{
  "schema": "ferrofinder.endpoint_parent_recovery.v4_variable_cell",
  "status": "complete",
  "input_atom_count": 28,
  "input_formula": "Al4Cs4O16Si4",
  "input_spacegroup": "Pna2_1",
  "input_pointgroup": "mm2",
  "input_is_polar_point_group": true,
  "input_energy_eV": -189.5622072003913,
  "input_cartesian_polarization_e_A2": [
    1.3449947681950719e-17,
    -1.58486183084193e-17,
    -0.000508165204260828
  ],
  "input_reduced_polarization": [
    7.054263031086974e-16,
    -7.947129134684322e-16,
    -0.04428842774439402
  ],
  "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": "Pnma",
      "spacegroup_number": 62,
      "pointgroup": "mmm",
      "has_inversion": true,
      "is_polar_point_group": false,
      "nonpolar_parent_hypothesis": true,
      "symmetry_tolerance_A": null,
      "target_reduced_polarization": [
        0.0,
        0.0,
        0.0
      ],
      "formal_class": [
        0.0,
        0.0,
        0.0
      ],
      "target_residual": 5.839751007145552e-16,
      "parent_symmetrization_rmsd_A": 0.09036055165463239,
      "parent_cell_rmsd_A": 0.0,
      "energy_eV": -189.55213076012112,
      "reduced_polarization": [
        -1.8547846762771783e-16,
        2.2892964585510392e-17,
        5.532635614908459e-16
      ],
      "cartesian_polarization_e_A2": [
        -3.536408657754283e-18,
        4.565445603248358e-19,
        6.34814341023105e-18
      ],
      "ranking_score": 0.09036055165463355
    },
    {
      "candidate_id": "symmetry_projection_00",
      "source": "spglib_refine_cell_from_polar_endpoint",
      "spacegroup": "Pnma",
      "spacegroup_number": 62,
      "pointgroup": "mmm",
      "has_inversion": true,
      "is_polar_point_group": false,
      "nonpolar_parent_hypothesis": true,
      "symmetry_tolerance_A": null,
      "target_reduced_polarization": [
        0.0,
        0.0,
        0.0
      ],
      "formal_class": [
        0.0,
        0.0,
        0.0
      ],
      "target_residual": 8.386683570661185e-16,
      "parent_symmetrization_rmsd_A": 1.3671207456673045,
      "parent_cell_rmsd_A": 3.480510000397754,
      "energy_eV": -189.25803814929074,
      "reduced_polarization": [
        -5.366713038736427e-16,
        5.722109437336832e-16,
        -2.9651839844089657e-16
      ],
      "cartesian_polarization_e_A2": [
        -1.0232395542518544e-17,
        6.565545581814306e-18,
        -5.913339067064541e-18
      ],
      "ranking_score": 2.237248245766745
    },
    {
      "candidate_id": "bec_projection_00",
      "source": "MACEField_BEC_backprojection",
      "spacegroup": "Pna2_1",
      "spacegroup_number": 33,
      "pointgroup": "mm2",
      "has_inversion": false,
      "is_polar_point_group": true,
      "nonpolar_parent_hypothesis": false,
      "symmetry_tolerance_A": null,
      "target_reduced_polarization": [
        0.0,
        0.0,
        0.0
      ],
      "formal_class": [
        0.0,
        0.0,
        0.0
      ],
      "target_residual": 1.219875239521763e-05,
      "parent_symmetrization_rmsd_A": 0.004079036060202629,
      "parent_cell_rmsd_A": 0.0008372165971471089,
      "energy_eV": -189.55453713506705,
      "reduced_polarization": [
        -1.312039829468891e-15,
        -1.2137916919341614e-16,
        -1.219875239521763e-05
      ],
      "cartesian_polarization_e_A2": [
        -2.5015876746564244e-17,
        -2.420423764007085e-18,
        -1.3998519575589708e-07
      ],
      "ranking_score": 0.5043127377142799
    },
    {
      "candidate_id": "inversion_parent_bec_00_00",
      "source": "same_species_inversion_center_projection_after_BEC",
      "spacegroup": "Pnma",
      "spacegroup_number": 62,
      "pointgroup": "mmm",
      "has_inversion": true,
      "is_polar_point_group": false,
      "nonpolar_parent_hypothesis": true,
      "symmetry_tolerance_A": null,
      "target_reduced_polarization": [
        0.0,
        0.0,
        0.0
      ],
      "formal_class": [
        0.0,
        0.0,
        0.0
      ],
      "target_residual": 3.449034921780593e-15,
      "parent_symmetrization_rmsd_A": 0.09036055749660625,
      "parent_cell_rmsd_A": 0.0008372165971471089,
      "energy_eV": -189.5520533047199,
      "reduced_polarization": [
        -2.797417052428589e-16,
        3.432857162794459e-15,
        -1.818740494426161e-16
      ],
      "cartesian_polarization_e_A2": [
        -5.3336284140994444e-18,
        6.84530624994339e-17,
        -2.0870719881258696e-18
      ],
      "ranking_score": 0.09056986164589992
    },
    {
      "candidate_id": "symmetry_parent_00_00",
      "source": "spglib_refine_cell_after_MACEField_BEC_backprojection",
      "spacegroup": "Pnma",
      "spacegroup_number": 62,
      "pointgroup": "mmm",
      "has_inversion": true,
      "is_polar_point_group": false,
      "nonpolar_parent_hypothesis": true,
      "symmetry_tolerance_A": null,
      "target_reduced_polarization": [
        0.0,
        0.0,
        0.0
      ],
      "formal_class": [
        0.0,
        0.0,
        0.0
      ],
      "target_residual": 1.6127634989092629e-15,
      "parent_symmetrization_rmsd_A": 1.367416737241446,
      "parent_cell_rmsd_A": 3.479758180986974,
      "energy_eV": -189.27279487697325,
      "reduced_polarization": [
        8.118590793461396e-16,
        3.915344119945169e-16,
        1.337382422092273e-15
      ],
      "cartesian_polarization_e_A2": [
        1.5479117245266866e-17,
        4.493002196659858e-18,
        2.6668142070497222e-17
      ],
      "ranking_score": 2.2373562824881925
    },
    {
      "candidate_id": "bec_projection_01",
      "source": "MACEField_BEC_backprojection",
      "spacegroup": "Pna2_1",
      "spacegroup_number": 33,
      "pointgroup": "mm2",
      "has_inversion": false,
      "is_polar_point_group": true,
      "nonpolar_parent_hypothesis": false,
      "symmetry_tolerance_A": null,
      "target_reduced_polarization": [
        0.0,
        0.0,
        -0.5
      ],
      "formal_class": [
        0.0,
        0.0,
        0.5
      ],
      "target_residual": 2.5442506892459082e-05,
      "parent_symmetrization_rmsd_A": 0.04202485599369556,
      "parent_cell_rmsd_A": 0.008622542860898556,
      "energy_eV": -188.7858359613725,
      "reduced_polarization": [
        -3.3313013114076135e-15,
        -2.9747392798332175e-15,
        -0.49997455749310754
      ],
      "cartesian_polarization_e_A2": [
        1.3412977233619548e-17,
        -3.521721737190222e-17,
        -0.005729637967123257
      ],
      "ranking_score": 0.5442313767227052
    },
    {
      "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": 5.487557631111407e-06,
      "parent_symmetrization_rmsd_A": 0.07510871925740185,
      "parent_cell_rmsd_A": 0.025602987267210296,
      "energy_eV": -186.50748266136648,
      "reduced_polarization": [
        6.304004980084891e-16,
        -0.4999987768279352,
        -5.349498934915147e-06
      ],
      "cartesian_polarization_e_A2": [
        9.739662436033825e-18,
        -0.009970475263197626,
        -4.2690152391111035e-05
      ],
      "ranking_score": 0.5815204411894667
    },
    {
      "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": 1.2252289519611978e-06,
      "parent_symmetrization_rmsd_A": 0.07775050838708619,
      "parent_cell_rmsd_A": 0.003895611991667364,
      "energy_eV": -186.49143195712134,
      "reduced_polarization": [
        0.4999992424127341,
        -1.4223208398238527e-15,
        -9.629369238112654e-07
      ],
      "cartesian_polarization_e_A2": [
        0.009533118585010686,
        1.855899734981771e-17,
        -6.3487049549600744e-06
      ],
      "ranking_score": 0.578726861842907
    },
    {
      "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": 4.862607416229433e-06,
      "parent_symmetrization_rmsd_A": 0.08678748432910931,
      "parent_cell_rmsd_A": 0.02739586757842614,
      "energy_eV": -185.8563353554065,
      "reduced_polarization": [
        1.187586810850408e-15,
        -0.49999594624929655,
        -0.49999731447284157
      ],
      "cartesian_polarization_e_A2": [
        -1.5379614418435703e-16,
        -0.010006753267674274,
        -0.005772916850844936
      ],
      "ranking_score": 0.5936461764385483
    },
    {
      "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": 1.8906075178842431e-06,
      "parent_symmetrization_rmsd_A": 0.08863559620643281,
      "parent_cell_rmsd_A": 0.009500082142660808,
      "energy_eV": -185.72831012158568,
      "reduced_polarization": [
        0.499998952274223,
        -1.5155217912213108e-15,
        -0.49999842625685614
      ],
      "cartesian_polarization_e_A2": [
        0.009537789320989965,
        1.998105079698352e-16,
        -0.005736204864463696
      ],
      "ranking_score": 0.5910143979571338
    },
    {
      "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": 1.3425377619378926e-06,
      "parent_symmetrization_rmsd_A": 0.10923936423554961,
      "parent_cell_rmsd_A": 0.026322309970530654,
      "energy_eV": -183.15316232623715,
      "reduced_polarization": [
        0.4999999768122071,
        -0.4999996672374151,
        -1.300438014899581e-06
      ],
      "cartesian_polarization_e_A2": [
        0.009533162540572737,
        -0.009970588700681054,
        -4.979098581887893e-05
      ],
      "ranking_score": 0.6158226268037061
    },
    {
      "candidate_id": "bec_projection_07",
      "source": "MACEField_BEC_backprojection",
      "spacegroup": "P1",
      "spacegroup_number": 1,
      "pointgroup": "1",
      "has_inversion": false,
      "is_polar_point_group": true,
      "nonpolar_parent_hypothesis": false,
      "symmetry_tolerance_A": null,
      "target_reduced_polarization": [
        0.5,
        -0.5,
        -0.5
      ],
      "formal_class": [
        0.5,
        0.5,
        0.5
      ],
      "target_residual": 4.330780371793287e-07,
      "parent_symmetrization_rmsd_A": 0.11796494086178971,
      "parent_cell_rmsd_A": 0.02823101851147652,
      "energy_eV": -182.492726613627,
      "reduced_polarization": [
        0.4999995706412289,
        -0.5000000150866758,
        -0.4999999454104022
      ],
      "cartesian_polarization_e_A2": [
        0.00953790310492924,
        -0.010007610457713008,
        -0.005780109435198428
      ],
      "ranking_score": 0.6250235616457331
    }
  ],
  "formal_branches": [
    {
      "orbit_id": 0,
      "formal_class": [
        0.0,
        0.0,
        0.0
      ],
      "formal_classes_in_orbit": [
        [
          0.0,
          0.0,
          0.0
        ]
      ],
      "target_reduced_polarization": [
        0.0,
        0.0,
        0.0
      ],
      "bec_backprojection": {
        "converged_to_target": true,
        "history": [
          {
            "iteration": 0,
            "reduced_polarization": [
              7.054263031086974e-16,
              -7.947129134684322e-16,
              -0.04428842774439402
            ],
            "branch_aligned_reduced_polarization": [
              7.054263031086974e-16,
              -7.947129134684322e-16,
              -0.04428842774439402
            ],
            "target_residual": 0.04428842774439402,
            "energy_eV": -189.5622072003913,
            "max_atomic_step_A": 0.005346841036584041,
            "max_log_strain_component": 0.00011446876057556579,
            "step_scale": 1.0,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 0.6565850236591441,
            "cell_principal_stretches": [
              1.000114475312374,
              0.9999868146479599,
              0.9998933842826749
            ],
            "cell_volume_ratio": 0.9999946619346706,
            "cell_rmsd_from_input_A": 0.0008372165971471089
          },
          {
            "iteration": 1,
            "reduced_polarization": [
              -1.312039829468891e-15,
              -1.2137916919341614e-16,
              -1.219875239521763e-05
            ],
            "branch_aligned_reduced_polarization": [
              -1.312039829468891e-15,
              -1.2137916919341614e-16,
              -1.219875239521763e-05
            ],
            "target_residual": 1.219875239521763e-05,
            "energy_eV": -189.55453713506705
          }
        ],
        "iterations": 1
      },
      "parent": {
        "candidate_id": "inversion_parent_endpoint_00",
        "source": "same_species_inversion_center_projection_from_endpoint",
        "spacegroup": "Pnma",
        "spacegroup_number": 62,
        "pointgroup": "mmm",
        "has_inversion": true,
        "is_polar_point_group": false,
        "nonpolar_parent_hypothesis": true,
        "symmetry_tolerance_A": null,
        "target_reduced_polarization": [
          0.0,
          0.0,
          0.0
        ],
        "formal_class": [
          0.0,
          0.0,
          0.0
        ],
        "target_residual": 5.839751007145552e-16,
        "parent_symmetrization_rmsd_A": 0.09036055165463239,
        "parent_cell_rmsd_A": 0.0,
        "energy_eV": -189.55213076012112,
        "reduced_polarization": [
          -1.8547846762771783e-16,
          2.2892964585510392e-17,
          5.532635614908459e-16
        ],
        "cartesian_polarization_e_A2": [
          -3.536408657754283e-18,
          4.565445603248358e-19,
          6.34814341023105e-18
        ],
        "ranking_score": 0.09036055165463355
      },
      "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": [
          -189.5622072003913,
          -189.560857993241,
          -189.55915673112213,
          -189.55735205128158,
          -189.55564188719242,
          -189.55417594694867,
          -189.55306092213044,
          -189.55236641589005,
          -189.55213076012114
        ],
        "cartesian_polarizations_e_A2": [
          [
            4.304562997348452e-18,
            3.087110836482223e-18,
            -0.0005081652042608221
          ],
          [
            -8.710580341435756e-18,
            4.314708432022337e-17,
            -0.00044402178983213737
          ],
          [
            -3.4929282234376326e-18,
            1.7471887856240938e-17,
            -0.00038006035143525713
          ],
          [
            2.405917365521357e-18,
            -4.1096257168287996e-17,
            -0.0003162893944273021
          ],
          [
            -1.9131391099326452e-18,
            -2.7697036659706707e-17,
            -0.0002527136875099361
          ],
          [
            -1.826178241299343e-18,
            -4.530298918842398e-17,
            -0.000189327889066149
          ],
          [
            -5.797391242220137e-20,
            -3.549452788049279e-17,
            -0.00012611057409673824
          ],
          [
            -2.8552151867934177e-18,
            6.398870583600476e-18,
            -6.302084493503817e-05
          ],
          [
            -8.768554253857957e-18,
            -3.1958119222738508e-18,
            1.734869329234376e-17
          ]
        ],
        "raw_reduced_polarization": [
          [
            2.2576682330095163e-16,
            1.5480004624487979e-16,
            -0.04428842774439351
          ],
          [
            -4.568547501813871e-16,
            2.163566843525855e-15,
            -0.038698098159872386
          ],
          [
            -1.8319799466508197e-16,
            8.761101208835803e-16,
            -0.033123628441922626
          ],
          [
            1.261861705991851e-16,
            -2.0607301930861815e-15,
            -0.027565759863049946
          ],
          [
            -1.003408103559785e-16,
            -1.388839851520964e-15,
            -0.02202490803277916
          ],
          [
            -9.577986443070676e-17,
            -2.2716725096240983e-15,
            -0.01650060740994963
          ],
          [
            -3.0406306168478333e-18,
            -1.779837151425871e-15,
            -0.010990990728717195
          ],
          [
            -1.4975105787975582e-16,
            3.208648845873917e-16,
            -0.005492493610136088
          ],
          [
            -4.598953807982348e-16,
            -1.6025075209857275e-16,
            1.5120011029784078e-15
          ]
        ],
        "unwrapped_reduced_polarization": [
          [
            2.2576682330095163e-16,
            1.5480004624487979e-16,
            -0.04428842774439351
          ],
          [
            -4.56854750181387e-16,
            2.163566843525855e-15,
            -0.038698098159872386
          ],
          [
            -1.8319799466508197e-16,
            8.761101208835802e-16,
            -0.033123628441922626
          ],
          [
            1.261861705991851e-16,
            -2.0607301930861815e-15,
            -0.027565759863049946
          ],
          [
            -1.0034081035597848e-16,
            -1.388839851520964e-15,
            -0.02202490803277916
          ],
          [
            -9.577986443070676e-17,
            -2.2716725096240983e-15,
            -0.01650060740994963
          ],
          [
            -3.040630616847831e-18,
            -1.779837151425871e-15,
            -0.010990990728717195
          ],
          [
            -1.4975105787975584e-16,
            3.208648845873916e-16,
            -0.005492493610136088
          ],
          [
            -4.598953807982348e-16,
            -1.602507520985728e-16,
            1.5118115093137874e-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": [
          [
            2.220446049250313e-16,
            1.1102230246251565e-16,
            -0.04428842774439351
          ],
          [
            -4.440892098500626e-16,
            2.1094237467877974e-15,
            -0.03869809815987241
          ],
          [
            -1.6653345369377348e-16,
            8.881784197001252e-16,
            -0.033123628441922626
          ],
          [
            1.1102230246251565e-16,
            -2.0539125955565396e-15,
            -0.027565759863049932
          ],
          [
            -1.1102230246251565e-16,
            -1.3877787807814457e-15,
            -0.022024908032779178
          ],
          [
            -1.1102230246251565e-16,
            -2.275957200481571e-15,
            -0.01650060740994963
          ],
          [
            0.0,
            -1.7763568394002505e-15,
            -0.010990990728717176
          ],
          [
            -1.6653345369377348e-16,
            3.3306690738754696e-16,
            -0.0054924936101360955
          ],
          [
            -4.440892098500626e-16,
            -1.6653345369377348e-16,
            1.5543122344752192e-15
          ]
        ]
      },
      "reflected": {
        "reached": true,
        "construction": "reflect_displacements_about_reconstructed_parent",
        "energies_eV": [
          -189.5521307601211,
          -189.55236641589005,
          -189.55306092213038,
          -189.5541759469487,
          -189.55564188719234,
          -189.55735205128164,
          -189.55915673112216,
          -189.56085799324106,
          -189.56220720039138
        ],
        "cartesian_polarizations_e_A2": [
          [
            -6.927882534453064e-18,
            2.7682543181601153e-18,
            1.5290619401355612e-17
          ],
          [
            -8.551152082274702e-19,
            5.797391242220137e-20,
            6.30208449350879e-05
          ],
          [
            3.478434745332082e-18,
            -2.8262282305823167e-19,
            0.00012611057409679237
          ],
          [
            -4.087160825765197e-18,
            -1.904443023069315e-17,
            0.00018932788906619313
          ],
          [
            -7.145284706036319e-18,
            -1.1877405307498507e-17,
            0.0002527136875099462
          ],
          [
            -2.4349043217324574e-18,
            -3.1675496399680275e-17,
            0.00031628939442731777
          ],
          [
            -8.580139038485803e-18,
            2.414613452384687e-17,
            0.00038006035143531443
          ],
          [
            -5.8118847203256874e-18,
            3.937153327372751e-17,
            0.0004440217898321798
          ],
          [
            -7.840971655102735e-18,
            -2.8805787734781307e-17,
            0.0005081652042608733
          ]
        ],
        "raw_reduced_polarization": [
          [
            -3.6335535871331614e-16,
            1.3881130907404714e-16,
            1.3326325510795491e-15
          ],
          [
            -4.484930159850554e-17,
            2.9070431219695735e-18,
            0.005492493610140423
          ],
          [
            1.8243783701087e-16,
            -1.417183521960167e-17,
            0.010990990728721912
          ],
          [
            -2.1436445848777226e-16,
            -9.54963665567005e-16,
            0.016500607409953478
          ],
          [
            -3.7475772352649546e-16,
            -5.955804596135164e-16,
            0.022024908032780045
          ],
          [
            -1.27706485907609e-16,
            -1.5883356857661258e-15,
            0.027565759863051313
          ],
          [
            -4.500133312934793e-16,
            1.2107834603003273e-15,
            0.03312362844192762
          ],
          [
            -3.048232193389953e-16,
            1.974245660207587e-15,
            0.038698098159876085
          ],
          [
            -4.112452909286695e-16,
            -1.444437051228632e-15,
            0.044288427744397965
          ]
        ],
        "unwrapped_reduced_polarization": [
          [
            -3.6335535871331614e-16,
            1.3881130907404714e-16,
            1.3326325510795491e-15
          ],
          [
            -4.484930159850554e-17,
            2.907043121969563e-18,
            0.005492493610140423
          ],
          [
            1.8243783701087e-16,
            -1.417183521960167e-17,
            0.010990990728721912
          ],
          [
            -2.1436445848777226e-16,
            -9.54963665567005e-16,
            0.016500607409953478
          ],
          [
            -3.7475772352649546e-16,
            -5.955804596135164e-16,
            0.022024908032780045
          ],
          [
            -1.2770648590760898e-16,
            -1.5883356857661258e-15,
            0.027565759863051313
          ],
          [
            -4.500133312934793e-16,
            1.2107834603003271e-15,
            0.03312362844192762
          ],
          [
            -3.048232193389953e-16,
            1.974245660207587e-15,
            0.038698098159876085
          ],
          [
            -4.112452909286695e-16,
            -1.444437051228632e-15,
            0.044288427744397965
          ]
        ],
        "gauge_integer_shift": [
          0,
          0,
          0
        ],
        "expected_opposite_endpoint_reduced_polarization": [
          -1.1455575848974213e-15,
          -4.753015504420254e-16,
          0.04428842774439653
        ],
        "actual_opposite_endpoint_branch_residual": 1.881898633995671e-15
      },
      "pnp_branch": {
        "construction": "incoming_path_concatenated_with_parent_reflection",
        "reduced_polarization": [
          [
            2.2576682330095163e-16,
            1.5480004624487979e-16,
            -0.04428842774439351
          ],
          [
            -4.568547501813871e-16,
            2.163566843525855e-15,
            -0.038698098159872386
          ],
          [
            -1.8319799466508197e-16,
            8.761101208835803e-16,
            -0.033123628441922626
          ],
          [
            1.261861705991851e-16,
            -2.0607301930861815e-15,
            -0.027565759863049946
          ],
          [
            -1.003408103559785e-16,
            -1.388839851520964e-15,
            -0.02202490803277916
          ],
          [
            -9.577986443070676e-17,
            -2.2716725096240983e-15,
            -0.01650060740994963
          ],
          [
            -3.0406306168478333e-18,
            -1.779837151425871e-15,
            -0.010990990728717195
          ],
          [
            -1.4975105787975582e-16,
            3.208648845873917e-16,
            -0.005492493610136088
          ],
          [
            -4.598953807982348e-16,
            -1.6025075209857275e-16,
            1.5120011029784078e-15
          ],
          [
            -4.484930159850554e-17,
            2.9070431219695735e-18,
            0.005492493610140423
          ],
          [
            1.8243783701087e-16,
            -1.417183521960167e-17,
            0.010990990728721912
          ],
          [
            -2.1436445848777226e-16,
            -9.54963665567005e-16,
            0.016500607409953478
          ],
          [
            -3.7475772352649546e-16,
            -5.955804596135164e-16,
            0.022024908032780045
          ],
          [
            -1.27706485907609e-16,
            -1.5883356857661258e-15,
            0.027565759863051313
          ],
          [
            -4.500133312934793e-16,
            1.2107834603003273e-15,
            0.03312362844192762
          ],
          [
            -3.048232193389953e-16,
            1.974245660207587e-15,
            0.038698098159876085
          ],
          [
            -4.112452909286695e-16,
            -1.444437051228632e-15,
            0.044288427744397965
          ]
        ],
        "unwrapped_reduced_polarization": [
          [
            2.2576682330095163e-16,
            1.5480004624487979e-16,
            -0.04428842774439351
          ],
          [
            -4.56854750181387e-16,
            2.163566843525855e-15,
            -0.038698098159872386
          ],
          [
            -1.8319799466508197e-16,
            8.761101208835802e-16,
            -0.033123628441922626
          ],
          [
            1.261861705991851e-16,
            -2.0607301930861815e-15,
            -0.027565759863049946
          ],
          [
            -1.0034081035597848e-16,
            -1.388839851520964e-15,
            -0.02202490803277916
          ],
          [
            -9.577986443070676e-17,
            -2.2716725096240983e-15,
            -0.01650060740994963
          ],
          [
            -3.040630616847831e-18,
            -1.779837151425871e-15,
            -0.010990990728717195
          ],
          [
            -1.4975105787975584e-16,
            3.208648845873916e-16,
            -0.005492493610136088
          ],
          [
            -4.598953807982348e-16,
            -1.602507520985728e-16,
            1.5118115093137874e-15
          ],
          [
            -4.484930159850554e-17,
            2.907043121969563e-18,
            0.005492493610140423
          ],
          [
            1.8243783701087e-16,
            -1.417183521960167e-17,
            0.010990990728721912
          ],
          [
            -2.1436445848777226e-16,
            -9.54963665567005e-16,
            0.016500607409953478
          ],
          [
            -3.7475772352649546e-16,
            -5.955804596135164e-16,
            0.022024908032780045
          ],
          [
            -1.2770648590760898e-16,
            -1.5883356857661258e-15,
            0.027565759863051313
          ],
          [
            -4.500133312934793e-16,
            1.2107834603003271e-15,
            0.03312362844192762
          ],
          [
            -3.048232193389953e-16,
            1.974245660207587e-15,
            0.038698098159876085
          ],
          [
            -4.112452909286695e-16,
            -1.444437051228632e-15,
            0.044288427744397965
          ]
        ],
        "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": [
          [
            2.220446049250313e-16,
            1.1102230246251565e-16,
            -0.04428842774439351
          ],
          [
            -4.440892098500626e-16,
            2.1094237467877974e-15,
            -0.03869809815987241
          ],
          [
            -1.6653345369377348e-16,
            8.881784197001252e-16,
            -0.033123628441922626
          ],
          [
            1.1102230246251565e-16,
            -2.0539125955565396e-15,
            -0.027565759863049932
          ],
          [
            -1.1102230246251565e-16,
            -1.3877787807814457e-15,
            -0.022024908032779178
          ],
          [
            -1.1102230246251565e-16,
            -2.275957200481571e-15,
            -0.01650060740994963
          ],
          [
            0.0,
            -1.7763568394002505e-15,
            -0.010990990728717176
          ],
          [
            -1.6653345369377348e-16,
            3.3306690738754696e-16,
            -0.0054924936101360955
          ],
          [
            -4.440892098500626e-16,
            -1.6653345369377348e-16,
            1.5543122344752192e-15
          ],
          [
            -5.551115123125783e-17,
            0.0,
            0.00549249361014037
          ],
          [
            2.220446049250313e-16,
            0.0,
            0.010990990728721894
          ],
          [
            -2.220446049250313e-16,
            -9.43689570931383e-16,
            0.016500607409953516
          ],
          [
            -3.885780586188048e-16,
            -6.106226635438361e-16,
            0.02202490803278001
          ],
          [
            -1.1102230246251565e-16,
            -1.609823385706477e-15,
            0.02756575986305132
          ],
          [
            -4.440892098500626e-16,
            1.2212453270876722e-15,
            0.03312362844192762
          ],
          [
            -2.7755575615628914e-16,
            1.9984014443252818e-15,
            0.038698098159876126
          ],
          [
            -3.885780586188048e-16,
            -1.4432899320127035e-15,
            0.04428842774439801
          ]
        ]
      },
      "incoming_structure_ids": [
        "incoming_00_000",
        "incoming_00_001",
        "incoming_00_002",
        "incoming_00_003",
        "incoming_00_004",
        "incoming_00_005",
        "incoming_00_006",
        "incoming_00_007",
        "incoming_00_008"
      ],
      "reflected_structure_ids": [
        "reflected_00_001",
        "reflected_00_002",
        "reflected_00_003",
        "reflected_00_004",
        "reflected_00_005",
        "reflected_00_006",
        "reflected_00_007",
        "reflected_00_008"
      ]
    },
    {
      "orbit_id": 1,
      "formal_class": [
        0.0,
        0.0,
        0.5
      ],
      "formal_classes_in_orbit": [
        [
          0.0,
          0.0,
          0.5
        ]
      ],
      "target_reduced_polarization": [
        0.0,
        0.0,
        -0.5
      ],
      "bec_backprojection": {
        "converged_to_target": true,
        "history": [
          {
            "iteration": 0,
            "reduced_polarization": [
              7.054263031086974e-16,
              -7.947129134684322e-16,
              -0.04428842774439402
            ],
            "branch_aligned_reduced_polarization": [
              7.054263031086974e-16,
              -7.947129134684322e-16,
              -0.04428842774439401
            ],
            "target_residual": 0.455711572255606,
            "energy_eV": -189.5622072003913,
            "max_atomic_step_A": 0.05501702046063111,
            "max_log_strain_component": 0.001177841289763206,
            "step_scale": 1.0,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 0.6565850236591441,
            "cell_principal_stretches": [
              1.0010976968872194,
              1.0001356825035643,
              0.9988228520930305
            ],
            "cell_volume_ratio": 1.000054928376785,
            "cell_rmsd_from_input_A": 0.008622542860898556
          },
          {
            "iteration": 1,
            "reduced_polarization": [
              -3.3313013114076135e-15,
              -2.9747392798332175e-15,
              -0.49997455749310754
            ],
            "branch_aligned_reduced_polarization": [
              -3.3313013114076135e-15,
              -2.9747392798332175e-15,
              -0.49997455749310754
            ],
            "target_residual": 2.5442506892459082e-05,
            "energy_eV": -188.7858359613725
          }
        ],
        "iterations": 1
      },
      "parent": {
        "candidate_id": "bec_projection_01",
        "source": "MACEField_BEC_backprojection",
        "spacegroup": "Pna2_1",
        "spacegroup_number": 33,
        "pointgroup": "mm2",
        "has_inversion": false,
        "is_polar_point_group": true,
        "nonpolar_parent_hypothesis": false,
        "symmetry_tolerance_A": null,
        "target_reduced_polarization": [
          0.0,
          0.0,
          -0.5
        ],
        "formal_class": [
          0.0,
          0.0,
          0.5
        ],
        "target_residual": 2.5442506892459082e-05,
        "parent_symmetrization_rmsd_A": 0.04202485599369556,
        "parent_cell_rmsd_A": 0.008622542860898556,
        "energy_eV": -188.7858359613725,
        "reduced_polarization": [
          -3.3313013114076135e-15,
          -2.9747392798332175e-15,
          -0.49997455749310754
        ],
        "cartesian_polarization_e_A2": [
          1.3412977233619548e-17,
          -3.521721737190222e-17,
          -0.005729637967123257
        ],
        "ranking_score": 0.5442313767227052
      },
      "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": [
              7.054263031086974e-16,
              -7.947129134684322e-16,
              -0.04428842774439402
            ],
            "branch_aligned_reduced_polarization": [
              7.054263031086974e-16,
              -7.771561172376096e-16,
              -0.04428842774439402
            ],
            "target_residual": 0.5019576325070371,
            "energy_eV": -189.5622072003913,
            "max_atomic_step_A": 0.1035669869487486,
            "max_log_strain_component": 0.004239068930557919,
            "step_scale": 1.0,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 0.6565850236591441,
            "cell_principal_stretches": [
              1.0042534541114017,
              0.9999868146479512,
              0.9957723752865265
            ],
            "cell_volume_ratio": 0.9999946619346898,
            "cell_rmsd_from_input_A": 0.025389829133315504
          },
          {
            "iteration": 1,
            "reduced_polarization": [
              -1.9416036444475867e-15,
              -0.4960310359813036,
              0.005570570486167468
            ],
            "branch_aligned_reduced_polarization": [
              -1.9416036444475867e-15,
              -0.4960310359813036,
              0.005570570486167468
            ],
            "target_residual": 0.006839877990364062,
            "energy_eV": -186.55443399916908,
            "max_atomic_step_A": 0.0010945712423529362,
            "max_log_strain_component": 3.6112295000734726e-05,
            "step_scale": 1.0,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 0.6565850236591441,
            "cell_principal_stretches": [
              1.0042888370705934,
              0.9999885497939407,
              0.9957362640898466
            ],
            "cell_volume_ratio": 0.9999953644077205,
            "cell_rmsd_from_input_A": 0.025602987267210296
          },
          {
            "iteration": 2,
            "reduced_polarization": [
              6.304004980084891e-16,
              -0.4999987768279352,
              -5.349498934915147e-06
            ],
            "branch_aligned_reduced_polarization": [
              6.304004980084891e-16,
              -0.4999987768279352,
              -5.349498934915147e-06
            ],
            "target_residual": 5.487557631111407e-06,
            "energy_eV": -186.50748266136648
          }
        ],
        "iterations": 2
      },
      "parent": {
        "candidate_id": "bec_projection_02",
        "source": "MACEField_BEC_backprojection",
        "spacegroup": "Pc",
        "spacegroup_number": 7,
        "pointgroup": "m",
        "has_inversion": false,
        "is_polar_point_group": true,
        "nonpolar_parent_hypothesis": false,
        "symmetry_tolerance_A": null,
        "target_reduced_polarization": [
          0.0,
          -0.5,
          0.0
        ],
        "formal_class": [
          0.0,
          0.5,
          0.0
        ],
        "target_residual": 5.487557631111407e-06,
        "parent_symmetrization_rmsd_A": 0.07510871925740185,
        "parent_cell_rmsd_A": 0.025602987267210296,
        "energy_eV": -186.50748266136648,
        "reduced_polarization": [
          6.304004980084891e-16,
          -0.4999987768279352,
          -5.349498934915147e-06
        ],
        "cartesian_polarization_e_A2": [
          9.739662436033825e-18,
          -0.009970475263197626,
          -4.2690152391111035e-05
        ],
        "ranking_score": 0.5815204411894667
      },
      "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": [
              7.054263031086974e-16,
              -7.947129134684322e-16,
              -0.04428842774439402
            ],
            "branch_aligned_reduced_polarization": [
              7.216449660063518e-16,
              -7.947129134684322e-16,
              -0.04428842774439402
            ],
            "target_residual": 0.5019576325070371,
            "energy_eV": -189.5622072003913,
            "max_atomic_step_A": 0.10179757728705201,
            "max_log_strain_component": 0.0006593273704928661,
            "step_scale": 1.0,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 0.6565850236591441,
            "cell_principal_stretches": [
              1.0007133055437794,
              0.9998933842826608,
              0.9993884191511649
            ],
            "cell_volume_ratio": 0.9999946619346542,
            "cell_rmsd_from_input_A": 0.00386601942313512
          },
          {
            "iteration": 1,
            "reduced_polarization": [
              0.4960629275211473,
              7.636332270830583e-16,
              0.00017677928458469455
            ],
            "branch_aligned_reduced_polarization": [
              0.4960629275211473,
              7.636332270830583e-16,
              0.00017677928458469455
            ],
            "target_residual": 0.003941039281610599,
            "energy_eV": -186.54345261423464,
            "max_atomic_step_A": 0.0008397175651641094,
            "max_log_strain_component": 5.4349640505266346e-06,
            "step_scale": 1.0,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 0.6565850236591441,
            "cell_principal_stretches": [
              1.0007184709001165,
              0.9998938507595385,
              0.9993828177639925
            ],
            "cell_volume_ratio": 0.9999946852915252,
            "cell_rmsd_from_input_A": 0.003895611991667364
          },
          {
            "iteration": 2,
            "reduced_polarization": [
              0.4999992424127341,
              -1.4223208398238527e-15,
              -9.629369238112654e-07
            ],
            "branch_aligned_reduced_polarization": [
              0.4999992424127341,
              -1.4223208398238527e-15,
              -9.629369238112654e-07
            ],
            "target_residual": 1.2252289519611978e-06,
            "energy_eV": -186.49143195712134
          }
        ],
        "iterations": 2
      },
      "parent": {
        "candidate_id": "bec_projection_03",
        "source": "MACEField_BEC_backprojection",
        "spacegroup": "Pc",
        "spacegroup_number": 7,
        "pointgroup": "m",
        "has_inversion": false,
        "is_polar_point_group": true,
        "nonpolar_parent_hypothesis": false,
        "symmetry_tolerance_A": null,
        "target_reduced_polarization": [
          0.5,
          0.0,
          0.0
        ],
        "formal_class": [
          0.5,
          0.0,
          0.0
        ],
        "target_residual": 1.2252289519611978e-06,
        "parent_symmetrization_rmsd_A": 0.07775050838708619,
        "parent_cell_rmsd_A": 0.003895611991667364,
        "energy_eV": -186.49143195712134,
        "reduced_polarization": [
          0.4999992424127341,
          -1.4223208398238527e-15,
          -9.629369238112654e-07
        ],
        "cartesian_polarization_e_A2": [
          0.009533118585010686,
          1.855899734981771e-17,
          -6.3487049549600744e-06
        ],
        "ranking_score": 0.578726861842907
      },
      "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": [
              7.054263031086974e-16,
              -7.947129134684322e-16,
              -0.04428842774439402
            ],
            "branch_aligned_reduced_polarization": [
              7.054263031086974e-16,
              -7.771561172376096e-16,
              -0.04428842774439401
            ],
            "target_residual": 0.6765153635267093,
            "energy_eV": -189.5622072003913,
            "max_atomic_step_A": 0.11747391091787594,
            "max_log_strain_component": 0.004239068930553304,
            "step_scale": 1.0,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 0.6565850236591441,
            "cell_principal_stretches": [
              1.0043581207275794,
              1.0001356825035557,
              0.9955803972633986
            ],
            "cell_volume_ratio": 1.0000549283768039,
            "cell_rmsd_from_input_A": 0.026837446529296788
          },
          {
            "iteration": 1,
            "reduced_polarization": [
              3.910031745757795e-15,
              -0.4907046113805665,
              -0.4902802051811559
            ],
            "branch_aligned_reduced_polarization": [
              3.910031745757795e-15,
              -0.4907046113805665,
              -0.4902802051811559
            ],
            "target_residual": 0.013449113759156138,
            "energy_eV": -186.0073160472881,
            "max_atomic_step_A": 0.002385664642698966,
            "max_log_strain_component": 8.678194484210571e-05,
            "step_scale": 1.0,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 0.6565850236591441,
            "cell_principal_stretches": [
              1.0044482879009946,
              1.0001388579475494,
              0.9954891450465259
            ],
            "cell_volume_ratio": 1.000056213839359,
            "cell_rmsd_from_input_A": 0.02739586757842614
          },
          {
            "iteration": 2,
            "reduced_polarization": [
              1.187586810850408e-15,
              -0.49999594624929655,
              -0.49999731447284157
            ],
            "branch_aligned_reduced_polarization": [
              1.187586810850408e-15,
              -0.49999594624929655,
              -0.49999731447284157
            ],
            "target_residual": 4.862607416229433e-06,
            "energy_eV": -185.8563353554065
          }
        ],
        "iterations": 2
      },
      "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": 4.862607416229433e-06,
        "parent_symmetrization_rmsd_A": 0.08678748432910931,
        "parent_cell_rmsd_A": 0.02739586757842614,
        "energy_eV": -185.8563353554065,
        "reduced_polarization": [
          1.187586810850408e-15,
          -0.49999594624929655,
          -0.49999731447284157
        ],
        "cartesian_polarization_e_A2": [
          -1.5379614418435703e-16,
          -0.010006753267674274,
          -0.005772916850844936
        ],
        "ranking_score": 0.5936461764385483
      },
      "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": [
              7.054263031086974e-16,
              -7.947129134684322e-16,
              -0.04428842774439402
            ],
            "branch_aligned_reduced_polarization": [
              7.216449660063518e-16,
              -7.947129134684322e-16,
              -0.04428842774439401
            ],
            "target_residual": 0.6765153635267094,
            "energy_eV": -189.5622072003913,
            "max_atomic_step_A": 0.11628530956630413,
            "max_log_strain_component": 0.001177841289763858,
            "step_scale": 1.0,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 0.6565850236591441,
            "cell_principal_stretches": [
              1.0010976968872052,
              1.0004096140395988,
              0.9985493550431591
            ],
            "cell_volume_ratio": 1.0000549283767683,
            "cell_rmsd_from_input_A": 0.009410637074825062
          },
          {
            "iteration": 1,
            "reduced_polarization": [
              0.4944167306675625,
              -8.860901742936882e-15,
              -0.49612007751317994
            ],
            "branch_aligned_reduced_polarization": [
              0.4944167306675625,
              -8.860901742936882e-15,
              -0.49612007751317994
            ],
            "target_residual": 0.006799021616546703,
            "energy_eV": -185.81557396897475,
            "max_atomic_step_A": 0.001275053766305828,
            "max_log_strain_component": 1.0667577279963676e-05,
            "step_scale": 1.0,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 0.6565850236591441,
            "cell_principal_stretches": [
              1.0011076441094846,
              1.0004146139322445,
              0.9985349394573463
            ],
            "cell_volume_ratio": 1.0000554258707408,
            "cell_rmsd_from_input_A": 0.009500082142660808
          },
          {
            "iteration": 2,
            "reduced_polarization": [
              0.499998952274223,
              -1.5155217912213108e-15,
              -0.49999842625685614
            ],
            "branch_aligned_reduced_polarization": [
              0.499998952274223,
              -1.5155217912213108e-15,
              -0.49999842625685614
            ],
            "target_residual": 1.8906075178842431e-06,
            "energy_eV": -185.72831012158568
          }
        ],
        "iterations": 2
      },
      "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": 1.8906075178842431e-06,
        "parent_symmetrization_rmsd_A": 0.08863559620643281,
        "parent_cell_rmsd_A": 0.009500082142660808,
        "energy_eV": -185.72831012158568,
        "reduced_polarization": [
          0.499998952274223,
          -1.5155217912213108e-15,
          -0.49999842625685614
        ],
        "cartesian_polarization_e_A2": [
          0.009537789320989965,
          1.998105079698352e-16,
          -0.005736204864463696
        ],
        "ranking_score": 0.5910143979571338
      },
      "branch_status": "awaiting_branch_sampling"
    },
    {
      "orbit_id": 6,
      "formal_class": [
        0.5,
        0.5,
        0.0
      ],
      "formal_classes_in_orbit": [
        [
          0.5,
          0.5,
          0.0
        ]
      ],
      "target_reduced_polarization": [
        0.5,
        -0.5,
        0.0
      ],
      "bec_backprojection": {
        "converged_to_target": true,
        "history": [
          {
            "iteration": 0,
            "reduced_polarization": [
              7.054263031086974e-16,
              -7.947129134684322e-16,
              -0.04428842774439402
            ],
            "branch_aligned_reduced_polarization": [
              7.216449660063518e-16,
              -7.771561172376096e-16,
              -0.04428842774439402
            ],
            "target_residual": 0.7084923886902872,
            "energy_eV": -189.5622072003913,
            "max_atomic_step_A": 0.12,
            "max_log_strain_component": 0.0033644242939401573,
            "step_scale": 0.793670579330793,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 0.6565850236591441,
            "cell_principal_stretches": [
              1.003415812555641,
              0.9999877847083153,
              0.9966037670608882
            ],
            "cell_volume_ratio": 0.9999957633322664,
            "cell_rmsd_from_input_A": 0.020372949836537455
          },
          {
            "iteration": 1,
            "reduced_polarization": [
              0.39328902652771297,
              -0.3922743418466809,
              -0.004942179329699435
            ],
            "branch_aligned_reduced_polarization": [
              0.39328902652771297,
              -0.3922743418466809,
              -0.004942179329699435
            ],
            "target_residual": 0.151711813714344,
            "energy_eV": -185.79474299317323,
            "max_atomic_step_A": 0.03412497204383858,
            "max_log_strain_component": 0.0009742014524986463,
            "step_scale": 1.0,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 0.6565850236591441,
            "cell_principal_stretches": [
              1.0044050074038169,
              0.9999876067069103,
              0.9956223665565379
            ],
            "cell_volume_ratio": 0.9999956970592683,
            "cell_rmsd_from_input_A": 0.026264877862341298
          },
          {
            "iteration": 2,
            "reduced_polarization": [
              0.49920861973814634,
              -0.498982077067922,
              0.0006103364422885922
            ],
            "branch_aligned_reduced_polarization": [
              0.49920861973814634,
              -0.498982077067922,
              0.0006103364422885922
            ],
            "target_residual": 0.0014265203774525205,
            "energy_eV": -183.17858359265864,
            "max_atomic_step_A": 0.00030810871085897696,
            "max_log_strain_component": 9.584830135732097e-06,
            "step_scale": 1.0,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 0.6565850236591441,
            "cell_principal_stretches": [
              1.0044145820685781,
              0.9999878489569883,
              0.9956127176911583
            ],
            "cell_volume_ratio": 0.9999957806025351,
            "cell_rmsd_from_input_A": 0.026322309970530654
          },
          {
            "iteration": 3,
            "reduced_polarization": [
              0.4999999768122071,
              -0.4999996672374151,
              -1.300438014899581e-06
            ],
            "branch_aligned_reduced_polarization": [
              0.4999999768122071,
              -0.4999996672374151,
              -1.300438014899581e-06
            ],
            "target_residual": 1.3425377619378926e-06,
            "energy_eV": -183.15316232623715
          }
        ],
        "iterations": 3
      },
      "parent": {
        "candidate_id": "bec_projection_06",
        "source": "MACEField_BEC_backprojection",
        "spacegroup": "P1",
        "spacegroup_number": 1,
        "pointgroup": "1",
        "has_inversion": false,
        "is_polar_point_group": true,
        "nonpolar_parent_hypothesis": false,
        "symmetry_tolerance_A": null,
        "target_reduced_polarization": [
          0.5,
          -0.5,
          0.0
        ],
        "formal_class": [
          0.5,
          0.5,
          0.0
        ],
        "target_residual": 1.3425377619378926e-06,
        "parent_symmetrization_rmsd_A": 0.10923936423554961,
        "parent_cell_rmsd_A": 0.026322309970530654,
        "energy_eV": -183.15316232623715,
        "reduced_polarization": [
          0.4999999768122071,
          -0.4999996672374151,
          -1.300438014899581e-06
        ],
        "cartesian_polarization_e_A2": [
          0.009533162540572737,
          -0.009970588700681054,
          -4.979098581887893e-05
        ],
        "ranking_score": 0.6158226268037061
      },
      "branch_status": "awaiting_branch_sampling"
    },
    {
      "orbit_id": 7,
      "formal_class": [
        0.5,
        0.5,
        0.5
      ],
      "formal_classes_in_orbit": [
        [
          0.5,
          0.5,
          0.5
        ]
      ],
      "target_reduced_polarization": [
        0.5,
        -0.5,
        -0.5
      ],
      "bec_backprojection": {
        "converged_to_target": true,
        "history": [
          {
            "iteration": 0,
            "reduced_polarization": [
              7.054263031086974e-16,
              -7.947129134684322e-16,
              -0.04428842774439402
            ],
            "branch_aligned_reduced_polarization": [
              7.216449660063518e-16,
              -7.771561172376096e-16,
              -0.04428842774439401
            ],
            "target_residual": 0.8412330456464933,
            "energy_eV": -189.5622072003913,
            "max_atomic_step_A": 0.12,
            "max_log_strain_component": 0.0031489703083992936,
            "step_scale": 0.7428447991732128,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 0.6565850236591441,
            "cell_principal_stretches": [
              1.0032640333240552,
              1.0001165833086396,
              0.9966710609398787
            ],
            "cell_volume_ratio": 1.0000408029708547,
            "cell_rmsd_from_input_A": 0.020124945558142406
          },
          {
            "iteration": 1,
            "reduced_polarization": [
              0.3677087898258843,
              -0.3650074210943048,
              -0.3760738144473316
            ],
            "branch_aligned_reduced_polarization": [
              0.3677087898258843,
              -0.3650074210943048,
              -0.3760738144473316
            ],
            "target_residual": 0.2260125220304769,
            "energy_eV": -185.98163464349318,
            "max_atomic_step_A": 0.04493822994935773,
            "max_log_strain_component": 0.001244464793398106,
            "step_scale": 1.0,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 0.6565850236591441,
            "cell_principal_stretches": [
              1.0045571266578346,
              1.000162884452518,
              0.9953583520332251
            ],
            "cell_volume_ratio": 1.0000571933532587,
            "cell_rmsd_from_input_A": 0.02809611596674968
          },
          {
            "iteration": 2,
            "reduced_polarization": [
              0.49864613631536264,
              -0.4979070501515139,
              -0.4974211268657351
            ],
            "branch_aligned_reduced_polarization": [
              0.49864613631536264,
              -0.4979070501515139,
              -0.4974211268657351
            ],
            "target_residual": 0.0035866380619587585,
            "energy_eV": -182.55064015173508,
            "max_atomic_step_A": 0.0006752690899976283,
            "max_log_strain_component": 2.0530370151590668e-05,
            "step_scale": 1.0,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 0.6565850236591441,
            "cell_principal_stretches": [
              1.0045787192059719,
              1.000163812731026,
              0.995336383944194
            ],
            "cell_volume_ratio": 1.000057545087646,
            "cell_rmsd_from_input_A": 0.02823101851147652
          },
          {
            "iteration": 3,
            "reduced_polarization": [
              0.4999995706412289,
              -0.5000000150866758,
              -0.4999999454104022
            ],
            "branch_aligned_reduced_polarization": [
              0.4999995706412289,
              -0.5000000150866758,
              -0.4999999454104022
            ],
            "target_residual": 4.330780371793287e-07,
            "energy_eV": -182.492726613627
          }
        ],
        "iterations": 3
      },
      "parent": {
        "candidate_id": "bec_projection_07",
        "source": "MACEField_BEC_backprojection",
        "spacegroup": "P1",
        "spacegroup_number": 1,
        "pointgroup": "1",
        "has_inversion": false,
        "is_polar_point_group": true,
        "nonpolar_parent_hypothesis": false,
        "symmetry_tolerance_A": null,
        "target_reduced_polarization": [
          0.5,
          -0.5,
          -0.5
        ],
        "formal_class": [
          0.5,
          0.5,
          0.5
        ],
        "target_residual": 4.330780371793287e-07,
        "parent_symmetrization_rmsd_A": 0.11796494086178971,
        "parent_cell_rmsd_A": 0.02823101851147652,
        "energy_eV": -182.492726613627,
        "reduced_polarization": [
          0.4999995706412289,
          -0.5000000150866758,
          -0.4999999454104022
        ],
        "cartesian_polarization_e_A2": [
          0.00953790310492924,
          -0.010007610457713008,
          -0.005780109435198428
        ],
        "ranking_score": 0.6250235616457331
      },
      "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
        ],
        "endpoint_rmsd_A": 0.09036055165463239,
        "minimum_distance_A_by_image": [
          1.6261814911448385,
          1.6261812247579925,
          1.6261809938893572,
          1.6259151797232014,
          1.6250633381482553,
          1.6244004858653578,
          1.6239268542987122,
          1.623642609040626,
          1.6235478495624422
        ],
        "minimum_distance_A": 1.6235478495624422,
        "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": [
          478.7597465131537,
          478.7597465131537,
          478.7597465131537,
          478.7597465131537,
          478.7597465131537,
          478.7597465131537,
          478.7597465131537,
          478.7597465131537,
          478.7597465131537
        ],
        "cell_deformation_log_strain_norm": 0.0
      },
      "parent_reduced_polarization": [
        -4.598953807982348e-16,
        -1.6025075209857275e-16,
        1.5120011029784078e-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": [
          -189.5622072003913,
          -189.560857993241,
          -189.55915673112213,
          -189.55735205128158,
          -189.55564188719242,
          -189.55417594694867,
          -189.55306092213044,
          -189.55236641589005,
          -189.55213076012114
        ],
        "cartesian_polarizations_e_A2": [
          [
            4.304562997348452e-18,
            3.087110836482223e-18,
            -0.0005081652042608221
          ],
          [
            -8.710580341435756e-18,
            4.314708432022337e-17,
            -0.00044402178983213737
          ],
          [
            -3.4929282234376326e-18,
            1.7471887856240938e-17,
            -0.00038006035143525713
          ],
          [
            2.405917365521357e-18,
            -4.1096257168287996e-17,
            -0.0003162893944273021
          ],
          [
            -1.9131391099326452e-18,
            -2.7697036659706707e-17,
            -0.0002527136875099361
          ],
          [
            -1.826178241299343e-18,
            -4.530298918842398e-17,
            -0.000189327889066149
          ],
          [
            -5.797391242220137e-20,
            -3.549452788049279e-17,
            -0.00012611057409673824
          ],
          [
            -2.8552151867934177e-18,
            6.398870583600476e-18,
            -6.302084493503817e-05
          ],
          [
            -8.768554253857957e-18,
            -3.1958119222738508e-18,
            1.734869329234376e-17
          ]
        ],
        "raw_reduced_polarization": [
          [
            2.2576682330095163e-16,
            1.5480004624487979e-16,
            -0.04428842774439351
          ],
          [
            -4.568547501813871e-16,
            2.163566843525855e-15,
            -0.038698098159872386
          ],
          [
            -1.8319799466508197e-16,
            8.761101208835803e-16,
            -0.033123628441922626
          ],
          [
            1.261861705991851e-16,
            -2.0607301930861815e-15,
            -0.027565759863049946
          ],
          [
            -1.003408103559785e-16,
            -1.388839851520964e-15,
            -0.02202490803277916
          ],
          [
            -9.577986443070676e-17,
            -2.2716725096240983e-15,
            -0.01650060740994963
          ],
          [
            -3.0406306168478333e-18,
            -1.779837151425871e-15,
            -0.010990990728717195
          ],
          [
            -1.4975105787975582e-16,
            3.208648845873917e-16,
            -0.005492493610136088
          ],
          [
            -4.598953807982348e-16,
            -1.6025075209857275e-16,
            1.5120011029784078e-15
          ]
        ],
        "unwrapped_reduced_polarization": [
          [
            2.2576682330095163e-16,
            1.5480004624487979e-16,
            -0.04428842774439351
          ],
          [
            -4.56854750181387e-16,
            2.163566843525855e-15,
            -0.038698098159872386
          ],
          [
            -1.8319799466508197e-16,
            8.761101208835802e-16,
            -0.033123628441922626
          ],
          [
            1.261861705991851e-16,
            -2.0607301930861815e-15,
            -0.027565759863049946
          ],
          [
            -1.0034081035597848e-16,
            -1.388839851520964e-15,
            -0.02202490803277916
          ],
          [
            -9.577986443070676e-17,
            -2.2716725096240983e-15,
            -0.01650060740994963
          ],
          [
            -3.040630616847831e-18,
            -1.779837151425871e-15,
            -0.010990990728717195
          ],
          [
            -1.4975105787975584e-16,
            3.208648845873916e-16,
            -0.005492493610136088
          ],
          [
            -4.598953807982348e-16,
            -1.602507520985728e-16,
            1.5118115093137874e-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": [
          [
            2.220446049250313e-16,
            1.1102230246251565e-16,
            -0.04428842774439351
          ],
          [
            -4.440892098500626e-16,
            2.1094237467877974e-15,
            -0.03869809815987241
          ],
          [
            -1.6653345369377348e-16,
            8.881784197001252e-16,
            -0.033123628441922626
          ],
          [
            1.1102230246251565e-16,
            -2.0539125955565396e-15,
            -0.027565759863049932
          ],
          [
            -1.1102230246251565e-16,
            -1.3877787807814457e-15,
            -0.022024908032779178
          ],
          [
            -1.1102230246251565e-16,
            -2.275957200481571e-15,
            -0.01650060740994963
          ],
          [
            0.0,
            -1.7763568394002505e-15,
            -0.010990990728717176
          ],
          [
            -1.6653345369377348e-16,
            3.3306690738754696e-16,
            -0.0054924936101360955
          ],
          [
            -4.440892098500626e-16,
            -1.6653345369377348e-16,
            1.5543122344752192e-15
          ]
        ]
      },
      "reflected": {
        "reached": true,
        "construction": "reflect_displacements_about_reconstructed_parent",
        "energies_eV": [
          -189.5521307601211,
          -189.55236641589005,
          -189.55306092213038,
          -189.5541759469487,
          -189.55564188719234,
          -189.55735205128164,
          -189.55915673112216,
          -189.56085799324106,
          -189.56220720039138
        ],
        "cartesian_polarizations_e_A2": [
          [
            -6.927882534453064e-18,
            2.7682543181601153e-18,
            1.5290619401355612e-17
          ],
          [
            -8.551152082274702e-19,
            5.797391242220137e-20,
            6.30208449350879e-05
          ],
          [
            3.478434745332082e-18,
            -2.8262282305823167e-19,
            0.00012611057409679237
          ],
          [
            -4.087160825765197e-18,
            -1.904443023069315e-17,
            0.00018932788906619313
          ],
          [
            -7.145284706036319e-18,
            -1.1877405307498507e-17,
            0.0002527136875099462
          ],
          [
            -2.4349043217324574e-18,
            -3.1675496399680275e-17,
            0.00031628939442731777
          ],
          [
            -8.580139038485803e-18,
            2.414613452384687e-17,
            0.00038006035143531443
          ],
          [
            -5.8118847203256874e-18,
            3.937153327372751e-17,
            0.0004440217898321798
          ],
          [
            -7.840971655102735e-18,
            -2.8805787734781307e-17,
            0.0005081652042608733
          ]
        ],
        "raw_reduced_polarization": [
          [
            -3.6335535871331614e-16,
            1.3881130907404714e-16,
            1.3326325510795491e-15
          ],
          [
            -4.484930159850554e-17,
            2.9070431219695735e-18,
            0.005492493610140423
          ],
          [
            1.8243783701087e-16,
            -1.417183521960167e-17,
            0.010990990728721912
          ],
          [
            -2.1436445848777226e-16,
            -9.54963665567005e-16,
            0.016500607409953478
          ],
          [
            -3.7475772352649546e-16,
            -5.955804596135164e-16,
            0.022024908032780045
          ],
          [
            -1.27706485907609e-16,
            -1.5883356857661258e-15,
            0.027565759863051313
          ],
          [
            -4.500133312934793e-16,
            1.2107834603003273e-15,
            0.03312362844192762
          ],
          [
            -3.048232193389953e-16,
            1.974245660207587e-15,
            0.038698098159876085
          ],
          [
            -4.112452909286695e-16,
            -1.444437051228632e-15,
            0.044288427744397965
          ]
        ],
        "unwrapped_reduced_polarization": [
          [
            -3.6335535871331614e-16,
            1.3881130907404714e-16,
            1.3326325510795491e-15
          ],
          [
            -4.484930159850554e-17,
            2.907043121969563e-18,
            0.005492493610140423
          ],
          [
            1.8243783701087e-16,
            -1.417183521960167e-17,
            0.010990990728721912
          ],
          [
            -2.1436445848777226e-16,
            -9.54963665567005e-16,
            0.016500607409953478
          ],
          [
            -3.7475772352649546e-16,
            -5.955804596135164e-16,
            0.022024908032780045
          ],
          [
            -1.2770648590760898e-16,
            -1.5883356857661258e-15,
            0.027565759863051313
          ],
          [
            -4.500133312934793e-16,
            1.2107834603003271e-15,
            0.03312362844192762
          ],
          [
            -3.048232193389953e-16,
            1.974245660207587e-15,
            0.038698098159876085
          ],
          [
            -4.112452909286695e-16,
            -1.444437051228632e-15,
            0.044288427744397965
          ]
        ],
        "gauge_integer_shift": [
          0,
          0,
          0
        ],
        "expected_opposite_endpoint_reduced_polarization": [
          -1.1455575848974213e-15,
          -4.753015504420254e-16,
          0.04428842774439653
        ],
        "actual_opposite_endpoint_branch_residual": 1.881898633995671e-15
      },
      "pnp_branch": {
        "construction": "incoming_path_concatenated_with_parent_reflection",
        "reduced_polarization": [
          [
            2.2576682330095163e-16,
            1.5480004624487979e-16,
            -0.04428842774439351
          ],
          [
            -4.568547501813871e-16,
            2.163566843525855e-15,
            -0.038698098159872386
          ],
          [
            -1.8319799466508197e-16,
            8.761101208835803e-16,
            -0.033123628441922626
          ],
          [
            1.261861705991851e-16,
            -2.0607301930861815e-15,
            -0.027565759863049946
          ],
          [
            -1.003408103559785e-16,
            -1.388839851520964e-15,
            -0.02202490803277916
          ],
          [
            -9.577986443070676e-17,
            -2.2716725096240983e-15,
            -0.01650060740994963
          ],
          [
            -3.0406306168478333e-18,
            -1.779837151425871e-15,
            -0.010990990728717195
          ],
          [
            -1.4975105787975582e-16,
            3.208648845873917e-16,
            -0.005492493610136088
          ],
          [
            -4.598953807982348e-16,
            -1.6025075209857275e-16,
            1.5120011029784078e-15
          ],
          [
            -4.484930159850554e-17,
            2.9070431219695735e-18,
            0.005492493610140423
          ],
          [
            1.8243783701087e-16,
            -1.417183521960167e-17,
            0.010990990728721912
          ],
          [
            -2.1436445848777226e-16,
            -9.54963665567005e-16,
            0.016500607409953478
          ],
          [
            -3.7475772352649546e-16,
            -5.955804596135164e-16,
            0.022024908032780045
          ],
          [
            -1.27706485907609e-16,
            -1.5883356857661258e-15,
            0.027565759863051313
          ],
          [
            -4.500133312934793e-16,
            1.2107834603003273e-15,
            0.03312362844192762
          ],
          [
            -3.048232193389953e-16,
            1.974245660207587e-15,
            0.038698098159876085
          ],
          [
            -4.112452909286695e-16,
            -1.444437051228632e-15,
            0.044288427744397965
          ]
        ],
        "unwrapped_reduced_polarization": [
          [
            2.2576682330095163e-16,
            1.5480004624487979e-16,
            -0.04428842774439351
          ],
          [
            -4.56854750181387e-16,
            2.163566843525855e-15,
            -0.038698098159872386
          ],
          [
            -1.8319799466508197e-16,
            8.761101208835802e-16,
            -0.033123628441922626
          ],
          [
            1.261861705991851e-16,
            -2.0607301930861815e-15,
            -0.027565759863049946
          ],
          [
            -1.0034081035597848e-16,
            -1.388839851520964e-15,
            -0.02202490803277916
          ],
          [
            -9.577986443070676e-17,
            -2.2716725096240983e-15,
            -0.01650060740994963
          ],
          [
            -3.040630616847831e-18,
            -1.779837151425871e-15,
            -0.010990990728717195
          ],
          [
            -1.4975105787975584e-16,
            3.208648845873916e-16,
            -0.005492493610136088
          ],
          [
            -4.598953807982348e-16,
            -1.602507520985728e-16,
            1.5118115093137874e-15
          ],
          [
            -4.484930159850554e-17,
            2.907043121969563e-18,
            0.005492493610140423
          ],
          [
            1.8243783701087e-16,
            -1.417183521960167e-17,
            0.010990990728721912
          ],
          [
            -2.1436445848777226e-16,
            -9.54963665567005e-16,
            0.016500607409953478
          ],
          [
            -3.7475772352649546e-16,
            -5.955804596135164e-16,
            0.022024908032780045
          ],
          [
            -1.2770648590760898e-16,
            -1.5883356857661258e-15,
            0.027565759863051313
          ],
          [
            -4.500133312934793e-16,
            1.2107834603003271e-15,
            0.03312362844192762
          ],
          [
            -3.048232193389953e-16,
            1.974245660207587e-15,
            0.038698098159876085
          ],
          [
            -4.112452909286695e-16,
            -1.444437051228632e-15,
            0.044288427744397965
          ]
        ],
        "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": [
          [
            2.220446049250313e-16,
            1.1102230246251565e-16,
            -0.04428842774439351
          ],
          [
            -4.440892098500626e-16,
            2.1094237467877974e-15,
            -0.03869809815987241
          ],
          [
            -1.6653345369377348e-16,
            8.881784197001252e-16,
            -0.033123628441922626
          ],
          [
            1.1102230246251565e-16,
            -2.0539125955565396e-15,
            -0.027565759863049932
          ],
          [
            -1.1102230246251565e-16,
            -1.3877787807814457e-15,
            -0.022024908032779178
          ],
          [
            -1.1102230246251565e-16,
            -2.275957200481571e-15,
            -0.01650060740994963
          ],
          [
            0.0,
            -1.7763568394002505e-15,
            -0.010990990728717176
          ],
          [
            -1.6653345369377348e-16,
            3.3306690738754696e-16,
            -0.0054924936101360955
          ],
          [
            -4.440892098500626e-16,
            -1.6653345369377348e-16,
            1.5543122344752192e-15
          ],
          [
            -5.551115123125783e-17,
            0.0,
            0.00549249361014037
          ],
          [
            2.220446049250313e-16,
            0.0,
            0.010990990728721894
          ],
          [
            -2.220446049250313e-16,
            -9.43689570931383e-16,
            0.016500607409953516
          ],
          [
            -3.885780586188048e-16,
            -6.106226635438361e-16,
            0.02202490803278001
          ],
          [
            -1.1102230246251565e-16,
            -1.609823385706477e-15,
            0.02756575986305132
          ],
          [
            -4.440892098500626e-16,
            1.2212453270876722e-15,
            0.03312362844192762
          ],
          [
            -2.7755575615628914e-16,
            1.9984014443252818e-15,
            0.038698098159876126
          ],
          [
            -3.885780586188048e-16,
            -1.4432899320127035e-15,
            0.04428842774439801
          ]
        ]
      },
      "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": "Pnma",
        "spacegroup_number": 62,
        "pointgroup": "mmm",
        "has_inversion": true,
        "is_polar_point_group": false,
        "nonpolar_parent_hypothesis": true,
        "symmetry_tolerance_A": null,
        "target_reduced_polarization": [
          0.0,
          0.0,
          0.0
        ],
        "formal_class": [
          0.0,
          0.0,
          0.0
        ],
        "target_residual": 5.839751007145552e-16,
        "parent_symmetrization_rmsd_A": 0.09036055165463239,
        "parent_cell_rmsd_A": 0.0,
        "energy_eV": -189.55213076012112,
        "reduced_polarization": [
          -1.8547846762771783e-16,
          2.2892964585510392e-17,
          5.532635614908459e-16
        ],
        "cartesian_polarization_e_A2": [
          -3.536408657754283e-18,
          4.565445603248358e-19,
          6.34814341023105e-18
        ],
        "ranking_score": 0.09036055165463355
      }
    }
  ],
  "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": 51,
      "full_response": 17,
      "energy_polarization": 34
    },
    "model_evaluations_for_recovery_and_path_properties": {
      "total": 76,
      "full_response": 42,
      "energy_polarization": 34
    },
    "elapsed_seconds": 587.7266595789697
  }
}