{
  "schema": "ferrofinder.endpoint_parent_recovery.v4_variable_cell",
  "status": "complete",
  "input_atom_count": 32,
  "input_formula": "Cd6O20Se6",
  "input_spacegroup": "P2_1",
  "input_pointgroup": "2",
  "input_is_polar_point_group": true,
  "input_energy_eV": -152.53207703576916,
  "input_cartesian_polarization_e_A2": [
    -0.0004905634905864617,
    7.430158027670126e-09,
    -3.2886140437540076e-08
  ],
  "input_reduced_polarization": [
    -0.04384857498709558,
    -2.0007828352177597e-07,
    -1.5385567183002936e-06
  ],
  "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": "P2_1/m",
      "spacegroup_number": 11,
      "pointgroup": "2/m",
      "has_inversion": true,
      "is_polar_point_group": false,
      "nonpolar_parent_hypothesis": true,
      "symmetry_tolerance_A": null,
      "target_reduced_polarization": [
        0.0,
        0.0,
        0.0
      ],
      "formal_class": [
        0.0,
        0.0,
        0.0
      ],
      "target_residual": 6.66948747710966e-16,
      "parent_symmetrization_rmsd_A": 0.5491824496640724,
      "parent_cell_rmsd_A": 0.0,
      "energy_eV": -137.63080412987657,
      "reduced_polarization": [
        -9.799617266510476e-17,
        -2.671906513280253e-16,
        6.031803528457492e-16
      ],
      "cartesian_polarization_e_A2": [
        -1.0963490727088656e-18,
        -8.99860537600004e-18,
        1.2892780329063347e-17
      ],
      "ranking_score": 0.5491824496640737
    },
    {
      "candidate_id": "inversion_parent_endpoint_01",
      "source": "same_species_inversion_center_projection_from_endpoint",
      "spacegroup": "P2_1/m",
      "spacegroup_number": 11,
      "pointgroup": "2/m",
      "has_inversion": true,
      "is_polar_point_group": false,
      "nonpolar_parent_hypothesis": true,
      "symmetry_tolerance_A": null,
      "target_reduced_polarization": [
        0.0,
        0.0,
        0.0
      ],
      "formal_class": [
        0.0,
        0.0,
        0.0
      ],
      "target_residual": 2.0116335566669416e-15,
      "parent_symmetrization_rmsd_A": 0.5505059452816402,
      "parent_cell_rmsd_A": 0.0,
      "energy_eV": -137.14330095715098,
      "reduced_polarization": [
        -1.3051308450398042e-15,
        -5.248219919587832e-16,
        1.4380072741090678e-15
      ],
      "cartesian_polarization_e_A2": [
        -1.460137628653171e-17,
        -1.9477993915139324e-17,
        3.073692935987355e-17
      ],
      "ranking_score": 0.5505059452816442
    },
    {
      "candidate_id": "inversion_parent_endpoint_02",
      "source": "same_species_inversion_center_projection_from_endpoint",
      "spacegroup": "P2_1/m",
      "spacegroup_number": 11,
      "pointgroup": "2/m",
      "has_inversion": true,
      "is_polar_point_group": false,
      "nonpolar_parent_hypothesis": true,
      "symmetry_tolerance_A": null,
      "target_reduced_polarization": [
        0.0,
        0.0,
        0.0
      ],
      "formal_class": [
        0.0,
        0.0,
        0.0
      ],
      "target_residual": 2.596069718051629e-15,
      "parent_symmetrization_rmsd_A": 0.5788465539370705,
      "parent_cell_rmsd_A": 0.0,
      "energy_eV": -135.29462889858553,
      "reduced_polarization": [
        1.9751955841070468e-15,
        -1.5075097554944649e-15,
        7.520603184570413e-16
      ],
      "cartesian_polarization_e_A2": [
        2.2097841049924147e-17,
        -3.189735078098748e-17,
        1.6075040299848172e-17
      ],
      "ranking_score": 0.5788465539370757
    },
    {
      "candidate_id": "bec_projection_00",
      "source": "MACEField_BEC_backprojection",
      "spacegroup": "P2_1",
      "spacegroup_number": 4,
      "pointgroup": "2",
      "has_inversion": false,
      "is_polar_point_group": true,
      "nonpolar_parent_hypothesis": false,
      "symmetry_tolerance_A": null,
      "target_reduced_polarization": [
        0.0,
        0.0,
        0.0
      ],
      "formal_class": [
        0.0,
        0.0,
        0.0
      ],
      "target_residual": 1.4345446171348154e-05,
      "parent_symmetrization_rmsd_A": 0.004274287100881192,
      "parent_cell_rmsd_A": 0.0005842111294521887,
      "energy_eV": -152.52370598153058,
      "reduced_polarization": [
        1.4345446049706201e-05,
        -1.648898522170148e-09,
        -8.781513534134053e-10
      ],
      "cartesian_polarization_e_A2": [
        1.6047508130663224e-07,
        -2.2782464208803556e-11,
        -1.8772407275896626e-11
      ],
      "ranking_score": 0.5044490307755869
    },
    {
      "candidate_id": "inversion_parent_bec_00_00",
      "source": "same_species_inversion_center_projection_after_BEC",
      "spacegroup": "P2_1/m",
      "spacegroup_number": 11,
      "pointgroup": "2/m",
      "has_inversion": true,
      "is_polar_point_group": false,
      "nonpolar_parent_hypothesis": true,
      "symmetry_tolerance_A": null,
      "target_reduced_polarization": [
        0.0,
        0.0,
        0.0
      ],
      "formal_class": [
        0.0,
        0.0,
        0.0
      ],
      "target_residual": 4.027638743540368e-15,
      "parent_symmetrization_rmsd_A": 0.5491828005041663,
      "parent_cell_rmsd_A": 0.0005842111294521887,
      "energy_eV": -137.6300669701973,
      "reduced_polarization": [
        1.3135647980050926e-15,
        -3.1670098414643942e-15,
        -2.1134024779906324e-15
      ],
      "cartesian_polarization_e_A2": [
        1.469416924108716e-17,
        -4.072221320688883e-17,
        -4.5178875001908483e-17
      ],
      "ranking_score": 0.5493288532865375
    },
    {
      "candidate_id": "inversion_parent_bec_00_01",
      "source": "same_species_inversion_center_projection_after_BEC",
      "spacegroup": "P2_1/m",
      "spacegroup_number": 11,
      "pointgroup": "2/m",
      "has_inversion": true,
      "is_polar_point_group": false,
      "nonpolar_parent_hypothesis": true,
      "symmetry_tolerance_A": null,
      "target_reduced_polarization": [
        0.0,
        0.0,
        0.0
      ],
      "formal_class": [
        0.0,
        0.0,
        0.0
      ],
      "target_residual": 3.680148018336019e-15,
      "parent_symmetrization_rmsd_A": 0.5505063023751716,
      "parent_cell_rmsd_A": 0.0005842111294521887,
      "energy_eV": -137.1266546577042,
      "reduced_polarization": [
        1.557312522506489e-15,
        -3.1615285104492963e-15,
        -1.059719123977318e-15
      ],
      "cartesian_polarization_e_A2": [
        1.742084890161835e-17,
        -4.812625197177771e-17,
        -2.2655290730353494e-17
      ],
      "ranking_score": 0.550652355157542
    },
    {
      "candidate_id": "bec_projection_01",
      "source": "MACEField_BEC_backprojection",
      "spacegroup": "P2_1",
      "spacegroup_number": 4,
      "pointgroup": "2",
      "has_inversion": false,
      "is_polar_point_group": true,
      "nonpolar_parent_hypothesis": false,
      "symmetry_tolerance_A": null,
      "target_reduced_polarization": [
        -0.5,
        0.0,
        0.0
      ],
      "formal_class": [
        0.5,
        0.0,
        0.0
      ],
      "target_residual": 1.2490063503778677e-06,
      "parent_symmetrization_rmsd_A": 0.04469700103306567,
      "parent_cell_rmsd_A": 0.006114288937589747,
      "energy_eV": -151.99834851087567,
      "reduced_polarization": [
        -0.5000012490063499,
        -2.5463532138995493e-11,
        2.326926018458212e-11
      ],
      "cartesian_polarization_e_A2": [
        -0.005600083945672675,
        -5.5506724289532395e-11,
        -7.745404858073033e-11
      ],
      "ranking_score": 0.5462280712801638
    },
    {
      "candidate_id": "bec_projection_02",
      "source": "MACEField_BEC_backprojection",
      "spacegroup": "P1",
      "spacegroup_number": 1,
      "pointgroup": "1",
      "has_inversion": false,
      "is_polar_point_group": true,
      "nonpolar_parent_hypothesis": false,
      "symmetry_tolerance_A": null,
      "target_reduced_polarization": [
        0.0,
        0.0,
        -0.5
      ],
      "formal_class": [
        0.0,
        0.0,
        0.5
      ],
      "target_residual": 0.00011305831381970193,
      "parent_symmetrization_rmsd_A": 0.10061481946878281,
      "parent_cell_rmsd_A": 0.014100383688801654,
      "energy_eV": -149.4779125304924,
      "reduced_polarization": [
        -6.337784212111709e-05,
        1.254635076317664e-05,
        -0.49990722058129977
      ],
      "cartesian_polarization_e_A2": [
        -7.112458719350128e-06,
        0.003558725669344175,
        -0.010686157412321538
      ],
      "ranking_score": 0.6043660320186226
    },
    {
      "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": 0.0005492031286286566,
      "parent_symmetrization_rmsd_A": 0.09075438152685905,
      "parent_cell_rmsd_A": 0.048100696003840655,
      "energy_eV": -149.74446544954827,
      "reduced_polarization": [
        -0.00026121772477318803,
        -0.4995269742945118,
        -9.816342856293216e-05
      ],
      "cartesian_polarization_e_A2": [
        -2.1343097792741172e-05,
        -0.008795215806298004,
        -2.4143169968300632e-06
      ],
      "ranking_score": 0.6038779617850765
    },
    {
      "candidate_id": "bec_projection_04",
      "source": "MACEField_BEC_backprojection",
      "spacegroup": "P1",
      "spacegroup_number": 1,
      "pointgroup": "1",
      "has_inversion": false,
      "is_polar_point_group": true,
      "nonpolar_parent_hypothesis": false,
      "symmetry_tolerance_A": null,
      "target_reduced_polarization": [
        -0.5,
        0.0,
        -0.5
      ],
      "formal_class": [
        0.5,
        0.0,
        0.5
      ],
      "target_residual": 3.085299149702375e-06,
      "parent_symmetrization_rmsd_A": 0.11097334534315623,
      "parent_cell_rmsd_A": 0.015890734830616652,
      "energy_eV": -148.9311741056393,
      "reduced_polarization": [
        -0.5000028452014322,
        -6.623738405702771e-07,
        -0.5000009925525419
      ],
      "cartesian_polarization_e_A2": [
        -0.005608166074503148,
        0.0035779901035410577,
        -0.01067897998226979
      ],
      "ranking_score": 0.6149521996491099
    },
    {
      "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": 2.550774497164488e-06,
      "parent_symmetrization_rmsd_A": 0.10296179104033196,
      "parent_cell_rmsd_A": 0.04929082484367017,
      "energy_eV": -148.90765474782734,
      "reduced_polarization": [
        -0.500002339202483,
        -0.5000010161629957,
        4.4665923897468984e-08
      ],
      "cartesian_polarization_e_A2": [
        -0.005619625786253935,
        -0.008810230724452271,
        4.3596983946594246e-05
      ],
      "ranking_score": 0.6152895988002438
    },
    {
      "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": 1.7980435528827708e-05,
      "parent_symmetrization_rmsd_A": 0.11409070353636348,
      "parent_cell_rmsd_A": 0.04414622233235505,
      "energy_eV": -147.7500927621333,
      "reduced_polarization": [
        1.7916148038261214e-05,
        -0.4999992673347085,
        -0.4999986692472626
      ],
      "cartesian_polarization_e_A2": [
        8.117436503335281e-05,
        -0.005245715010462235,
        -0.010689593371357177
      ],
      "ranking_score": 0.6251632199905099
    },
    {
      "candidate_id": "bec_projection_07",
      "source": "MACEField_BEC_backprojection",
      "spacegroup": "P1",
      "spacegroup_number": 1,
      "pointgroup": "1",
      "has_inversion": false,
      "is_polar_point_group": true,
      "nonpolar_parent_hypothesis": false,
      "symmetry_tolerance_A": null,
      "target_reduced_polarization": [
        -0.5,
        -0.5,
        -0.5
      ],
      "formal_class": [
        0.5,
        0.5,
        0.5
      ],
      "target_residual": 3.017800308162939e-05,
      "parent_symmetrization_rmsd_A": 0.12190923506854393,
      "parent_cell_rmsd_A": 0.04425027960387887,
      "energy_eV": -147.4383366300476,
      "reduced_polarization": [
        -0.49996991906874594,
        -0.5000006996238974,
        -0.49999768483882084
      ],
      "cartesian_polarization_e_A2": [
        -0.005519674526622256,
        -0.005232594377736119,
        -0.010635482384855703
      ],
      "ranking_score": 0.6330321609756768
    }
  ],
  "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": [
              -0.04384857498709558,
              -2.0007828352177597e-07,
              -1.5385567183002936e-06
            ],
            "branch_aligned_reduced_polarization": [
              -0.04384857498709558,
              -2.0007828352177597e-07,
              -1.5385567183002936e-06
            ],
            "target_residual": 0.04384857501454446,
            "energy_eV": -152.53207703576916,
            "max_atomic_step_A": 0.005510620593269122,
            "max_log_strain_component": 0.00012296568221424527,
            "step_scale": 1.0,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 0.8575016604268295,
            "cell_principal_stretches": [
              1.0001026477602075,
              1.0000037173665313,
              0.9998770418774612
            ],
            "cell_volume_ratio": 0.9999833943072761,
            "cell_rmsd_from_input_A": 0.0005842111294521887
          },
          {
            "iteration": 1,
            "reduced_polarization": [
              1.4345446049706201e-05,
              -1.648898522170148e-09,
              -8.781513534134053e-10
            ],
            "branch_aligned_reduced_polarization": [
              1.4345446049706201e-05,
              -1.648898522170148e-09,
              -8.781513534134053e-10
            ],
            "target_residual": 1.4345446171348154e-05,
            "energy_eV": -152.52370598153058
          }
        ],
        "iterations": 1
      },
      "parent": {
        "candidate_id": "bec_projection_00",
        "source": "MACEField_BEC_backprojection",
        "spacegroup": "P2_1",
        "spacegroup_number": 4,
        "pointgroup": "2",
        "has_inversion": false,
        "is_polar_point_group": true,
        "nonpolar_parent_hypothesis": false,
        "symmetry_tolerance_A": null,
        "target_reduced_polarization": [
          0.0,
          0.0,
          0.0
        ],
        "formal_class": [
          0.0,
          0.0,
          0.0
        ],
        "target_residual": 1.4345446171348154e-05,
        "parent_symmetrization_rmsd_A": 0.004274287100881192,
        "parent_cell_rmsd_A": 0.0005842111294521887,
        "energy_eV": -152.52370598153058,
        "reduced_polarization": [
          1.4345446049706201e-05,
          -1.648898522170148e-09,
          -8.781513534134053e-10
        ],
        "cartesian_polarization_e_A2": [
          1.6047508130663224e-07,
          -2.2782464208803556e-11,
          -1.8772407275896626e-11
        ],
        "ranking_score": 0.5044490307755869
      },
      "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": [
          -152.5320770357692,
          -152.53159497880932,
          -152.53095174468638,
          -152.53014730750198,
          -152.5291816386782,
          -152.52805470695517,
          -152.52676647838948,
          -152.5253169163529,
          -152.52370598153055
        ],
        "cartesian_polarizations_e_A2": [
          [
            -0.0004905634905864242,
            7.430158038633617e-09,
            -3.288614042976241e-08
          ],
          [
            -0.00042922894123214466,
            6.50015179879701e-09,
            -2.8776257290059264e-08
          ],
          [
            -0.00036789239372611734,
            5.569677029005544e-09,
            -2.466674810734201e-08
          ],
          [
            -0.00030655399720859737,
            4.638737679214976e-09,
            -2.0557634762899273e-08
          ],
          [
            -0.00024521390117276536,
            3.7073379483583727e-09,
            -1.644893914041189e-08
          ],
          [
            -0.00018387225548015704,
            2.775481892221842e-09,
            -1.2340683153415293e-08
          ],
          [
            -0.00012252921037560403,
            1.843173690870133e-09,
            -8.232888674659189e-09
          ],
          [
            -6.118491650280562e-05,
            9.104174819150129e-10,
            -4.125577803157472e-09
          ],
          [
            1.604750813333544e-07,
            -2.278242337268206e-11,
            -1.8772350004944853e-11
          ]
        ],
        "raw_reduced_polarization": [
          [
            -0.04384857498709222,
            -2.0007828275199346e-07,
            -1.5385567179364205e-06
          ],
          [
            -0.03836675171502692,
            -1.7511985700266977e-07,
            -1.3462606298145437e-06
          ],
          [
            -0.03288460406502446,
            -1.5020528330863528e-07,
            -1.1539871425659764e-06
          ],
          [
            -0.027402145358352815,
            -1.2533475009955157e-07,
            -9.617372789188225e-07
          ],
          [
            -0.021919388948536185,
            -1.0050843163919259e-07,
            -7.695120616681294e-07
          ],
          [
            -0.016436348222736635,
            -7.572651081470768e-08,
            -5.773125149604037e-07
          ],
          [
            -0.010953036603091588,
            -5.0989162612717766e-08,
            -3.851396609890975e-07
          ],
          [
            -0.005469467548108296,
            -2.6296568638863968e-08,
            -1.9299453248740649e-07
          ],
          [
            1.4345446052094992e-05,
            -1.6488951200117763e-09,
            -8.781486743366744e-10
          ]
        ],
        "unwrapped_reduced_polarization": [
          [
            -0.04384857498709222,
            -2.0007828275199346e-07,
            -1.5385567179364205e-06
          ],
          [
            -0.03836675171502692,
            -1.7511985700266977e-07,
            -1.3462606298145437e-06
          ],
          [
            -0.03288460406502446,
            -1.5020528330863528e-07,
            -1.1539871425659764e-06
          ],
          [
            -0.027402145358352815,
            -1.2533475009955157e-07,
            -9.617372789188225e-07
          ],
          [
            -0.021919388948536185,
            -1.0050843163919259e-07,
            -7.695120616681294e-07
          ],
          [
            -0.016436348222736635,
            -7.572651081470768e-08,
            -5.773125149604037e-07
          ],
          [
            -0.010953036603091588,
            -5.0989162612717766e-08,
            -3.851396609890975e-07
          ],
          [
            -0.005469467548108296,
            -2.6296568638863968e-08,
            -1.9299453248740649e-07
          ],
          [
            1.4345446052095243e-05,
            -1.6488951200117771e-09,
            -8.781486743366643e-10
          ]
        ],
        "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": [
          [
            -0.043848574987092215,
            -2.0007828277490702e-07,
            -1.5385567179171389e-06
          ],
          [
            -0.0383667517150269,
            -1.7511985700435773e-07,
            -1.3462606298086932e-06
          ],
          [
            -0.03288460406502447,
            -1.5020528332243543e-07,
            -1.153987142565871e-06
          ],
          [
            -0.027402145358352836,
            -1.2533475007847628e-07,
            -9.617372789261225e-07
          ],
          [
            -0.021919388948536178,
            -1.0050843163300627e-07,
            -7.695120616824092e-07
          ],
          [
            -0.016436348222736652,
            -7.572651083975757e-08,
            -5.773125149599601e-07
          ],
          [
            -0.010953036603091604,
            -5.09891626143677e-08,
            -3.851396609966251e-07
          ],
          [
            -0.005469467548108287,
            -2.629656864483465e-08,
            -1.9299453246635068e-07
          ],
          [
            1.4345446052055344e-05,
            -1.6488951315452027e-09,
            -8.781486648956616e-10
          ]
        ]
      },
      "reflected": {
        "reached": true,
        "construction": "reflect_displacements_about_reconstructed_parent",
        "energies_eV": [
          -152.52370598153055,
          -152.52198598232522,
          -152.52010373549427,
          -152.51805919374925,
          -152.51585230708116,
          -152.5134830227591,
          -152.51095128532825,
          -152.50825703660854,
          -152.50540021569316
        ],
        "cartesian_polarizations_e_A2": [
          [
            1.6047508132973782e-07,
            -2.2782422290553317e-11,
            -1.8772328490516827e-11
          ],
          [
            6.128925760361039e-05,
            -9.566314052680466e-10,
            4.0793892196687135e-09
          ],
          [
            0.00012242350036741808,
            -1.8912334870863633e-09,
            8.1768411948818e-09
          ],
          [
            0.0001835630481024165,
            -2.826584188469266e-09,
            1.2273561544091228e-08
          ],
          [
            0.0002447077450988788,
            -3.762678965392883e-09,
            1.6369528210834506e-08
          ],
          [
            0.0003058574351931517,
            -4.699513262594251e-09,
            2.046471894825859e-08
          ],
          [
            0.0003670119617532766,
            -5.637082381667277e-09,
            2.45591121209159e-08
          ],
          [
            0.00042817116766479945,
            -6.575381668298243e-09,
            2.8652685413508754e-08
          ],
          [
            0.0004893348953167154,
            -7.514406323664842e-09,
            3.274541687202587e-08
          ]
        ],
        "raw_reduced_polarization": [
          [
            1.4345446051771691e-05,
            -1.6488946516870284e-09,
            -8.781476678814317e-10
          ],
          [
            0.005478794851264156,
            2.2798500604248864e-08,
            1.9083386237116412e-07
          ],
          [
            0.010943587055629228,
            4.7199834545041944e-08,
            3.825177646675092e-07
          ],
          [
            0.016408708162955424,
            7.155494313488423e-08,
            5.741725262395157e-07
          ],
          [
            0.021874144238513155,
            9.586366587896794e-08,
            7.657971139008273e-07
          ],
          [
            0.027339881307738085,
            1.2012583924796243e-07,
            9.57390485512733e-07
          ],
          [
            0.03280590535494837,
            1.443413193343995e-07,
            1.1489516274943724e-06
          ],
          [
            0.0382722023220793,
            1.6850994679634076e-07,
            1.340479494414456e-06
          ],
          [
            0.04373875810742959,
            1.9263157726066542e-07,
            1.5319730576984586e-06
          ]
        ],
        "unwrapped_reduced_polarization": [
          [
            1.4345446051771691e-05,
            -1.6488946516870284e-09,
            -8.781476678814317e-10
          ],
          [
            0.005478794851264156,
            2.2798500604248864e-08,
            1.9083386237116412e-07
          ],
          [
            0.010943587055629228,
            4.7199834545041944e-08,
            3.825177646675092e-07
          ],
          [
            0.016408708162955424,
            7.155494313488423e-08,
            5.741725262395157e-07
          ],
          [
            0.021874144238513155,
            9.586366587896794e-08,
            7.657971139008273e-07
          ],
          [
            0.027339881307738085,
            1.2012583924796243e-07,
            9.57390485512733e-07
          ],
          [
            0.03280590535494837,
            1.443413193343995e-07,
            1.1489516274943724e-06
          ],
          [
            0.0382722023220793,
            1.6850994679634076e-07,
            1.340479494414456e-06
          ],
          [
            0.04373875810742959,
            1.9263157726066542e-07,
            1.5319730576984586e-06
          ]
        ],
        "gauge_integer_shift": [
          0,
          0,
          0
        ],
        "expected_opposite_endpoint_reduced_polarization": [
          0.04387726282779963,
          1.9678027945179551e-07,
          1.5368002135346195e-06
        ],
        "actual_opposite_endpoint_branch_residual": 0.00013850472051629093
      },
      "pnp_branch": {
        "construction": "incoming_path_concatenated_with_parent_reflection",
        "reduced_polarization": [
          [
            -0.04384857498709222,
            -2.0007828275199346e-07,
            -1.5385567179364205e-06
          ],
          [
            -0.03836675171502692,
            -1.7511985700266977e-07,
            -1.3462606298145437e-06
          ],
          [
            -0.03288460406502446,
            -1.5020528330863528e-07,
            -1.1539871425659764e-06
          ],
          [
            -0.027402145358352815,
            -1.2533475009955157e-07,
            -9.617372789188225e-07
          ],
          [
            -0.021919388948536185,
            -1.0050843163919259e-07,
            -7.695120616681294e-07
          ],
          [
            -0.016436348222736635,
            -7.572651081470768e-08,
            -5.773125149604037e-07
          ],
          [
            -0.010953036603091588,
            -5.0989162612717766e-08,
            -3.851396609890975e-07
          ],
          [
            -0.005469467548108296,
            -2.6296568638863968e-08,
            -1.9299453248740649e-07
          ],
          [
            1.4345446052094992e-05,
            -1.6488951200117763e-09,
            -8.781486743366744e-10
          ],
          [
            0.005478794851264156,
            2.2798500604248864e-08,
            1.9083386237116412e-07
          ],
          [
            0.010943587055629228,
            4.7199834545041944e-08,
            3.825177646675092e-07
          ],
          [
            0.016408708162955424,
            7.155494313488423e-08,
            5.741725262395157e-07
          ],
          [
            0.021874144238513155,
            9.586366587896794e-08,
            7.657971139008273e-07
          ],
          [
            0.027339881307738085,
            1.2012583924796243e-07,
            9.57390485512733e-07
          ],
          [
            0.03280590535494837,
            1.443413193343995e-07,
            1.1489516274943724e-06
          ],
          [
            0.0382722023220793,
            1.6850994679634076e-07,
            1.340479494414456e-06
          ],
          [
            0.04373875810742959,
            1.9263157726066542e-07,
            1.5319730576984586e-06
          ]
        ],
        "unwrapped_reduced_polarization": [
          [
            -0.04384857498709222,
            -2.0007828275199346e-07,
            -1.5385567179364205e-06
          ],
          [
            -0.03836675171502692,
            -1.7511985700266977e-07,
            -1.3462606298145437e-06
          ],
          [
            -0.03288460406502446,
            -1.5020528330863528e-07,
            -1.1539871425659764e-06
          ],
          [
            -0.027402145358352815,
            -1.2533475009955157e-07,
            -9.617372789188225e-07
          ],
          [
            -0.021919388948536185,
            -1.0050843163919259e-07,
            -7.695120616681294e-07
          ],
          [
            -0.016436348222736635,
            -7.572651081470768e-08,
            -5.773125149604037e-07
          ],
          [
            -0.010953036603091588,
            -5.0989162612717766e-08,
            -3.851396609890975e-07
          ],
          [
            -0.005469467548108296,
            -2.6296568638863968e-08,
            -1.9299453248740649e-07
          ],
          [
            1.4345446052095243e-05,
            -1.6488951200117771e-09,
            -8.781486743366643e-10
          ],
          [
            0.005478794851264156,
            2.2798500604248864e-08,
            1.9083386237116412e-07
          ],
          [
            0.010943587055629228,
            4.7199834545041944e-08,
            3.825177646675092e-07
          ],
          [
            0.016408708162955424,
            7.155494313488423e-08,
            5.741725262395157e-07
          ],
          [
            0.021874144238513155,
            9.586366587896794e-08,
            7.657971139008273e-07
          ],
          [
            0.027339881307738085,
            1.2012583924796243e-07,
            9.57390485512733e-07
          ],
          [
            0.03280590535494837,
            1.443413193343995e-07,
            1.1489516274943724e-06
          ],
          [
            0.0382722023220793,
            1.6850994679634076e-07,
            1.340479494414456e-06
          ],
          [
            0.04373875810742959,
            1.9263157726066542e-07,
            1.5319730576984586e-06
          ]
        ],
        "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": [
          [
            -0.043848574987092215,
            -2.0007828277490702e-07,
            -1.5385567179171389e-06
          ],
          [
            -0.0383667517150269,
            -1.7511985700435773e-07,
            -1.3462606298086932e-06
          ],
          [
            -0.03288460406502447,
            -1.5020528332243543e-07,
            -1.153987142565871e-06
          ],
          [
            -0.027402145358352836,
            -1.2533475007847628e-07,
            -9.617372789261225e-07
          ],
          [
            -0.021919388948536178,
            -1.0050843163300627e-07,
            -7.695120616824092e-07
          ],
          [
            -0.016436348222736652,
            -7.572651083975757e-08,
            -5.773125149599601e-07
          ],
          [
            -0.010953036603091604,
            -5.09891626143677e-08,
            -3.851396609966251e-07
          ],
          [
            -0.005469467548108287,
            -2.629656864483465e-08,
            -1.9299453246635068e-07
          ],
          [
            1.4345446052055344e-05,
            -1.6488951315452027e-09,
            -8.781486648956616e-10
          ],
          [
            0.005478794851264124,
            2.279850064290656e-08,
            1.9083386237905842e-07
          ],
          [
            0.010943587055629256,
            4.7199834596334256e-08,
            3.8251776468545273e-07
          ],
          [
            0.016408708162955477,
            7.155494308186405e-08,
            5.741725261909636e-07
          ],
          [
            0.021874144238513193,
            9.58636658943135e-08,
            7.657971139440889e-07
          ],
          [
            0.027339881307738123,
            1.2012583927578646e-07,
            9.573904855564308e-07
          ],
          [
            0.03280590535494832,
            1.4434131934137895e-07,
            1.1489516275053901e-06
          ],
          [
            0.038272202322079285,
            1.6850994677408693e-07,
            1.340479494404967e-06
          ],
          [
            0.043738758107429554,
            1.926315772449172e-07,
            1.5319730577445512e-06
          ]
        ]
      },
      "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": [
              -0.04384857498709558,
              -2.0007828352177597e-07,
              -1.5385567183002936e-06
            ],
            "branch_aligned_reduced_polarization": [
              -0.0438485749870956,
              -2.0007828352177597e-07,
              -1.5385567183002936e-06
            ],
            "target_residual": 0.45615142501554296,
            "energy_eV": -152.53207703576916,
            "max_atomic_step_A": 0.05732565194782224,
            "max_log_strain_component": 0.0012791971277416165,
            "step_scale": 1.0,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 0.8575016604268295,
            "cell_principal_stretches": [
              1.0012800156494963,
              0.9999613295058735,
              0.9989327924342928
            ],
            "cell_volume_ratio": 1.000172763370709,
            "cell_rmsd_from_input_A": 0.006074062133931708
          },
          {
            "iteration": 1,
            "reduced_polarization": [
              -0.4970635787448067,
              3.6486399438756745e-08,
              2.0109586531106006e-08
            ],
            "branch_aligned_reduced_polarization": [
              -0.4970635787448067,
              3.6486399438756745e-08,
              2.0109586531106006e-08
            ],
            "target_residual": 0.002936421255488817,
            "energy_eV": -152.0055768683398,
            "max_atomic_step_A": 0.0003790784064374398,
            "max_log_strain_component": 8.476127200948877e-06,
            "step_scale": 1.0,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 0.8575016604268295,
            "cell_principal_stretches": [
              1.0012885026622353,
              0.9999610732751186,
              0.9989257247773159
            ],
            "cell_volume_ratio": 1.0001739082228958,
            "cell_rmsd_from_input_A": 0.006114288937589747
          },
          {
            "iteration": 2,
            "reduced_polarization": [
              -0.5000012490063499,
              -2.5463532138995493e-11,
              2.326926018458212e-11
            ],
            "branch_aligned_reduced_polarization": [
              -0.5000012490063499,
              -2.5463532138995493e-11,
              2.326926018458212e-11
            ],
            "target_residual": 1.2490063503778677e-06,
            "energy_eV": -151.99834851087567
          }
        ],
        "iterations": 2
      },
      "parent": {
        "candidate_id": "bec_projection_01",
        "source": "MACEField_BEC_backprojection",
        "spacegroup": "P2_1",
        "spacegroup_number": 4,
        "pointgroup": "2",
        "has_inversion": false,
        "is_polar_point_group": true,
        "nonpolar_parent_hypothesis": false,
        "symmetry_tolerance_A": null,
        "target_reduced_polarization": [
          -0.5,
          0.0,
          0.0
        ],
        "formal_class": [
          0.5,
          0.0,
          0.0
        ],
        "target_residual": 1.2490063503778677e-06,
        "parent_symmetrization_rmsd_A": 0.04469700103306567,
        "parent_cell_rmsd_A": 0.006114288937589747,
        "energy_eV": -151.99834851087567,
        "reduced_polarization": [
          -0.5000012490063499,
          -2.5463532138995493e-11,
          2.326926018458212e-11
        ],
        "cartesian_polarization_e_A2": [
          -0.005600083945672675,
          -5.5506724289532395e-11,
          -7.745404858073033e-11
        ],
        "ranking_score": 0.5462280712801638
      },
      "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": [
              -0.04384857498709558,
              -2.0007828352177597e-07,
              -1.5385567183002936e-06
            ],
            "branch_aligned_reduced_polarization": [
              -0.04384857498709558,
              -2.0007828352177597e-07,
              -1.538556718305717e-06
            ],
            "target_residual": 0.5019174822359627,
            "energy_eV": -152.53207703576916,
            "max_atomic_step_A": 0.12,
            "max_log_strain_component": 0.0024918124459118287,
            "step_scale": 0.9542971197500247,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 0.8575016604268295,
            "cell_principal_stretches": [
              1.002475784614981,
              1.0000513270342486,
              0.997463314348184
            ],
            "cell_volume_ratio": 0.9999841422618849,
            "cell_rmsd_from_input_A": 0.013228717788679848
          },
          {
            "iteration": 1,
            "reduced_polarization": [
              -0.00808937115022673,
              0.0009254012793461832,
              -0.469549430081218
            ],
            "branch_aligned_reduced_polarization": [
              -0.00808937115022673,
              0.0009254012793461832,
              -0.469549430081218
            ],
            "target_residual": 0.031520334730338224,
            "energy_eV": -149.85573360536677,
            "max_atomic_step_A": 0.008348002560972598,
            "max_log_strain_component": 0.00016918308380043162,
            "step_scale": 1.0,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 0.8575016604268295,
            "cell_principal_stretches": [
              1.0026415543308045,
              1.0000624373961482,
              0.9972836477949804
            ],
            "cell_volume_ratio": 0.9999804590118049,
            "cell_rmsd_from_input_A": 0.014100383688801654
          },
          {
            "iteration": 2,
            "reduced_polarization": [
              -6.337784212111709e-05,
              1.254635076317664e-05,
              -0.49990722058129977
            ],
            "branch_aligned_reduced_polarization": [
              -6.337784212111709e-05,
              1.254635076317664e-05,
              -0.49990722058129977
            ],
            "target_residual": 0.00011305831381970193,
            "energy_eV": -149.4779125304924
          }
        ],
        "iterations": 2
      },
      "parent": {
        "candidate_id": "bec_projection_02",
        "source": "MACEField_BEC_backprojection",
        "spacegroup": "P1",
        "spacegroup_number": 1,
        "pointgroup": "1",
        "has_inversion": false,
        "is_polar_point_group": true,
        "nonpolar_parent_hypothesis": false,
        "symmetry_tolerance_A": null,
        "target_reduced_polarization": [
          0.0,
          0.0,
          -0.5
        ],
        "formal_class": [
          0.0,
          0.0,
          0.5
        ],
        "target_residual": 0.00011305831381970193,
        "parent_symmetrization_rmsd_A": 0.10061481946878281,
        "parent_cell_rmsd_A": 0.014100383688801654,
        "energy_eV": -149.4779125304924,
        "reduced_polarization": [
          -6.337784212111709e-05,
          1.254635076317664e-05,
          -0.49990722058129977
        ],
        "cartesian_polarization_e_A2": [
          -7.112458719350128e-06,
          0.003558725669344175,
          -0.010686157412321538
        ],
        "ranking_score": 0.6043660320186226
      },
      "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": [
              -0.04384857498709558,
              -2.0007828352177597e-07,
              -1.5385567183002936e-06
            ],
            "branch_aligned_reduced_polarization": [
              -0.04384857498709558,
              -2.00078283496552e-07,
              -1.5385567183002936e-06
            ],
            "target_residual": 0.5019188155992188,
            "energy_eV": -152.53207703576916,
            "max_atomic_step_A": 0.12,
            "max_log_strain_component": 0.005563010436078854,
            "step_scale": 0.8241534800539474,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 0.8575016604268295,
            "cell_principal_stretches": [
              1.0057972593999118,
              1.0000588421416459,
              0.9941640358087442
            ],
            "cell_volume_ratio": 0.9999863004837812,
            "cell_rmsd_from_input_A": 0.038964439825430026
          },
          {
            "iteration": 1,
            "reduced_polarization": [
              -0.0067835226151567885,
              -0.40827853436198636,
              0.00022301475414918478
            ],
            "branch_aligned_reduced_polarization": [
              -0.0067835226151567885,
              -0.40827853436198636,
              0.00022301475414918478
            ],
            "target_residual": 0.09197224132006476,
            "energy_eV": -150.6874629979742,
            "max_atomic_step_A": 0.028531550341434803,
            "max_log_strain_component": 0.0013040050951257185,
            "step_scale": 1.0,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 0.8575016604268295,
            "cell_principal_stretches": [
              1.0071645852116689,
              1.0000670846865938,
              0.9928042721601309
            ],
            "cell_volume_ratio": 0.9999843821054202,
            "cell_rmsd_from_input_A": 0.048100696003840655
          },
          {
            "iteration": 2,
            "reduced_polarization": [
              -0.00026121772477318803,
              -0.4995269742945118,
              -9.816342856293216e-05
            ],
            "branch_aligned_reduced_polarization": [
              -0.00026121772477318803,
              -0.4995269742945118,
              -9.816342856293216e-05
            ],
            "target_residual": 0.0005492031286286566,
            "energy_eV": -149.74446544954827
          }
        ],
        "iterations": 2
      },
      "parent": {
        "candidate_id": "bec_projection_03",
        "source": "MACEField_BEC_backprojection",
        "spacegroup": "P1",
        "spacegroup_number": 1,
        "pointgroup": "1",
        "has_inversion": false,
        "is_polar_point_group": true,
        "nonpolar_parent_hypothesis": false,
        "symmetry_tolerance_A": null,
        "target_reduced_polarization": [
          0.0,
          -0.5,
          0.0
        ],
        "formal_class": [
          0.0,
          0.5,
          0.0
        ],
        "target_residual": 0.0005492031286286566,
        "parent_symmetrization_rmsd_A": 0.09075438152685905,
        "parent_cell_rmsd_A": 0.048100696003840655,
        "energy_eV": -149.74446544954827,
        "reduced_polarization": [
          -0.00026121772477318803,
          -0.4995269742945118,
          -9.816342856293216e-05
        ],
        "cartesian_polarization_e_A2": [
          -2.1343097792741172e-05,
          -0.008795215806298004,
          -2.4143169968300632e-06
        ],
        "ranking_score": 0.6038779617850765
      },
      "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": [
              -0.04384857498709558,
              -2.0007828352177597e-07,
              -1.5385567183002936e-06
            ],
            "branch_aligned_reduced_polarization": [
              -0.0438485749870956,
              -2.0007828352177597e-07,
              -1.538556718305717e-06
            ],
            "target_residual": 0.6768105968341455,
            "energy_eV": -152.53207703576916,
            "max_atomic_step_A": 0.12,
            "max_log_strain_component": 0.0021268621416326975,
            "step_scale": 0.8145318401908203,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 0.8575016604268295,
            "cell_principal_stretches": [
              1.0025846861210674,
              0.9995984657499384,
              0.9979630404962615
            ],
            "cell_volume_ratio": 1.0001407096493506,
            "cell_rmsd_from_input_A": 0.012327169649356508
          },
          {
            "iteration": 1,
            "reduced_polarization": [
              -0.4101905997895325,
              -0.003313080814039525,
              -0.4024878303754729
            ],
            "branch_aligned_reduced_polarization": [
              -0.4101905997895325,
              -0.003313080814039525,
              -0.4024878303754729
            ],
            "target_residual": 0.1326096832645596,
            "energy_eV": -150.27519393893013,
            "max_atomic_step_A": 0.031097098855446665,
            "max_log_strain_component": 0.0005771238953496889,
            "step_scale": 1.0,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 0.8575016604268295,
            "cell_principal_stretches": [
              1.003293014466649,
              0.9994524612171195,
              0.9974423913908125
            ],
            "cell_volume_ratio": 1.0001790467807068,
            "cell_rmsd_from_input_A": 0.015844548966691758
          },
          {
            "iteration": 2,
            "reduced_polarization": [
              -0.49848732445196997,
              -8.859922188556606e-05,
              -0.49897535549528443
            ],
            "branch_aligned_reduced_polarization": [
              -0.49848732445196997,
              -8.859922188556606e-05,
              -0.49897535549528443
            ],
            "target_residual": 0.0018291893004198567,
            "energy_eV": -148.94899010386607,
            "max_atomic_step_A": 0.00039510338009723467,
            "max_log_strain_component": 6.736276811846295e-06,
            "step_scale": 1.0,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 0.8575016604268295,
            "cell_principal_stretches": [
              1.003302299358794,
              0.9994498546601518,
              0.9974364345044101
            ],
            "cell_volume_ratio": 1.0001797211090144,
            "cell_rmsd_from_input_A": 0.015890734830616652
          },
          {
            "iteration": 3,
            "reduced_polarization": [
              -0.5000028452014322,
              -6.623738405702771e-07,
              -0.5000009925525419
            ],
            "branch_aligned_reduced_polarization": [
              -0.5000028452014322,
              -6.623738405702771e-07,
              -0.5000009925525419
            ],
            "target_residual": 3.085299149702375e-06,
            "energy_eV": -148.9311741056393
          }
        ],
        "iterations": 3
      },
      "parent": {
        "candidate_id": "bec_projection_04",
        "source": "MACEField_BEC_backprojection",
        "spacegroup": "P1",
        "spacegroup_number": 1,
        "pointgroup": "1",
        "has_inversion": false,
        "is_polar_point_group": true,
        "nonpolar_parent_hypothesis": false,
        "symmetry_tolerance_A": null,
        "target_reduced_polarization": [
          -0.5,
          0.0,
          -0.5
        ],
        "formal_class": [
          0.5,
          0.0,
          0.5
        ],
        "target_residual": 3.085299149702375e-06,
        "parent_symmetrization_rmsd_A": 0.11097334534315623,
        "parent_cell_rmsd_A": 0.015890734830616652,
        "energy_eV": -148.9311741056393,
        "reduced_polarization": [
          -0.5000028452014322,
          -6.623738405702771e-07,
          -0.5000009925525419
        ],
        "cartesian_polarization_e_A2": [
          -0.005608166074503148,
          0.0035779901035410577,
          -0.01067897998226979
        ],
        "ranking_score": 0.6149521996491099
      },
      "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": [
              -0.04384857498709558,
              -2.0007828352177597e-07,
              -1.5385567183002936e-06
            ],
            "branch_aligned_reduced_polarization": [
              -0.0438485749870956,
              -2.00078283496552e-07,
              -1.5385567183002936e-06
            ],
            "target_residual": 0.676811585646572,
            "energy_eV": -152.53207703576916,
            "max_atomic_step_A": 0.12,
            "max_log_strain_component": 0.005123150036415556,
            "step_scale": 0.7589900162645535,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 0.8575016604268295,
            "cell_principal_stretches": [
              1.0057658628681776,
              0.9994433965806728,
              0.9949513435894332
            ],
            "cell_volume_ratio": 1.0001311101808328,
            "cell_rmsd_from_input_A": 0.0361966136952687
          },
          {
            "iteration": 1,
            "reduced_polarization": [
              -0.38385062539665465,
              -0.374661026595265,
              -0.004074978171500623
            ],
            "branch_aligned_reduced_polarization": [
              -0.38385062539665465,
              -0.374661026595265,
              -0.004074978171500623
            ],
            "target_residual": 0.1709302223774348,
            "energy_eV": -150.58267401826436,
            "max_atomic_step_A": 0.04083439343041413,
            "max_log_strain_component": 0.0018078335090509741,
            "step_scale": 1.0,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 0.8575016604268295,
            "cell_principal_stretches": [
              1.0078344005223574,
              0.9992286550845793,
              0.9931715375491335
            ],
            "cell_volume_ratio": 1.0001803615856308,
            "cell_rmsd_from_input_A": 0.04913815663570144
          },
          {
            "iteration": 2,
            "reduced_polarization": [
              -0.49825851463325593,
              -0.49867061193737455,
              -0.00036687816828835694
            ],
            "branch_aligned_reduced_polarization": [
              -0.49825851463325593,
              -0.49867061193737455,
              -0.00036687816828835694
            ],
            "target_residual": 0.002221405747269367,
            "energy_eV": -148.93122668190784,
            "max_atomic_step_A": 0.0004982849558898596,
            "max_log_strain_component": 2.0312142109546937e-05,
            "step_scale": 1.0,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 0.8575016604268295,
            "cell_principal_stretches": [
              1.0078591348178665,
              0.9992250166803207,
              0.9931515602781827
            ],
            "cell_volume_ratio": 1.000181147405244,
            "cell_rmsd_from_input_A": 0.04929082484367017
          },
          {
            "iteration": 3,
            "reduced_polarization": [
              -0.500002339202483,
              -0.5000010161629957,
              4.4665923897468984e-08
            ],
            "branch_aligned_reduced_polarization": [
              -0.500002339202483,
              -0.5000010161629957,
              4.4665923897468984e-08
            ],
            "target_residual": 2.550774497164488e-06,
            "energy_eV": -148.90765474782734
          }
        ],
        "iterations": 3
      },
      "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": 2.550774497164488e-06,
        "parent_symmetrization_rmsd_A": 0.10296179104033196,
        "parent_cell_rmsd_A": 0.04929082484367017,
        "energy_eV": -148.90765474782734,
        "reduced_polarization": [
          -0.500002339202483,
          -0.5000010161629957,
          4.4665923897468984e-08
        ],
        "cartesian_polarization_e_A2": [
          -0.005619625786253935,
          -0.008810230724452271,
          4.3596983946594246e-05
        ],
        "ranking_score": 0.6152895988002438
      },
      "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": [
              -0.04384857498709558,
              -2.0007828352177597e-07,
              -1.5385567183002936e-06
            ],
            "branch_aligned_reduced_polarization": [
              -0.04384857498709558,
              -2.00078283496552e-07,
              -1.538556718305717e-06
            ],
            "target_residual": 0.7084638021069279,
            "energy_eV": -152.53207703576916,
            "max_atomic_step_A": 0.12,
            "max_log_strain_component": 0.0047869049838037865,
            "step_scale": 0.6825257468219822,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 0.8575016604268295,
            "cell_principal_stretches": [
              1.004795997370035,
              1.000024030102221,
              0.9951916809014183
            ],
            "cell_volume_ratio": 0.9999886468376806,
            "cell_rmsd_from_input_A": 0.028960452499325245
          },
          {
            "iteration": 1,
            "reduced_polarization": [
              -0.024968909985824524,
              -0.33644634959651115,
              -0.33735453552862477
            ],
            "branch_aligned_reduced_polarization": [
              -0.024968909985824524,
              -0.33644634959651115,
              -0.33735453552862477
            ],
            "target_residual": 0.23200601315331515,
            "energy_eV": -150.47464050513207,
            "max_atomic_step_A": 0.05985451315693152,
            "max_log_strain_component": 0.002457259372376664,
            "step_scale": 1.0,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 0.8575016604268295,
            "cell_principal_stretches": [
              1.007250052463728,
              1.000061136495998,
              0.9927127755663406
            ],
            "cell_volume_ratio": 0.9999711262640338,
            "cell_rmsd_from_input_A": 0.0438356714808057
          },
          {
            "iteration": 2,
            "reduced_polarization": [
              -0.0015834991678825515,
              -0.4968493874832815,
              -0.4968879493119326
            ],
            "branch_aligned_reduced_polarization": [
              -0.0015834991678825515,
              -0.4968493874832815,
              -0.4968879493119326
            ],
            "target_residual": 0.004703050959780137,
            "energy_eV": -147.81451345196726,
            "max_atomic_step_A": 0.0012171890474696513,
            "max_log_strain_component": 5.1310267456162233e-05,
            "step_scale": 1.0,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 0.8575016604268295,
            "cell_principal_stretches": [
              1.0073006764458192,
              1.000062986722858,
              0.9926601775954965
            ],
            "cell_volume_ratio": 0.9999702492547671,
            "cell_rmsd_from_input_A": 0.04414622233235505
          },
          {
            "iteration": 3,
            "reduced_polarization": [
              1.7916148038261214e-05,
              -0.4999992673347085,
              -0.4999986692472626
            ],
            "branch_aligned_reduced_polarization": [
              1.7916148038261214e-05,
              -0.4999992673347085,
              -0.4999986692472626
            ],
            "target_residual": 1.7980435528827708e-05,
            "energy_eV": -147.7500927621333
          }
        ],
        "iterations": 3
      },
      "parent": {
        "candidate_id": "bec_projection_06",
        "source": "MACEField_BEC_backprojection",
        "spacegroup": "P1",
        "spacegroup_number": 1,
        "pointgroup": "1",
        "has_inversion": false,
        "is_polar_point_group": true,
        "nonpolar_parent_hypothesis": false,
        "symmetry_tolerance_A": null,
        "target_reduced_polarization": [
          0.0,
          -0.5,
          -0.5
        ],
        "formal_class": [
          0.0,
          0.5,
          0.5
        ],
        "target_residual": 1.7980435528827708e-05,
        "parent_symmetrization_rmsd_A": 0.11409070353636348,
        "parent_cell_rmsd_A": 0.04414622233235505,
        "energy_eV": -147.7500927621333,
        "reduced_polarization": [
          1.7916148038261214e-05,
          -0.4999992673347085,
          -0.4999986692472626
        ],
        "cartesian_polarization_e_A2": [
          8.117436503335281e-05,
          -0.005245715010462235,
          -0.010689593371357177
        ],
        "ranking_score": 0.6251632199905099
      },
      "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": [
              -0.04384857498709558,
              -2.0007828352177597e-07,
              -1.5385567183002936e-06
            ],
            "branch_aligned_reduced_polarization": [
              -0.0438485749870956,
              -2.00078283496552e-07,
              -1.538556718305717e-06
            ],
            "target_residual": 0.841470370190602,
            "energy_eV": -152.53207703576916,
            "max_atomic_step_A": 0.12000000000000001,
            "max_log_strain_component": 0.004419604947938696,
            "step_scale": 0.6301564999585453,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 0.8575016604268295,
            "cell_principal_stretches": [
              1.0046673822447363,
              0.9997739035927725,
              0.9956877634093426
            ],
            "cell_volume_ratio": 1.000108846643807,
            "cell_rmsd_from_input_A": 0.027010962207608572
          },
          {
            "iteration": 1,
            "reduced_polarization": [
              -0.3347972106497298,
              -0.31252603848635574,
              -0.31514658846142823
            ],
            "branch_aligned_reduced_polarization": [
              -0.3347972106497298,
              -0.31252603848635574,
              -0.31514658846142823
            ],
            "target_residual": 0.3108202561162604,
            "energy_eV": -150.63864893262013,
            "max_atomic_step_A": 0.07582753327167528,
            "max_log_strain_component": 0.0027493695406216236,
            "step_scale": 1.0,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 0.8575016604268295,
            "cell_principal_stretches": [
              1.0075676439526478,
              0.9996411651877812,
              0.993015319204781
            ],
            "cell_volume_ratio": 1.000171080547493,
            "cell_rmsd_from_input_A": 0.04383202591237351
          },
          {
            "iteration": 2,
            "reduced_polarization": [
              -0.49444496010189565,
              -0.49580921474923323,
              -0.49601003955890643
            ],
            "branch_aligned_reduced_polarization": [
              -0.49444496010189565,
              -0.49580921474923323,
              -0.49601003955890643
            ],
            "target_residual": 0.00802128004803891,
            "energy_eV": -147.53100108732792,
            "max_atomic_step_A": 0.001937046791546841,
            "max_log_strain_component": 6.752160089097808e-05,
            "step_scale": 1.0,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 0.8575016604268295,
            "cell_principal_stretches": [
              1.0076411546057495,
              0.999636095236982,
              0.9929502898099324
            ],
            "cell_volume_ratio": 1.0001734761005308,
            "cell_rmsd_from_input_A": 0.04425027960387887
          },
          {
            "iteration": 3,
            "reduced_polarization": [
              -0.49996991906874594,
              -0.5000006996238974,
              -0.49999768483882084
            ],
            "branch_aligned_reduced_polarization": [
              -0.49996991906874594,
              -0.5000006996238974,
              -0.49999768483882084
            ],
            "target_residual": 3.017800308162939e-05,
            "energy_eV": -147.4383366300476
          }
        ],
        "iterations": 3
      },
      "parent": {
        "candidate_id": "bec_projection_07",
        "source": "MACEField_BEC_backprojection",
        "spacegroup": "P1",
        "spacegroup_number": 1,
        "pointgroup": "1",
        "has_inversion": false,
        "is_polar_point_group": true,
        "nonpolar_parent_hypothesis": false,
        "symmetry_tolerance_A": null,
        "target_reduced_polarization": [
          -0.5,
          -0.5,
          -0.5
        ],
        "formal_class": [
          0.5,
          0.5,
          0.5
        ],
        "target_residual": 3.017800308162939e-05,
        "parent_symmetrization_rmsd_A": 0.12190923506854393,
        "parent_cell_rmsd_A": 0.04425027960387887,
        "energy_eV": -147.4383366300476,
        "reduced_polarization": [
          -0.49996991906874594,
          -0.5000006996238974,
          -0.49999768483882084
        ],
        "cartesian_polarization_e_A2": [
          -0.005519674526622256,
          -0.005232594377736119,
          -0.010635482384855703
        ],
        "ranking_score": 0.6330321609756768
      },
      "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": 0.004274287100881192,
        "minimum_distance_A_by_image": [
          1.6633119427032181,
          1.6629116020612804,
          1.6625116331159824,
          1.6621120360944661,
          1.6617128112238415,
          1.6613139587311985,
          1.660915478843588,
          1.6605173717880368,
          1.6601196377915395
        ],
        "minimum_distance_A": 1.6601196377915395,
        "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": [
          487.3400670470018,
          487.3390554622268,
          487.3380438795516,
          487.33703229897657,
          487.33602072050047,
          487.33500914412497,
          487.3339975698492,
          487.33298599767323,
          487.33197442759615
        ],
        "cell_deformation_log_strain_norm": 0.0001602181608315816
      },
      "parent_reduced_polarization": [
        1.4345446052094992e-05,
        -1.6488951200117763e-09,
        -8.781486743366744e-10
      ],
      "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": [
          -152.5320770357692,
          -152.53159497880932,
          -152.53095174468638,
          -152.53014730750198,
          -152.5291816386782,
          -152.52805470695517,
          -152.52676647838948,
          -152.5253169163529,
          -152.52370598153055
        ],
        "cartesian_polarizations_e_A2": [
          [
            -0.0004905634905864242,
            7.430158038633617e-09,
            -3.288614042976241e-08
          ],
          [
            -0.00042922894123214466,
            6.50015179879701e-09,
            -2.8776257290059264e-08
          ],
          [
            -0.00036789239372611734,
            5.569677029005544e-09,
            -2.466674810734201e-08
          ],
          [
            -0.00030655399720859737,
            4.638737679214976e-09,
            -2.0557634762899273e-08
          ],
          [
            -0.00024521390117276536,
            3.7073379483583727e-09,
            -1.644893914041189e-08
          ],
          [
            -0.00018387225548015704,
            2.775481892221842e-09,
            -1.2340683153415293e-08
          ],
          [
            -0.00012252921037560403,
            1.843173690870133e-09,
            -8.232888674659189e-09
          ],
          [
            -6.118491650280562e-05,
            9.104174819150129e-10,
            -4.125577803157472e-09
          ],
          [
            1.604750813333544e-07,
            -2.278242337268206e-11,
            -1.8772350004944853e-11
          ]
        ],
        "raw_reduced_polarization": [
          [
            -0.04384857498709222,
            -2.0007828275199346e-07,
            -1.5385567179364205e-06
          ],
          [
            -0.03836675171502692,
            -1.7511985700266977e-07,
            -1.3462606298145437e-06
          ],
          [
            -0.03288460406502446,
            -1.5020528330863528e-07,
            -1.1539871425659764e-06
          ],
          [
            -0.027402145358352815,
            -1.2533475009955157e-07,
            -9.617372789188225e-07
          ],
          [
            -0.021919388948536185,
            -1.0050843163919259e-07,
            -7.695120616681294e-07
          ],
          [
            -0.016436348222736635,
            -7.572651081470768e-08,
            -5.773125149604037e-07
          ],
          [
            -0.010953036603091588,
            -5.0989162612717766e-08,
            -3.851396609890975e-07
          ],
          [
            -0.005469467548108296,
            -2.6296568638863968e-08,
            -1.9299453248740649e-07
          ],
          [
            1.4345446052094992e-05,
            -1.6488951200117763e-09,
            -8.781486743366744e-10
          ]
        ],
        "unwrapped_reduced_polarization": [
          [
            -0.04384857498709222,
            -2.0007828275199346e-07,
            -1.5385567179364205e-06
          ],
          [
            -0.03836675171502692,
            -1.7511985700266977e-07,
            -1.3462606298145437e-06
          ],
          [
            -0.03288460406502446,
            -1.5020528330863528e-07,
            -1.1539871425659764e-06
          ],
          [
            -0.027402145358352815,
            -1.2533475009955157e-07,
            -9.617372789188225e-07
          ],
          [
            -0.021919388948536185,
            -1.0050843163919259e-07,
            -7.695120616681294e-07
          ],
          [
            -0.016436348222736635,
            -7.572651081470768e-08,
            -5.773125149604037e-07
          ],
          [
            -0.010953036603091588,
            -5.0989162612717766e-08,
            -3.851396609890975e-07
          ],
          [
            -0.005469467548108296,
            -2.6296568638863968e-08,
            -1.9299453248740649e-07
          ],
          [
            1.4345446052095243e-05,
            -1.6488951200117771e-09,
            -8.781486743366643e-10
          ]
        ],
        "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": [
          [
            -0.043848574987092215,
            -2.0007828277490702e-07,
            -1.5385567179171389e-06
          ],
          [
            -0.0383667517150269,
            -1.7511985700435773e-07,
            -1.3462606298086932e-06
          ],
          [
            -0.03288460406502447,
            -1.5020528332243543e-07,
            -1.153987142565871e-06
          ],
          [
            -0.027402145358352836,
            -1.2533475007847628e-07,
            -9.617372789261225e-07
          ],
          [
            -0.021919388948536178,
            -1.0050843163300627e-07,
            -7.695120616824092e-07
          ],
          [
            -0.016436348222736652,
            -7.572651083975757e-08,
            -5.773125149599601e-07
          ],
          [
            -0.010953036603091604,
            -5.09891626143677e-08,
            -3.851396609966251e-07
          ],
          [
            -0.005469467548108287,
            -2.629656864483465e-08,
            -1.9299453246635068e-07
          ],
          [
            1.4345446052055344e-05,
            -1.6488951315452027e-09,
            -8.781486648956616e-10
          ]
        ]
      },
      "reflected": {
        "reached": true,
        "construction": "reflect_displacements_about_reconstructed_parent",
        "energies_eV": [
          -152.52370598153055,
          -152.52198598232522,
          -152.52010373549427,
          -152.51805919374925,
          -152.51585230708116,
          -152.5134830227591,
          -152.51095128532825,
          -152.50825703660854,
          -152.50540021569316
        ],
        "cartesian_polarizations_e_A2": [
          [
            1.6047508132973782e-07,
            -2.2782422290553317e-11,
            -1.8772328490516827e-11
          ],
          [
            6.128925760361039e-05,
            -9.566314052680466e-10,
            4.0793892196687135e-09
          ],
          [
            0.00012242350036741808,
            -1.8912334870863633e-09,
            8.1768411948818e-09
          ],
          [
            0.0001835630481024165,
            -2.826584188469266e-09,
            1.2273561544091228e-08
          ],
          [
            0.0002447077450988788,
            -3.762678965392883e-09,
            1.6369528210834506e-08
          ],
          [
            0.0003058574351931517,
            -4.699513262594251e-09,
            2.046471894825859e-08
          ],
          [
            0.0003670119617532766,
            -5.637082381667277e-09,
            2.45591121209159e-08
          ],
          [
            0.00042817116766479945,
            -6.575381668298243e-09,
            2.8652685413508754e-08
          ],
          [
            0.0004893348953167154,
            -7.514406323664842e-09,
            3.274541687202587e-08
          ]
        ],
        "raw_reduced_polarization": [
          [
            1.4345446051771691e-05,
            -1.6488946516870284e-09,
            -8.781476678814317e-10
          ],
          [
            0.005478794851264156,
            2.2798500604248864e-08,
            1.9083386237116412e-07
          ],
          [
            0.010943587055629228,
            4.7199834545041944e-08,
            3.825177646675092e-07
          ],
          [
            0.016408708162955424,
            7.155494313488423e-08,
            5.741725262395157e-07
          ],
          [
            0.021874144238513155,
            9.586366587896794e-08,
            7.657971139008273e-07
          ],
          [
            0.027339881307738085,
            1.2012583924796243e-07,
            9.57390485512733e-07
          ],
          [
            0.03280590535494837,
            1.443413193343995e-07,
            1.1489516274943724e-06
          ],
          [
            0.0382722023220793,
            1.6850994679634076e-07,
            1.340479494414456e-06
          ],
          [
            0.04373875810742959,
            1.9263157726066542e-07,
            1.5319730576984586e-06
          ]
        ],
        "unwrapped_reduced_polarization": [
          [
            1.4345446051771691e-05,
            -1.6488946516870284e-09,
            -8.781476678814317e-10
          ],
          [
            0.005478794851264156,
            2.2798500604248864e-08,
            1.9083386237116412e-07
          ],
          [
            0.010943587055629228,
            4.7199834545041944e-08,
            3.825177646675092e-07
          ],
          [
            0.016408708162955424,
            7.155494313488423e-08,
            5.741725262395157e-07
          ],
          [
            0.021874144238513155,
            9.586366587896794e-08,
            7.657971139008273e-07
          ],
          [
            0.027339881307738085,
            1.2012583924796243e-07,
            9.57390485512733e-07
          ],
          [
            0.03280590535494837,
            1.443413193343995e-07,
            1.1489516274943724e-06
          ],
          [
            0.0382722023220793,
            1.6850994679634076e-07,
            1.340479494414456e-06
          ],
          [
            0.04373875810742959,
            1.9263157726066542e-07,
            1.5319730576984586e-06
          ]
        ],
        "gauge_integer_shift": [
          0,
          0,
          0
        ],
        "expected_opposite_endpoint_reduced_polarization": [
          0.04387726282779963,
          1.9678027945179551e-07,
          1.5368002135346195e-06
        ],
        "actual_opposite_endpoint_branch_residual": 0.00013850472051629093
      },
      "pnp_branch": {
        "construction": "incoming_path_concatenated_with_parent_reflection",
        "reduced_polarization": [
          [
            -0.04384857498709222,
            -2.0007828275199346e-07,
            -1.5385567179364205e-06
          ],
          [
            -0.03836675171502692,
            -1.7511985700266977e-07,
            -1.3462606298145437e-06
          ],
          [
            -0.03288460406502446,
            -1.5020528330863528e-07,
            -1.1539871425659764e-06
          ],
          [
            -0.027402145358352815,
            -1.2533475009955157e-07,
            -9.617372789188225e-07
          ],
          [
            -0.021919388948536185,
            -1.0050843163919259e-07,
            -7.695120616681294e-07
          ],
          [
            -0.016436348222736635,
            -7.572651081470768e-08,
            -5.773125149604037e-07
          ],
          [
            -0.010953036603091588,
            -5.0989162612717766e-08,
            -3.851396609890975e-07
          ],
          [
            -0.005469467548108296,
            -2.6296568638863968e-08,
            -1.9299453248740649e-07
          ],
          [
            1.4345446052094992e-05,
            -1.6488951200117763e-09,
            -8.781486743366744e-10
          ],
          [
            0.005478794851264156,
            2.2798500604248864e-08,
            1.9083386237116412e-07
          ],
          [
            0.010943587055629228,
            4.7199834545041944e-08,
            3.825177646675092e-07
          ],
          [
            0.016408708162955424,
            7.155494313488423e-08,
            5.741725262395157e-07
          ],
          [
            0.021874144238513155,
            9.586366587896794e-08,
            7.657971139008273e-07
          ],
          [
            0.027339881307738085,
            1.2012583924796243e-07,
            9.57390485512733e-07
          ],
          [
            0.03280590535494837,
            1.443413193343995e-07,
            1.1489516274943724e-06
          ],
          [
            0.0382722023220793,
            1.6850994679634076e-07,
            1.340479494414456e-06
          ],
          [
            0.04373875810742959,
            1.9263157726066542e-07,
            1.5319730576984586e-06
          ]
        ],
        "unwrapped_reduced_polarization": [
          [
            -0.04384857498709222,
            -2.0007828275199346e-07,
            -1.5385567179364205e-06
          ],
          [
            -0.03836675171502692,
            -1.7511985700266977e-07,
            -1.3462606298145437e-06
          ],
          [
            -0.03288460406502446,
            -1.5020528330863528e-07,
            -1.1539871425659764e-06
          ],
          [
            -0.027402145358352815,
            -1.2533475009955157e-07,
            -9.617372789188225e-07
          ],
          [
            -0.021919388948536185,
            -1.0050843163919259e-07,
            -7.695120616681294e-07
          ],
          [
            -0.016436348222736635,
            -7.572651081470768e-08,
            -5.773125149604037e-07
          ],
          [
            -0.010953036603091588,
            -5.0989162612717766e-08,
            -3.851396609890975e-07
          ],
          [
            -0.005469467548108296,
            -2.6296568638863968e-08,
            -1.9299453248740649e-07
          ],
          [
            1.4345446052095243e-05,
            -1.6488951200117771e-09,
            -8.781486743366643e-10
          ],
          [
            0.005478794851264156,
            2.2798500604248864e-08,
            1.9083386237116412e-07
          ],
          [
            0.010943587055629228,
            4.7199834545041944e-08,
            3.825177646675092e-07
          ],
          [
            0.016408708162955424,
            7.155494313488423e-08,
            5.741725262395157e-07
          ],
          [
            0.021874144238513155,
            9.586366587896794e-08,
            7.657971139008273e-07
          ],
          [
            0.027339881307738085,
            1.2012583924796243e-07,
            9.57390485512733e-07
          ],
          [
            0.03280590535494837,
            1.443413193343995e-07,
            1.1489516274943724e-06
          ],
          [
            0.0382722023220793,
            1.6850994679634076e-07,
            1.340479494414456e-06
          ],
          [
            0.04373875810742959,
            1.9263157726066542e-07,
            1.5319730576984586e-06
          ]
        ],
        "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": [
          [
            -0.043848574987092215,
            -2.0007828277490702e-07,
            -1.5385567179171389e-06
          ],
          [
            -0.0383667517150269,
            -1.7511985700435773e-07,
            -1.3462606298086932e-06
          ],
          [
            -0.03288460406502447,
            -1.5020528332243543e-07,
            -1.153987142565871e-06
          ],
          [
            -0.027402145358352836,
            -1.2533475007847628e-07,
            -9.617372789261225e-07
          ],
          [
            -0.021919388948536178,
            -1.0050843163300627e-07,
            -7.695120616824092e-07
          ],
          [
            -0.016436348222736652,
            -7.572651083975757e-08,
            -5.773125149599601e-07
          ],
          [
            -0.010953036603091604,
            -5.09891626143677e-08,
            -3.851396609966251e-07
          ],
          [
            -0.005469467548108287,
            -2.629656864483465e-08,
            -1.9299453246635068e-07
          ],
          [
            1.4345446052055344e-05,
            -1.6488951315452027e-09,
            -8.781486648956616e-10
          ],
          [
            0.005478794851264124,
            2.279850064290656e-08,
            1.9083386237905842e-07
          ],
          [
            0.010943587055629256,
            4.7199834596334256e-08,
            3.8251776468545273e-07
          ],
          [
            0.016408708162955477,
            7.155494308186405e-08,
            5.741725261909636e-07
          ],
          [
            0.021874144238513193,
            9.58636658943135e-08,
            7.657971139440889e-07
          ],
          [
            0.027339881307738123,
            1.2012583927578646e-07,
            9.573904855564308e-07
          ],
          [
            0.03280590535494832,
            1.4434131934137895e-07,
            1.1489516275053901e-06
          ],
          [
            0.038272202322079285,
            1.6850994677408693e-07,
            1.340479494404967e-06
          ],
          [
            0.043738758107429554,
            1.926315772449172e-07,
            1.5319730577445512e-06
          ]
        ]
      },
      "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": "P2_1",
        "spacegroup_number": 4,
        "pointgroup": "2",
        "has_inversion": false,
        "is_polar_point_group": true,
        "nonpolar_parent_hypothesis": false,
        "symmetry_tolerance_A": null,
        "target_reduced_polarization": [
          0.0,
          0.0,
          0.0
        ],
        "formal_class": [
          0.0,
          0.0,
          0.0
        ],
        "target_residual": 1.4345446171348154e-05,
        "parent_symmetrization_rmsd_A": 0.004274287100881192,
        "parent_cell_rmsd_A": 0.0005842111294521887,
        "energy_eV": -152.52370598153058,
        "reduced_polarization": [
          1.4345446049706201e-05,
          -1.648898522170148e-09,
          -8.781513534134053e-10
        ],
        "cartesian_polarization_e_A2": [
          1.6047508130663224e-07,
          -2.2782464208803556e-11,
          -1.8772407275896626e-11
        ],
        "ranking_score": 0.5044490307755869
      }
    }
  ],
  "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": 55,
      "full_response": 20,
      "energy_polarization": 35
    },
    "model_evaluations_for_recovery_and_path_properties": {
      "total": 80,
      "full_response": 45,
      "energy_polarization": 35
    },
    "elapsed_seconds": 784.0512130539864
  }
}