations": 4
      },
      "parent": {
        "candidate_id": "bec_projection_03",
        "source": "MACEField_BEC_backprojection",
        "spacegroup": "P1",
        "spacegroup_number": 1,
        "pointgroup": "1",
        "has_inversion": false,
        "is_polar_point_group": true,
        "nonpolar_parent_hypothesis": false,
        "symmetry_tolerance_A": null,
        "target_reduced_polarization": [
          0.0,
          0.5,
          0.0
        ],
        "formal_class": [
          0.0,
          0.5,
          0.0
        ],
        "target_residual": 0.0004670454935148821,
        "parent_symmetrization_rmsd_A": 0.2284746259576941,
        "parent_cell_rmsd_A": 0.2753660038168413,
        "energy_eV": -129.3152243998772,
        "reduced_polarization": [
          8.221313830746546e-05,
          0.499834835658041,
          0.0004290608733588322
        ],
        "cartesian_polarization_e_A2": [
          -0.000451468463934174,
          0.015227853408950805,
          2.7317785319988072e-05
        ],
        "ranking_score": 0.7982502178989342
      },
      "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": [
              0.10885109055045711,
              1.3824676480015927e-10,
              -0.048403891353765986
            ],
            "branch_aligned_reduced_polarization": [
              0.10885109055045711,
              1.3824676480015927e-10,
              -0.04840389135376599
            ],
            "target_residual": 0.5974416412571089,
            "energy_eV": -136.11461798537022,
            "max_atomic_step_A": 0.12000000000000001,
            "max_log_strain_component": 0.01924728938170628,
            "step_scale": 0.9039583541849681,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 2.3195488914165274,
            "cell_principal_stretches": [
              1.007135933221375,
              0.997208018507535,
              0.9686631978487034
            ],
            "cell_volume_ratio": 0.9728517249636843,
            "cell_rmsd_from_input_A": 0.10149318179400467
          },
          {
            "iteration": 1,
            "reduced_polarization": [
              0.4807434598600926,
              -6.681439726558711e-12,
              -0.4776192380700831
            ],
            "branch_aligned_reduced_polarization": [
              0.4807434598600926,
              -6.681439726558711e-12,
              -0.4776192380700831
            ],
            "target_residual": 0.02952478353389712,
            "energy_eV": -134.2450676013645,
            "max_atomic_step_A": 0.006122426659022074,
            "max_log_strain_component": 0.0009479570940132921,
            "step_scale": 1.0,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 2.3195488914165274,
            "cell_principal_stretches": [
              1.0074887018710423,
              0.9970707116025781,
              0.9671454447089524
            ],
            "cell_volume_ratio": 0.9715338448291763,
            "cell_rmsd_from_input_A": 0.1063633378162019
          },
          {
            "iteration": 2,
            "reduced_polarization": [
              0.500805199625307,
              -6.588474445343033e-13,
              -0.5008032982335474
            ],
            "branch_aligned_reduced_polarization": [
              0.500805199625307,
              -6.588474445343033e-13,
              -0.5008032982335474
            ],
            "target_residual": 0.0011373805381731023,
            "energy_eV": -133.96490329230858,
            "max_atomic_step_A": 0.00023498292734824055,
            "max_log_strain_component": 3.55973059724223e-05,
            "step_scale": 1.0,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 2.3195488914165274,
            "cell_principal_stretches": [
              1.0074759422644521,
              0.9970763020520151,
              0.9672029386720951
            ],
            "cell_volume_ratio": 0.97158474221387,
            "cell_rmsd_from_input_A": 0.10617575185736569
          },
          {
            "iteration": 3,
            "reduced_polarization": [
              0.49997102379074104,
              1.8930219011326e-14,
              -0.499971346860589
            ],
            "branch_aligned_reduced_polarization": [
              0.49997102379074104,
              1.8930219011326e-14,
              -0.499971346860589
            ],
            "target_residual": 4.075074356528363e-05,
            "energy_eV": -133.97609219605698
          }
        ],
        "iterations": 3
      },
      "parent": {
        "candidate_id": "bec_projection_04",
        "source": "MACEField_BEC_backprojection",
        "spacegroup": "Cc",
        "spacegroup_number": 9,
        "pointgroup": "m",
        "has_inversion": false,
        "is_polar_point_group": true,
        "nonpolar_parent_hypothesis": false,
        "symmetry_tolerance_A": null,
        "target_reduced_polarization": [
          0.5,
          0.0,
          -0.5
        ],
        "formal_class": [
          0.5,
          0.0,
          0.5
        ],
        "target_residual": 4.075074356528363e-05,
        "parent_symmetrization_rmsd_A": 0.08604352094870757,
        "parent_cell_rmsd_A": 0.10617575185736569,
        "energy_eV": -133.97609219605698,
        "reduced_polarization": [
          0.49997102379074104,
          1.8930219011326e-14,
          -0.499971346860589
        ],
        "cartesian_polarization_e_A2": [
          0.007135792342807811,
          -4.657619217124015e-13,
          -0.0049947246157864
        ],
        "ranking_score": 0.6126689604001796
      },
      "branch_status": "awaiting_branch_sampling"
    },
    {
      "orbit_id": 5,
      "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": [
              0.10885109055045711,
              1.3824676480015927e-10,
              -0.048403891353765986
            ],
            "branch_aligned_reduced_polarization": [
              0.10885109055045711,
              1.382467473831639e-10,
              -0.048403891353765986
            ],
            "target_residual": 0.6366634950454653,
            "energy_eV": -136.11461798537022,
            "max_atomic_step_A": 0.12,
            "max_log_strain_component": 0.011219938929241816,
            "step_scale": 0.4295721004823433,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 2.3195488914165274,
            "cell_principal_stretches": [
              1.009278465298794,
              0.998578316802013,
              0.9861881883309401
            ],
            "cell_volume_ratio": 0.9939234451909637,
            "cell_rmsd_from_input_A": 0.10564345157889564
          },
          {
            "iteration": 1,
            "reduced_polarization": [
              0.2711117620780955,
              0.21047473921339277,
              -0.006011043570686786
            ],
            "branch_aligned_reduced_polarization": [
              0.2711117620780955,
              0.21047473921339277,
              -0.006011043570686786
            ],
            "target_residual": 0.3691217072150539,
            "energy_eV": -134.80494580405778,
            "max_atomic_step_A": 0.12000000000000001,
            "max_log_strain_component": 0.01147869164571652,
            "step_scale": 0.667480902847046,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 2.3195488914165274,
            "cell_principal_stretches": [
              1.0186169252489756,
              0.9965233245580211,
              0.970800053454458
            ],
            "cell_volume_ratio": 0.9854353737363251,
            "cell_rmsd_from_input_A": 0.21314416805544809
          },
          {
            "iteration": 2,
            "reduced_polarization": [
              0.4270725212022936,
              0.39009326371750236,
              0.015559259731171693
            ],
            "branch_aligned_reduced_polarization": [
              0.4270725212022936,
              0.39009326371750236,
              0.015559259731171693
            ],
            "target_residual": 0.13281565573170379,
            "energy_eV": -131.12248224087563,
            "max_atomic_step_A": 0.08020290732378503,
            "max_log_strain_component": 0.008031243201436274,
            "step_scale": 1.0,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 2.3195488914165274,
            "cell_principal_stretches": [
              1.0255372886802845,
              0.995275621703276,
              0.960502428092859
            ],
            "cell_volume_ratio": 0.9803773965351952,
            "cell_rmsd_from_input_A": 0.2866011204318901
          },
          {
            "iteration": 3,
            "reduced_polarization": [
              0.5121327332883333,
              0.49493206530348777,
              0.014671237782918768
            ],
            "branch_aligned_reduced_polarization": [
              0.5121327332883333,
              0.49493206530348777,
              0.014671237782918768
            ],
            "target_residual": 0.019701076042107114,
            "energy_eV": -128.39529590024136,
            "max_atomic_step_A": 0.005368327292356538,
            "max_log_strain_component": 0.0004523249193411047,
            "step_scale": 1.0,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 2.3195488914165274,
            "cell_principal_stretches": [
              1.0260508317467454,
              0.9952433364072772,
              0.9599775672036532
            ],
            "cell_volume_ratio": 0.9803005352823257,
            "cell_rmsd_from_input_A": 0.2905950597332013
          },
          {
            "iteration": 4,
            "reduced_polarization": [
              0.5003493249794255,
              0.4997817824469068,
              0.0007772988007609961
            ],
            "branch_aligned_reduced_polarization": [
              0.5003493249794255,
              0.4997817824469068,
              0.0007772988007609961
            ],
            "target_residual": 0.0008796819126213241,
            "energy_eV": -128.31239902812018
          }
        ],
        "iterations": 4
      },
      "parent": {
        "candidate_id": "bec_projection_05",
        "source": "MACEField_BEC_backprojection",
        "spacegroup": "P1",
        "spacegroup_number": 1,
        "pointgroup": "1",
        "has_inversion": false,
        "is_polar_point_group": true,
        "nonpolar_parent_hypothesis": false,
        "symmetry_tolerance_A": null,
        "target_reduced_polarization": [
          0.5,
          0.5,
          0.0
        ],
        "formal_class": [
          0.5,
          0.5,
          0.0
        ],
        "target_residual": 0.0008796819126213241,
        "parent_symmetrization_rmsd_A": 0.24345141256117983,
        "parent_cell_rmsd_A": 0.2905950597332013,
        "energy_eV": -128.31239902812018,
        "reduced_polarization": [
          0.5003493249794255,
          0.4997817824469068,
          0.0007772988007609961
        ],
        "cartesian_polarization_e_A2": [
          0.004878508777489372,
          0.015316219975035086,
          8.891297671606612e-05
        ],
        "ranking_score": 0.8178595413197228
      },
      "branch_status": "awaiting_branch_sampling"
    },
    {
      "orbit_id": 6,
      "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": [
              0.10885109055045711,
              1.3824676480015927e-10,
              -0.048403891353765986
            ],
            "branch_aligned_reduced_polarization": [
              0.10885109055045711,
              1.382467473831639e-10,
              -0.04840389135376599
            ],
            "target_residual": 0.6824863406107101,
            "energy_eV": -136.11461798537022,
            "max_atomic_step_A": 0.12,
            "max_log_strain_component": 0.01132353419255511,
            "step_scale": 0.433538400288278,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 2.3195488914165274,
            "cell_principal_stretches": [
              1.0109210163962443,
              0.998821037046519,
              0.985952626243294
            ],
            "cell_volume_ratio": 0.9955451348130353,
            "cell_rmsd_from_input_A": 0.10650401510971336
          },
          {
            "iteration": 1,
            "reduced_polarization": [
              0.053675054139626636,
              0.210732378098838,
              -0.22670708610396412
            ],
            "branch_aligned_reduced_polarization": [
              0.053675054139626636,
              0.210732378098838,
              -0.22670708610396412
            ],
            "target_residual": 0.40155421215949355,
            "energy_eV": -134.80170006713263,
            "max_atomic_step_A": 0.12,
            "max_log_strain_component": 0.011657782318736407,
            "step_scale": 0.6708885121093644,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 2.3195488914165274,
            "cell_principal_stretches": [
              1.0220037184300395,
              0.9971884538399268,
              0.9701422229932576
            ],
            "cell_volume_ratio": 0.9887013423288044,
            "cell_rmsd_from_input_A": 0.21613767163537662
          },
          {
            "iteration": 2,
            "reduced_polarization": [
              0.028111122462941483,
              0.38698469014448483,
              -0.39178788545052046
            ],
            "branch_aligned_reduced_polarization": [
              0.028111122462941483,
              0.38698469014448483,
              -0.39178788545052046
            ],
            "target_residual": 0.15897344810733105,
            "energy_eV": -131.27774140365676,
            "max_atomic_step_A": 0.07970821740736803,
            "max_log_strain_component": 0.008688295501621916,
            "step_scale": 1.0,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 2.3195488914165274,
            "cell_principal_stretches": [
              1.0305079772865622,
              0.9961911546446746,
              0.9593023485222814
            ],
            "cell_volume_ratio": 0.9848034173937569,
            "cell_rmsd_from_input_A": 0.2967471702032335
          },
          {
            "iteration": 3,
            "reduced_polarization": [
              0.012865422038584888,
              0.48920626332631756,
              -0.4847415535244391
            ],
            "branch_aligned_reduced_polarization": [
              0.012865422038584888,
              0.48920626332631756,
              -0.4847415535244391
            ],
            "target_residual": 0.022690174623815923,
            "energy_eV": -128.47698849931447,
            "max_atomic_step_A": 0.008098386483962189,
            "max_log_strain_component": 0.000978927859969393,
            "step_scale": 1.0,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 2.3195488914165274,
            "cell_principal_stretches": [
              1.0315436221402998,
              0.9961197575015442,
              0.9581720860970796
            ],
            "cell_volume_ratio": 0.9845610869809448,
            "cell_rmsd_from_input_A": 0.30585820457127205
          },
          {
            "iteration": 4,
            "reduced_polarization": [
              0.0010757900771694953,
              0.49915883571545716,
              -0.49769726416324545
            ],
            "branch_aligned_reduced_polarization": [
              0.0010757900771694953,
              0.49915883571545716,
              -0.49769726416324545
            ],
            "target_residual": 0.002677213846072165,
            "energy_eV": -128.15230293792024,
            "max_atomic_step_A": 0.0005426973947678071,
            "max_log_strain_component": 0.00015348432197430858,
            "step_scale": 1.0,
            "strain_jacobian_refreshed": true,
            "strain_jacobian_frobenius_norm": 5.803945221328013,
            "cell_principal_stretches": [
              1.031279166101352,
              0.9961430271634033,
              0.9582121733017782
            ],
            "cell_volume_ratio": 0.984372851217043,
            "cell_rmsd_from_input_A": 0.3050967804552599
          },
          {
            "iteration": 5,
            "reduced_polarization": [
              -2.5140623404783076e-06,
              0.5000001725878165,
              -0.5000029151178599
            ],
            "branch_aligned_reduced_polarization": [
              -2.5140623404783076e-06,
              0.5000001725878165,
              -0.5000029151178599
            ],
            "target_residual": 3.853337273481937e-06,
            "energy_eV": -128.1204303928584
          }
        ],
        "iterations": 5
      },
      "parent": {
        "candidate_id": "bec_projection_06",
        "source": "MACEField_BEC_backprojection",
        "spacegroup": "P1",
        "spacegroup_number": 1,
        "pointgroup": "1",
        "has_inversion": false,
        "is_polar_point_group": true,
        "nonpolar_parent_hypothesis": false,
        "symmetry_tolerance_A": null,
        "target_reduced_polarization": [
          0.0,
          0.5,
          -0.5
        ],
        "formal_class": [
          0.0,
          0.5,
          0.5
        ],
        "target_residual": 3.853337273481937e-06,
        "parent_symmetrization_rmsd_A": 0.2529732331196209,
        "parent_cell_rmsd_A": 0.3050967804552599,
        "energy_eV": -128.1204303928584,
        "reduced_polarization": [
          -2.5140623404783076e-06,
          0.5000001725878165,
          -0.5000029151178599
        ],
        "cartesian_polarization_e_A2": [
          0.0012688997336535895,
          0.01540106185139676,
          -0.005035286573705311
        ],
        "ranking_score": 0.8292551349079829
      },
      "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": [
              0.10885109055045711,
              1.3824676480015927e-10,
              -0.048403891353765986
            ],
            "branch_aligned_reduced_polarization": [
              0.10885109055045711,
              1.382467473831639e-10,
              -0.04840389135376599
            ],
            "target_residual": 0.7790613034734437,
            "energy_eV": -136.11461798537022,
            "max_atomic_step_A": 0.12,
            "max_log_strain_component": 0.011620252145709544,
            "step_scale": 0.44489868897817353,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 2.3195488914165274,
            "cell_principal_stretches": [
              1.0099149353856305,
              0.9972166549534355,
              0.9795861499125692
            ],
            "cell_volume_ratio": 0.9865451237038929,
            "cell_rmsd_from_input_A": 0.11710083518403695
          },
          {
            "iteration": 1,
            "reduced_polarization": [
              0.27640699952691916,
              0.214051622597217,
              -0.23009334016685382
            ],
            "branch_aligned_reduced_polarization": [
              0.27640699952691916,
              0.214051622597217,
              -0.2300933401668538
            ],
            "target_residual": 0.45233826880126476,
            "energy_eV": -134.5424708045157,
            "max_atomic_step_A": 0.11999999999999998,
            "max_log_strain_component": 0.011500650494075837,
            "step_scale": 0.6354948286958949,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 2.3195488914165274,
            "cell_principal_stretches": [
              1.0199057852966842,
              0.9945006383543851,
              0.9597672550545068
            ],
            "cell_volume_ratio": 0.9734890038679298,
            "cell_rmsd_from_input_A": 0.22919624019451937
          },
          {
            "iteration": 2,
            "reduced_polarization": [
              0.4436612027221548,
              0.37856592565528774,
              -0.40730268758059307
            ],
            "branch_aligned_reduced_polarization": [
              0.4436612027221548,
              0.37856592565528774,
              -0.40730268758059307
            ],
            "target_residual": 0.16282839500668295,
            "energy_eV": -129.99486813824996,
            "max_atomic_step_A": 0.09733410784183333,
            "max_log_strain_component": 0.009795369617999223,
            "step_scale": 1.0,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 2.3195488914165274,
            "cell_principal_stretches": [
              1.0286120054302985,
              0.9930386060361871,
              0.9478242501525607
            ],
            "cell_volume_ratio": 0.9681564376259667,
            "cell_rmsd_from_input_A": 0.3158243994814633
          },
          {
            "iteration": 3,
            "reduced_polarization": [
              0.5191600542477183,
              0.4865050111733832,
              -0.48621096309663675
            ],
            "branch_aligned_reduced_polarization": [
              0.5191600542477183,
              0.4865050111733832,
              -0.48621096309663675
            ],
            "target_residual": 0.02719117395274307,
            "energy_eV": -125.70754824044816,
            "max_atomic_step_A": 0.011789333513041659,
            "max_log_strain_component": 0.0013774484845025803,
            "step_scale": 1.0,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 2.3195488914165274,
            "cell_principal_stretches": [
              1.0300207210705008,
              0.9929629661321637,
              0.9464723796049612
            ],
            "cell_volume_ratio": 0.9680258559683037,
            "cell_rmsd_from_input_A": 0.32755519912709313
          },
          {
            "iteration": 4,
            "reduced_polarization": [
              0.5011238769466565,
              0.499177829855721,
              -0.49663785838126134
            ],
            "branch_aligned_reduced_polarization": [
              0.5011238769466565,
              0.499177829855721,
              -0.49663785838126134
            ],
            "target_residual": 0.003639101455280446,
            "energy_eV": -125.36595702328694,
            "max_atomic_step_A": 0.0008119438696460654,
            "max_log_strain_component": 0.00012892025253485122,
            "step_scale": 1.0,
            "strain_jacobian_refreshed": true,
            "strain_jacobian_frobenius_norm": 6.3471045035385085,
            "cell_principal_stretches": [
              1.0297357035199337,
              0.9929793722977521,
              0.9465400843097801
            ],
            "cell_volume_ratio": 0.9678432112541021,
            "cell_rmsd_from_input_A": 0.3268130564926751
          },
          {
            "iteration": 5,
            "reduced_polarization": [
              0.499996966162749,
              0.5000001201432874,
              -0.5000038038778186
            ],
            "branch_aligned_reduced_polarization": [
              0.499996966162749,
              0.5000001201432874,
              -0.5000038038778186
            ],
            "target_residual": 4.867041127206118e-06,
            "energy_eV": -125.31784877831413
          }
        ],
        "iterations": 5
      },
      "parent": {
        "candidate_id": "bec_projection_07",
        "source": "MACEField_BEC_backprojection",
        "spacegroup": "P1",
        "spacegroup_number": 1,
        "pointgroup": "1",
        "has_inversion": false,
        "is_polar_point_group": true,
        "nonpolar_parent_hypothesis": false,
        "symmetry_tolerance_A": null,
        "target_reduced_polarization": [
          0.5,
          0.5,
          -0.5
        ],
        "formal_class": [
          0.5,
          0.5,
          0.5
        ],
        "target_residual": 4.867041127206118e-06,
        "parent_symmetrization_rmsd_A": 0.26760713842810346,
        "parent_cell_rmsd_A": 0.3268130564926751,
        "energy_eV": -125.31784877831413,
        "reduced_polarization": [
          0.499996966162749,
          0.5000001201432874,
          -0.5000038038778186
        ],
        "cartesian_polarization_e_A2": [
          0.006603630105753847,
          0.015431355454343414,
          -0.004957133719768818
        ],
        "ranking_score": 0.8493201366335266
      },
      "branch_status": "awaiting_branch_sampling"
    }
  ],
  "sampled_polarization_branches": [
    {
      "orbit_id": 0,
      "candidate_id": "bec_projection_00",
      "formal_class": [
        0.0,
        0.0,
        0.0
      ],
      "construction": "MACEField-BEC-parent plus variable-cell P-N-P path and symmetric log-strain continuation beyond both polar endpoints",
      "geometry_diagnostics": {
        "collision_aware": false,
        "permutations_tested": 1,
        "selected_order": [
          0,
          1,
          2,
          3,
          4,
          5,
          6,
          7,
          8,
          9,
          10,
          11,
          12,
          13,
          14,
          15,
          16,
          17,
          18,
          19,
          20,
          21,
          22,
          23,
          24,
          25,
          26,
          27,
          28,
          29,
          30,
          31
        ],
        "endpoint_rmsd_A": 0.01718171949171929,
        "minimum_distance_A_by_image": [
          2.054981786633608,
          2.056029347502753,
          2.0570006459703167,
          2.0553116416754134,
          2.0536302834513482,
          2.0519566182857454,
          2.0502906933281038,
          2.0486325558889127,
          2.0469822534387667
        ],
        "minimum_distance_A": 2.0469822534387667,
        "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": [
          553.8835646755166,
          554.2964002544048,
          554.7095435391475,
          555.12299475909,
          555.5367541437549,
          555.9508219228286,
          556.3651983261732,
          556.7798835838208,
          557.1948779259752
        ],
        "cell_deformation_log_strain_norm": 0.0063547541500469885
      },
      "parent_reduced_polarization": [
        0.00049904805295213,
        -1.1858862011894517e-12,
        -0.0007095094357392071
      ],
      "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": [
          -136.1146179853702,
          -136.10081561655335,
          -136.08505608925202,
          -136.06739776775618,
          -136.04789796715616,
          -136.0266129739889,
          -136.00359806416566,
          -135.9789075178408,
          -135.95259462976534
        ],
        "cartesian_polarizations_e_A2": [
          [
            0.0013334211818576748,
            4.208650551904071e-12,
            -0.00048826818408783453
          ],
          [
            0.0011672411309668707,
            3.6854766693242666e-12,
            -0.0004281988669518816
          ],
          [
            0.001001193870793636,
            3.160134781160733e-12,
            -0.0003681000299374867
          ],
          [
            0.0008352816450527612,
            2.6328031531333457e-12,
            -0.0003079752310518325
          ],
          [
            0.0006695079588507994,
            2.1033207874487677e-12,
            -0.0002478290300922622
          ],
          [
            0.0005038775510526901,
            1.5716502311336715e-12,
            -0.00018766698911083695
          ],
          [
            0.00033839635440688066,
            1.0378720034092199e-12,
            -0.00012749566230752624
          ],
          [
            0.00017307144664603218,
            5.020797890084044e-13,
            -6.732257581483446e-05
          ],
          [
            7.910996551327186e-06,
            -3.5727213700517464e-14,
            -7.156198358879447e-06
          ]
        ],
        "raw_reduced_polarization": [
          [
            0.10885109055045719,
            1.3824698249103875e-10,
            -0.04840389135377225
          ],
          [
            0.09528764634232711,
            1.210398791845314e-10,
            -0.042419008908741625
          ],
          [
            0.08172934999078785,
            1.0376764345749899e-10,
            -0.03643979161081588
          ],
          [
            0.06817630250577647,
            8.643598368007922e-11,
            -0.030466580705636293
          ],
          [
            0.05462868892340489,
            6.903944855684656e-11,
            -0.024499817024509835
          ],
          [
            0.04108677567682448,
            5.157664215467489e-11,
            -0.018540041011050088
          ],
          [
            0.027550907169335677,
            3.405005274693965e-11,
            -0.012587891707358502
          ],
          [
            0.01402150183815107,
            1.646260649290383e-11,
            -0.0066441047448697246
          ],
          [
            0.00049904805295213,
            -1.1858862011894517e-12,
            -0.0007095094357392071
          ]
        ],
        "unwrapped_reduced_polarization": [
          [
            0.10885109055045719,
            1.3824698249103875e-10,
            -0.04840389135377225
          ],
          [
            0.09528764634232711,
            1.210398791845314e-10,
            -0.042419008908741625
          ],
          [
            0.08172934999078785,
            1.0376764345749899e-10,
            -0.03643979161081588
          ],
          [
            0.06817630250577647,
            8.643598368007922e-11,
            -0.030466580705636293
          ],
          [
            0.05462868892340489,
            6.903944855684656e-11,
            -0.024499817024509835
          ],
          [
            0.04108677567682448,
            5.157664215467489e-11,
            -0.018540041011050088
          ],
          [
            0.027550907169335677,
            3.405005274693965e-11,
            -0.012587891707358502
          ],
          [
            0.01402150183815107,
            1.646260649290383e-11,
            -0.0066441047448697246
          ],
          [
            0.0004990480529521307,
            -1.1858862011894515e-12,
            -0.0007095094357392074
          ]
        ],
        "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": [
          [
            0.10885109055045716,
            1.3824696942776882e-10,
            -0.048403891353772266
          ],
          [
            0.09528764634232711,
            1.2103984481370844e-10,
            -0.04241900890874162
          ],
          [
            0.08172934999078785,
            1.0376766113040503e-10,
            -0.0364397916108159
          ],
          [
            0.06817630250577644,
            8.643596949298171e-11,
            -0.030466580705636293
          ],
          [
            0.05462868892340489,
            6.903944083092028e-11,
            -0.024499817024509818
          ],
          [
            0.041086775676824505,
            5.1576631854288735e-11,
            -0.018540041011050112
          ],
          [
            0.027550907169335725,
            3.40500960760437e-11,
            -0.012587891707358523
          ],
          [
            0.014021501838151096,
            1.6462609053746746e-11,
            -0.0066441047448697055
          ],
          [
            0.0004990480529520891,
            -1.185884723753361e-12,
            -0.0007095094357392195
          ]
        ]
      },
      "reflected": {
        "reached": true,
        "construction": "reflect_displacements_about_reconstructed_parent",
        "energies_eV": [
          -135.95259462976537,
          -135.93939658611157,
          -135.92515984023214,
          -135.90988311437687,
          -135.89356466532024,
          -135.87620226344293,
          -135.85779317161297,
          -135.83833412505578,
          -135.8178213135909
        ],
        "cartesian_polarizations_e_A2": [
          [
            7.910996551344072e-06,
            -3.5785233449045374e-14,
            -7.156198358900393e-06
          ],
          [
            -0.0001329469839053867,
            -4.614255615893766e-13,
            3.0899171472154025e-05
          ],
          [
            -0.0002739896274171361,
            -8.859845633211295e-13,
            6.890603575781341e-05
          ],
          [
            -0.0004152193990727277,
            -1.3098430995573624e-12,
            0.0001068653380532347
          ],
          [
            -0.0005566393714132267,
            -1.7324967250747153e-12,
            0.00014477847499009213
          ],
          [
            -0.0006982532747704074,
            -2.154275745192504e-12,
            0.0001826472724731105
          ],
          [
            -0.000840065517109554,
            -2.5750322076830953e-12,
            0.0002204739466682243
          ],
          [
            -0.0009820811782852536,
            -2.9946880510989467e-12,
            0.0002582610555590398
          ],
          [
            -0.0011243059845508785,
            -3.4134054485397555e-12,
            0.00029601144688684274
          ]
        ],
        "raw_reduced_polarization": [
          [
            0.0004990480529529979,
            -1.1878019643695467e-12,
            -0.000709509435741286
          ],
          [
            -0.011494482329148315,
            -1.514865215381725e-11,
            0.0030328778559502887
          ],
          [
            -0.02349843631338219,
            -2.9079259707950563e-11,
            0.0067790420594900196
          ],
          [
            -0.03551299132355698,
            -4.2992274756548583e-11,
            0.010529097731544979
          ],
          [
            -0.04753836626472356,
            -5.6871158986950906e-11,
            0.014283204531909472
          ],
          [
            -0.059574827087474344,
            -7.072689147582618e-11,
            0.018041564873186484
          ],
          [
            -0.07162268997795257,
            -8.455469381245319e-11,
            0.021804420084495006
          ],
          [
            -0.08368232244121618,
            -9.835209885855863e-11,
            0.025572045657809184
          ],
          [
            -0.09575414263298367,
            -1.1212453907953913e-10,
            0.02934474614878077
          ]
        ],
        "unwrapped_reduced_polarization": [
          [
            0.0004990480529529979,
            -1.1878019643695467e-12,
            -0.000709509435741286
          ],
          [
            -0.011494482329148315,
            -1.514865215381725e-11,
            0.0030328778559502887
          ],
          [
            -0.02349843631338219,
            -2.9079259707950563e-11,
            0.0067790420594900196
          ],
          [
            -0.03551299132355698,
            -4.2992274756548583e-11,
            0.010529097731544979
          ],
          [
            -0.04753836626472356,
            -5.6871158986950906e-11,
            0.014283204531909472
          ],
          [
            -0.059574827087474344,
            -7.072689147582618e-11,
            0.018041564873186484
          ],
          [
            -0.07162268997795257,
            -8.455469381245319e-11,
            0.021804420084495006
          ],
          [
            -0.08368232244121618,
            -9.835209885855863e-11,
            0.025572045657809184
          ],
          [
            -0.09575414263298367,
            -1.1212453907953913e-10,
            0.02934474614878077
          ]
        ],
        "gauge_integer_shift": [
          0,
          0,
          0
        ],
        "expected_opposite_endpoint_reduced_polarization": [
          -0.10785211443123463,
          -1.4059413839100983e-10,
          0.04698504876210779
        ],
        "actual_opposite_endpoint_branch_residual": 0.021390212666568504
      },
      "pnp_branch": {
        "construction": "incoming_path_concatenated_with_parent_reflection",
        "reduced_polarization": [
          [
            0.10885109055045719,
            1.3824698249103875e-10,
            -0.04840389135377225
          ],
          [
            0.09528764634232711,
            1.210398791845314e-10,
            -0.042419008908741625
          ],
          [
            0.08172934999078785,
            1.0376764345749899e-10,
            -0.03643979161081588
          ],
          [
            0.06817630250577647,
            8.643598368007922e-11,
            -0.030466580705636293
          ],
          [
            0.05462868892340489,
            6.903944855684656e-11,
            -0.024499817024509835
          ],
          [
            0.04108677567682448,
            5.157664215467489e-11,
            -0.018540041011050088
          ],
          [
            0.027550907169335677,
            3.405005274693965e-11,
            -0.012587891707358502
          ],
          [
            0.01402150183815107,
            1.646260649290383e-11,
            -0.0066441047448697246
          ],
          [
            0.00049904805295213,
            -1.1858862011894517e-12,
            -0.0007095094357392071
          ],
          [
            -0.011494482329148315,
            -1.514865215381725e-11,
            0.0030328778559502887
          ],
          [
            -0.02349843631338219,
            -2.9079259707950563e-11,
            0.0067790420594900196
          ],
          [
            -0.03551299132355698,
            -4.2992274756548583e-11,
            0.010529097731544979
          ],
          [
            -0.04753836626472356,
            -5.6871158986950906e-11,
            0.014283204531909472
          ],
          [
            -0.059574827087474344,
            -7.072689147582618e-11,
            0.018041564873186484
          ],
          [
            -0.07162268997795257,
            -8.455469381245319e-11,
            0.021804420084495006
          ],
          [
            -0.08368232244121618,
            -9.835209885855863e-11,
            0.025572045657809184
          ],
          [
            -0.09575414263298367,
            -1.1212453907953913e-10,
            0.02934474614878077
          ]
        ],
        "unwrapped_reduced_polarization": [
          [
            0.10885109055045719,
            1.3824698249103875e-10,
            -0.04840389135377225
          ],
          [
            0.09528764634232711,
            1.210398791845314e-10,
            -0.042419008908741625
          ],
          [
            0.08172934999078785,
            1.0376764345749899e-10,
            -0.03643979161081588
          ],
          [
            0.06817630250577647,
            8.643598368007922e-11,
            -0.030466580705636293
          ],
          [
            0.05462868892340489,
            6.903944855684656e-11,
            -0.024499817024509835
          ],
          [
            0.04108677567682448,
            5.157664215467489e-11,
            -0.018540041011050088
          ],
          [
            0.027550907169335677,
            3.405005274693965e-11,
            -0.012587891707358502
          ],
          [
            0.01402150183815107,
            1.646260649290383e-11,
            -0.0066441047448697246
          ],
          [
            0.0004990480529521307,
            -1.1858862011894515e-12,
            -0.0007095094357392074
          ],
          [
            -0.011494482329148315,
            -1.514865215381725e-11,
            0.0030328778559502887
          ],
          [
            -0.02349843631338219,
            -2.9079259707950563e-11,
            0.0067790420594900196
          ],
          [
            -0.03551299132355698,
            -4.2992274756548583e-11,
            0.010529097731544979
          ],
          [
            -0.04753836626472356,
            -5.6871158986950906e-11,
            0.014283204531909472
          ],
          [
            -0.059574827087474344,
            -7.072689147582618e-11,
            0.018041564873186484
          ],
          [
            -0.07162268997795257,
            -8.455469381245319e-11,
            0.021804420084495006
          ],
          [
            -0.08368232244121618,
            -9.835209885855863e-11,
            0.025572045657809184
          ],
          [
            -0.09575414263298367,
            -1.1212453907953913e-10,
            0.02934474614878077
          ]
        ],
        "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": [
          [
            0.10885109055045716,
            1.3824696942776882e-10,
            -0.048403891353772266
          ],
          [
            0.09528764634232711,
            1.2103984481370844e-10,
            -0.04241900890874162
          ],
          [
            0.08172934999078785,
            1.0376766113040503e-10,
            -0.0364397916108159
          ],
          [
            0.06817630250577644,
            8.643596949298171e-11,
            -0.030466580705636293
          ],
          [
            0.05462868892340489,
            6.903944083092028e-11,
            -0.024499817024509818
          ],
          [
            0.041086775676824505,
            5.1576631854288735e-11,
            -0.018540041011050112
          ],
          [
            0.027550907169335725,
            3.40500960760437e-11,
            -0.012587891707358523
          ],
          [
            0.014021501838151096,
            1.6462609053746746e-11,
            -0.0066441047448697055
          ],
          [
            0.0004990480529520891,
            -1.185884723753361e-12,
            -0.0007095094357392195
          ],
          [
            -0.011494482329148292,
            -1.5148660104102873e-11,
            0.0030328778559503
          ],
          [
            -0.023498436313382165,
            -2.9079239016738256e-11,
            0.006779042059489981
          ],
          [
            -0.03551299132355701,
            -4.299227640558456e-11,
            0.010529097731544979
          ],
          [
            -0.047538366264723575,
            -5.6871174436423644e-11,
            0.014283204531909455
          ],
          [
            -0.05957482708747436,
            -7.072686880604806e-11,
            0.018041564873186533
          ],
          [
            -0.07162268997795257,
            -8.455469657775438e-11,
            0.021804420084495013
          ],
          [
            -0.0836823224412162,
            -9.835210423858598e-11,
            0.02557204565780924
          ],
          [
            -0.09575414263298365,
            -1.1212453188136351e-10,
            0.029344746148780798
          ]
        ]
      },
      "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": "Cc",
        "spacegroup_number": 9,
        "pointgroup": "m",
        "has_inversion": false,
        "is_polar_point_group": true,
        "nonpolar_parent_hypothesis": false,
        "symmetry_tolerance_A": null,
        "target_reduced_polarization": [
          0.0,
          0.0,
          0.0
        ],
        "formal_class": [
          0.0,
          0.0,
          0.0
        ],
        "target_residual": 0.0008674402564783212,
        "parent_symmetrization_rmsd_A": 0.01718171949171929,
        "parent_cell_rmsd_A": 0.022533379012042918,
        "energy_eV": -135.95259462976534,
        "reduced_polarization": [
          0.0004990480529539278,
          -1.1871047811817705e-12,
          -0.0007095094357385739
        ],
        "cartesian_polarization_e_A2": [
          7.910996551343873e-06,
          -3.57641189430078e-14,
          -7.156198358873145e-06
        ],
        "ranking_score": 0.5245499447576867
      }
    }
  ],
  "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": 83,
      "full_response": 27,
      "energy_polarization": 56
    },
    "model_evaluations_for_recovery_and_path_properties": {
      "total": 108,
      "full_response": 52,
      "energy_polarization": 56
    },
    "elapsed_seconds": 797.4404899370275
  }
}
