{
  "schema": "ferrofinder.endpoint_parent_recovery.v4_variable_cell",
  "status": "complete",
  "input_atom_count": 5,
  "input_formula": "HfO3Sr",
  "input_spacegroup": "P4mm",
  "input_pointgroup": "4mm",
  "input_is_polar_point_group": true,
  "input_energy_eV": -41.426235577751456,
  "input_cartesian_polarization_e_A2": [
    2.213260031061063e-21,
    -4.885739321607145e-19,
    0.009465458134545461
  ],
  "input_reduced_polarization": [
    3.801819211082765e-20,
    -8.392460602256297e-18,
    0.16218855578490116
  ],
  "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": [
        0.0,
        0.5,
        0.5
      ],
      "target_reduced_polarization": [
        0.0,
        0.5,
        0.5
      ]
    },
    {
      "orbit_id": 4,
      "representative_formal_class": [
        0.5,
        0.5,
        0.0
      ],
      "target_reduced_polarization": [
        0.5,
        0.5,
        0.0
      ]
    },
    {
      "orbit_id": 5,
      "representative_formal_class": [
        0.5,
        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": "P4/mmm",
      "spacegroup_number": 123,
      "pointgroup": "4/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": 1.3550610227833532e-17,
      "parent_symmetrization_rmsd_A": 0.13120323592499078,
      "parent_cell_rmsd_A": 0.0,
      "energy_eV": -41.41022714897762,
      "reduced_polarization": [
        7.476356420372805e-19,
        3.608083491849168e-18,
        1.304000812918718e-17
      ],
      "cartesian_polarization_e_A2": [
        4.352421807681182e-20,
        2.1004752035451678e-19,
        7.610256495818944e-19
      ],
      "ranking_score": 0.1312032359249908
    },
    {
      "candidate_id": "symmetry_projection_00",
      "source": "spglib_refine_cell_from_polar_endpoint",
      "spacegroup": "Pm-3m",
      "spacegroup_number": 221,
      "pointgroup": "m-3m",
      "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": 1.2176302820636404e-17,
      "parent_symmetrization_rmsd_A": 0.13120323592499017,
      "parent_cell_rmsd_A": 0.005614922762763027,
      "energy_eV": -41.41043330807792,
      "reduced_polarization": [
        3.615606134334009e-18,
        -1.4862532397906993e-18,
        1.1531729877534245e-17
      ],
      "cartesian_polarization_e_A2": [
        2.1065979055450277e-19,
        -8.659510593040065e-20,
        6.718850755517748e-19
      ],
      "ranking_score": 0.13260696661568094
    },
    {
      "candidate_id": "bec_projection_00",
      "source": "MACEField_BEC_backprojection",
      "spacegroup": "P4mm",
      "spacegroup_number": 99,
      "pointgroup": "4mm",
      "has_inversion": false,
      "is_polar_point_group": true,
      "nonpolar_parent_hypothesis": false,
      "symmetry_tolerance_A": null,
      "target_reduced_polarization": [
        0.0,
        0.0,
        0.0
      ],
      "formal_class": [
        0.0,
        0.0,
        0.0
      ],
      "target_residual": 0.0005829561674475733,
      "parent_symmetrization_rmsd_A": 0.03857992375667842,
      "parent_cell_rmsd_A": 0.0014476307394993124,
      "energy_eV": -41.37966631709628,
      "reduced_polarization": [
        1.2326729454962242e-16,
        1.4229280234331132e-16,
        0.0005829561674475733
      ],
      "cartesian_polarization_e_A2": [
        7.141218128014362e-18,
        8.255766266338088e-18,
        3.401456273913498e-05
      ],
      "ranking_score": 0.5401077437764484
    },
    {
      "candidate_id": "inversion_parent_bec_00_00",
      "source": "same_species_inversion_center_projection_after_BEC",
      "spacegroup": "P4/mmm",
      "spacegroup_number": 123,
      "pointgroup": "4/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": 3.2073955646327485e-16,
      "parent_symmetrization_rmsd_A": 0.13120323592499078,
      "parent_cell_rmsd_A": 0.0014476307394993124,
      "energy_eV": -41.40912089998496,
      "reduced_polarization": [
        -1.3327836266760673e-16,
        -8.261500964762319e-17,
        2.797954633403181e-16
      ],
      "cartesian_polarization_e_A2": [
        -7.754202945337848e-18,
        -4.8065832916845045e-18,
        1.6325619100291095e-17
      ],
      "ranking_score": 0.13156514360986624
    },
    {
      "candidate_id": "symmetry_parent_00_00",
      "source": "spglib_refine_cell_after_MACEField_BEC_backprojection",
      "spacegroup": "Pm-3m",
      "spacegroup_number": 221,
      "pointgroup": "m-3m",
      "has_inversion": true,
      "is_polar_point_group": false,
      "nonpolar_parent_hypothesis": true,
      "symmetry_tolerance_A": null,
      "target_reduced_polarization": [
        0.0,
        0.0,
        0.0
      ],
      "formal_class": [
        0.0,
        0.0,
        0.0
      ],
      "target_residual": 3.614789179325889e-18,
      "parent_symmetrization_rmsd_A": 0.13120323592499017,
      "parent_cell_rmsd_A": 0.005728521016806148,
      "energy_eV": -41.40939642744895,
      "reduced_polarization": [
        -2.413497534615787e-18,
        -2.6602416763863537e-18,
        4.0601069516968737e-19
      ],
      "cartesian_polarization_e_A2": [
        -1.4055319791239224e-19,
        -1.5492266698977534e-19,
        2.3644565935642266e-20
      ],
      "ranking_score": 0.1326353661791917
    },
    {
      "candidate_id": "bec_projection_01",
      "source": "MACEField_BEC_backprojection",
      "spacegroup": "P4mm",
      "spacegroup_number": 99,
      "pointgroup": "4mm",
      "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": 1.11637313002233e-05,
      "parent_symmetrization_rmsd_A": 0.08385403388574295,
      "parent_cell_rmsd_A": 0.003144298855009493,
      "energy_eV": -41.156472809237705,
      "reduced_polarization": [
        -1.7188508859816736e-16,
        8.545874764029979e-16,
        0.4999888362686998
      ],
      "cartesian_polarization_e_A2": [
        4.702011947590077e-17,
        9.259157178916045e-17,
        0.029193275347526845
      ],
      "ranking_score": 0.5846624360620958
    },
    {
      "candidate_id": "bec_projection_02",
      "source": "MACEField_BEC_backprojection",
      "spacegroup": "Pm",
      "spacegroup_number": 6,
      "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": 1.83323070332163e-05,
      "parent_symmetrization_rmsd_A": 0.13522872139033063,
      "parent_cell_rmsd_A": 0.0019611112274656194,
      "energy_eV": -40.666029300249505,
      "reduced_polarization": [
        3.1864985653026205e-16,
        0.4999828874406216,
        6.575240883817166e-06
      ],
      "cartesian_polarization_e_A2": [
        2.0308038926997232e-17,
        0.029088409523501665,
        9.620611553669902e-06
      ],
      "ranking_score": 0.6357556638112635
    },
    {
      "candidate_id": "bec_projection_03",
      "source": "MACEField_BEC_backprojection",
      "spacegroup": "Pm",
      "spacegroup_number": 6,
      "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": 7.085968588544717e-05,
      "parent_symmetrization_rmsd_A": 0.1633425795961537,
      "parent_cell_rmsd_A": 0.003809194211591342,
      "energy_eV": -40.39996529163049,
      "reduced_polarization": [
        -5.564813769048454e-16,
        0.49993411325198145,
        0.49997392258603074
      ],
      "cartesian_polarization_e_A2": [
        7.692942974963759e-18,
        0.029157597761144124,
        0.029204023981084053
      ],
      "ranking_score": 0.6644365975208224
    },
    {
      "candidate_id": "bec_projection_04",
      "source": "MACEField_BEC_backprojection",
      "spacegroup": "Cm",
      "spacegroup_number": 8,
      "pointgroup": "m",
      "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": 1.2310158643039884e-06,
      "parent_symmetrization_rmsd_A": 0.20032976607366118,
      "parent_cell_rmsd_A": 0.0025080483848914366,
      "energy_eV": -39.82089343625056,
      "reduced_polarization": [
        0.49999950170091795,
        0.4999995017008978,
        1.0093542924749848e-06
      ],
      "cartesian_polarization_e_A2": [
        0.029088392878170978,
        0.029088392878293692,
        2.0381909580161157e-05
      ],
      "ranking_score": 0.7009592402016126
    },
    {
      "candidate_id": "bec_projection_05",
      "source": "MACEField_BEC_backprojection",
      "spacegroup": "Cm",
      "spacegroup_number": 8,
      "pointgroup": "m",
      "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": 1.3274873358967923e-05,
      "parent_symmetrization_rmsd_A": 0.23096426801407408,
      "parent_cell_rmsd_A": 0.0046341666610729085,
      "energy_eV": -39.5409258148883,
      "reduced_polarization": [
        0.49999240046040977,
        0.4999924004605348,
        0.5000077920639519
      ],
      "cartesian_polarization_e_A2": [
        0.029169138184536796,
        0.02916913818415291,
        0.029220669472279654
      ],
      "ranking_score": 0.7321493594260602
    }
  ],
  "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": [
              3.801819211082765e-20,
              -8.392460602256297e-18,
              0.16218855578490116
            ],
            "branch_aligned_reduced_polarization": [
              3.801819211082765e-20,
              -8.392460602256297e-18,
              0.16218855578490116
            ],
            "target_residual": 0.16218855578490116,
            "energy_eV": -41.426235577751456,
            "max_atomic_step_A": 0.05244955071984266,
            "max_log_strain_component": 0.0005002255003774747,
            "step_scale": 1.0,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 0.39960934799932685,
            "cell_principal_stretches": [
              1.000500350634017,
              1.0001064325561333,
              1.0001064325522744
            ],
            "cell_volume_ratio": 1.0007133335831733,
            "cell_rmsd_from_input_A": 0.0014476307394993124
          },
          {
            "iteration": 1,
            "reduced_polarization": [
              1.2326729454962242e-16,
              1.4229280234331132e-16,
              0.0005829561674475733
            ],
            "branch_aligned_reduced_polarization": [
              1.2326729454962242e-16,
              1.4229280234331132e-16,
              0.0005829561674475733
            ],
            "target_residual": 0.0005829561674475733,
            "energy_eV": -41.37966631709628
          }
        ],
        "iterations": 1
      },
      "parent": {
        "candidate_id": "inversion_parent_endpoint_00",
        "source": "same_species_inversion_center_projection_from_endpoint",
        "spacegroup": "P4/mmm",
        "spacegroup_number": 123,
        "pointgroup": "4/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": 1.3550610227833532e-17,
        "parent_symmetrization_rmsd_A": 0.13120323592499078,
        "parent_cell_rmsd_A": 0.0,
        "energy_eV": -41.41022714897762,
        "reduced_polarization": [
          7.476356420372805e-19,
          3.608083491849168e-18,
          1.304000812918718e-17
        ],
        "cartesian_polarization_e_A2": [
          4.352421807681182e-20,
          2.1004752035451678e-19,
          7.610256495818944e-19
        ],
        "ranking_score": 0.1312032359249908
      },
      "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": [
          -41.426235577751456,
          -41.42288810494926,
          -41.419794661758296,
          -41.41703163927629,
          -41.414668005784215,
          -41.412763483322294,
          -41.41136676585149,
          -41.410513925463334,
          -41.410227148977626
        ],
        "cartesian_polarizations_e_A2": [
          [
            2.937861999565669e-17,
            2.9982133911068135e-17,
            0.00946545813454547
          ],
          [
            3.006714150259478e-17,
            2.91893540304398e-17,
            0.008277346791794137
          ],
          [
            1.6344565204812227e-17,
            1.5698067899702272e-17,
            0.007091060153895778
          ],
          [
            3.50708792979587e-17,
            3.4505500641611594e-17,
            0.005906443572688264
          ],
          [
            3.615345930091114e-17,
            3.6764442497906055e-17,
            0.004723292760074892
          ],
          [
            3.2125008916118665e-17,
            3.293875826297309e-17,
            0.0035413620047148407
          ],
          [
            3.723995317252305e-17,
            3.855989765130638e-17,
            0.002360373168331362
          ],
          [
            5.818021340098197e-17,
            5.866055332715925e-17,
            0.0011800246835077441
          ],
          [
            3.269956073020537e-17,
            3.287858612490591e-17,
            4.7466450455316564e-17
          ]
        ],
        "raw_reduced_polarization": [
          [
            5.046501555492388e-16,
            5.150169934515481e-16,
            0.16218855578490132
          ],
          [
            5.16477208202722e-16,
            5.013990464501387e-16,
            0.141830527673275
          ],
          [
            2.807581627119513e-16,
            2.6965297922701784e-16,
            0.1215037654803851
          ],
          [
            6.024287286325897e-16,
            5.927169577287158e-16,
            0.10120561934378292
          ],
          [
            6.210247064887725e-16,
            6.315198476985039e-16,
            0.08093258883159314
          ],
          [
            5.518261493881169e-16,
            5.658042986180293e-16,
            0.06068046373370854
          ],
          [
            6.396879146787183e-16,
            6.623612120164708e-16,
            0.04044447821156399
          ],
          [
            9.993884582405202e-16,
            1.0076394795103318e-15,
            0.020219464973403174
          ],
          [
            5.616954918689011e-16,
            5.647706939477004e-16,
            8.133272513758835e-16
          ]
        ],
        "unwrapped_reduced_polarization": [
          [
            5.046501555492388e-16,
            5.150169934515481e-16,
            0.16218855578490132
          ],
          [
            5.16477208202722e-16,
            5.013990464501387e-16,
            0.141830527673275
          ],
          [
            2.807581627119513e-16,
            2.6965297922701784e-16,
            0.1215037654803851
          ],
          [
            6.024287286325897e-16,
            5.927169577287158e-16,
            0.10120561934378292
          ],
          [
            6.210247064887725e-16,
            6.315198476985039e-16,
            0.08093258883159314
          ],
          [
            5.518261493881169e-16,
            5.658042986180293e-16,
            0.06068046373370854
          ],
          [
            6.396879146787183e-16,
            6.623612120164708e-16,
            0.04044447821156399
          ],
          [
            9.993884582405202e-16,
            1.0076394795103318e-15,
            0.020219464973403174
          ],
          [
            5.616954918689011e-16,
            5.647706939477004e-16,
            8.118505867571457e-16
          ]
        ],
        "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": [
          [
            5.551115123125783e-16,
            5.551115123125783e-16,
            0.16218855578490132
          ],
          [
            5.551115123125783e-16,
            5.551115123125783e-16,
            0.14183052767327498
          ],
          [
            3.3306690738754696e-16,
            2.220446049250313e-16,
            0.1215037654803851
          ],
          [
            5.551115123125783e-16,
            5.551115123125783e-16,
            0.10120561934378292
          ],
          [
            6.661338147750939e-16,
            6.661338147750939e-16,
            0.08093258883159316
          ],
          [
            5.551115123125783e-16,
            5.551115123125783e-16,
            0.0606804637337085
          ],
          [
            6.661338147750939e-16,
            6.661338147750939e-16,
            0.04044447821156394
          ],
          [
            9.992007221626409e-16,
            9.992007221626409e-16,
            0.02021946497340321
          ],
          [
            5.551115123125783e-16,
            5.551115123125783e-16,
            7.771561172376096e-16
          ]
        ]
      },
      "reflected": {
        "reached": true,
        "construction": "reflect_displacements_about_reconstructed_parent",
        "energies_eV": [
          -41.410227148977626,
          -41.41051392546333,
          -41.41136676585149,
          -41.412763483322294,
          -41.41466800578422,
          -41.41703163927629,
          -41.419794661758296,
          -41.42288810494925,
          -41.42623557775146
        ],
        "cartesian_polarizations_e_A2": [
          [
            1.855937462396959e-17,
            1.7791389380702898e-17,
            3.8518639779136357e-17
          ],
          [
            1.795652467614215e-19,
            8.446896508830252e-19,
            -0.0011800246835076277
          ],
          [
            4.565980084119275e-18,
            5.576833871868636e-18,
            -0.0023603731683312984
          ],
          [
            3.41166309557683e-17,
            3.39673894107687e-17,
            -0.0035413620047147682
          ],
          [
            4.9585517899325287e-17,
            4.9044816220437844e-17,
            -0.004723292760074858
          ],
          [
            -3.873970552784633e-18,
            -4.376839593222568e-18,
            -0.005906443572688251
          ],
          [
            5.974040689715526e-17,
            5.862459819209712e-17,
            -0.007091060153895722
          ],
          [
            3.349604882354485e-17,
            3.28668543866196e-17,
            -0.008277346791794165
          ],
          [
            2.4256410772750052e-17,
            2.4114314739827506e-17,
            -0.009465458134545471
          ]
        ],
        "raw_reduced_polarization": [
          [
            3.188029693793483e-16,
            3.0561093134177695e-16,
            6.600084716213232e-16
          ],
          [
            3.0844753675559182e-18,
            1.4509625155026705e-17,
            -0.020219464973401182
          ],
          [
            7.843195357801603e-17,
            9.579585703231949e-17,
            -0.0404444782115629
          ],
          [
            5.860371631203164e-16,
            5.834735720153022e-16,
            -0.0606804637337073
          ],
          [
            8.517533949717005e-16,
            8.424655119330613e-16,
            -0.08093258883159256
          ],
          [
            -6.654498551480503e-17,
            -7.518299980939809e-17,
            -0.10120561934378268
          ],
          [
            1.0261886241655079e-15,
            1.0070218615111005e-15,
            -0.12150376548038415
          ],
          [
            5.753771365566471e-16,
            5.645691724483267e-16,
            -0.1418305276732755
          ],
          [
            4.1666359656594643e-16,
            4.14222747229664e-16,
            -0.16218855578490135
          ]
        ],
        "unwrapped_reduced_polarization": [
          [
            3.188029693793483e-16,
            3.0561093134177695e-16,
            6.600084716213232e-16
          ],
          [
            3.0844753675559098e-18,
            1.450962515502673e-17,
            -0.020219464973401182
          ],
          [
            7.843195357801603e-17,
            9.579585703231949e-17,
            -0.0404444782115629
          ],
          [
            5.860371631203164e-16,
            5.834735720153022e-16,
            -0.0606804637337073
          ],
          [
            8.517533949717005e-16,
            8.424655119330613e-16,
            -0.08093258883159256
          ],
          [
            -6.654498551480509e-17,
            -7.518299980939801e-17,
            -0.10120561934378268
          ],
          [
            1.0261886241655079e-15,
            1.0070218615111005e-15,
            -0.12150376548038415
          ],
          [
            5.753771365566471e-16,
            5.645691724483267e-16,
            -0.1418305276732755
          ],
          [
            4.1666359656594643e-16,
            4.14222747229664e-16,
            -0.16218855578490135
          ]
        ],
        "gauge_integer_shift": [
          0,
          0,
          0
        ],
        "expected_opposite_endpoint_reduced_polarization": [
          6.187408281885635e-16,
          6.145243944438525e-16,
          -0.16218855578489969
        ],
        "actual_opposite_endpoint_branch_residual": 1.6894659148188217e-15
      },
      "pnp_branch": {
        "construction": "incoming_path_concatenated_with_parent_reflection",
        "reduced_polarization": [
          [
            5.046501555492388e-16,
            5.150169934515481e-16,
            0.16218855578490132
          ],
          [
            5.16477208202722e-16,
            5.013990464501387e-16,
            0.141830527673275
          ],
          [
            2.807581627119513e-16,
            2.6965297922701784e-16,
            0.1215037654803851
          ],
          [
            6.024287286325897e-16,
            5.927169577287158e-16,
            0.10120561934378292
          ],
          [
            6.210247064887725e-16,
            6.315198476985039e-16,
            0.08093258883159314
          ],
          [
            5.518261493881169e-16,
            5.658042986180293e-16,
            0.06068046373370854
          ],
          [
            6.396879146787183e-16,
            6.623612120164708e-16,
            0.04044447821156399
          ],
          [
            9.993884582405202e-16,
            1.0076394795103318e-15,
            0.020219464973403174
          ],
          [
            5.616954918689011e-16,
            5.647706939477004e-16,
            8.133272513758835e-16
          ],
          [
            3.0844753675559182e-18,
            1.4509625155026705e-17,
            -0.020219464973401182
          ],
          [
            7.843195357801603e-17,
            9.579585703231949e-17,
            -0.0404444782115629
          ],
          [
            5.860371631203164e-16,
            5.834735720153022e-16,
            -0.0606804637337073
          ],
          [
            8.517533949717005e-16,
            8.424655119330613e-16,
            -0.08093258883159256
          ],
          [
            -6.654498551480503e-17,
            -7.518299980939809e-17,
            -0.10120561934378268
          ],
          [
            1.0261886241655079e-15,
            1.0070218615111005e-15,
            -0.12150376548038415
          ],
          [
            5.753771365566471e-16,
            5.645691724483267e-16,
            -0.1418305276732755
          ],
          [
            4.1666359656594643e-16,
            4.14222747229664e-16,
            -0.16218855578490135
          ]
        ],
        "unwrapped_reduced_polarization": [
          [
            5.046501555492388e-16,
            5.150169934515481e-16,
            0.16218855578490132
          ],
          [
            5.16477208202722e-16,
            5.013990464501387e-16,
            0.141830527673275
          ],
          [
            2.807581627119513e-16,
            2.6965297922701784e-16,
            0.1215037654803851
          ],
          [
            6.024287286325897e-16,
            5.927169577287158e-16,
            0.10120561934378292
          ],
          [
            6.210247064887725e-16,
            6.315198476985039e-16,
            0.08093258883159314
          ],
          [
            5.518261493881169e-16,
            5.658042986180293e-16,
            0.06068046373370854
          ],
          [
            6.396879146787183e-16,
            6.623612120164708e-16,
            0.04044447821156399
          ],
          [
            9.993884582405202e-16,
            1.0076394795103318e-15,
            0.020219464973403174
          ],
          [
            5.616954918689011e-16,
            5.647706939477004e-16,
            8.118505867571457e-16
          ],
          [
            3.084475367555959e-18,
            1.450962515502673e-17,
            -0.020219464973401182
          ],
          [
            7.843195357801603e-17,
            9.579585703231949e-17,
            -0.0404444782115629
          ],
          [
            5.860371631203164e-16,
            5.834735720153022e-16,
            -0.0606804637337073
          ],
          [
            8.517533949717005e-16,
            8.424655119330613e-16,
            -0.08093258883159256
          ],
          [
            -6.654498551480509e-17,
            -7.518299980939801e-17,
            -0.10120561934378268
          ],
          [
            1.0261886241655079e-15,
            1.0070218615111005e-15,
            -0.12150376548038415
          ],
          [
            5.753771365566471e-16,
            5.645691724483267e-16,
            -0.1418305276732755
          ],
          [
            4.1666359656594643e-16,
            4.14222747229664e-16,
            -0.16218855578490135
          ]
        ],
        "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": [
          [
            5.551115123125783e-16,
            5.551115123125783e-16,
            0.16218855578490132
          ],
          [
            5.551115123125783e-16,
            5.551115123125783e-16,
            0.14183052767327498
          ],
          [
            3.3306690738754696e-16,
            2.220446049250313e-16,
            0.1215037654803851
          ],
          [
            5.551115123125783e-16,
            5.551115123125783e-16,
            0.10120561934378292
          ],
          [
            6.661338147750939e-16,
            6.661338147750939e-16,
            0.08093258883159316
          ],
          [
            5.551115123125783e-16,
            5.551115123125783e-16,
            0.0606804637337085
          ],
          [
            6.661338147750939e-16,
            6.661338147750939e-16,
            0.04044447821156394
          ],
          [
            9.992007221626409e-16,
            9.992007221626409e-16,
            0.02021946497340321
          ],
          [
            5.551115123125783e-16,
            5.551115123125783e-16,
            7.771561172376096e-16
          ],
          [
            0.0,
            0.0,
            -0.020219464973401158
          ],
          [
            1.1102230246251565e-16,
            1.1102230246251565e-16,
            -0.040444478211562884
          ],
          [
            5.551115123125783e-16,
            5.551115123125783e-16,
            -0.06068046373370728
          ],
          [
            8.881784197001252e-16,
            8.881784197001252e-16,
            -0.08093258883159254
          ],
          [
            -5.551115123125783e-17,
            -5.551115123125783e-17,
            -0.1012056193437827
          ],
          [
            9.992007221626409e-16,
            9.992007221626409e-16,
            -0.12150376548038416
          ],
          [
            5.551115123125783e-16,
            5.551115123125783e-16,
            -0.14183052767327553
          ],
          [
            4.440892098500626e-16,
            4.440892098500626e-16,
            -0.16218855578490132
          ]
        ]
      },
      "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": [
              3.801819211082765e-20,
              -8.392460602256297e-18,
              0.16218855578490116
            ],
            "branch_aligned_reduced_polarization": [
              3.801819211082765e-20,
              -8.392460602256297e-18,
              0.16218855578490116
            ],
            "target_residual": 0.33781144421509884,
            "energy_eV": -41.426235577751456,
            "max_atomic_step_A": 0.10924358005013186,
            "max_log_strain_component": 0.0010418854641004607,
            "step_scale": 1.0,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 0.39960934799932685,
            "cell_principal_stretches": [
              0.9997783552831156,
              0.9997783552750815,
              0.9989586571101099
            ],
            "cell_volume_ratio": 0.9985158783598402,
            "cell_rmsd_from_input_A": 0.0030108260314892755
          },
          {
            "iteration": 1,
            "reduced_polarization": [
              2.1432175095650842e-16,
              4.0953145310468674e-16,
              0.4877038101198617
            ],
            "branch_aligned_reduced_polarization": [
              2.1432175095650842e-16,
              4.0953145310468674e-16,
              0.4877038101198617
            ],
            "target_residual": 0.012296189880138308,
            "energy_eV": -41.18153903627826,
            "max_atomic_step_A": 0.0043033549098100065,
            "max_log_strain_component": 4.623481662029338e-05,
            "step_scale": 1.0,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 0.39960934799932685,
            "cell_principal_stretches": [
              0.9997685206928101,
              0.9997685206844197,
              0.9989124715074867
            ],
            "cell_volume_ratio": 0.9984500698898083,
            "cell_rmsd_from_input_A": 0.003144298855009493
          },
          {
            "iteration": 2,
            "reduced_polarization": [
              -1.7188508859816736e-16,
              8.545874764029979e-16,
              0.4999888362686998
            ],
            "branch_aligned_reduced_polarization": [
              -1.7188508859816736e-16,
              8.545874764029979e-16,
              0.4999888362686998
            ],
            "target_residual": 1.11637313002233e-05,
            "energy_eV": -41.156472809237705
          }
        ],
        "iterations": 2
      },
      "parent": {
        "candidate_id": "bec_projection_01",
        "source": "MACEField_BEC_backprojection",
        "spacegroup": "P4mm",
        "spacegroup_number": 99,
        "pointgroup": "4mm",
        "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": 1.11637313002233e-05,
        "parent_symmetrization_rmsd_A": 0.08385403388574295,
        "parent_cell_rmsd_A": 0.003144298855009493,
        "energy_eV": -41.156472809237705,
        "reduced_polarization": [
          -1.7188508859816736e-16,
          8.545874764029979e-16,
          0.4999888362686998
        ],
        "cartesian_polarization_e_A2": [
          4.702011947590077e-17,
          9.259157178916045e-17,
          0.029193275347526845
        ],
        "ranking_score": 0.5846624360620958
      },
      "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
        ],
        [
          0.5,
          0.0,
          0.0
        ]
      ],
      "target_reduced_polarization": [
        0.0,
        0.5,
        0.0
      ],
      "bec_backprojection": {
        "converged_to_target": true,
        "history": [
          {
            "iteration": 0,
            "reduced_polarization": [
              3.801819211082765e-20,
              -8.392460602256297e-18,
              0.16218855578490116
            ],
            "branch_aligned_reduced_polarization": [
              3.801819211082765e-20,
              0.0,
              0.16218855578490116
            ],
            "target_residual": 0.5256473415014976,
            "energy_eV": -41.426235577751456,
            "max_atomic_step_A": 0.12,
            "max_log_strain_component": 0.0003547835899212422,
            "step_scale": 0.7092473087707253,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 0.39960934799932685,
            "cell_principal_stretches": [
              1.000460295165938,
              1.0000754858333263,
              0.9999700777621358
            ],
            "cell_volume_ratio": 1.0005058774743585,
            "cell_rmsd_from_input_A": 0.0012939678298676193
          },
          {
            "iteration": 1,
            "reduced_polarization": [
              -1.5658485798536366e-15,
              0.3424203413784341,
              0.04769833629254886
            ],
            "branch_aligned_reduced_polarization": [
              -1.5658485798536366e-15,
              0.3424203413784341,
              0.04769833629254886
            ],
            "target_residual": 0.16464045704615357,
            "energy_eV": -41.15431156961969,
            "max_atomic_step_A": 0.05757517199170141,
            "max_log_strain_component": 0.00016323287610645008,
            "step_scale": 1.0,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 0.39960934799932685,
            "cell_principal_stretches": [
              1.0006865104673153,
              1.0001102181294341,
              0.9999419552837462
            ],
            "cell_volume_ratio": 1.0007387132961179,
            "cell_rmsd_from_input_A": 0.0019316881065242443
          },
          {
            "iteration": 2,
            "reduced_polarization": [
              1.56789721070009e-15,
              0.49267081362914333,
              0.0014829158694213266
            ],
            "branch_aligned_reduced_polarization": [
              1.56789721070009e-15,
              0.49267081362914333,
              0.0014829158694213266
            ],
            "target_residual": 0.007477701005959834,
            "energy_eV": -40.697433533480435,
            "max_atomic_step_A": 0.002809176212631232,
            "max_log_strain_component": 6.326871768865277e-06,
            "step_scale": 1.0,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 0.39960934799932685,
            "cell_principal_stretches": [
              1.0006968684274153,
              1.0001115643701712,
              0.9999392776054903
            ],
            "cell_volume_ratio": 1.0007477390540673,
            "cell_rmsd_from_input_A": 0.0019611112274656194
          },
          {
            "iteration": 3,
            "reduced_polarization": [
              3.1864985653026205e-16,
              0.4999828874406216,
              6.575240883817166e-06
            ],
            "branch_aligned_reduced_polarization": [
              3.1864985653026205e-16,
              0.4999828874406216,
              6.575240883817166e-06
            ],
            "target_residual": 1.83323070332163e-05,
            "energy_eV": -40.666029300249505
          }
        ],
        "iterations": 3
      },
      "parent": {
        "candidate_id": "bec_projection_02",
        "source": "MACEField_BEC_backprojection",
        "spacegroup": "Pm",
        "spacegroup_number": 6,
        "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": 1.83323070332163e-05,
        "parent_symmetrization_rmsd_A": 0.13522872139033063,
        "parent_cell_rmsd_A": 0.0019611112274656194,
        "energy_eV": -40.666029300249505,
        "reduced_polarization": [
          3.1864985653026205e-16,
          0.4999828874406216,
          6.575240883817166e-06
        ],
        "cartesian_polarization_e_A2": [
          2.0308038926997232e-17,
          0.029088409523501665,
          9.620611553669902e-06
        ],
        "ranking_score": 0.6357556638112635
      },
      "branch_status": "awaiting_branch_sampling"
    },
    {
      "orbit_id": 3,
      "formal_class": [
        0.0,
        0.5,
        0.5
      ],
      "formal_classes_in_orbit": [
        [
          0.0,
          0.5,
          0.5
        ],
        [
          0.5,
          0.0,
          0.5
        ]
      ],
      "target_reduced_polarization": [
        0.0,
        0.5,
        0.5
      ],
      "bec_backprojection": {
        "converged_to_target": true,
        "history": [
          {
            "iteration": 0,
            "reduced_polarization": [
              3.801819211082765e-20,
              -8.392460602256297e-18,
              0.16218855578490116
            ],
            "branch_aligned_reduced_polarization": [
              3.801819211082765e-20,
              0.0,
              0.16218855578490116
            ],
            "target_residual": 0.6034207254003552,
            "energy_eV": -41.426235577751456,
            "max_atomic_step_A": 0.11999999999999998,
            "max_log_strain_component": 0.0006429837846886594,
            "step_scale": 0.6171348068895667,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 0.39960934799932685,
            "cell_principal_stretches": [
              0.999917937694781,
              0.9998632095260777,
              0.9993025254008417
            ],
            "cell_volume_ratio": 0.9990838364834667,
            "cell_rmsd_from_input_A": 0.001980687507670429
          },
          {
            "iteration": 1,
            "reduced_polarization": [
              2.2503618084216355e-15,
              0.2956307043490521,
              0.3607253366235371
            ],
            "branch_aligned_reduced_polarization": [
              2.2503618084216355e-15,
              0.2956307043490521,
              0.3607253366235371
            ],
            "target_residual": 0.24731405310554352,
            "energy_eV": -41.17882920982824,
            "max_atomic_step_A": 0.08680812378688692,
            "max_log_strain_component": 0.000546498113770897,
            "step_scale": 1.0,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 0.39960934799932685,
            "cell_principal_stretches": [
              0.9998467867133787,
              0.999746960440072,
              0.9987115023643368
            ],
            "cell_volume_ratio": 0.9983058116926887,
            "cell_rmsd_from_input_A": 0.003658741604646392
          },
          {
            "iteration": 2,
            "reduced_polarization": [
              -1.855430681220152e-15,
              0.4864226641589442,
              0.4905133813491536
            ],
            "branch_aligned_reduced_polarization": [
              -1.855430681220152e-15,
              0.4864226641589442,
              0.4905133813491536
            ],
            "target_residual": 0.016563211704479445,
            "energy_eV": -40.477861604504305,
            "max_atomic_step_A": 0.00634364929604994,
            "max_log_strain_component": 4.912139559326009e-05,
            "step_scale": 1.0,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 0.39960934799932685,
            "cell_principal_stretches": [
              0.9998402712283587,
              0.9997365121779607,
              0.9986585162797783
            ],
            "cell_volume_ratio": 0.9982359094543958,
            "cell_rmsd_from_input_A": 0.003809194211591342
          },
          {
            "iteration": 3,
            "reduced_polarization": [
              -5.564813769048454e-16,
              0.49993411325198145,
              0.49997392258603074
            ],
            "branch_aligned_reduced_polarization": [
              -5.564813769048454e-16,
              0.49993411325198145,
              0.49997392258603074
            ],
            "target_residual": 7.085968588544717e-05,
            "energy_eV": -40.39996529163049
          }
        ],
        "iterations": 3
      },
      "parent": {
        "candidate_id": "bec_projection_03",
        "source": "MACEField_BEC_backprojection",
        "spacegroup": "Pm",
        "spacegroup_number": 6,
        "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": 7.085968588544717e-05,
        "parent_symmetrization_rmsd_A": 0.1633425795961537,
        "parent_cell_rmsd_A": 0.003809194211591342,
        "energy_eV": -40.39996529163049,
        "reduced_polarization": [
          -5.564813769048454e-16,
          0.49993411325198145,
          0.49997392258603074
        ],
        "cartesian_polarization_e_A2": [
          7.692942974963759e-18,
          0.029157597761144124,
          0.029204023981084053
        ],
        "ranking_score": 0.6644365975208224
      },
      "branch_status": "awaiting_branch_sampling"
    },
    {
      "orbit_id": 4,
      "formal_class": [
        0.5,
        0.5,
        0.0
      ],
      "formal_classes_in_orbit": [
        [
          0.5,
          0.5,
          0.0
        ]
      ],
      "target_reduced_polarization": [
        0.5,
        0.5,
        0.0
      ],
      "bec_backprojection": {
        "converged_to_target": true,
        "history": [
          {
            "iteration": 0,
            "reduced_polarization": [
              3.801819211082765e-20,
              -8.392460602256297e-18,
              0.16218855578490116
            ],
            "branch_aligned_reduced_polarization": [
              0.0,
              0.0,
              0.16218855578490116
            ],
            "target_residual": 0.7254689019024813,
            "energy_eV": -41.426235577751456,
            "max_atomic_step_A": 0.11999999999999998,
            "max_log_strain_component": 0.00025712321019336857,
            "step_scale": 0.5140145994143013,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 0.39960934799932685,
            "cell_principal_stretches": [
              1.0003858586139212,
              1.0000547064719147,
              0.999926046730811
            ],
            "cell_volume_ratio": 1.0003666003428207,
            "cell_rmsd_from_input_A": 0.0010977216542172462
          },
          {
            "iteration": 1,
            "reduced_polarization": [
              0.24857147654428252,
              0.24857147668447693,
              0.07838151397434613
            ],
            "branch_aligned_reduced_polarization": [
              0.24857147654428252,
              0.24857147668447693,
              0.07838151397434613
            ],
            "target_residual": 0.36411023945593374,
            "energy_eV": -41.18068010545674,
            "max_atomic_step_A": 0.12,
            "max_log_strain_component": 0.0002456576406988723,
            "step_scale": 0.9502980984326167,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 0.39960934799932685,
            "cell_principal_stretches": [
              1.000787705854902,
              1.00010697628304,
              0.9998223714127357
            ],
            "cell_volume_ratio": 1.0007169788804295,
            "cell_rmsd_from_input_A": 0.002254314605002407
          },
          {
            "iteration": 2,
            "reduced_polarization": [
              0.4643912693487492,
              0.4643912695401702,
              0.009302626961290843
            ],
            "branch_aligned_reduced_polarization": [
              0.4643912693487492,
              0.4643912695401702,
              0.009302626961290843
            ],
            "target_residual": 0.05121037250338135,
            "energy_eV": -40.13602357844088,
            "max_atomic_step_A": 0.020403531831255473,
            "max_log_strain_component": 4.8282677466661155e-05,
            "step_scale": 1.0,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 0.39960934799932685,
            "cell_principal_stretches": [
              1.0008729586152598,
              1.0001172499522815,
              0.9997957496608528
            ],
            "cell_volume_ratio": 1.000785858311408,
            "cell_rmsd_from_input_A": 0.0025024108929573726
          },
          {
            "iteration": 3,
            "reduced_polarization": [
              0.49929650411001875,
              0.4992965041072786,
              0.00022215076090764958
            ],
            "branch_aligned_reduced_polarization": [
              0.49929650411001875,
              0.4992965041072786,
              0.00022215076090764958
            ],
            "target_residual": 0.0010193938879884637,
            "energy_eV": -39.827639979000075,
            "max_atomic_step_A": 0.000414796449286973,
            "max_log_strain_component": 1.2074375725210464e-06,
            "step_scale": 1.0,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 0.39960934799932685,
            "cell_principal_stretches": [
              1.000874917769949,
              1.0001175068742298,
              0.9997952566470555
            ],
            "cell_volume_ratio": 1.0007875808866886,
            "cell_rmsd_from_input_A": 0.0025080483848914366
          },
          {
            "iteration": 4,
            "reduced_polarization": [
              0.49999950170091795,
              0.4999995017008978,
              1.0093542924749848e-06
            ],
            "branch_aligned_reduced_polarization": [
              0.49999950170091795,
              0.4999995017008978,
              1.0093542924749848e-06
            ],
            "target_residual": 1.2310158643039884e-06,
            "energy_eV": -39.82089343625056
          }
        ],
        "iterations": 4
      },
      "parent": {
        "candidate_id": "bec_projection_04",
        "source": "MACEField_BEC_backprojection",
        "spacegroup": "Cm",
        "spacegroup_number": 8,
        "pointgroup": "m",
        "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": 1.2310158643039884e-06,
        "parent_symmetrization_rmsd_A": 0.20032976607366118,
        "parent_cell_rmsd_A": 0.0025080483848914366,
        "energy_eV": -39.82089343625056,
        "reduced_polarization": [
          0.49999950170091795,
          0.4999995017008978,
          1.0093542924749848e-06
        ],
        "cartesian_polarization_e_A2": [
          0.029088392878170978,
          0.029088392878293692,
          2.0381909580161157e-05
        ],
        "ranking_score": 0.7009592402016126
      },
      "branch_status": "awaiting_branch_sampling"
    },
    {
      "orbit_id": 5,
      "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": [
              3.801819211082765e-20,
              -8.392460602256297e-18,
              0.16218855578490116
            ],
            "branch_aligned_reduced_polarization": [
              0.0,
              0.0,
              0.16218855578490116
            ],
            "target_residual": 0.7836559014278466,
            "energy_eV": -41.426235577751456,
            "max_atomic_step_A": 0.12,
            "max_log_strain_component": 0.0004954300190138443,
            "step_scale": 0.4755129388829775,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 0.39960934799932685,
            "cell_principal_stretches": [
              0.9999724999626726,
              0.999894598940617,
              0.999426828107784
            ],
            "cell_volume_ratio": 0.9992940060831189,
            "cell_rmsd_from_input_A": 0.0016148989280973553
          },
          {
            "iteration": 1,
            "reduced_polarization": [
              0.2282665830627845,
              0.22826658306539868,
              0.3143471234955879
            ],
            "branch_aligned_reduced_polarization": [
              0.22826658306278447,
              0.2282665830653987,
              0.3143471234955879
            ],
            "target_residual": 0.42678459474738656,
            "energy_eV": -41.19468674869963,
            "max_atomic_step_A": 0.12,
            "max_log_strain_component": 0.0005962206174470946,
            "step_scale": 0.8028197956097712,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 0.39960934799932685,
            "cell_principal_stretches": [
              0.9999325031821727,
              0.9997677697519469,
              0.998744380192739
            ],
            "cell_volume_ratio": 0.9984450451252207,
            "cell_rmsd_from_input_A": 0.0035382381691130785
          },
          {
            "iteration": 2,
            "reduced_polarization": [
              0.4250750420887129,
              0.42507504213453023,
              0.44762184581642134
            ],
            "branch_aligned_reduced_polarization": [
              0.4250750420887129,
              0.42507504213453023,
              0.44762184581642134
            ],
            "target_residual": 0.11819885644467674,
            "energy_eV": -40.248205559242656,
            "max_atomic_step_A": 0.04742649214698887,
            "max_log_strain_component": 0.0003230940695269584,
            "step_scale": 1.0,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 0.39960934799932685,
            "cell_principal_stretches": [
              0.9999088194227082,
              0.9996990472854114,
              0.9983767608985802
            ],
            "cell_volume_ratio": 0.9979852915292909,
            "cell_rmsd_from_input_A": 0.004574329186238887
          },
          {
            "iteration": 3,
            "reduced_polarization": [
              0.49648258458121813,
              0.4964825845729487,
              0.4975201469481689
            ],
            "branch_aligned_reduced_polarization": [
              0.49648258458121813,
              0.4964825845729487,
              0.4975201469481689
            ],
            "target_residual": 0.005558245557135731,
            "energy_eV": -39.57900069089638,
            "max_atomic_step_A": 0.0023497318013649153,
            "max_log_strain_component": 1.8685654387774465e-05,
            "step_scale": 1.0,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 0.39960934799932685,
            "cell_principal_stretches": [
              0.9999074256776762,
              0.9996950729705241,
              0.9983555283457533
            ],
            "cell_volume_ratio": 0.9979587088556514,
            "cell_rmsd_from_input_A": 0.0046341666610729085
          },
          {
            "iteration": 4,
            "reduced_polarization": [
              0.49999240046040977,
              0.4999924004605348,
              0.5000077920639519
            ],
            "branch_aligned_reduced_polarization": [
              0.49999240046040977,
              0.4999924004605348,
              0.5000077920639519
            ],
            "target_residual": 1.3274873358967923e-05,
            "energy_eV": -39.5409258148883
          }
        ],
        "iterations": 4
      },
      "parent": {
        "candidate_id": "bec_projection_05",
        "source": "MACEField_BEC_backprojection",
        "spacegroup": "Cm",
        "spacegroup_number": 8,
        "pointgroup": "m",
        "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": 1.3274873358967923e-05,
        "parent_symmetrization_rmsd_A": 0.23096426801407408,
        "parent_cell_rmsd_A": 0.0046341666610729085,
        "energy_eV": -39.5409258148883,
        "reduced_polarization": [
          0.49999240046040977,
          0.4999924004605348,
          0.5000077920639519
        ],
        "cartesian_polarization_e_A2": [
          0.029169138184536796,
          0.02916913818415291,
          0.029220669472279654
        ],
        "ranking_score": 0.7321493594260602
      },
      "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
        ],
        "endpoint_rmsd_A": 0.13120323592499078,
        "minimum_distance_A_by_image": [
          2.0443805899999994,
          2.0481910787499995,
          2.0520015674999987,
          2.055812056249999,
          2.0596225449999994,
          2.063433033749999,
          2.067243522499999,
          2.0697316232487757,
          2.069708999999999
        ],
        "minimum_distance_A": 2.0443805899999994,
        "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": [
          71.10469919595096,
          71.10469919595096,
          71.10469919595096,
          71.10469919595096,
          71.10469919595096,
          71.10469919595096,
          71.10469919595096,
          71.10469919595096,
          71.10469919595096
        ],
        "cell_deformation_log_strain_norm": 0.0
      },
      "parent_reduced_polarization": [
        5.616954918689011e-16,
        5.647706939477004e-16,
        8.133272513758835e-16
      ],
      "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": [
          -41.426235577751456,
          -41.42288810494926,
          -41.419794661758296,
          -41.41703163927629,
          -41.414668005784215,
          -41.412763483322294,
          -41.41136676585149,
          -41.410513925463334,
          -41.410227148977626
        ],
        "cartesian_polarizations_e_A2": [
          [
            2.937861999565669e-17,
            2.9982133911068135e-17,
            0.00946545813454547
          ],
          [
            3.006714150259478e-17,
            2.91893540304398e-17,
            0.008277346791794137
          ],
          [
            1.6344565204812227e-17,
            1.5698067899702272e-17,
            0.007091060153895778
          ],
          [
            3.50708792979587e-17,
            3.4505500641611594e-17,
            0.005906443572688264
          ],
          [
            3.615345930091114e-17,
            3.6764442497906055e-17,
            0.004723292760074892
          ],
          [
            3.2125008916118665e-17,
            3.293875826297309e-17,
            0.0035413620047148407
          ],
          [
            3.723995317252305e-17,
            3.855989765130638e-17,
            0.002360373168331362
          ],
          [
            5.818021340098197e-17,
            5.866055332715925e-17,
            0.0011800246835077441
          ],
          [
            3.269956073020537e-17,
            3.287858612490591e-17,
            4.7466450455316564e-17
          ]
        ],
        "raw_reduced_polarization": [
          [
            5.046501555492388e-16,
            5.150169934515481e-16,
            0.16218855578490132
          ],
          [
            5.16477208202722e-16,
            5.013990464501387e-16,
            0.141830527673275
          ],
          [
            2.807581627119513e-16,
            2.6965297922701784e-16,
            0.1215037654803851
          ],
          [
            6.024287286325897e-16,
            5.927169577287158e-16,
            0.10120561934378292
          ],
          [
            6.210247064887725e-16,
            6.315198476985039e-16,
            0.08093258883159314
          ],
          [
            5.518261493881169e-16,
            5.658042986180293e-16,
            0.06068046373370854
          ],
          [
            6.396879146787183e-16,
            6.623612120164708e-16,
            0.04044447821156399
          ],
          [
            9.993884582405202e-16,
            1.0076394795103318e-15,
            0.020219464973403174
          ],
          [
            5.616954918689011e-16,
            5.647706939477004e-16,
            8.133272513758835e-16
          ]
        ],
        "unwrapped_reduced_polarization": [
          [
            5.046501555492388e-16,
            5.150169934515481e-16,
            0.16218855578490132
          ],
          [
            5.16477208202722e-16,
            5.013990464501387e-16,
            0.141830527673275
          ],
          [
            2.807581627119513e-16,
            2.6965297922701784e-16,
            0.1215037654803851
          ],
          [
            6.024287286325897e-16,
            5.927169577287158e-16,
            0.10120561934378292
          ],
          [
            6.210247064887725e-16,
            6.315198476985039e-16,
            0.08093258883159314
          ],
          [
            5.518261493881169e-16,
            5.658042986180293e-16,
            0.06068046373370854
          ],
          [
            6.396879146787183e-16,
            6.623612120164708e-16,
            0.04044447821156399
          ],
          [
            9.993884582405202e-16,
            1.0076394795103318e-15,
            0.020219464973403174
          ],
          [
            5.616954918689011e-16,
            5.647706939477004e-16,
            8.118505867571457e-16
          ]
        ],
        "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": [
          [
            5.551115123125783e-16,
            5.551115123125783e-16,
            0.16218855578490132
          ],
          [
            5.551115123125783e-16,
            5.551115123125783e-16,
            0.14183052767327498
          ],
          [
            3.3306690738754696e-16,
            2.220446049250313e-16,
            0.1215037654803851
          ],
          [
            5.551115123125783e-16,
            5.551115123125783e-16,
            0.10120561934378292
          ],
          [
            6.661338147750939e-16,
            6.661338147750939e-16,
            0.08093258883159316
          ],
          [
            5.551115123125783e-16,
            5.551115123125783e-16,
            0.0606804637337085
          ],
          [
            6.661338147750939e-16,
            6.661338147750939e-16,
            0.04044447821156394
          ],
          [
            9.992007221626409e-16,
            9.992007221626409e-16,
            0.02021946497340321
          ],
          [
            5.551115123125783e-16,
            5.551115123125783e-16,
            7.771561172376096e-16
          ]
        ]
      },
      "reflected": {
        "reached": true,
        "construction": "reflect_displacements_about_reconstructed_parent",
        "energies_eV": [
          -41.410227148977626,
          -41.41051392546333,
          -41.41136676585149,
          -41.412763483322294,
          -41.41466800578422,
          -41.41703163927629,
          -41.419794661758296,
          -41.42288810494925,
          -41.42623557775146
        ],
        "cartesian_polarizations_e_A2": [
          [
            1.855937462396959e-17,
            1.7791389380702898e-17,
            3.8518639779136357e-17
          ],
          [
            1.795652467614215e-19,
            8.446896508830252e-19,
            -0.0011800246835076277
          ],
          [
            4.565980084119275e-18,
            5.576833871868636e-18,
            -0.0023603731683312984
          ],
          [
            3.41166309557683e-17,
            3.39673894107687e-17,
            -0.0035413620047147682
          ],
          [
            4.9585517899325287e-17,
            4.9044816220437844e-17,
            -0.004723292760074858
          ],
          [
            -3.873970552784633e-18,
            -4.376839593222568e-18,
            -0.005906443572688251
          ],
          [
            5.974040689715526e-17,
            5.862459819209712e-17,
            -0.007091060153895722
          ],
          [
            3.349604882354485e-17,
            3.28668543866196e-17,
            -0.008277346791794165
          ],
          [
            2.4256410772750052e-17,
            2.4114314739827506e-17,
            -0.009465458134545471
          ]
        ],
        "raw_reduced_polarization": [
          [
            3.188029693793483e-16,
            3.0561093134177695e-16,
            6.600084716213232e-16
          ],
          [
            3.0844753675559182e-18,
            1.4509625155026705e-17,
            -0.020219464973401182
          ],
          [
            7.843195357801603e-17,
            9.579585703231949e-17,
            -0.0404444782115629
          ],
          [
            5.860371631203164e-16,
            5.834735720153022e-16,
            -0.0606804637337073
          ],
          [
            8.517533949717005e-16,
            8.424655119330613e-16,
            -0.08093258883159256
          ],
          [
            -6.654498551480503e-17,
            -7.518299980939809e-17,
            -0.10120561934378268
          ],
          [
            1.0261886241655079e-15,
            1.0070218615111005e-15,
            -0.12150376548038415
          ],
          [
            5.753771365566471e-16,
            5.645691724483267e-16,
            -0.1418305276732755
          ],
          [
            4.1666359656594643e-16,
            4.14222747229664e-16,
            -0.16218855578490135
          ]
        ],
        "unwrapped_reduced_polarization": [
          [
            3.188029693793483e-16,
            3.0561093134177695e-16,
            6.600084716213232e-16
          ],
          [
            3.0844753675559098e-18,
            1.450962515502673e-17,
            -0.020219464973401182
          ],
          [
            7.843195357801603e-17,
            9.579585703231949e-17,
            -0.0404444782115629
          ],
          [
            5.860371631203164e-16,
            5.834735720153022e-16,
            -0.0606804637337073
          ],
          [
            8.517533949717005e-16,
            8.424655119330613e-16,
            -0.08093258883159256
          ],
          [
            -6.654498551480509e-17,
            -7.518299980939801e-17,
            -0.10120561934378268
          ],
          [
            1.0261886241655079e-15,
            1.0070218615111005e-15,
            -0.12150376548038415
          ],
          [
            5.753771365566471e-16,
            5.645691724483267e-16,
            -0.1418305276732755
          ],
          [
            4.1666359656594643e-16,
            4.14222747229664e-16,
            -0.16218855578490135
          ]
        ],
        "gauge_integer_shift": [
          0,
          0,
          0
        ],
        "expected_opposite_endpoint_reduced_polarization": [
          6.187408281885635e-16,
          6.145243944438525e-16,
          -0.16218855578489969
        ],
        "actual_opposite_endpoint_branch_residual": 1.6894659148188217e-15
      },
      "pnp_branch": {
        "construction": "incoming_path_concatenated_with_parent_reflection",
        "reduced_polarization": [
          [
            5.046501555492388e-16,
            5.150169934515481e-16,
            0.16218855578490132
          ],
          [
            5.16477208202722e-16,
            5.013990464501387e-16,
            0.141830527673275
          ],
          [
            2.807581627119513e-16,
            2.6965297922701784e-16,
            0.1215037654803851
          ],
          [
            6.024287286325897e-16,
            5.927169577287158e-16,
            0.10120561934378292
          ],
          [
            6.210247064887725e-16,
            6.315198476985039e-16,
            0.08093258883159314
          ],
          [
            5.518261493881169e-16,
            5.658042986180293e-16,
            0.06068046373370854
          ],
          [
            6.396879146787183e-16,
            6.623612120164708e-16,
            0.04044447821156399
          ],
          [
            9.993884582405202e-16,
            1.0076394795103318e-15,
            0.020219464973403174
          ],
          [
            5.616954918689011e-16,
            5.647706939477004e-16,
            8.133272513758835e-16
          ],
          [
            3.0844753675559182e-18,
            1.4509625155026705e-17,
            -0.020219464973401182
          ],
          [
            7.843195357801603e-17,
            9.579585703231949e-17,
            -0.0404444782115629
          ],
          [
            5.860371631203164e-16,
            5.834735720153022e-16,
            -0.0606804637337073
          ],
          [
            8.517533949717005e-16,
            8.424655119330613e-16,
            -0.08093258883159256
          ],
          [
            -6.654498551480503e-17,
            -7.518299980939809e-17,
            -0.10120561934378268
          ],
          [
            1.0261886241655079e-15,
            1.0070218615111005e-15,
            -0.12150376548038415
          ],
          [
            5.753771365566471e-16,
            5.645691724483267e-16,
            -0.1418305276732755
          ],
          [
            4.1666359656594643e-16,
            4.14222747229664e-16,
            -0.16218855578490135
          ]
        ],
        "unwrapped_reduced_polarization": [
          [
            5.046501555492388e-16,
            5.150169934515481e-16,
            0.16218855578490132
          ],
          [
            5.16477208202722e-16,
            5.013990464501387e-16,
            0.141830527673275
          ],
          [
            2.807581627119513e-16,
            2.6965297922701784e-16,
            0.1215037654803851
          ],
          [
            6.024287286325897e-16,
            5.927169577287158e-16,
            0.10120561934378292
          ],
          [
            6.210247064887725e-16,
            6.315198476985039e-16,
            0.08093258883159314
          ],
          [
            5.518261493881169e-16,
            5.658042986180293e-16,
            0.06068046373370854
          ],
          [
            6.396879146787183e-16,
            6.623612120164708e-16,
            0.04044447821156399
          ],
          [
            9.993884582405202e-16,
            1.0076394795103318e-15,
            0.020219464973403174
          ],
          [
            5.616954918689011e-16,
            5.647706939477004e-16,
            8.118505867571457e-16
          ],
          [
            3.084475367555959e-18,
            1.450962515502673e-17,
            -0.020219464973401182
          ],
          [
            7.843195357801603e-17,
            9.579585703231949e-17,
            -0.0404444782115629
          ],
          [
            5.860371631203164e-16,
            5.834735720153022e-16,
            -0.0606804637337073
          ],
          [
            8.517533949717005e-16,
            8.424655119330613e-16,
            -0.08093258883159256
          ],
          [
            -6.654498551480509e-17,
            -7.518299980939801e-17,
            -0.10120561934378268
          ],
          [
            1.0261886241655079e-15,
            1.0070218615111005e-15,
            -0.12150376548038415
          ],
          [
            5.753771365566471e-16,
            5.645691724483267e-16,
            -0.1418305276732755
          ],
          [
            4.1666359656594643e-16,
            4.14222747229664e-16,
            -0.16218855578490135
          ]
        ],
        "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": [
          [
            5.551115123125783e-16,
            5.551115123125783e-16,
            0.16218855578490132
          ],
          [
            5.551115123125783e-16,
            5.551115123125783e-16,
            0.14183052767327498
          ],
          [
            3.3306690738754696e-16,
            2.220446049250313e-16,
            0.1215037654803851
          ],
          [
            5.551115123125783e-16,
            5.551115123125783e-16,
            0.10120561934378292
          ],
          [
            6.661338147750939e-16,
            6.661338147750939e-16,
            0.08093258883159316
          ],
          [
            5.551115123125783e-16,
            5.551115123125783e-16,
            0.0606804637337085
          ],
          [
            6.661338147750939e-16,
            6.661338147750939e-16,
            0.04044447821156394
          ],
          [
            9.992007221626409e-16,
            9.992007221626409e-16,
            0.02021946497340321
          ],
          [
            5.551115123125783e-16,
            5.551115123125783e-16,
            7.771561172376096e-16
          ],
          [
            0.0,
            0.0,
            -0.020219464973401158
          ],
          [
            1.1102230246251565e-16,
            1.1102230246251565e-16,
            -0.040444478211562884
          ],
          [
            5.551115123125783e-16,
            5.551115123125783e-16,
            -0.06068046373370728
          ],
          [
            8.881784197001252e-16,
            8.881784197001252e-16,
            -0.08093258883159254
          ],
          [
            -5.551115123125783e-17,
            -5.551115123125783e-17,
            -0.1012056193437827
          ],
          [
            9.992007221626409e-16,
            9.992007221626409e-16,
            -0.12150376548038416
          ],
          [
            5.551115123125783e-16,
            5.551115123125783e-16,
            -0.14183052767327553
          ],
          [
            4.440892098500626e-16,
            4.440892098500626e-16,
            -0.16218855578490132
          ]
        ]
      },
      "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": "P4/mmm",
        "spacegroup_number": 123,
        "pointgroup": "4/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": 1.3550610227833532e-17,
        "parent_symmetrization_rmsd_A": 0.13120323592499078,
        "parent_cell_rmsd_A": 0.0,
        "energy_eV": -41.41022714897762,
        "reduced_polarization": [
          7.476356420372805e-19,
          3.608083491849168e-18,
          1.304000812918718e-17
        ],
        "cartesian_polarization_e_A2": [
          4.352421807681182e-20,
          2.1004752035451678e-19,
          7.610256495818944e-19
        ],
        "ranking_score": 0.1312032359249908
      }
    }
  ],
  "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": 52,
      "full_response": 18,
      "energy_polarization": 34
    },
    "model_evaluations_for_recovery_and_path_properties": {
      "total": 77,
      "full_response": 43,
      "energy_polarization": 34
    },
    "elapsed_seconds": 66.95934897399275
  }
}