{
  "schema": "ferrofinder.endpoint_parent_recovery.v4_variable_cell",
  "status": "complete",
  "input_atom_count": 36,
  "input_formula": "H2Cs6F24S4",
  "input_spacegroup": "Pba2",
  "input_pointgroup": "mm2",
  "input_is_polar_point_group": true,
  "input_energy_eV": -147.0307900367688,
  "input_cartesian_polarization_e_A2": [
    -4.39193925289459e-18,
    -7.103484356855597e-18,
    -0.0003591201418238804
  ],
  "input_reduced_polarization": [
    -3.138946583768895e-16,
    -4.790392100875958e-16,
    -0.039354648485049284
  ],
  "input_formal_targets": [
    {
      "orbit_id": 0,
      "representative_formal_class": [
        0.0,
        0.0,
        0.0
      ],
      "target_reduced_polarization": [
        0.0,
        0.0,
        0.0
      ]
    },
    {
      "orbit_id": 1,
      "representative_formal_class": [
        0.0,
        0.0,
        0.5
      ],
      "target_reduced_polarization": [
        0.0,
        0.0,
        -0.5
      ]
    },
    {
      "orbit_id": 2,
      "representative_formal_class": [
        0.0,
        0.5,
        0.0
      ],
      "target_reduced_polarization": [
        0.0,
        -0.5,
        0.0
      ]
    },
    {
      "orbit_id": 3,
      "representative_formal_class": [
        0.5,
        0.0,
        0.0
      ],
      "target_reduced_polarization": [
        -0.5,
        0.0,
        0.0
      ]
    },
    {
      "orbit_id": 4,
      "representative_formal_class": [
        0.0,
        0.5,
        0.5
      ],
      "target_reduced_polarization": [
        0.0,
        -0.5,
        -0.5
      ]
    },
    {
      "orbit_id": 5,
      "representative_formal_class": [
        0.5,
        0.0,
        0.5
      ],
      "target_reduced_polarization": [
        -0.5,
        0.0,
        -0.5
      ]
    },
    {
      "orbit_id": 6,
      "representative_formal_class": [
        0.5,
        0.5,
        0.0
      ],
      "target_reduced_polarization": [
        -0.5,
        -0.5,
        0.0
      ]
    },
    {
      "orbit_id": 7,
      "representative_formal_class": [
        0.5,
        0.5,
        0.5
      ],
      "target_reduced_polarization": [
        -0.5,
        -0.5,
        -0.5
      ]
    }
  ],
  "parent_candidates": [
    {
      "candidate_id": "inversion_parent_endpoint_00",
      "source": "same_species_inversion_center_projection_from_endpoint",
      "spacegroup": "Pbam",
      "spacegroup_number": 55,
      "pointgroup": "mmm",
      "has_inversion": true,
      "is_polar_point_group": false,
      "nonpolar_parent_hypothesis": true,
      "symmetry_tolerance_A": null,
      "target_reduced_polarization": [
        0.0,
        0.0,
        0.0
      ],
      "formal_class": [
        0.0,
        0.0,
        0.0
      ],
      "target_residual": 1.0204620596421558e-15,
      "parent_symmetrization_rmsd_A": 0.04295456241051995,
      "parent_cell_rmsd_A": 0.0,
      "energy_eV": -147.03924448737496,
      "reduced_polarization": [
        -2.0471390763710185e-16,
        -6.696247022729834e-17,
        9.974723348394767e-16
      ],
      "cartesian_polarization_e_A2": [
        -2.864308208409515e-18,
        -9.929601789152985e-19,
        9.102162518083061e-18
      ],
      "ranking_score": 0.04295456241052199
    },
    {
      "candidate_id": "symmetry_projection_00",
      "source": "spglib_refine_cell_from_polar_endpoint",
      "spacegroup": "Pbam",
      "spacegroup_number": 55,
      "pointgroup": "mmm",
      "has_inversion": true,
      "is_polar_point_group": false,
      "nonpolar_parent_hypothesis": true,
      "symmetry_tolerance_A": null,
      "target_reduced_polarization": [
        0.0,
        0.0,
        0.0
      ],
      "formal_class": [
        0.0,
        0.0,
        0.0
      ],
      "target_residual": 7.684897774070885e-16,
      "parent_symmetrization_rmsd_A": 0.06332420490094653,
      "parent_cell_rmsd_A": 1.8223050854092006e-15,
      "energy_eV": -146.94189354224534,
      "reduced_polarization": [
        -6.892034890449098e-16,
        -3.399633103847456e-16,
        -1.904199683020959e-19
      ],
      "cartesian_polarization_e_A2": [
        -9.643170968312037e-18,
        -5.041182446800748e-18,
        -1.737625633950872e-21
      ],
      "ranking_score": 0.06332420490094853
    },
    {
      "candidate_id": "bec_projection_00",
      "source": "MACEField_BEC_backprojection",
      "spacegroup": "Pba2",
      "spacegroup_number": 32,
      "pointgroup": "mm2",
      "has_inversion": false,
      "is_polar_point_group": true,
      "nonpolar_parent_hypothesis": false,
      "symmetry_tolerance_A": null,
      "target_reduced_polarization": [
        0.0,
        0.0,
        0.0
      ],
      "formal_class": [
        0.0,
        0.0,
        0.0
      ],
      "target_residual": 1.4720815794268301e-05,
      "parent_symmetrization_rmsd_A": 0.008254404758309122,
      "parent_cell_rmsd_A": 0.00065737182337599,
      "energy_eV": -147.01817777974483,
      "reduced_polarization": [
        -2.728618213111642e-17,
        4.841925083855813e-16,
        -1.4720815794268301e-05
      ],
      "cartesian_polarization_e_A2": [
        -3.818912591709983e-19,
        7.179555672414768e-18,
        -1.3434111215488964e-07
      ],
      "ranking_score": 0.5084481893457417
    },
    {
      "candidate_id": "inversion_parent_bec_00_00",
      "source": "same_species_inversion_center_projection_after_BEC",
      "spacegroup": "Pbam",
      "spacegroup_number": 55,
      "pointgroup": "mmm",
      "has_inversion": true,
      "is_polar_point_group": false,
      "nonpolar_parent_hypothesis": true,
      "symmetry_tolerance_A": null,
      "target_reduced_polarization": [
        0.0,
        0.0,
        0.0
      ],
      "formal_class": [
        0.0,
        0.0,
        0.0
      ],
      "target_residual": 2.644597493738635e-15,
      "parent_symmetrization_rmsd_A": 0.04295461563671935,
      "parent_cell_rmsd_A": 0.00065737182337599,
      "energy_eV": -147.0383918503955,
      "reduced_polarization": [
        -2.456746903825804e-17,
        9.889876182131077e-16,
        -2.4525896180109077e-15
      ],
      "cartesian_polarization_e_A2": [
        -3.437021332538985e-19,
        1.4664624352166335e-17,
        -2.238215745294558e-17
      ],
      "ranking_score": 0.04311895859256864
    },
    {
      "candidate_id": "symmetry_parent_00_00",
      "source": "spglib_refine_cell_after_MACEField_BEC_backprojection",
      "spacegroup": "Pbam",
      "spacegroup_number": 55,
      "pointgroup": "mmm",
      "has_inversion": true,
      "is_polar_point_group": false,
      "nonpolar_parent_hypothesis": true,
      "symmetry_tolerance_A": null,
      "target_reduced_polarization": [
        0.0,
        0.0,
        0.0
      ],
      "formal_class": [
        0.0,
        0.0,
        0.0
      ],
      "target_residual": 9.979773954516865e-16,
      "parent_symmetrization_rmsd_A": 0.06559699439271047,
      "parent_cell_rmsd_A": 0.0006573718233757014,
      "energy_eV": -146.90825917241017,
      "reduced_polarization": [
        -8.789694478134164e-16,
        4.7260215609923205e-16,
        -4.335169370033508e-18
      ],
      "cartesian_polarization_e_A2": [
        -1.2296898545306149e-17,
        7.00770460578782e-18,
        -3.956244563408464e-20
      ],
      "ranking_score": 0.0657613373485564
    },
    {
      "candidate_id": "bec_projection_01",
      "source": "MACEField_BEC_backprojection",
      "spacegroup": "Pba2",
      "spacegroup_number": 32,
      "pointgroup": "mm2",
      "has_inversion": false,
      "is_polar_point_group": true,
      "nonpolar_parent_hypothesis": false,
      "symmetry_tolerance_A": null,
      "target_reduced_polarization": [
        0.0,
        0.0,
        -0.5
      ],
      "formal_class": [
        0.0,
        0.0,
        0.5
      ],
      "target_residual": 0.0007408801804287823,
      "parent_symmetrization_rmsd_A": 0.09981242265326641,
      "parent_cell_rmsd_A": 0.00796343238049416,
      "energy_eV": -145.31149053983256,
      "reduced_polarization": [
        -2.239396565968707e-15,
        -1.882465003261362e-15,
        -0.4992591198195712
      ],
      "cartesian_polarization_e_A2": [
        3.1905992636188544e-17,
        -2.3919941784735365e-17,
        -0.004551619699383095
      ],
      "ranking_score": 0.6032850411092475
    },
    {
      "candidate_id": "symmetry_parent_01_00",
      "source": "spglib_refine_cell_after_MACEField_BEC_backprojection",
      "spacegroup": "Pbam",
      "spacegroup_number": 55,
      "pointgroup": "mmm",
      "has_inversion": true,
      "is_polar_point_group": false,
      "nonpolar_parent_hypothesis": true,
      "symmetry_tolerance_A": null,
      "target_reduced_polarization": [
        0.0,
        0.0,
        -0.5
      ],
      "formal_class": [
        0.0,
        0.0,
        0.5
      ],
      "target_residual": 0.4999999999999991,
      "parent_symmetrization_rmsd_A": 0.05342348052295785,
      "parent_cell_rmsd_A": 0.007963432380493872,
      "energy_eV": -146.8167823547656,
      "reduced_polarization": [
        7.090452940659445e-17,
        -2.5753710391620926e-18,
        -8.703858079803177e-16
      ],
      "cartesian_polarization_e_A2": [
        9.934800102286254e-19,
        -3.8210769624177896e-20,
        -7.935088278604514e-18
      ],
      "ranking_score": 1.0554143386180797
    },
    {
      "candidate_id": "bec_projection_02",
      "source": "MACEField_BEC_backprojection",
      "spacegroup": "Pc",
      "spacegroup_number": 7,
      "pointgroup": "m",
      "has_inversion": false,
      "is_polar_point_group": true,
      "nonpolar_parent_hypothesis": false,
      "symmetry_tolerance_A": null,
      "target_reduced_polarization": [
        0.0,
        -0.5,
        0.0
      ],
      "formal_class": [
        0.0,
        0.5,
        0.0
      ],
      "target_residual": 0.000200412379418273,
      "parent_symmetrization_rmsd_A": 0.16113434969095072,
      "parent_cell_rmsd_A": 0.0039675334564321625,
      "energy_eV": -140.9639295328011,
      "reduced_polarization": [
        -3.3419973443637213e-15,
        -0.49980796602328853,
        5.734172662618798e-05
      ],
      "cartesian_polarization_e_A2": [
        -1.5174583660320745e-16,
        -0.007411181834382396,
        -3.530624855448826e-06
      ],
      "ranking_score": 0.6625270578138953
    },
    {
      "candidate_id": "bec_projection_03",
      "source": "MACEField_BEC_backprojection",
      "spacegroup": "Pc",
      "spacegroup_number": 7,
      "pointgroup": "m",
      "has_inversion": false,
      "is_polar_point_group": true,
      "nonpolar_parent_hypothesis": false,
      "symmetry_tolerance_A": null,
      "target_reduced_polarization": [
        -0.5,
        0.0,
        0.0
      ],
      "formal_class": [
        0.5,
        0.0,
        0.0
      ],
      "target_residual": 5.1386766063961526e-05,
      "parent_symmetrization_rmsd_A": 0.16998048343698768,
      "parent_cell_rmsd_A": 0.0011272043214164509,
      "energy_eV": -142.30148453337915,
      "reduced_polarization": [
        -0.49994901624486887,
        3.572629138818636e-15,
        6.423117564034776e-06
      ],
      "cartesian_polarization_e_A2": [
        -0.006994261526663972,
        2.755713993901983e-16,
        -8.261725722540162e-07
      ],
      "ranking_score": 0.6703650580494698
    },
    {
      "candidate_id": "bec_projection_04",
      "source": "MACEField_BEC_backprojection",
      "spacegroup": "Pc",
      "spacegroup_number": 7,
      "pointgroup": "m",
      "has_inversion": false,
      "is_polar_point_group": true,
      "nonpolar_parent_hypothesis": false,
      "symmetry_tolerance_A": null,
      "target_reduced_polarization": [
        0.0,
        -0.5,
        -0.5
      ],
      "formal_class": [
        0.0,
        0.5,
        0.5
      ],
      "target_residual": 3.42881041635235e-06,
      "parent_symmetrization_rmsd_A": 0.1989311244706572,
      "parent_cell_rmsd_A": 0.009948126828116376,
      "energy_eV": -138.26594398729173,
      "reduced_polarization": [
        -7.262658862422507e-16,
        -0.49999733546165187,
        -0.4999978419971588
      ],
      "cartesian_polarization_e_A2": [
        -4.9079568739833525e-16,
        -0.007421640702793932,
        -0.004561989599305948
      ],
      "ranking_score": 0.701425013798519
    },
    {
      "candidate_id": "bec_projection_05",
      "source": "MACEField_BEC_backprojection",
      "spacegroup": "Pc",
      "spacegroup_number": 7,
      "pointgroup": "m",
      "has_inversion": false,
      "is_polar_point_group": true,
      "nonpolar_parent_hypothesis": false,
      "symmetry_tolerance_A": null,
      "target_reduced_polarization": [
        -0.5,
        0.0,
        -0.5
      ],
      "formal_class": [
        0.5,
        0.0,
        0.5
      ],
      "target_residual": 0.000735207462619507,
      "parent_symmetrization_rmsd_A": 0.20167503272301288,
      "parent_cell_rmsd_A": 0.008637126985759136,
      "energy_eV": -139.886809423743,
      "reduced_polarization": [
        -0.49946080171883617,
        -4.680438833371857e-15,
        -0.4995002048152679
      ],
      "cartesian_polarization_e_A2": [
        -0.006999569931292761,
        1.5821823729240446e-16,
        -0.004554381201173258
      ],
      "ranking_score": 0.7053047293946917
    },
    {
      "candidate_id": "bec_projection_06",
      "source": "MACEField_BEC_backprojection",
      "spacegroup": "P1",
      "spacegroup_number": 1,
      "pointgroup": "1",
      "has_inversion": false,
      "is_polar_point_group": true,
      "nonpolar_parent_hypothesis": false,
      "symmetry_tolerance_A": null,
      "target_reduced_polarization": [
        -0.5,
        -0.5,
        0.0
      ],
      "formal_class": [
        0.5,
        0.5,
        0.0
      ],
      "target_residual": 6.907838317585876e-05,
      "parent_symmetrization_rmsd_A": 0.25907361809114743,
      "parent_cell_rmsd_A": 0.004642535485661896,
      "energy_eV": -131.78039843276684,
      "reduced_polarization": [
        -0.4999798051189816,
        -0.4999815032228372,
        6.341812861818568e-05
      ],
      "cartesian_polarization_e_A2": [
        -0.006994787355979234,
        -0.007413686195923092,
        -5.073566325851863e-06
      ],
      "ranking_score": 0.7603724087289145
    },
    {
      "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": 3.4547488009679596e-07,
      "parent_symmetrization_rmsd_A": 0.2891875317015818,
      "parent_cell_rmsd_A": 0.010965618093133966,
      "energy_eV": -129.26619526470412,
      "reduced_polarization": [
        -0.4999997904599428,
        -0.49999983829450495,
        -0.4999997779702946
      ],
      "cartesian_polarization_e_A2": [
        -0.007009151178245136,
        -0.007422175763960916,
        -0.004562705135122509
      ],
      "ranking_score": 0.7919296271746255
    }
  ],
  "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": [
              -3.138946583768895e-16,
              -4.790392100875958e-16,
              -0.039354648485049284
            ],
            "branch_aligned_reduced_polarization": [
              -3.138946583768895e-16,
              -4.790392100875958e-16,
              -0.039354648485049284
            ],
            "target_residual": 0.039354648485049284,
            "energy_eV": -147.0307900367688,
            "max_atomic_step_A": 0.011917241937724287,
            "max_log_strain_component": 0.00011996634028961537,
            "step_scale": 1.0,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 0.12178817011209728,
            "cell_principal_stretches": [
              1.0001199735365387,
              0.9999965191188148,
              0.9999267274212026
            ],
            "cell_volume_ratio": 1.000043211123256,
            "cell_rmsd_from_input_A": 0.00065737182337599
          },
          {
            "iteration": 1,
            "reduced_polarization": [
              -2.728618213111642e-17,
              4.841925083855813e-16,
              -1.4720815794268301e-05
            ],
            "branch_aligned_reduced_polarization": [
              -2.728618213111642e-17,
              4.841925083855813e-16,
              -1.4720815794268301e-05
            ],
            "target_residual": 1.4720815794268301e-05,
            "energy_eV": -147.01817777974483
          }
        ],
        "iterations": 1
      },
      "parent": {
        "candidate_id": "inversion_parent_endpoint_00",
        "source": "same_species_inversion_center_projection_from_endpoint",
        "spacegroup": "Pbam",
        "spacegroup_number": 55,
        "pointgroup": "mmm",
        "has_inversion": true,
        "is_polar_point_group": false,
        "nonpolar_parent_hypothesis": true,
        "symmetry_tolerance_A": null,
        "target_reduced_polarization": [
          0.0,
          0.0,
          0.0
        ],
        "formal_class": [
          0.0,
          0.0,
          0.0
        ],
        "target_residual": 1.0204620596421558e-15,
        "parent_symmetrization_rmsd_A": 0.04295456241051995,
        "parent_cell_rmsd_A": 0.0,
        "energy_eV": -147.03924448737496,
        "reduced_polarization": [
          -2.0471390763710185e-16,
          -6.696247022729834e-17,
          9.974723348394767e-16
        ],
        "cartesian_polarization_e_A2": [
          -2.864308208409515e-18,
          -9.929601789152985e-19,
          9.102162518083061e-18
        ],
        "ranking_score": 0.04295456241052199
      },
      "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": [
          -147.0307900367688,
          -147.03284734042882,
          -147.03459607958976,
          -147.03604847411236,
          -147.037216632906,
          -147.03811182256524,
          -147.03874370420482,
          -147.0391196935474,
          -147.03924448737496
        ],
        "cartesian_polarizations_e_A2": [
          [
            -1.1686377490310821e-17,
            -1.768232933991474e-17,
            -0.0003591201418238796
          ],
          [
            -3.895459163436941e-18,
            -1.2030094475319964e-17,
            -0.00031407981151966563
          ],
          [
            -6.4542411629494404e-18,
            -5.0029916706886195e-18,
            -0.0002691037878628357
          ],
          [
            -1.0655226535283396e-17,
            -7.294438237416232e-18,
            -0.0002241803316680458
          ],
          [
            -9.356740147471082e-18,
            -7.485392117976866e-18,
            -0.0001792984549005723
          ],
          [
            -1.5696408982084142e-17,
            -7.065293580743471e-18,
            -0.00013444806988749798
          ],
          [
            -1.6612987608775187e-17,
            -6.988912028519217e-18,
            -8.962014033301318e-05
          ],
          [
            -1.1113515848628918e-17,
            -3.208025193418657e-18,
            -4.4806576309735636e-05
          ],
          [
            -1.451249492260821e-17,
            -6.5306227151736944e-18,
            1.754131640201001e-17
          ]
        ],
        "raw_reduced_polarization": [
          [
            -8.352327431593756e-16,
            -1.192447065970736e-15,
            -0.0393546484850492
          ],
          [
            -2.7841091438645855e-16,
            -8.112760815999607e-16,
            -0.03441884522497434
          ],
          [
            -4.612886718756028e-16,
            -3.373878307606186e-16,
            -0.02949008909261056
          ],
          [
            -7.615357364100189e-16,
            -4.919166082082302e-16,
            -0.02456709363404198
          ],
          [
            -6.687320982811992e-16,
            -5.047940063288644e-16,
            -0.019648654711171838
          ],
          [
            -1.121832213851318e-15,
            -4.76463730463469e-16,
            -0.014733666853224598
          ],
          [
            -1.1873406642951906e-15,
            -4.713127712152153e-16,
            -0.009821139805954457
          ],
          [
            -7.942899616319552e-16,
            -2.1634028842665622e-16,
            -0.004910187024132339
          ],
          [
            -1.0372171320279828e-15,
            -4.4040701572569295e-16,
            1.922288004955974e-15
          ]
        ],
        "unwrapped_reduced_polarization": [
          [
            -8.352327431593756e-16,
            -1.192447065970736e-15,
            -0.0393546484850492
          ],
          [
            -2.7841091438645855e-16,
            -8.112760815999607e-16,
            -0.03441884522497434
          ],
          [
            -4.612886718756028e-16,
            -3.3738783076061864e-16,
            -0.02949008909261056
          ],
          [
            -7.615357364100189e-16,
            -4.919166082082302e-16,
            -0.02456709363404198
          ],
          [
            -6.687320982811992e-16,
            -5.047940063288644e-16,
            -0.019648654711171838
          ],
          [
            -1.121832213851318e-15,
            -4.76463730463469e-16,
            -0.014733666853224598
          ],
          [
            -1.1873406642951906e-15,
            -4.713127712152153e-16,
            -0.009821139805954457
          ],
          [
            -7.942899616319552e-16,
            -2.163402884266562e-16,
            -0.004910187024132339
          ],
          [
            -1.0372171320279828e-15,
            -4.4040701572569295e-16,
            1.9220736113823023e-15
          ]
        ],
        "berry_integer_shifts": [
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ]
        ],
        "folded_reduced_polarization": [
          [
            -8.326672684688674e-16,
            -1.1657341758564144e-15,
            -0.039354648485049215
          ],
          [
            -2.7755575615628914e-16,
            -8.326672684688674e-16,
            -0.03441884522497435
          ],
          [
            -4.440892098500626e-16,
            -3.3306690738754696e-16,
            -0.029490089092610583
          ],
          [
            -7.771561172376096e-16,
            -4.996003610813204e-16,
            -0.02456709363404197
          ],
          [
            -6.661338147750939e-16,
            -4.996003610813204e-16,
            -0.01964865471117183
          ],
          [
            -1.1102230246251565e-15,
            -4.996003610813204e-16,
            -0.01473366685322458
          ],
          [
            -1.1657341758564144e-15,
            -4.440892098500626e-16,
            -0.009821139805954449
          ],
          [
            -7.771561172376096e-16,
            -2.220446049250313e-16,
            -0.0049101870241323176
          ],
          [
            -1.0547118733938987e-15,
            -4.440892098500626e-16,
            1.887379141862766e-15
          ]
        ]
      },
      "reflected": {
        "reached": true,
        "construction": "reflect_displacements_about_reconstructed_parent",
        "energies_eV": [
          -147.03924448737496,
          -147.03911969354735,
          -147.03874370420488,
          -147.03811182256524,
          -147.037216632906,
          -147.03604847411236,
          -147.0345960795897,
          -147.03284734042882,
          -147.0307900367688
        ],
        "cartesian_polarizations_e_A2": [
          [
            -1.2984863878123134e-18,
            -4.048222267885448e-18,
            1.0350883045917259e-17
          ],
          [
            -8.058253759658769e-18,
            -3.819077611212687e-19,
            4.480657630974152e-05
          ],
          [
            -1.0884371191956158e-17,
            -2.8452128203534515e-17,
            8.96201403330271e-05
          ],
          [
            -1.1228088176965299e-17,
            -7.905490655210262e-18,
            0.00013444806988751189
          ],
          [
            -1.7491375459354106e-17,
            -2.0393874443875747e-17,
            0.00017929845490061275
          ],
          [
            -2.1654170055575934e-17,
            -1.0311509550274255e-17,
            0.00022418033166807298
          ],
          [
            -2.3449136532845898e-17,
            7.752727550761754e-18,
            0.00026910378786286113
          ],
          [
            -9.776838684704479e-18,
            -1.8331572533820896e-17,
            0.0003140798115196991
          ],
          [
            -1.1609995938086567e-17,
            8.17282608799515e-18,
            0.0003591201418239043
          ]
        ],
        "raw_reduced_polarization": [
          [
            -9.280363812881949e-17,
            -2.730008401574471e-16,
            1.1343150003034503e-15
          ],
          [
            -5.759284601523798e-16,
            -2.5754796241268593e-17,
            0.004910187024132984
          ],
          [
            -7.77912849020987e-16,
            -1.9187323199745102e-15,
            0.009821139805955982
          ],
          [
            -8.024785179374392e-16,
            -5.331242821942599e-16,
            0.014733666853226123
          ],
          [
            -1.2501195959705687e-15,
            -1.375306119283743e-15,
            0.01964865471117627
          ],
          [
            -1.54763714173649e-15,
            -6.95379498514252e-16,
            0.02456709363404496
          ],
          [
            -1.6759245238557405e-15,
            5.228223636977525e-16,
            0.029490089092613348
          ],
          [
            -6.987568047346409e-16,
            -1.2362302195808925e-15,
            0.03441884522497801
          ],
          [
            -8.297737056223861e-16,
            5.51152639563148e-16,
            0.03935464848505191
          ]
        ],
        "unwrapped_reduced_polarization": [
          [
            -9.280363812881949e-17,
            -2.730008401574471e-16,
            1.1343150003034503e-15
          ],
          [
            -5.759284601523798e-16,
            -2.575479624126859e-17,
            0.004910187024132984
          ],
          [
            -7.77912849020987e-16,
            -1.9187323199745102e-15,
            0.009821139805955982
          ],
          [
            -8.024785179374392e-16,
            -5.331242821942599e-16,
            0.014733666853226123
          ],
          [
            -1.2501195959705687e-15,
            -1.375306119283743e-15,
            0.01964865471117627
          ],
          [
            -1.54763714173649e-15,
            -6.95379498514252e-16,
            0.02456709363404496
          ],
          [
            -1.6759245238557405e-15,
            5.228223636977526e-16,
            0.029490089092613348
          ],
          [
            -6.987568047346409e-16,
            -1.2362302195808925e-15,
            0.03441884522497801
          ],
          [
            -8.297737056223861e-16,
            5.511526395631482e-16,
            0.03935464848505191
          ]
        ],
        "gauge_integer_shift": [
          0,
          0,
          0
        ],
        "expected_opposite_endpoint_reduced_polarization": [
          -1.2392015208965901e-15,
          3.1163303451935005e-16,
          0.039354648485053045
        ],
        "actual_opposite_endpoint_branch_residual": 1.2328812074675005e-15
      },
      "pnp_branch": {
        "construction": "incoming_path_concatenated_with_parent_reflection",
        "reduced_polarization": [
          [
            -8.352327431593756e-16,
            -1.192447065970736e-15,
            -0.0393546484850492
          ],
          [
            -2.7841091438645855e-16,
            -8.112760815999607e-16,
            -0.03441884522497434
          ],
          [
            -4.612886718756028e-16,
            -3.373878307606186e-16,
            -0.02949008909261056
          ],
          [
            -7.615357364100189e-16,
            -4.919166082082302e-16,
            -0.02456709363404198
          ],
          [
            -6.687320982811992e-16,
            -5.047940063288644e-16,
            -0.019648654711171838
          ],
          [
            -1.121832213851318e-15,
            -4.76463730463469e-16,
            -0.014733666853224598
          ],
          [
            -1.1873406642951906e-15,
            -4.713127712152153e-16,
            -0.009821139805954457
          ],
          [
            -7.942899616319552e-16,
            -2.1634028842665622e-16,
            -0.004910187024132339
          ],
          [
            -1.0372171320279828e-15,
            -4.4040701572569295e-16,
            1.922288004955974e-15
          ],
          [
            -5.759284601523798e-16,
            -2.5754796241268593e-17,
            0.004910187024132984
          ],
          [
            -7.77912849020987e-16,
            -1.9187323199745102e-15,
            0.009821139805955982
          ],
          [
            -8.024785179374392e-16,
            -5.331242821942599e-16,
            0.014733666853226123
          ],
          [
            -1.2501195959705687e-15,
            -1.375306119283743e-15,
            0.01964865471117627
          ],
          [
            -1.54763714173649e-15,
            -6.95379498514252e-16,
            0.02456709363404496
          ],
          [
            -1.6759245238557405e-15,
            5.228223636977525e-16,
            0.029490089092613348
          ],
          [
            -6.987568047346409e-16,
            -1.2362302195808925e-15,
            0.03441884522497801
          ],
          [
            -8.297737056223861e-16,
            5.51152639563148e-16,
            0.03935464848505191
          ]
        ],
        "unwrapped_reduced_polarization": [
          [
            -8.352327431593756e-16,
            -1.192447065970736e-15,
            -0.0393546484850492
          ],
          [
            -2.7841091438645855e-16,
            -8.112760815999607e-16,
            -0.03441884522497434
          ],
          [
            -4.612886718756028e-16,
            -3.3738783076061864e-16,
            -0.02949008909261056
          ],
          [
            -7.615357364100189e-16,
            -4.919166082082302e-16,
            -0.02456709363404198
          ],
          [
            -6.687320982811992e-16,
            -5.047940063288644e-16,
            -0.019648654711171838
          ],
          [
            -1.121832213851318e-15,
            -4.76463730463469e-16,
            -0.014733666853224598
          ],
          [
            -1.1873406642951906e-15,
            -4.713127712152153e-16,
            -0.009821139805954457
          ],
          [
            -7.942899616319552e-16,
            -2.163402884266562e-16,
            -0.004910187024132339
          ],
          [
            -1.0372171320279828e-15,
            -4.4040701572569295e-16,
            1.9220736113823023e-15
          ],
          [
            -5.759284601523798e-16,
            -2.575479624126859e-17,
            0.004910187024132984
          ],
          [
            -7.77912849020987e-16,
            -1.9187323199745102e-15,
            0.009821139805955982
          ],
          [
            -8.024785179374392e-16,
            -5.331242821942599e-16,
            0.014733666853226123
          ],
          [
            -1.2501195959705687e-15,
            -1.375306119283743e-15,
            0.01964865471117627
          ],
          [
            -1.54763714173649e-15,
            -6.95379498514252e-16,
            0.02456709363404496
          ],
          [
            -1.6759245238557405e-15,
            5.228223636977526e-16,
            0.029490089092613348
          ],
          [
            -6.987568047346409e-16,
            -1.2362302195808925e-15,
            0.03441884522497801
          ],
          [
            -8.297737056223861e-16,
            5.511526395631482e-16,
            0.03935464848505191
          ]
        ],
        "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": [
          [
            -8.326672684688674e-16,
            -1.1657341758564144e-15,
            -0.039354648485049215
          ],
          [
            -2.7755575615628914e-16,
            -8.326672684688674e-16,
            -0.03441884522497435
          ],
          [
            -4.440892098500626e-16,
            -3.3306690738754696e-16,
            -0.029490089092610583
          ],
          [
            -7.771561172376096e-16,
            -4.996003610813204e-16,
            -0.02456709363404197
          ],
          [
            -6.661338147750939e-16,
            -4.996003610813204e-16,
            -0.01964865471117183
          ],
          [
            -1.1102230246251565e-15,
            -4.996003610813204e-16,
            -0.01473366685322458
          ],
          [
            -1.1657341758564144e-15,
            -4.440892098500626e-16,
            -0.009821139805954449
          ],
          [
            -7.771561172376096e-16,
            -2.220446049250313e-16,
            -0.0049101870241323176
          ],
          [
            -1.0547118733938987e-15,
            -4.440892098500626e-16,
            1.887379141862766e-15
          ],
          [
            -5.551115123125783e-16,
            0.0,
            0.004910187024133039
          ],
          [
            -7.771561172376096e-16,
            -1.942890293094024e-15,
            0.009821139805956003
          ],
          [
            -7.771561172376096e-16,
            -5.551115123125783e-16,
            0.01473366685322608
          ],
          [
            -1.27675647831893e-15,
            -1.3877787807814457e-15,
            0.019648654711176272
          ],
          [
            -1.5543122344752192e-15,
            -7.216449660063518e-16,
            0.024567093634044967
          ],
          [
            -1.6653345369377348e-15,
            5.551115123125783e-16,
            0.029490089092613303
          ],
          [
            -7.216449660063518e-16,
            -1.2212453270876722e-15,
            0.03441884522497807
          ],
          [
            -8.326672684688674e-16,
            5.551115123125783e-16,
            0.03935464848505188
          ]
        ]
      },
      "incoming_structure_ids": [
        "incoming_00_000",
        "incoming_00_001",
        "incoming_00_002",
        "incoming_00_003",
        "incoming_00_004",
        "incoming_00_005",
        "incoming_00_006",
        "incoming_00_007",
        "incoming_00_008"
      ],
      "reflected_structure_ids": [
        "reflected_00_001",
        "reflected_00_002",
        "reflected_00_003",
        "reflected_00_004",
        "reflected_00_005",
        "reflected_00_006",
        "reflected_00_007",
        "reflected_00_008"
      ]
    },
    {
      "orbit_id": 1,
      "formal_class": [
        0.0,
        0.0,
        0.5
      ],
      "formal_classes_in_orbit": [
        [
          0.0,
          0.0,
          0.5
        ]
      ],
      "target_reduced_polarization": [
        0.0,
        0.0,
        -0.5
      ],
      "bec_backprojection": {
        "converged_to_target": true,
        "history": [
          {
            "iteration": 0,
            "reduced_polarization": [
              -3.138946583768895e-16,
              -4.790392100875958e-16,
              -0.039354648485049284
            ],
            "branch_aligned_reduced_polarization": [
              -3.138946583768895e-16,
              -4.790392100875958e-16,
              -0.03935464848504927
            ],
            "target_residual": 0.46064535151495073,
            "energy_eV": -147.0307900367688,
            "max_atomic_step_A": 0.12000000000000001,
            "max_log_strain_component": 0.0012079943421458212,
            "step_scale": 0.8602701116571638,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 0.12178817011209728,
            "cell_principal_stretches": [
              1.0007381134307705,
              1.0000350512133511,
              0.9987927349893139
            ],
            "cell_volume_ratio": 0.9995649920593501,
            "cell_rmsd_from_input_A": 0.006620119236066701
          },
          {
            "iteration": 1,
            "reduced_polarization": [
              -7.166302305612699e-15,
              -9.987748691034562e-16,
              -0.4284624334038859
            ],
            "branch_aligned_reduced_polarization": [
              -7.166302305612699e-15,
              -9.987748691034562e-16,
              -0.4284624334038859
            ],
            "target_residual": 0.0715375665961141,
            "energy_eV": -145.8065419967562,
            "max_atomic_step_A": 0.021650225841516123,
            "max_log_strain_component": 0.0002450878713474458,
            "step_scale": 1.0,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 0.12178817011209728,
            "cell_principal_stretches": [
              1.000887934449244,
              1.000042162842991,
              0.9985479729993009
            ],
            "cell_volume_ratio": 0.9994767571486343,
            "cell_rmsd_from_input_A": 0.00796343238049416
          },
          {
            "iteration": 2,
            "reduced_polarization": [
              -2.239396565968707e-15,
              -1.882465003261362e-15,
              -0.4992591198195712
            ],
            "branch_aligned_reduced_polarization": [
              -2.239396565968707e-15,
              -1.882465003261362e-15,
              -0.4992591198195712
            ],
            "target_residual": 0.0007408801804287823,
            "energy_eV": -145.31149053983256
          }
        ],
        "iterations": 2
      },
      "parent": {
        "candidate_id": "bec_projection_01",
        "source": "MACEField_BEC_backprojection",
        "spacegroup": "Pba2",
        "spacegroup_number": 32,
        "pointgroup": "mm2",
        "has_inversion": false,
        "is_polar_point_group": true,
        "nonpolar_parent_hypothesis": false,
        "symmetry_tolerance_A": null,
        "target_reduced_polarization": [
          0.0,
          0.0,
          -0.5
        ],
        "formal_class": [
          0.0,
          0.0,
          0.5
        ],
        "target_residual": 0.0007408801804287823,
        "parent_symmetrization_rmsd_A": 0.09981242265326641,
        "parent_cell_rmsd_A": 0.00796343238049416,
        "energy_eV": -145.31149053983256,
        "reduced_polarization": [
          -2.239396565968707e-15,
          -1.882465003261362e-15,
          -0.4992591198195712
        ],
        "cartesian_polarization_e_A2": [
          3.1905992636188544e-17,
          -2.3919941784735365e-17,
          -0.004551619699383095
        ],
        "ranking_score": 0.6032850411092475
      },
      "branch_status": "awaiting_branch_sampling"
    },
    {
      "orbit_id": 2,
      "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": [
              -3.138946583768895e-16,
              -4.790392100875958e-16,
              -0.039354648485049284
            ],
            "branch_aligned_reduced_polarization": [
              -3.138946583768895e-16,
              -4.996003610813204e-16,
              -0.039354648485049284
            ],
            "target_residual": 0.5015463970136574,
            "energy_eV": -147.0307900367688,
            "max_atomic_step_A": 0.12,
            "max_log_strain_component": 0.00028365869280101686,
            "step_scale": 0.6305509681815392,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 0.12178817011209728,
            "cell_principal_stretches": [
              1.0003230934696823,
              0.9999537972791044,
              0.9997504398742886
            ],
            "cell_volume_ratio": 1.0000272465981128,
            "cell_rmsd_from_input_A": 0.00208124718428228
          },
          {
            "iteration": 1,
            "reduced_polarization": [
              4.608415793847115e-15,
              -0.2959707077686083,
              -0.012076097798056275
            ],
            "branch_aligned_reduced_polarization": [
              4.608415793847115e-15,
              -0.2959707077686083,
              -0.012076097798056275
            ],
            "target_residual": 0.20438636017716755,
            "energy_eV": -145.38292439582648,
            "max_atomic_step_A": 0.102826010850952,
            "max_log_strain_component": 0.00023560885927520302,
            "step_scale": 1.0,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 0.12178817011209728,
            "cell_principal_stretches": [
              1.0005706481154943,
              0.9999387786851591,
              0.999526952872964
            ],
            "cell_volume_ratio": 1.0000361037714312,
            "cell_rmsd_from_input_A": 0.003773904798637249
          },
          {
            "iteration": 2,
            "reduced_polarization": [
              1.2100000916358746e-14,
              -0.4829362332534983,
              0.0007176448569083293
            ],
            "branch_aligned_reduced_polarization": [
              1.2100000916358746e-14,
              -0.4829362332534983,
              0.0007176448569083293
            ],
            "target_residual": 0.017078850948458544,
            "energy_eV": -141.40016267192095,
            "max_atomic_step_A": 0.00979523544870922,
            "max_log_strain_component": 2.771351407617464e-05,
            "step_scale": 1.0,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 0.12178817011209728,
            "cell_principal_stretches": [
              1.0005956521984585,
              0.9999417545609859,
              0.9994972468403539
            ],
            "cell_volume_ratio": 1.0000343487402708,
            "cell_rmsd_from_input_A": 0.0039675334564321625
          },
          {
            "iteration": 3,
            "reduced_polarization": [
              -3.3419973443637213e-15,
              -0.49980796602328853,
              5.734172662618798e-05
            ],
            "branch_aligned_reduced_polarization": [
              -3.3419973443637213e-15,
              -0.49980796602328853,
              5.734172662618798e-05
            ],
            "target_residual": 0.000200412379418273,
            "energy_eV": -140.9639295328011
          }
        ],
        "iterations": 3
      },
      "parent": {
        "candidate_id": "bec_projection_02",
        "source": "MACEField_BEC_backprojection",
        "spacegroup": "Pc",
        "spacegroup_number": 7,
        "pointgroup": "m",
        "has_inversion": false,
        "is_polar_point_group": true,
        "nonpolar_parent_hypothesis": false,
        "symmetry_tolerance_A": null,
        "target_reduced_polarization": [
          0.0,
          -0.5,
          0.0
        ],
        "formal_class": [
          0.0,
          0.5,
          0.0
        ],
        "target_residual": 0.000200412379418273,
        "parent_symmetrization_rmsd_A": 0.16113434969095072,
        "parent_cell_rmsd_A": 0.0039675334564321625,
        "energy_eV": -140.9639295328011,
        "reduced_polarization": [
          -3.3419973443637213e-15,
          -0.49980796602328853,
          5.734172662618798e-05
        ],
        "cartesian_polarization_e_A2": [
          -1.5174583660320745e-16,
          -0.007411181834382396,
          -3.530624855448826e-06
        ],
        "ranking_score": 0.6625270578138953
      },
      "branch_status": "awaiting_branch_sampling"
    },
    {
      "orbit_id": 3,
      "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": [
              -3.138946583768895e-16,
              -4.790392100875958e-16,
              -0.039354648485049284
            ],
            "branch_aligned_reduced_polarization": [
              -3.3306690738754696e-16,
              -4.790392100875958e-16,
              -0.039354648485049284
            ],
            "target_residual": 0.5015463970136577,
            "energy_eV": -147.0307900367688,
            "max_atomic_step_A": 0.12,
            "max_log_strain_component": 6.959207175605678e-05,
            "step_scale": 0.5800966469551263,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 0.12178817011209728,
            "cell_principal_stretches": [
              1.0001024947823474,
              0.9999979807509806,
              0.9999245986498887
            ],
            "cell_volume_ratio": 1.0000250664002792,
            "cell_rmsd_from_input_A": 0.0006040973491782787
          },
          {
            "iteration": 1,
            "reduced_polarization": [
              -0.2873396918048548,
              -8.337365446149333e-15,
              -0.017212823845738898
            ],
            "branch_aligned_reduced_polarization": [
              -0.2873396918048548,
              -8.337365446149333e-15,
              -0.017212823845738898
            ],
            "target_residual": 0.2133557779540985,
            "energy_eV": -145.52552232603728,
            "max_atomic_step_A": 0.09110473912016166,
            "max_log_strain_component": 5.9439449912658905e-05,
            "step_scale": 1.0,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 0.12178817011209728,
            "cell_principal_stretches": [
              1.000185859328774,
              0.99999625608863,
              0.9998643863962204
            ],
            "cell_volume_ratio": 1.0000464764205501,
            "cell_rmsd_from_input_A": 0.0010917012856097778
          },
          {
            "iteration": 2,
            "reduced_polarization": [
              -0.48814710419368684,
              -1.4973547162627112e-14,
              -0.001185351634464634
            ],
            "branch_aligned_reduced_polarization": [
              -0.48814710419368684,
              -1.4973547162627112e-14,
              -0.001185351634464634
            ],
            "target_residual": 0.011912019035102488,
            "energy_eV": -142.51961335817572,
            "max_atomic_step_A": 0.005571535139028207,
            "max_log_strain_component": 4.3668699888111616e-06,
            "step_scale": 1.0,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 0.12178817011209728,
            "cell_principal_stretches": [
              1.0001919369769938,
              0.9999961293820523,
              0.9998600100912397
            ],
            "cell_volume_ratio": 1.0000480493800827,
            "cell_rmsd_from_input_A": 0.0011272043214164509
          },
          {
            "iteration": 3,
            "reduced_polarization": [
              -0.49994901624486887,
              3.572629138818636e-15,
              6.423117564034776e-06
            ],
            "branch_aligned_reduced_polarization": [
              -0.49994901624486887,
              3.572629138818636e-15,
              6.423117564034776e-06
            ],
            "target_residual": 5.1386766063961526e-05,
            "energy_eV": -142.30148453337915
          }
        ],
        "iterations": 3
      },
      "parent": {
        "candidate_id": "bec_projection_03",
        "source": "MACEField_BEC_backprojection",
        "spacegroup": "Pc",
        "spacegroup_number": 7,
        "pointgroup": "m",
        "has_inversion": false,
        "is_polar_point_group": true,
        "nonpolar_parent_hypothesis": false,
        "symmetry_tolerance_A": null,
        "target_reduced_polarization": [
          -0.5,
          0.0,
          0.0
        ],
        "formal_class": [
          0.5,
          0.0,
          0.0
        ],
        "target_residual": 5.1386766063961526e-05,
        "parent_symmetrization_rmsd_A": 0.16998048343698768,
        "parent_cell_rmsd_A": 0.0011272043214164509,
        "energy_eV": -142.30148453337915,
        "reduced_polarization": [
          -0.49994901624486887,
          3.572629138818636e-15,
          6.423117564034776e-06
        ],
        "cartesian_polarization_e_A2": [
          -0.006994261526663972,
          2.755713993901983e-16,
          -8.261725722540162e-07
        ],
        "ranking_score": 0.6703650580494698
      },
      "branch_status": "awaiting_branch_sampling"
    },
    {
      "orbit_id": 4,
      "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": [
              -3.138946583768895e-16,
              -4.790392100875958e-16,
              -0.039354648485049284
            ],
            "branch_aligned_reduced_polarization": [
              -3.138946583768895e-16,
              -4.996003610813204e-16,
              -0.03935464848504927
            ],
            "target_residual": 0.6798486154081157,
            "energy_eV": -147.0307900367688,
            "max_atomic_step_A": 0.12,
            "max_log_strain_component": 0.000739112226745089,
            "step_scale": 0.5263569005673475,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 0.12178817011209728,
            "cell_principal_stretches": [
              1.0004515505741154,
              1.0000891436779589,
              0.9991935191837875
            ],
            "cell_volume_ratio": 0.9997338175967357,
            "cell_rmsd_from_input_A": 0.004393033749915454
          },
          {
            "iteration": 1,
            "reduced_polarization": [
              2.1887050388014312e-14,
              -0.2512834670140718,
              -0.2726355652980879
            ],
            "branch_aligned_reduced_polarization": [
              2.1887050388014312e-14,
              -0.2512834670140718,
              -0.2726355652980879
            ],
            "target_residual": 0.336978485882794,
            "energy_eV": -145.4385551418261,
            "max_atomic_step_A": 0.12,
            "max_log_strain_component": 0.0006943925564397223,
            "step_scale": 0.8935112286955457,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 0.12178817011209728,
            "cell_principal_stretches": [
              1.0008759660374813,
              1.000182531088626,
              0.9984268134468938
            ],
            "cell_volume_ratio": 0.9994838049990518,
            "cell_rmsd_from_input_A": 0.008570428964671733
          },
          {
            "iteration": 2,
            "reduced_polarization": [
              3.190601407957617e-14,
              -0.44594002235138475,
              -0.4570941791544238
            ],
            "branch_aligned_reduced_polarization": [
              3.190601407957617e-14,
              -0.44594002235138475,
              -0.4570941791544238
            ],
            "target_residual": 0.06901732134617702,
            "energy_eV": -140.13210002591552,
            "max_atomic_step_A": 0.026784321691787644,
            "max_log_strain_component": 0.00021615417538625167,
            "step_scale": 1.0,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 0.12178817011209728,
            "cell_principal_stretches": [
              1.0010081170627723,
              1.0002199737808584,
              0.9981799155506026
            ],
            "cell_volume_ratio": 0.999405992520887,
            "cell_rmsd_from_input_A": 0.00991496611268682
          },
          {
            "iteration": 3,
            "reduced_polarization": [
              1.3354729889268178e-14,
              -0.4986482203065045,
              -0.4990828519757111
            ],
            "branch_aligned_reduced_polarization": [
              1.3354729889268178e-14,
              -0.4986482203065045,
              -0.4990828519757111
            ],
            "target_residual": 0.001633544868745189,
            "energy_eV": -138.31146741722216,
            "max_atomic_step_A": 0.000634257955446595,
            "max_log_strain_component": 5.1965813341758785e-06,
            "step_scale": 1.0,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 0.12178817011209728,
            "cell_principal_stretches": [
              1.0010112943318423,
              1.0002210315332762,
              0.9981738233587578
            ],
            "cell_volume_ratio": 0.9994041218989024,
            "cell_rmsd_from_input_A": 0.009948126828116376
          },
          {
            "iteration": 4,
            "reduced_polarization": [
              -7.262658862422507e-16,
              -0.49999733546165187,
              -0.4999978419971588
            ],
            "branch_aligned_reduced_polarization": [
              -7.262658862422507e-16,
              -0.49999733546165187,
              -0.4999978419971588
            ],
            "target_residual": 3.42881041635235e-06,
            "energy_eV": -138.26594398729173
          }
        ],
        "iterations": 4
      },
      "parent": {
        "candidate_id": "bec_projection_04",
        "source": "MACEField_BEC_backprojection",
        "spacegroup": "Pc",
        "spacegroup_number": 7,
        "pointgroup": "m",
        "has_inversion": false,
        "is_polar_point_group": true,
        "nonpolar_parent_hypothesis": false,
        "symmetry_tolerance_A": null,
        "target_reduced_polarization": [
          0.0,
          -0.5,
          -0.5
        ],
        "formal_class": [
          0.0,
          0.5,
          0.5
        ],
        "target_residual": 3.42881041635235e-06,
        "parent_symmetrization_rmsd_A": 0.1989311244706572,
        "parent_cell_rmsd_A": 0.009948126828116376,
        "energy_eV": -138.26594398729173,
        "reduced_polarization": [
          -7.262658862422507e-16,
          -0.49999733546165187,
          -0.4999978419971588
        ],
        "cartesian_polarization_e_A2": [
          -4.9079568739833525e-16,
          -0.007421640702793932,
          -0.004561989599305948
        ],
        "ranking_score": 0.701425013798519
      },
      "branch_status": "awaiting_branch_sampling"
    },
    {
      "orbit_id": 5,
      "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": [
              -3.138946583768895e-16,
              -4.790392100875958e-16,
              -0.039354648485049284
            ],
            "branch_aligned_reduced_polarization": [
              -3.3306690738754696e-16,
              -4.790392100875958e-16,
              -0.03935464848504927
            ],
            "target_residual": 0.6798486154081158,
            "energy_eV": -147.0307900367688,
            "max_atomic_step_A": 0.12,
            "max_log_strain_component": 0.0006737014828021901,
            "step_scale": 0.47977480491258157,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 0.12178817011209728,
            "cell_principal_stretches": [
              1.0004145801622053,
              1.0000195479982836,
              0.9993235290494322
            ],
            "cell_volume_ratio": 0.9997573716335616,
            "cell_rmsd_from_input_A": 0.003712171051818995
          },
          {
            "iteration": 1,
            "reduced_polarization": [
              -0.23841670091147482,
              -1.0328154951973952e-14,
              -0.2557368503047308
            ],
            "branch_aligned_reduced_polarization": [
              -0.23841670091147482,
              -1.0328154951973952e-14,
              -0.2557368503047308
            ],
            "target_residual": 0.3578970643370665,
            "energy_eV": -145.59936432353402,
            "max_atomic_step_A": 0.12,
            "max_log_strain_component": 0.0007241655163692527,
            "step_scale": 0.9043112114026314,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 0.12178817011209728,
            "cell_principal_stretches": [
              1.0008601113077427,
              1.0000405606778147,
              0.9985971913314442
            ],
            "cell_volume_ratio": 0.9994966346842906,
            "cell_rmsd_from_input_A": 0.0077008918262070165
          },
          {
            "iteration": 2,
            "reduced_polarization": [
              -0.46057394810665847,
              -1.7925504476867696e-14,
              -0.45992186585288364
            ],
            "branch_aligned_reduced_polarization": [
              -0.46057394810665847,
              -1.7925504476867696e-14,
              -0.45992186585288364
            ],
            "target_residual": 0.05621983995539932,
            "energy_eV": -140.95300987342023,
            "max_atomic_step_A": 0.022039296008664142,
            "max_log_strain_component": 0.0001700780025019447,
            "step_scale": 1.0,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 0.12178817011209728,
            "cell_principal_stretches": [
              1.0009646843624684,
              1.0000454957939533,
              0.9984267729558683
            ],
            "cell_volume_ratio": 0.9994354076895822,
            "cell_rmsd_from_input_A": 0.008637126985759136
          },
          {
            "iteration": 3,
            "reduced_polarization": [
              -0.49946080171883617,
              -4.680438833371857e-15,
              -0.4995002048152679
            ],
            "branch_aligned_reduced_polarization": [
              -0.49946080171883617,
              -4.680438833371857e-15,
              -0.4995002048152679
            ],
            "target_residual": 0.000735207462619507,
            "energy_eV": -139.886809423743
          }
        ],
        "iterations": 3
      },
      "parent": {
        "candidate_id": "bec_projection_05",
        "source": "MACEField_BEC_backprojection",
        "spacegroup": "Pc",
        "spacegroup_number": 7,
        "pointgroup": "m",
        "has_inversion": false,
        "is_polar_point_group": true,
        "nonpolar_parent_hypothesis": false,
        "symmetry_tolerance_A": null,
        "target_reduced_polarization": [
          -0.5,
          0.0,
          -0.5
        ],
        "formal_class": [
          0.5,
          0.0,
          0.5
        ],
        "target_residual": 0.000735207462619507,
        "parent_symmetrization_rmsd_A": 0.20167503272301288,
        "parent_cell_rmsd_A": 0.008637126985759136,
        "energy_eV": -139.886809423743,
        "reduced_polarization": [
          -0.49946080171883617,
          -4.680438833371857e-15,
          -0.4995002048152679
        ],
        "cartesian_polarization_e_A2": [
          -0.006999569931292761,
          1.5821823729240446e-16,
          -0.004554381201173258
        ],
        "ranking_score": 0.7053047293946917
      },
      "branch_status": "awaiting_branch_sampling"
    },
    {
      "orbit_id": 6,
      "formal_class": [
        0.5,
        0.5,
        0.0
      ],
      "formal_classes_in_orbit": [
        [
          0.5,
          0.5,
          0.0
        ]
      ],
      "target_reduced_polarization": [
        -0.5,
        -0.5,
        0.0
      ],
      "bec_backprojection": {
        "converged_to_target": true,
        "history": [
          {
            "iteration": 0,
            "reduced_polarization": [
              -3.138946583768895e-16,
              -4.790392100875958e-16,
              -0.039354648485049284
            ],
            "branch_aligned_reduced_polarization": [
              -3.3306690738754696e-16,
              -4.996003610813204e-16,
              -0.039354648485049284
            ],
            "target_residual": 0.7082010931630796,
            "energy_eV": -147.0307900367688,
            "max_atomic_step_A": 0.11999999999999998,
            "max_log_strain_component": 0.00017224417600100392,
            "step_scale": 0.38288525863231865,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 0.12178817011209728,
            "cell_principal_stretches": [
              1.0002013807920502,
              0.9999737983549531,
              0.9998413985938177
            ],
            "cell_volume_ratio": 1.000016544681491,
            "cell_rmsd_from_input_A": 0.0013010278337907647
          },
          {
            "iteration": 1,
            "reduced_polarization": [
              -0.18765430417719264,
              -0.18546481347028004,
              -0.023433598423682398
            ],
            "branch_aligned_reduced_polarization": [
              -0.18765430417719264,
              -0.18546481347028004,
              -0.023433598423682398
            ],
            "target_residual": 0.44389340026565144,
            "energy_eV": -145.7698595416259,
            "max_atomic_step_A": 0.12,
            "max_log_strain_component": 0.00018658777569982875,
            "step_scale": 0.5829722190562653,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 0.12178817011209728,
            "cell_principal_stretches": [
              1.000412846127898,
              0.999951922164892,
              0.9996656246340245
            ],
            "cell_volume_ratio": 1.000030251115172,
            "cell_rmsd_from_input_A": 0.002695748122266133
          },
          {
            "iteration": 2,
            "reduced_polarization": [
              -0.3565179383897854,
              -0.3467931784061032,
              -0.01074803986046865
            ],
            "branch_aligned_reduced_polarization": [
              -0.3565179383897854,
              -0.3467931784061032,
              -0.01074803986046865
            ],
            "target_residual": 0.21017838268400432,
            "energy_eV": -141.17855177997998,
            "max_atomic_step_A": 0.1118470372347902,
            "max_log_strain_component": 0.00023587212931457097,
            "step_scale": 1.0,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 0.12178817011209728,
            "cell_principal_stretches": [
              1.0006715723609216,
              0.9999306425264773,
              0.999441382907427
            ],
            "cell_volume_ratio": 1.000043214834754,
            "cell_rmsd_from_input_A": 0.004433179940721902
          },
          {
            "iteration": 3,
            "reduced_polarization": [
              -0.49236607552938827,
              -0.4849982750557143,
              -7.110684312714704e-05
            ],
            "branch_aligned_reduced_polarization": [
              -0.49236607552938827,
              -0.4849982750557143,
              -7.110684312714704e-05
            ],
            "target_residual": 0.016832516458038824,
            "energy_eV": -132.47163962802824,
            "max_atomic_step_A": 0.009367622005478615,
            "max_log_strain_component": 2.9353039101643386e-05,
            "step_scale": 1.0,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 0.12178817011209728,
            "cell_principal_stretches": [
              1.0007007126795602,
              0.9999307987297537,
              0.9994119281306132
            ],
            "cell_volume_ratio": 1.0000430197041406,
            "cell_rmsd_from_input_A": 0.004642535485661896
          },
          {
            "iteration": 4,
            "reduced_polarization": [
              -0.4999798051189816,
              -0.4999815032228372,
              6.341812861818568e-05
            ],
            "branch_aligned_reduced_polarization": [
              -0.4999798051189816,
              -0.4999815032228372,
              6.341812861818568e-05
            ],
            "target_residual": 6.907838317585876e-05,
            "energy_eV": -131.78039843276684
          }
        ],
        "iterations": 4
      },
      "parent": {
        "candidate_id": "bec_projection_06",
        "source": "MACEField_BEC_backprojection",
        "spacegroup": "P1",
        "spacegroup_number": 1,
        "pointgroup": "1",
        "has_inversion": false,
        "is_polar_point_group": true,
        "nonpolar_parent_hypothesis": false,
        "symmetry_tolerance_A": null,
        "target_reduced_polarization": [
          -0.5,
          -0.5,
          0.0
        ],
        "formal_class": [
          0.5,
          0.5,
          0.0
        ],
        "target_residual": 6.907838317585876e-05,
        "parent_symmetrization_rmsd_A": 0.25907361809114743,
        "parent_cell_rmsd_A": 0.004642535485661896,
        "energy_eV": -131.78039843276684,
        "reduced_polarization": [
          -0.4999798051189816,
          -0.4999815032228372,
          6.341812861818568e-05
        ],
        "cartesian_polarization_e_A2": [
          -0.006994787355979234,
          -0.007413686195923092,
          -5.073566325851863e-06
        ],
        "ranking_score": 0.7603724087289145
      },
      "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": [
              -3.138946583768895e-16,
              -4.790392100875958e-16,
              -0.039354648485049284
            ],
            "branch_aligned_reduced_polarization": [
              -3.3306690738754696e-16,
              -4.996003610813204e-16,
              -0.03935464848504927
            ],
            "target_residual": 0.8439159554554776,
            "energy_eV": -147.0307900367688,
            "max_atomic_step_A": 0.12,
            "max_log_strain_component": 0.0004907027023475183,
            "step_scale": 0.34945268683645386,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 0.12178817011209728,
            "cell_principal_stretches": [
              1.0003022143635991,
              1.0000586457860563,
              0.999462587468642
            ],
            "cell_volume_ratio": 0.9998232714016051,
            "cell_rmsd_from_input_A": 0.002930266490109606
          },
          {
            "iteration": 1,
            "reduced_polarization": [
              -0.17177851875100966,
              -0.17000433706524135,
              -0.19548901324081044
            ],
            "branch_aligned_reduced_polarization": [
              -0.1717785187510097,
              -0.17000433706524132,
              -0.19548901324081047
            ],
            "target_residual": 0.5561954866466353,
            "energy_eV": -145.77815454292644,
            "max_atomic_step_A": 0.11999999999999998,
            "max_log_strain_component": 0.0005189934633508445,
            "step_scale": 0.5152099017207188,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 0.12178817011209728,
            "cell_principal_stretches": [
              1.000621886274658,
              1.0001224301602298,
              0.9988928193595183
            ],
            "cell_volume_ratio": 0.9996363877549971,
            "cell_rmsd_from_input_A": 0.006037955881893467
          },
          {
            "iteration": 2,
            "reduced_polarization": [
              -0.3291785870525888,
              -0.32265763311141993,
              -0.3399335992963281
            ],
            "branch_aligned_reduced_polarization": [
              -0.3291785870525888,
              -0.32265763311141993,
              -0.3399335992963281
            ],
            "target_residual": 0.2936860957710157,
            "energy_eV": -141.21288809906582,
            "max_atomic_step_A": 0.12,
            "max_log_strain_component": 0.0005859347430144743,
            "step_scale": 0.8724320080007814,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 0.12178817011209728,
            "cell_principal_stretches": [
              1.0009832071169669,
              1.0002155926158496,
              0.9982285535747952
            ],
            "cell_volume_ratio": 0.9994254412948077,
            "cell_rmsd_from_input_A": 0.009659720511620125
          },
          {
            "iteration": 3,
            "reduced_polarization": [
              -0.4672441910192771,
              -0.45768517825537147,
              -0.45647454885995087
            ],
            "branch_aligned_reduced_polarization": [
              -0.4672441910192771,
              -0.45768517825537147,
              -0.45647454885995087
            ],
            "target_residual": 0.06897790992923819,
            "energy_eV": -132.04182126436774,
            "max_atomic_step_A": 0.03691909319363952,
            "max_log_strain_component": 0.00028013164877582953,
            "step_scale": 1.0,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 0.12178817011209728,
            "cell_principal_stretches": [
              1.0011548314082963,
              1.0002478453908885,
              0.9979245536276866
            ],
            "cell_volume_ratio": 0.9993246048720059,
            "cell_rmsd_from_input_A": 0.011318249438284014
          },
          {
            "iteration": 4,
            "reduced_polarization": [
              -0.4993125783063892,
              -0.49917344824558213,
              -0.49954252426575957
            ],
            "branch_aligned_reduced_polarization": [
              -0.4993125783063892,
              -0.49917344824558213,
              -0.49954252426575957
            ],
            "target_residual": 0.0011683408898933664,
            "energy_eV": -129.31316642110414,
            "max_atomic_step_A": 0.0004211175109916656,
            "max_log_strain_component": 0.0001335431762547523,
            "step_scale": 1.0,
            "strain_jacobian_refreshed": true,
            "strain_jacobian_frobenius_norm": 3.3662294220258815,
            "cell_principal_stretches": [
              1.0011090925253432,
              1.0001088797747026,
              0.9979083200613897
            ],
            "cell_volume_ratio": 0.9991238652583677,
            "cell_rmsd_from_input_A": 0.010965618093133966
          },
          {
            "iteration": 5,
            "reduced_polarization": [
              -0.4999997904599428,
              -0.49999983829450495,
              -0.4999997779702946
            ],
            "branch_aligned_reduced_polarization": [
              -0.4999997904599428,
              -0.49999983829450495,
              -0.4999997779702946
            ],
            "target_residual": 3.4547488009679596e-07,
            "energy_eV": -129.26619526470412
          }
        ],
        "iterations": 5
      },
      "parent": {
        "candidate_id": "bec_projection_07",
        "source": "MACEField_BEC_backprojection",
        "spacegroup": "P1",
        "spacegroup_number": 1,
        "pointgroup": "1",
        "has_inversion": false,
        "is_polar_point_group": true,
        "nonpolar_parent_hypothesis": false,
        "symmetry_tolerance_A": null,
        "target_reduced_polarization": [
          -0.5,
          -0.5,
          -0.5
        ],
        "formal_class": [
          0.5,
          0.5,
          0.5
        ],
        "target_residual": 3.4547488009679596e-07,
        "parent_symmetrization_rmsd_A": 0.2891875317015818,
        "parent_cell_rmsd_A": 0.010965618093133966,
        "energy_eV": -129.26619526470412,
        "reduced_polarization": [
          -0.4999997904599428,
          -0.49999983829450495,
          -0.4999997779702946
        ],
        "cartesian_polarization_e_A2": [
          -0.007009151178245136,
          -0.007422175763960916,
          -0.004562705135122509
        ],
        "ranking_score": 0.7919296271746255
      },
      "branch_status": "awaiting_branch_sampling"
    }
  ],
  "sampled_polarization_branches": [
    {
      "orbit_id": 0,
      "candidate_id": "inversion_parent_endpoint_00",
      "formal_class": [
        0.0,
        0.0,
        0.0
      ],
      "construction": "MACEField-BEC-parent plus variable-cell P-N-P path and symmetric log-strain continuation beyond both polar endpoints",
      "geometry_diagnostics": {
        "collision_aware": false,
        "permutations_tested": 1,
        "selected_order": [
          0,
          1,
          2,
          3,
          4,
          5,
          6,
          7,
          8,
          9,
          10,
          11,
          12,
          13,
          14,
          15,
          16,
          17,
          18,
          19,
          20,
          21,
          22,
          23,
          24,
          25,
          26,
          27,
          28,
          29,
          30,
          31,
          32,
          33,
          34,
          35
        ],
        "endpoint_rmsd_A": 0.04295456241051995,
        "minimum_distance_A_by_image": [
          1.144017464826621,
          1.1440100140338274,
          1.1440035566408202,
          1.143998092664422,
          1.143993622118867,
          1.1439901450158014,
          1.143987661364284,
          1.1439861711707853,
          1.1439856744391879
        ],
        "minimum_distance_A": 1.1439856744391879,
        "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": [
          726.7612350725592,
          726.7612350725592,
          726.7612350725592,
          726.7612350725592,
          726.7612350725592,
          726.7612350725592,
          726.7612350725592,
          726.7612350725592,
          726.7612350725592
        ],
        "cell_deformation_log_strain_norm": 0.0
      },
      "parent_reduced_polarization": [
        -1.0372171320279828e-15,
        -4.4040701572569295e-16,
        1.922288004955974e-15
      ],
      "incoming": {
        "reached": true,
        "construction": "variable_cell_linear_interpolation",
        "continuation_fractions": [
          0.0,
          0.125,
          0.25,
          0.375,
          0.5,
          0.625,
          0.75,
          0.875,
          1.0
        ],
        "energies_eV": [
          -147.0307900367688,
          -147.03284734042882,
          -147.03459607958976,
          -147.03604847411236,
          -147.037216632906,
          -147.03811182256524,
          -147.03874370420482,
          -147.0391196935474,
          -147.03924448737496
        ],
        "cartesian_polarizations_e_A2": [
          [
            -1.1686377490310821e-17,
            -1.768232933991474e-17,
            -0.0003591201418238796
          ],
          [
            -3.895459163436941e-18,
            -1.2030094475319964e-17,
            -0.00031407981151966563
          ],
          [
            -6.4542411629494404e-18,
            -5.0029916706886195e-18,
            -0.0002691037878628357
          ],
          [
            -1.0655226535283396e-17,
            -7.294438237416232e-18,
            -0.0002241803316680458
          ],
          [
            -9.356740147471082e-18,
            -7.485392117976866e-18,
            -0.0001792984549005723
          ],
          [
            -1.5696408982084142e-17,
            -7.065293580743471e-18,
            -0.00013444806988749798
          ],
          [
            -1.6612987608775187e-17,
            -6.988912028519217e-18,
            -8.962014033301318e-05
          ],
          [
            -1.1113515848628918e-17,
            -3.208025193418657e-18,
            -4.4806576309735636e-05
          ],
          [
            -1.451249492260821e-17,
            -6.5306227151736944e-18,
            1.754131640201001e-17
          ]
        ],
        "raw_reduced_polarization": [
          [
            -8.352327431593756e-16,
            -1.192447065970736e-15,
            -0.0393546484850492
          ],
          [
            -2.7841091438645855e-16,
            -8.112760815999607e-16,
            -0.03441884522497434
          ],
          [
            -4.612886718756028e-16,
            -3.373878307606186e-16,
            -0.02949008909261056
          ],
          [
            -7.615357364100189e-16,
            -4.919166082082302e-16,
            -0.02456709363404198
          ],
          [
            -6.687320982811992e-16,
            -5.047940063288644e-16,
            -0.019648654711171838
          ],
          [
            -1.121832213851318e-15,
            -4.76463730463469e-16,
            -0.014733666853224598
          ],
          [
            -1.1873406642951906e-15,
            -4.713127712152153e-16,
            -0.009821139805954457
          ],
          [
            -7.942899616319552e-16,
            -2.1634028842665622e-16,
            -0.004910187024132339
          ],
          [
            -1.0372171320279828e-15,
            -4.4040701572569295e-16,
            1.922288004955974e-15
          ]
        ],
        "unwrapped_reduced_polarization": [
          [
            -8.352327431593756e-16,
            -1.192447065970736e-15,
            -0.0393546484850492
          ],
          [
            -2.7841091438645855e-16,
            -8.112760815999607e-16,
            -0.03441884522497434
          ],
          [
            -4.612886718756028e-16,
            -3.3738783076061864e-16,
            -0.02949008909261056
          ],
          [
            -7.615357364100189e-16,
            -4.919166082082302e-16,
            -0.02456709363404198
          ],
          [
            -6.687320982811992e-16,
            -5.047940063288644e-16,
            -0.019648654711171838
          ],
          [
            -1.121832213851318e-15,
            -4.76463730463469e-16,
            -0.014733666853224598
          ],
          [
            -1.1873406642951906e-15,
            -4.713127712152153e-16,
            -0.009821139805954457
          ],
          [
            -7.942899616319552e-16,
            -2.163402884266562e-16,
            -0.004910187024132339
          ],
          [
            -1.0372171320279828e-15,
            -4.4040701572569295e-16,
            1.9220736113823023e-15
          ]
        ],
        "berry_integer_shifts": [
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ]
        ],
        "folded_reduced_polarization": [
          [
            -8.326672684688674e-16,
            -1.1657341758564144e-15,
            -0.039354648485049215
          ],
          [
            -2.7755575615628914e-16,
            -8.326672684688674e-16,
            -0.03441884522497435
          ],
          [
            -4.440892098500626e-16,
            -3.3306690738754696e-16,
            -0.029490089092610583
          ],
          [
            -7.771561172376096e-16,
            -4.996003610813204e-16,
            -0.02456709363404197
          ],
          [
            -6.661338147750939e-16,
            -4.996003610813204e-16,
            -0.01964865471117183
          ],
          [
            -1.1102230246251565e-15,
            -4.996003610813204e-16,
            -0.01473366685322458
          ],
          [
            -1.1657341758564144e-15,
            -4.440892098500626e-16,
            -0.009821139805954449
          ],
          [
            -7.771561172376096e-16,
            -2.220446049250313e-16,
            -0.0049101870241323176
          ],
          [
            -1.0547118733938987e-15,
            -4.440892098500626e-16,
            1.887379141862766e-15
          ]
        ]
      },
      "reflected": {
        "reached": true,
        "construction": "reflect_displacements_about_reconstructed_parent",
        "energies_eV": [
          -147.03924448737496,
          -147.03911969354735,
          -147.03874370420488,
          -147.03811182256524,
          -147.037216632906,
          -147.03604847411236,
          -147.0345960795897,
          -147.03284734042882,
          -147.0307900367688
        ],
        "cartesian_polarizations_e_A2": [
          [
            -1.2984863878123134e-18,
            -4.048222267885448e-18,
            1.0350883045917259e-17
          ],
          [
            -8.058253759658769e-18,
            -3.819077611212687e-19,
            4.480657630974152e-05
          ],
          [
            -1.0884371191956158e-17,
            -2.8452128203534515e-17,
            8.96201403330271e-05
          ],
          [
            -1.1228088176965299e-17,
            -7.905490655210262e-18,
            0.00013444806988751189
          ],
          [
            -1.7491375459354106e-17,
            -2.0393874443875747e-17,
            0.00017929845490061275
          ],
          [
            -2.1654170055575934e-17,
            -1.0311509550274255e-17,
            0.00022418033166807298
          ],
          [
            -2.3449136532845898e-17,
            7.752727550761754e-18,
            0.00026910378786286113
          ],
          [
            -9.776838684704479e-18,
            -1.8331572533820896e-17,
            0.0003140798115196991
          ],
          [
            -1.1609995938086567e-17,
            8.17282608799515e-18,
            0.0003591201418239043
          ]
        ],
        "raw_reduced_polarization": [
          [
            -9.280363812881949e-17,
            -2.730008401574471e-16,
            1.1343150003034503e-15
          ],
          [
            -5.759284601523798e-16,
            -2.5754796241268593e-17,
            0.004910187024132984
          ],
          [
            -7.77912849020987e-16,
            -1.9187323199745102e-15,
            0.009821139805955982
          ],
          [
            -8.024785179374392e-16,
            -5.331242821942599e-16,
            0.014733666853226123
          ],
          [
            -1.2501195959705687e-15,
            -1.375306119283743e-15,
            0.01964865471117627
          ],
          [
            -1.54763714173649e-15,
            -6.95379498514252e-16,
            0.02456709363404496
          ],
          [
            -1.6759245238557405e-15,
            5.228223636977525e-16,
            0.029490089092613348
          ],
          [
            -6.987568047346409e-16,
            -1.2362302195808925e-15,
            0.03441884522497801
          ],
          [
            -8.297737056223861e-16,
            5.51152639563148e-16,
            0.03935464848505191
          ]
        ],
        "unwrapped_reduced_polarization": [
          [
            -9.280363812881949e-17,
            -2.730008401574471e-16,
            1.1343150003034503e-15
          ],
          [
            -5.759284601523798e-16,
            -2.575479624126859e-17,
            0.004910187024132984
          ],
          [
            -7.77912849020987e-16,
            -1.9187323199745102e-15,
            0.009821139805955982
          ],
          [
            -8.024785179374392e-16,
            -5.331242821942599e-16,
            0.014733666853226123
          ],
          [
            -1.2501195959705687e-15,
            -1.375306119283743e-15,
            0.01964865471117627
          ],
          [
            -1.54763714173649e-15,
            -6.95379498514252e-16,
            0.02456709363404496
          ],
          [
            -1.6759245238557405e-15,
            5.228223636977526e-16,
            0.029490089092613348
          ],
          [
            -6.987568047346409e-16,
            -1.2362302195808925e-15,
            0.03441884522497801
          ],
          [
            -8.297737056223861e-16,
            5.511526395631482e-16,
            0.03935464848505191
          ]
        ],
        "gauge_integer_shift": [
          0,
          0,
          0
        ],
        "expected_opposite_endpoint_reduced_polarization": [
          -1.2392015208965901e-15,
          3.1163303451935005e-16,
          0.039354648485053045
        ],
        "actual_opposite_endpoint_branch_residual": 1.2328812074675005e-15
      },
      "pnp_branch": {
        "construction": "incoming_path_concatenated_with_parent_reflection",
        "reduced_polarization": [
          [
            -8.352327431593756e-16,
            -1.192447065970736e-15,
            -0.0393546484850492
          ],
          [
            -2.7841091438645855e-16,
            -8.112760815999607e-16,
            -0.03441884522497434
          ],
          [
            -4.612886718756028e-16,
            -3.373878307606186e-16,
            -0.02949008909261056
          ],
          [
            -7.615357364100189e-16,
            -4.919166082082302e-16,
            -0.02456709363404198
          ],
          [
            -6.687320982811992e-16,
            -5.047940063288644e-16,
            -0.019648654711171838
          ],
          [
            -1.121832213851318e-15,
            -4.76463730463469e-16,
            -0.014733666853224598
          ],
          [
            -1.1873406642951906e-15,
            -4.713127712152153e-16,
            -0.009821139805954457
          ],
          [
            -7.942899616319552e-16,
            -2.1634028842665622e-16,
            -0.004910187024132339
          ],
          [
            -1.0372171320279828e-15,
            -4.4040701572569295e-16,
            1.922288004955974e-15
          ],
          [
            -5.759284601523798e-16,
            -2.5754796241268593e-17,
            0.004910187024132984
          ],
          [
            -7.77912849020987e-16,
            -1.9187323199745102e-15,
            0.009821139805955982
          ],
          [
            -8.024785179374392e-16,
            -5.331242821942599e-16,
            0.014733666853226123
          ],
          [
            -1.2501195959705687e-15,
            -1.375306119283743e-15,
            0.01964865471117627
          ],
          [
            -1.54763714173649e-15,
            -6.95379498514252e-16,
            0.02456709363404496
          ],
          [
            -1.6759245238557405e-15,
            5.228223636977525e-16,
            0.029490089092613348
          ],
          [
            -6.987568047346409e-16,
            -1.2362302195808925e-15,
            0.03441884522497801
          ],
          [
            -8.297737056223861e-16,
            5.51152639563148e-16,
            0.03935464848505191
          ]
        ],
        "unwrapped_reduced_polarization": [
          [
            -8.352327431593756e-16,
            -1.192447065970736e-15,
            -0.0393546484850492
          ],
          [
            -2.7841091438645855e-16,
            -8.112760815999607e-16,
            -0.03441884522497434
          ],
          [
            -4.612886718756028e-16,
            -3.3738783076061864e-16,
            -0.02949008909261056
          ],
          [
            -7.615357364100189e-16,
            -4.919166082082302e-16,
            -0.02456709363404198
          ],
          [
            -6.687320982811992e-16,
            -5.047940063288644e-16,
            -0.019648654711171838
          ],
          [
            -1.121832213851318e-15,
            -4.76463730463469e-16,
            -0.014733666853224598
          ],
          [
            -1.1873406642951906e-15,
            -4.713127712152153e-16,
            -0.009821139805954457
          ],
          [
            -7.942899616319552e-16,
            -2.163402884266562e-16,
            -0.004910187024132339
          ],
          [
            -1.0372171320279828e-15,
            -4.4040701572569295e-16,
            1.9220736113823023e-15
          ],
          [
            -5.759284601523798e-16,
            -2.575479624126859e-17,
            0.004910187024132984
          ],
          [
            -7.77912849020987e-16,
            -1.9187323199745102e-15,
            0.009821139805955982
          ],
          [
            -8.024785179374392e-16,
            -5.331242821942599e-16,
            0.014733666853226123
          ],
          [
            -1.2501195959705687e-15,
            -1.375306119283743e-15,
            0.01964865471117627
          ],
          [
            -1.54763714173649e-15,
            -6.95379498514252e-16,
            0.02456709363404496
          ],
          [
            -1.6759245238557405e-15,
            5.228223636977526e-16,
            0.029490089092613348
          ],
          [
            -6.987568047346409e-16,
            -1.2362302195808925e-15,
            0.03441884522497801
          ],
          [
            -8.297737056223861e-16,
            5.511526395631482e-16,
            0.03935464848505191
          ]
        ],
        "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": [
          [
            -8.326672684688674e-16,
            -1.1657341758564144e-15,
            -0.039354648485049215
          ],
          [
            -2.7755575615628914e-16,
            -8.326672684688674e-16,
            -0.03441884522497435
          ],
          [
            -4.440892098500626e-16,
            -3.3306690738754696e-16,
            -0.029490089092610583
          ],
          [
            -7.771561172376096e-16,
            -4.996003610813204e-16,
            -0.02456709363404197
          ],
          [
            -6.661338147750939e-16,
            -4.996003610813204e-16,
            -0.01964865471117183
          ],
          [
            -1.1102230246251565e-15,
            -4.996003610813204e-16,
            -0.01473366685322458
          ],
          [
            -1.1657341758564144e-15,
            -4.440892098500626e-16,
            -0.009821139805954449
          ],
          [
            -7.771561172376096e-16,
            -2.220446049250313e-16,
            -0.0049101870241323176
          ],
          [
            -1.0547118733938987e-15,
            -4.440892098500626e-16,
            1.887379141862766e-15
          ],
          [
            -5.551115123125783e-16,
            0.0,
            0.004910187024133039
          ],
          [
            -7.771561172376096e-16,
            -1.942890293094024e-15,
            0.009821139805956003
          ],
          [
            -7.771561172376096e-16,
            -5.551115123125783e-16,
            0.01473366685322608
          ],
          [
            -1.27675647831893e-15,
            -1.3877787807814457e-15,
            0.019648654711176272
          ],
          [
            -1.5543122344752192e-15,
            -7.216449660063518e-16,
            0.024567093634044967
          ],
          [
            -1.6653345369377348e-15,
            5.551115123125783e-16,
            0.029490089092613303
          ],
          [
            -7.216449660063518e-16,
            -1.2212453270876722e-15,
            0.03441884522497807
          ],
          [
            -8.326672684688674e-16,
            5.551115123125783e-16,
            0.03935464848505188
          ]
        ]
      },
      "incoming_structure_ids": [
        "incoming_00_000",
        "incoming_00_001",
        "incoming_00_002",
        "incoming_00_003",
        "incoming_00_004",
        "incoming_00_005",
        "incoming_00_006",
        "incoming_00_007",
        "incoming_00_008"
      ],
      "reflected_structure_ids": [
        "reflected_00_001",
        "reflected_00_002",
        "reflected_00_003",
        "reflected_00_004",
        "reflected_00_005",
        "reflected_00_006",
        "reflected_00_007",
        "reflected_00_008"
      ],
      "positive_extension_structure_ids": [
        "extension_plus_00_000",
        "extension_plus_00_001",
        "extension_plus_00_002",
        "extension_plus_00_003"
      ],
      "negative_extension_structure_ids": [
        "extension_minus_00_000",
        "extension_minus_00_001",
        "extension_minus_00_002",
        "extension_minus_00_003"
      ],
      "extension": {
        "enabled": true,
        "fraction_beyond_polar_endpoint": 0.35,
        "images_per_side": 4,
        "construction": "continue fractional atomic displacements and symmetric log strain beyond +P; reflect these structures about N for the -P side",
        "positive_path_coordinates": [
          1.35,
          1.2625,
          1.175,
          1.0875
        ],
        "negative_path_coordinates": [
          -1.0875,
          -1.175,
          -1.2625,
          -1.35
        ]
      },
      "branch_coordinates": [
        1.35,
        1.2625,
        1.175,
        1.0875,
        1.0,
        0.875,
        0.75,
        0.625,
        0.5,
        0.375,
        0.25,
        0.125,
        0.0,
        -0.125,
        -0.25,
        -0.375,
        -0.5,
        -0.625,
        -0.75,
        -0.875,
        -1.0,
        -1.0875,
        -1.175,
        -1.2625,
        -1.35
      ],
      "parent": {
        "candidate_id": "inversion_parent_endpoint_00",
        "source": "same_species_inversion_center_projection_from_endpoint",
        "spacegroup": "Pbam",
        "spacegroup_number": 55,
        "pointgroup": "mmm",
        "has_inversion": true,
        "is_polar_point_group": false,
        "nonpolar_parent_hypothesis": true,
        "symmetry_tolerance_A": null,
        "target_reduced_polarization": [
          0.0,
          0.0,
          0.0
        ],
        "formal_class": [
          0.0,
          0.0,
          0.0
        ],
        "target_residual": 1.0204620596421558e-15,
        "parent_symmetrization_rmsd_A": 0.04295456241051995,
        "parent_cell_rmsd_A": 0.0,
        "energy_eV": -147.03924448737496,
        "reduced_polarization": [
          -2.0471390763710185e-16,
          -6.696247022729834e-17,
          9.974723348394767e-16
        ],
        "cartesian_polarization_e_A2": [
          -2.864308208409515e-18,
          -9.929601789152985e-19,
          9.102162518083061e-18
        ],
        "ranking_score": 0.04295456241052199
      }
    }
  ],
  "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": 73,
      "full_response": 26,
      "energy_polarization": 47
    },
    "model_evaluations_for_recovery_and_path_properties": {
      "total": 98,
      "full_response": 51,
      "energy_polarization": 47
    },
    "elapsed_seconds": 703.0208168009995
  }
}
