{
  "schema": "ferrofinder.endpoint_parent_recovery.v4_variable_cell",
  "status": "complete",
  "input_atom_count": 18,
  "input_formula": "K2Li2O10Si4",
  "input_spacegroup": "P2_1",
  "input_pointgroup": "2",
  "input_is_polar_point_group": true,
  "input_energy_eV": -119.22742062566527,
  "input_cartesian_polarization_e_A2": [
    1.391250926610665e-10,
    -0.0010255477608689502,
    -8.483199343671534e-11
  ],
  "input_reduced_polarization": [
    5.406203805838582e-09,
    -0.05162436938372586,
    -2.510672541994593e-09
  ],
  "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,
        0.5,
        0.0
      ],
      "target_reduced_polarization": [
        0.0,
        -0.5,
        0.0
      ]
    },
    {
      "orbit_id": 2,
      "representative_formal_class": [
        0.5,
        0.0,
        0.0
      ],
      "target_reduced_polarization": [
        0.5,
        0.0,
        0.0
      ]
    },
    {
      "orbit_id": 3,
      "representative_formal_class": [
        0.0,
        0.0,
        0.5
      ],
      "target_reduced_polarization": [
        0.0,
        0.0,
        -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": [
        0.0,
        0.5,
        0.5
      ],
      "target_reduced_polarization": [
        0.0,
        -0.5,
        -0.5
      ]
    },
    {
      "orbit_id": 6,
      "representative_formal_class": [
        0.5,
        0.0,
        0.5
      ],
      "target_reduced_polarization": [
        0.5,
        0.0,
        -0.5
      ]
    },
    {
      "orbit_id": 7,
      "representative_formal_class": [
        0.5,
        0.5,
        0.5
      ],
      "target_reduced_polarization": [
        0.5,
        -0.5,
        -0.5
      ]
    }
  ],
  "parent_candidates": [
    {
      "candidate_id": "inversion_parent_endpoint_00",
      "source": "same_species_inversion_center_projection_from_endpoint",
      "spacegroup": "P2_1/m",
      "spacegroup_number": 11,
      "pointgroup": "2/m",
      "has_inversion": true,
      "is_polar_point_group": false,
      "nonpolar_parent_hypothesis": true,
      "symmetry_tolerance_A": null,
      "target_reduced_polarization": [
        0.0,
        0.0,
        0.0
      ],
      "formal_class": [
        0.0,
        0.0,
        0.0
      ],
      "target_residual": 7.462475374655307e-16,
      "parent_symmetrization_rmsd_A": 0.39809216009749443,
      "parent_cell_rmsd_A": 0.0,
      "energy_eV": -112.75464902921549,
      "reduced_polarization": [
        -9.216221085842965e-17,
        -5.516760619322125e-18,
        7.40514064292721e-16
      ],
      "cartesian_polarization_e_A2": [
        -3.792760716993195e-18,
        -1.0959361960127595e-19,
        2.5020899058373018e-17
      ],
      "ranking_score": 0.39809216009749593
    },
    {
      "candidate_id": "inversion_parent_endpoint_01",
      "source": "same_species_inversion_center_projection_from_endpoint",
      "spacegroup": "P2_1/m",
      "spacegroup_number": 11,
      "pointgroup": "2/m",
      "has_inversion": true,
      "is_polar_point_group": false,
      "nonpolar_parent_hypothesis": true,
      "symmetry_tolerance_A": null,
      "target_reduced_polarization": [
        0.0,
        0.0,
        0.0
      ],
      "formal_class": [
        0.0,
        0.0,
        0.0
      ],
      "target_residual": 3.5025349551316542e-15,
      "parent_symmetrization_rmsd_A": 0.4828372964614371,
      "parent_cell_rmsd_A": 0.0,
      "energy_eV": -108.5133312252145,
      "reduced_polarization": [
        3.303092882489057e-15,
        -1.153182880434986e-15,
        1.6582450313780257e-16
      ],
      "cartesian_polarization_e_A2": [
        8.154095045539522e-17,
        -2.2908640531991167e-17,
        5.60297009129554e-18
      ],
      "ranking_score": 0.4828372964614441
    },
    {
      "candidate_id": "inversion_parent_endpoint_02",
      "source": "same_species_inversion_center_projection_from_endpoint",
      "spacegroup": "P2_1/m",
      "spacegroup_number": 11,
      "pointgroup": "2/m",
      "has_inversion": true,
      "is_polar_point_group": false,
      "nonpolar_parent_hypothesis": true,
      "symmetry_tolerance_A": null,
      "target_reduced_polarization": [
        0.0,
        0.0,
        0.0
      ],
      "formal_class": [
        0.0,
        0.0,
        0.0
      ],
      "target_residual": 1.2935371054422763e-15,
      "parent_symmetrization_rmsd_A": 0.4862933974768126,
      "parent_cell_rmsd_A": 0.0,
      "energy_eV": -110.12382091137124,
      "reduced_polarization": [
        -5.310974077548586e-16,
        6.6927482649087675e-18,
        1.1794613150725693e-15
      ],
      "cartesian_polarization_e_A2": [
        -1.5567301450345203e-17,
        1.3295528989648967e-19,
        3.985229171288372e-17
      ],
      "ranking_score": 0.4862933974768152
    },
    {
      "candidate_id": "bec_projection_00",
      "source": "MACEField_BEC_backprojection",
      "spacegroup": "P2_1",
      "spacegroup_number": 4,
      "pointgroup": "2",
      "has_inversion": false,
      "is_polar_point_group": true,
      "nonpolar_parent_hypothesis": false,
      "symmetry_tolerance_A": null,
      "target_reduced_polarization": [
        0.0,
        0.0,
        0.0
      ],
      "formal_class": [
        0.0,
        0.0,
        0.0
      ],
      "target_residual": 0.00018618322728352154,
      "parent_symmetrization_rmsd_A": 0.006076959207795058,
      "parent_cell_rmsd_A": 0.0020606367005953055,
      "energy_eV": -119.21870485575252,
      "reduced_polarization": [
        2.1745177904391163e-11,
        0.00018618322728352027,
        8.117266100618141e-13
      ],
      "cartesian_polarization_e_A2": [
        5.372541554772181e-13,
        3.69708051732421e-06,
        2.7490022853706957e-14
      ],
      "ranking_score": 0.5069644848375109
    },
    {
      "candidate_id": "inversion_parent_bec_00_00",
      "source": "same_species_inversion_center_projection_after_BEC",
      "spacegroup": "P2_1/m",
      "spacegroup_number": 11,
      "pointgroup": "2/m",
      "has_inversion": true,
      "is_polar_point_group": false,
      "nonpolar_parent_hypothesis": true,
      "symmetry_tolerance_A": null,
      "target_reduced_polarization": [
        0.0,
        0.0,
        0.0
      ],
      "formal_class": [
        0.0,
        0.0,
        0.0
      ],
      "target_residual": 6.256684637892516e-15,
      "parent_symmetrization_rmsd_A": 0.3980927767282817,
      "parent_cell_rmsd_A": 0.0020606367005953055,
      "energy_eV": -112.80637404986791,
      "reduced_polarization": [
        9.828921446394208e-16,
        6.174543491023292e-15,
        -2.3460257353281904e-16
      ],
      "cartesian_polarization_e_A2": [
        2.485513124019776e-17,
        1.2260924239293976e-16,
        -7.92646554357104e-18
      ],
      "ranking_score": 0.398607935903443
    },
    {
      "candidate_id": "inversion_parent_bec_00_01",
      "source": "same_species_inversion_center_projection_after_BEC",
      "spacegroup": "P2_1/m",
      "spacegroup_number": 11,
      "pointgroup": "2/m",
      "has_inversion": true,
      "is_polar_point_group": false,
      "nonpolar_parent_hypothesis": true,
      "symmetry_tolerance_A": null,
      "target_reduced_polarization": [
        0.0,
        0.0,
        0.0
      ],
      "formal_class": [
        0.0,
        0.0,
        0.0
      ],
      "target_residual": 2.7792456164334367e-15,
      "parent_symmetrization_rmsd_A": 0.482837345344,
      "parent_cell_rmsd_A": 0.0020606367005953055,
      "energy_eV": -108.49824603298914,
      "reduced_polarization": [
        -5.32175218703147e-16,
        2.5795864796548856e-15,
        -8.869776361580068e-16
      ],
      "cartesian_polarization_e_A2": [
        -1.1393964703799247e-17,
        5.122340533060472e-17,
        -2.9976672403728805e-17
      ],
      "ranking_score": 0.4833525045191544
    },
    {
      "candidate_id": "bec_projection_01",
      "source": "MACEField_BEC_backprojection",
      "spacegroup": "P2_1",
      "spacegroup_number": 4,
      "pointgroup": "2",
      "has_inversion": false,
      "is_polar_point_group": true,
      "nonpolar_parent_hypothesis": false,
      "symmetry_tolerance_A": null,
      "target_reduced_polarization": [
        0.0,
        -0.5,
        0.0
      ],
      "formal_class": [
        0.0,
        0.5,
        0.0
      ],
      "target_residual": 3.5840936333853e-05,
      "parent_symmetrization_rmsd_A": 0.054241939661388704,
      "parent_cell_rmsd_A": 0.01853631696546476,
      "energy_eV": -118.38440204606233,
      "reduced_polarization": [
        -3.649797643333413e-13,
        -0.49996415906366615,
        2.5231668005764225e-13
      ],
      "cartesian_polarization_e_A2": [
        1.2229878119602606e-12,
        -0.009969724052236567,
        -1.57385287633855e-13
      ],
      "ranking_score": 0.5589477007754226
    },
    {
      "candidate_id": "bec_projection_02",
      "source": "MACEField_BEC_backprojection",
      "spacegroup": "P1",
      "spacegroup_number": 1,
      "pointgroup": "1",
      "has_inversion": false,
      "is_polar_point_group": true,
      "nonpolar_parent_hypothesis": false,
      "symmetry_tolerance_A": null,
      "target_reduced_polarization": [
        0.5,
        0.0,
        0.0
      ],
      "formal_class": [
        0.5,
        0.0,
        0.0
      ],
      "target_residual": 3.528042222135087e-05,
      "parent_symmetrization_rmsd_A": 0.07950485131630149,
      "parent_cell_rmsd_A": 0.0428330825439861,
      "energy_eV": -116.49807716817345,
      "reduced_polarization": [
        0.499978114544031,
        2.101605220169746e-05,
        1.8001682115901705e-05
      ],
      "cartesian_polarization_e_A2": [
        0.012403719716659132,
        0.00012358201864211214,
        1.978987419274719e-06
      ],
      "ranking_score": 0.5902836827967407
    },
    {
      "candidate_id": "bec_projection_03",
      "source": "MACEField_BEC_backprojection",
      "spacegroup": "P1",
      "spacegroup_number": 1,
      "pointgroup": "1",
      "has_inversion": false,
      "is_polar_point_group": true,
      "nonpolar_parent_hypothesis": false,
      "symmetry_tolerance_A": null,
      "target_reduced_polarization": [
        0.0,
        0.0,
        -0.5
      ],
      "formal_class": [
        0.0,
        0.0,
        0.5
      ],
      "target_residual": 1.601743965363147e-06,
      "parent_symmetrization_rmsd_A": 0.10079601475579975,
      "parent_cell_rmsd_A": 0.007214420142497463,
      "energy_eV": -115.33991822750367,
      "reduced_polarization": [
        -1.4575144817902764e-06,
        4.5373220597489107e-07,
        -0.4999995148584215
      ],
      "cartesian_polarization_e_A2": [
        0.0010173811129768685,
        -1.7401106652214755e-06,
        -0.016898037511846938
      ],
      "ranking_score": 0.6026028232793549
    },
    {
      "candidate_id": "bec_projection_04",
      "source": "MACEField_BEC_backprojection",
      "spacegroup": "P1",
      "spacegroup_number": 1,
      "pointgroup": "1",
      "has_inversion": false,
      "is_polar_point_group": true,
      "nonpolar_parent_hypothesis": false,
      "symmetry_tolerance_A": null,
      "target_reduced_polarization": [
        0.5,
        -0.5,
        0.0
      ],
      "formal_class": [
        0.5,
        0.5,
        0.0
      ],
      "target_residual": 0.00021833498820167252,
      "parent_symmetrization_rmsd_A": 0.09416309208094531,
      "parent_cell_rmsd_A": 0.045134328676004615,
      "energy_eV": -114.92281359800158,
      "reduced_polarization": [
        0.5000640076880359,
        -0.4998122229361498,
        -9.117542013676291e-05
      ],
      "cartesian_polarization_e_A2": [
        0.012242409218107177,
        -0.009846875399956758,
        -6.411817149824642e-06
      ],
      "ranking_score": 0.6058833442263498
    },
    {
      "candidate_id": "bec_projection_05",
      "source": "MACEField_BEC_backprojection",
      "spacegroup": "P1",
      "spacegroup_number": 1,
      "pointgroup": "1",
      "has_inversion": false,
      "is_polar_point_group": true,
      "nonpolar_parent_hypothesis": false,
      "symmetry_tolerance_A": null,
      "target_reduced_polarization": [
        0.0,
        -0.5,
        -0.5
      ],
      "formal_class": [
        0.0,
        0.5,
        0.5
      ],
      "target_residual": 1.67957795991362e-05,
      "parent_symmetrization_rmsd_A": 0.11495135108043489,
      "parent_cell_rmsd_A": 0.02029786398428768,
      "energy_eV": -113.73610774439489,
      "reduced_polarization": [
        8.297178142949762e-06,
        -0.49998556160796886,
        -0.49999781187688597
      ],
      "cartesian_polarization_e_A2": [
        0.0010104088814515291,
        -0.009973202886030628,
        -0.01686531485163681
      ],
      "ranking_score": 0.6200594086357051
    },
    {
      "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,
        0.0,
        -0.5
      ],
      "formal_class": [
        0.5,
        0.0,
        0.5
      ],
      "target_residual": 3.366106480420695e-05,
      "parent_symmetrization_rmsd_A": 0.13494247137252197,
      "parent_cell_rmsd_A": 0.050927862093357305,
      "energy_eV": -111.1329108240389,
      "reduced_polarization": [
        0.4999725975485993,
        -1.8510928040338043e-05,
        -0.4999937136271133
      ],
      "cartesian_polarization_e_A2": [
        0.013422794169444934,
        0.00016521719856877164,
        -0.016897973524688453
      ],
      "ranking_score": 0.6477417590254697
    },
    {
      "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": 2.75486566776967e-06,
      "parent_symmetrization_rmsd_A": 0.1441639491673684,
      "parent_cell_rmsd_A": 0.0520345270207427,
      "energy_eV": -108.77352802140646,
      "reduced_polarization": [
        0.500000922276586,
        -0.49999741068198356,
        -0.4999998152760002
      ],
      "cartesian_polarization_e_A2": [
        0.013247607831439372,
        -0.009812914285873293,
        -0.016869926033925363
      ],
      "ranking_score": 0.6571780906538897
    }
  ],
  "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": [
              5.406203805838582e-09,
              -0.05162436938372586,
              -2.510672541994593e-09
            ],
            "branch_aligned_reduced_polarization": [
              5.406203805838582e-09,
              -0.05162436938372586,
              -2.510672541994593e-09
            ],
            "target_residual": 0.05162436938372621,
            "energy_eV": -119.22742062566527,
            "max_atomic_step_A": 0.00852443937666747,
            "max_log_strain_component": 0.0005841085395623784,
            "step_scale": 1.0,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 2.1391672092387974,
            "cell_principal_stretches": [
              1.000400371407093,
              1.0000205666839397,
              0.9994160620186211
            ],
            "cell_volume_ratio": 0.9998367625374185,
            "cell_rmsd_from_input_A": 0.0020606367005953055
          },
          {
            "iteration": 1,
            "reduced_polarization": [
              2.1745177904391163e-11,
              0.00018618322728352027,
              8.117266100618141e-13
            ],
            "branch_aligned_reduced_polarization": [
              2.1745177904391163e-11,
              0.00018618322728352027,
              8.117266100618141e-13
            ],
            "target_residual": 0.00018618322728352154,
            "energy_eV": -119.21870485575252
          }
        ],
        "iterations": 1
      },
      "parent": {
        "candidate_id": "inversion_parent_endpoint_00",
        "source": "same_species_inversion_center_projection_from_endpoint",
        "spacegroup": "P2_1/m",
        "spacegroup_number": 11,
        "pointgroup": "2/m",
        "has_inversion": true,
        "is_polar_point_group": false,
        "nonpolar_parent_hypothesis": true,
        "symmetry_tolerance_A": null,
        "target_reduced_polarization": [
          0.0,
          0.0,
          0.0
        ],
        "formal_class": [
          0.0,
          0.0,
          0.0
        ],
        "target_residual": 7.462475374655307e-16,
        "parent_symmetrization_rmsd_A": 0.39809216009749443,
        "parent_cell_rmsd_A": 0.0,
        "energy_eV": -112.75464902921549,
        "reduced_polarization": [
          -9.216221085842965e-17,
          -5.516760619322125e-18,
          7.40514064292721e-16
        ],
        "cartesian_polarization_e_A2": [
          -3.792760716993195e-18,
          -1.0959361960127595e-19,
          2.5020899058373018e-17
        ],
        "ranking_score": 0.39809216009749593
      },
      "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": [
          -119.22742062566527,
          -118.86939100055557,
          -118.03934265475783,
          -116.92998439864097,
          -115.7202317496577,
          -114.57366546439566,
          -113.61993922830808,
          -112.97942651748109,
          -112.75464902921549
        ],
        "cartesian_polarizations_e_A2": [
          [
            1.3912509417534038e-10,
            -0.0010255477608689598,
            -8.483198495607407e-11
          ],
          [
            1.2045605724520739e-10,
            -0.004218580221489486,
            -7.605196266989055e-11
          ],
          [
            1.0141727460193136e-10,
            -0.007252414005550464,
            -6.612175673048407e-11
          ],
          [
            8.224963079048165e-11,
            -0.009977125891292255,
            -5.5452354803868836e-11
          ],
          [
            6.318966818258619e-11,
            -0.012062981205879416,
            -4.4560101692413606e-11
          ],
          [
            4.4774929490086095e-11,
            -0.012842533665229416,
            -3.386265733844104e-11
          ],
          [
            2.7625468000182623e-11,
            -0.011297819914398769,
            -2.3403231928891053e-11
          ],
          [
            1.2737696523697504e-11,
            -0.006772422706961249,
            -1.2319500896379838e-11
          ],
          [
            5.1457007339504694e-17,
            1.1946856897715041e-17,
            5.2419349610980575e-17
          ]
        ],
        "raw_reduced_polarization": [
          [
            5.406203887548531e-09,
            -0.051624369383726346,
            -2.510672291003047e-09
          ],
          [
            4.674420755060886e-09,
            -0.2123563152675856,
            -2.250820317956272e-09
          ],
          [
            3.9305184715183345e-09,
            -0.36507446442963565,
            -1.956927714724941e-09
          ],
          [
            3.1832152450390983e-09,
            -0.5022319311229269,
            -1.6411579989438251e-09
          ],
          [
            2.4407979204625817e-09,
            -0.6072304200767878,
            -1.3187928192573832e-09
          ],
          [
            1.7239360584191464e-09,
            -0.6464717949313119,
            -1.002193164799541e-09
          ],
          [
            1.0575383439773287e-09,
            -0.5687134726885391,
            -6.926378765533935e-10
          ],
          [
            4.838982627050095e-10,
            -0.3409125004092098,
            -3.6460575047894624e-10
          ],
          [
            2.203309619287723e-15,
            6.013849154519932e-16,
            1.5513937184051124e-15
          ]
        ],
        "unwrapped_reduced_polarization": [
          [
            5.406203887548531e-09,
            -0.051624369383726346,
            -2.510672291003047e-09
          ],
          [
            4.674420755060886e-09,
            -0.21235631526758558,
            -2.250820317956272e-09
          ],
          [
            3.9305184715183345e-09,
            -0.36507446442963565,
            -1.956927714724941e-09
          ],
          [
            3.1832152450390983e-09,
            -0.5022319311229269,
            -1.6411579989438251e-09
          ],
          [
            2.4407979204625817e-09,
            -0.6072304200767878,
            -1.3187928192573832e-09
          ],
          [
            1.7239360584191464e-09,
            -0.6464717949313119,
            -1.002193164799541e-09
          ],
          [
            1.0575383439773287e-09,
            -0.5687134726885391,
            -6.926378765533935e-10
          ],
          [
            4.838982627050095e-10,
            -0.3409125004092098,
            -3.6460575047894624e-10
          ],
          [
            2.203309619298305e-15,
            6.106226635438361e-16,
            1.5513937184006558e-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": [
          [
            5.406203928970399e-09,
            -0.05162436938372633,
            -2.510672281186288e-09
          ],
          [
            4.674420739370078e-09,
            -0.21235631526758558,
            -2.2508203079141254e-09
          ],
          [
            3.930518466255251e-09,
            -0.36507446442963565,
            -1.9569277309727795e-09
          ],
          [
            3.1832152469490893e-09,
            0.49776806887707314,
            -1.64115798728659e-09
          ],
          [
            2.4407978971296984e-09,
            0.39276957992321215,
            -1.318792797189161e-09
          ],
          [
            1.7239361049803392e-09,
            0.3535282050686881,
            -1.0021931617920643e-09
          ],
          [
            1.057538390192292e-09,
            0.4312865273114609,
            -6.926378914862141e-10
          ],
          [
            4.838982547994419e-10,
            -0.3409125004092098,
            -3.646057344930398e-10
          ],
          [
            2.220446049250313e-15,
            6.661338147750939e-16,
            1.5543122344752192e-15
          ]
        ]
      },
      "reflected": {
        "reached": true,
        "construction": "reflect_displacements_about_reconstructed_parent",
        "energies_eV": [
          -112.75464902921547,
          -112.97942651748109,
          -113.61993922830807,
          -114.57366546439565,
          -115.7202317496577,
          -116.92998439864098,
          -118.03934265475786,
          -118.86939100055555,
          -119.22742062566529
        ],
        "cartesian_polarizations_e_A2": [
          [
            5.4287425785022004e-17,
            -1.6629960824843986e-18,
            6.328815644176705e-17
          ],
          [
            -1.2737664766402546e-11,
            0.006772422706961232,
            1.2319515954205967e-11
          ],
          [
            -2.7625412240939247e-11,
            0.011297819914398752,
            2.340333337108814e-11
          ],
          [
            -4.477494098158499e-11,
            0.01284253366522942,
            3.386268134038946e-11
          ],
          [
            -6.318959340293085e-11,
            0.012062981205879375,
            4.4560104862482265e-11
          ],
          [
            -8.22496143174463e-11,
            0.009977125891292292,
            5.5452363408340915e-11
          ],
          [
            -1.0141729212222154e-10,
            0.007252414005550508,
            6.61217626743628e-11
          ],
          [
            -1.20455972021308e-10,
            0.00421858022148948,
            7.605200574885929e-11
          ],
          [
            -1.391250588587942e-10,
            0.0010255477608689708,
            8.48320612393892e-11
          ]
        ],
        "raw_reduced_polarization": [
          [
            2.343921799777614e-15,
            -8.371245818246601e-17,
            1.8730649861521763e-15
          ],
          [
            -4.838969449585724e-10,
            0.3409125004092089,
            3.6460619612768173e-10
          ],
          [
            -1.057535847902249e-09,
            0.5687134726885382,
            6.926408788185592e-10
          ],
          [
            -1.7239364636362522e-09,
            0.6464717949313121,
            1.0021938751569238e-09
          ],
          [
            -2.4407948960451876e-09,
            0.6072304200767858,
            1.3187929130781695e-09
          ],
          [
            -3.1832145595720873e-09,
            0.5022319311229287,
            1.6411582536002457e-09
          ],
          [
            -3.9305191638561044e-09,
            0.36507446442963787,
            1.9569278906389156e-09
          ],
          [
            -4.67441721226358e-09,
            0.2123563152675853,
            2.2508215929137447e-09
          ],
          [
            -5.406202277336748e-09,
            0.0516243693837269,
            2.5106745486704314e-09
          ]
        ],
        "unwrapped_reduced_polarization": [
          [
            2.343921799777614e-15,
            -8.371245818246601e-17,
            1.8730649861521763e-15
          ],
          [
            -4.838969449585724e-10,
            0.3409125004092089,
            3.6460619612768173e-10
          ],
          [
            -1.057535847902249e-09,
            0.5687134726885382,
            6.926408788185592e-10
          ],
          [
            -1.7239364636362522e-09,
            0.6464717949313121,
            1.0021938751569238e-09
          ],
          [
            -2.4407948960451876e-09,
            0.6072304200767858,
            1.3187929130781695e-09
          ],
          [
            -3.1832145595720873e-09,
            0.5022319311229287,
            1.6411582536002457e-09
          ],
          [
            -3.9305191638561044e-09,
            0.36507446442963787,
            1.9569278906389156e-09
          ],
          [
            -4.67441721226358e-09,
            0.2123563152675853,
            2.2508215929137447e-09
          ],
          [
            -5.406202277336748e-09,
            0.05162436938372689,
            2.5106745486704314e-09
          ]
        ],
        "gauge_integer_shift": [
          0,
          0,
          0
        ],
        "expected_opposite_endpoint_reduced_polarization": [
          -5.406199480929292e-09,
          0.051624369383727546,
          2.5106753937904842e-09
        ],
        "actual_opposite_endpoint_branch_residual": 2.9947721964455615e-15
      },
      "pnp_branch": {
        "construction": "incoming_path_concatenated_with_parent_reflection",
        "reduced_polarization": [
          [
            5.406203887548531e-09,
            -0.051624369383726346,
            -2.510672291003047e-09
          ],
          [
            4.674420755060886e-09,
            -0.2123563152675856,
            -2.250820317956272e-09
          ],
          [
            3.9305184715183345e-09,
            -0.36507446442963565,
            -1.956927714724941e-09
          ],
          [
            3.1832152450390983e-09,
            -0.5022319311229269,
            -1.6411579989438251e-09
          ],
          [
            2.4407979204625817e-09,
            -0.6072304200767878,
            -1.3187928192573832e-09
          ],
          [
            1.7239360584191464e-09,
            -0.6464717949313119,
            -1.002193164799541e-09
          ],
          [
            1.0575383439773287e-09,
            -0.5687134726885391,
            -6.926378765533935e-10
          ],
          [
            4.838982627050095e-10,
            -0.3409125004092098,
            -3.6460575047894624e-10
          ],
          [
            2.203309619287723e-15,
            6.013849154519932e-16,
            1.5513937184051124e-15
          ],
          [
            -4.838969449585724e-10,
            0.3409125004092089,
            3.6460619612768173e-10
          ],
          [
            -1.057535847902249e-09,
            0.5687134726885382,
            6.926408788185592e-10
          ],
          [
            -1.7239364636362522e-09,
            0.6464717949313121,
            1.0021938751569238e-09
          ],
          [
            -2.4407948960451876e-09,
            0.6072304200767858,
            1.3187929130781695e-09
          ],
          [
            -3.1832145595720873e-09,
            0.5022319311229287,
            1.6411582536002457e-09
          ],
          [
            -3.9305191638561044e-09,
            0.36507446442963787,
            1.9569278906389156e-09
          ],
          [
            -4.67441721226358e-09,
            0.2123563152675853,
            2.2508215929137447e-09
          ],
          [
            -5.406202277336748e-09,
            0.0516243693837269,
            2.5106745486704314e-09
          ]
        ],
        "unwrapped_reduced_polarization": [
          [
            5.406203887548531e-09,
            -0.051624369383726346,
            -2.510672291003047e-09
          ],
          [
            4.674420755060886e-09,
            -0.21235631526758558,
            -2.250820317956272e-09
          ],
          [
            3.9305184715183345e-09,
            -0.36507446442963565,
            -1.956927714724941e-09
          ],
          [
            3.1832152450390983e-09,
            -0.5022319311229269,
            -1.6411579989438251e-09
          ],
          [
            2.4407979204625817e-09,
            -0.6072304200767878,
            -1.3187928192573832e-09
          ],
          [
            1.7239360584191464e-09,
            -0.6464717949313119,
            -1.002193164799541e-09
          ],
          [
            1.0575383439773287e-09,
            -0.5687134726885391,
            -6.926378765533935e-10
          ],
          [
            4.838982627050095e-10,
            -0.3409125004092098,
            -3.6460575047894624e-10
          ],
          [
            2.203309619298305e-15,
            6.106226635438361e-16,
            1.5513937184006558e-15
          ],
          [
            -4.838969449585724e-10,
            0.3409125004092089,
            3.6460619612768173e-10
          ],
          [
            -1.057535847902249e-09,
            0.5687134726885382,
            6.926408788185592e-10
          ],
          [
            -1.7239364636362522e-09,
            0.6464717949313121,
            1.0021938751569238e-09
          ],
          [
            -2.4407948960451876e-09,
            0.6072304200767858,
            1.3187929130781695e-09
          ],
          [
            -3.1832145595720873e-09,
            0.5022319311229287,
            1.6411582536002457e-09
          ],
          [
            -3.9305191638561044e-09,
            0.36507446442963787,
            1.9569278906389156e-09
          ],
          [
            -4.67441721226358e-09,
            0.2123563152675853,
            2.2508215929137447e-09
          ],
          [
            -5.406202277336748e-09,
            0.05162436938372689,
            2.5106745486704314e-09
          ]
        ],
        "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": [
          [
            5.406203928970399e-09,
            -0.05162436938372633,
            -2.510672281186288e-09
          ],
          [
            4.674420739370078e-09,
            -0.21235631526758558,
            -2.2508203079141254e-09
          ],
          [
            3.930518466255251e-09,
            -0.36507446442963565,
            -1.9569277309727795e-09
          ],
          [
            3.1832152469490893e-09,
            0.49776806887707314,
            -1.64115798728659e-09
          ],
          [
            2.4407978971296984e-09,
            0.39276957992321215,
            -1.318792797189161e-09
          ],
          [
            1.7239361049803392e-09,
            0.3535282050686881,
            -1.0021931617920643e-09
          ],
          [
            1.057538390192292e-09,
            0.4312865273114609,
            -6.926378914862141e-10
          ],
          [
            4.838982547994419e-10,
            -0.3409125004092098,
            -3.646057344930398e-10
          ],
          [
            2.220446049250313e-15,
            6.661338147750939e-16,
            1.5543122344752192e-15
          ],
          [
            -4.838969225318124e-10,
            0.34091250040920884,
            3.6460623409340087e-10
          ],
          [
            -1.0575358366793353e-09,
            -0.43128652731146166,
            6.926408335772294e-10
          ],
          [
            -1.7239364380472466e-09,
            -0.3535282050686879,
            1.0021938834370303e-09
          ],
          [
            -2.440794899527532e-09,
            -0.39276957992321426,
            1.3187929637226148e-09
          ],
          [
            -3.1832145808152745e-09,
            -0.49776806887707137,
            1.641158209331195e-09
          ],
          [
            -3.930519187900217e-09,
            0.36507446442963787,
            1.956927841995082e-09
          ],
          [
            -4.674417186656399e-09,
            0.21235631526758536,
            2.250821640181755e-09
          ],
          [
            -5.406202263635862e-09,
            0.05162436938372683,
            2.5106745571434885e-09
          ]
        ]
      },
      "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,
        0.5,
        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": [
              5.406203805838582e-09,
              -0.05162436938372586,
              -2.510672541994593e-09
            ],
            "branch_aligned_reduced_polarization": [
              5.406203805838582e-09,
              -0.05162436938372583,
              -2.510672541994593e-09
            ],
            "target_residual": 0.4483756306162742,
            "energy_eV": -119.22742062566527,
            "max_atomic_step_A": 0.07403772538916385,
            "max_log_strain_component": 0.005073186130912701,
            "step_scale": 1.0,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 2.1391672092387974,
            "cell_principal_stretches": [
              1.0050860765289165,
              0.9998213889756319,
              0.9965293674160616
            ],
            "cell_volume_ratio": 1.0014188956344108,
            "cell_rmsd_from_input_A": 0.017908065440760953
          },
          {
            "iteration": 1,
            "reduced_polarization": [
              -2.2122943912573992e-10,
              -0.48602966203284476,
              -7.455993795203913e-12
            ],
            "branch_aligned_reduced_polarization": [
              -2.2122943912573992e-10,
              -0.48602966203284476,
              -7.455993795203913e-12
            ],
            "target_residual": 0.013970337967155246,
            "energy_eV": -118.43337170688913,
            "max_atomic_step_A": 0.0024298048130750654,
            "max_log_strain_component": 0.00017787440159919515,
            "step_scale": 1.0,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 2.1391672092387974,
            "cell_principal_stretches": [
              1.0052648715143881,
              0.999815127152914,
              0.9964079000377488
            ],
            "cell_volume_ratio": 1.0014686810065492,
            "cell_rmsd_from_input_A": 0.01853631696546476
          },
          {
            "iteration": 2,
            "reduced_polarization": [
              -3.649797643333413e-13,
              -0.49996415906366615,
              2.5231668005764225e-13
            ],
            "branch_aligned_reduced_polarization": [
              -3.649797643333413e-13,
              -0.49996415906366615,
              2.5231668005764225e-13
            ],
            "target_residual": 3.5840936333853e-05,
            "energy_eV": -118.38440204606233
          }
        ],
        "iterations": 2
      },
      "parent": {
        "candidate_id": "bec_projection_01",
        "source": "MACEField_BEC_backprojection",
        "spacegroup": "P2_1",
        "spacegroup_number": 4,
        "pointgroup": "2",
        "has_inversion": false,
        "is_polar_point_group": true,
        "nonpolar_parent_hypothesis": false,
        "symmetry_tolerance_A": null,
        "target_reduced_polarization": [
          0.0,
          -0.5,
          0.0
        ],
        "formal_class": [
          0.0,
          0.5,
          0.0
        ],
        "target_residual": 3.5840936333853e-05,
        "parent_symmetrization_rmsd_A": 0.054241939661388704,
        "parent_cell_rmsd_A": 0.01853631696546476,
        "energy_eV": -118.38440204606233,
        "reduced_polarization": [
          -3.649797643333413e-13,
          -0.49996415906366615,
          2.5231668005764225e-13
        ],
        "cartesian_polarization_e_A2": [
          1.2229878119602606e-12,
          -0.009969724052236567,
          -1.57385287633855e-13
        ],
        "ranking_score": 0.5589477007754226
      },
      "branch_status": "awaiting_branch_sampling"
    },
    {
      "orbit_id": 2,
      "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": [
              5.406203805838582e-09,
              -0.05162436938372586,
              -2.510672541994593e-09
            ],
            "branch_aligned_reduced_polarization": [
              5.4062038179480965e-09,
              -0.05162436938372586,
              -2.510672541994593e-09
            ],
            "target_residual": 0.5026580051168623,
            "energy_eV": -119.22742062566527,
            "max_atomic_step_A": 0.11102453552315057,
            "max_log_strain_component": 0.009848174641866225,
            "step_scale": 1.0,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 2.1391672092387974,
            "cell_principal_stretches": [
              1.0098177495880956,
              1.0000489907562542,
              0.9900675469132569
            ],
            "cell_volume_ratio": 0.9998367625236927,
            "cell_rmsd_from_input_A": 0.04239919564240999
          },
          {
            "iteration": 1,
            "reduced_polarization": [
              0.49668740304056513,
              -0.019837418490952916,
              -0.0013276954701966683
            ],
            "branch_aligned_reduced_polarization": [
              0.49668740304056513,
              -0.019837418490952916,
              -0.0013276954701966683
            ],
            "target_residual": 0.020155873740982766,
            "energy_eV": -116.51724270787696,
            "max_atomic_step_A": 0.003607470250648363,
            "max_log_strain_component": 0.00023123934030439607,
            "step_scale": 1.0,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 2.1391672092387974,
            "cell_principal_stretches": [
              1.0098781870940132,
              1.0000683277613456,
              0.9899251731595173
            ],
            "cell_volume_ratio": 0.9997721467544037,
            "cell_rmsd_from_input_A": 0.0428330825439861
          },
          {
            "iteration": 2,
            "reduced_polarization": [
              0.499978114544031,
              2.101605220169746e-05,
              1.8001682115901705e-05
            ],
            "branch_aligned_reduced_polarization": [
              0.499978114544031,
              2.101605220169746e-05,
              1.8001682115901705e-05
            ],
            "target_residual": 3.528042222135087e-05,
            "energy_eV": -116.49807716817345
          }
        ],
        "iterations": 2
      },
      "parent": {
        "candidate_id": "bec_projection_02",
        "source": "MACEField_BEC_backprojection",
        "spacegroup": "P1",
        "spacegroup_number": 1,
        "pointgroup": "1",
        "has_inversion": false,
        "is_polar_point_group": true,
        "nonpolar_parent_hypothesis": false,
        "symmetry_tolerance_A": null,
        "target_reduced_polarization": [
          0.5,
          0.0,
          0.0
        ],
        "formal_class": [
          0.5,
          0.0,
          0.0
        ],
        "target_residual": 3.528042222135087e-05,
        "parent_symmetrization_rmsd_A": 0.07950485131630149,
        "parent_cell_rmsd_A": 0.0428330825439861,
        "energy_eV": -116.49807716817345,
        "reduced_polarization": [
          0.499978114544031,
          2.101605220169746e-05,
          1.8001682115901705e-05
        ],
        "cartesian_polarization_e_A2": [
          0.012403719716659132,
          0.00012358201864211214,
          1.978987419274719e-06
        ],
        "ranking_score": 0.5902836827967407
      },
      "branch_status": "awaiting_branch_sampling"
    },
    {
      "orbit_id": 3,
      "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": [
              5.406203805838582e-09,
              -0.05162436938372586,
              -2.510672541994593e-09
            ],
            "branch_aligned_reduced_polarization": [
              5.406203805838582e-09,
              -0.05162436938372586,
              -2.510672558742044e-09
            ],
            "target_residual": 0.5026580079970823,
            "energy_eV": -119.22742062566527,
            "max_atomic_step_A": 0.12,
            "max_log_strain_component": 0.0012582372123361798,
            "step_scale": 0.7793277365643898,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 2.1391672092387974,
            "cell_principal_stretches": [
              1.0012518059994704,
              1.0000187954092405,
              0.9986039311806277
            ],
            "cell_volume_ratio": 0.9998727822376894,
            "cell_rmsd_from_input_A": 0.005596539870262299
          },
          {
            "iteration": 1,
            "reduced_polarization": [
              0.0011224955328277399,
              -0.014705751114196227,
              -0.3871144527981712
            ],
            "branch_aligned_reduced_polarization": [
              0.0011224955328277399,
              -0.014705751114196227,
              -0.3871144527981712
            ],
            "target_residual": 0.11384492030437819,
            "energy_eV": -117.05493533410605,
            "max_atomic_step_A": 0.03703063969487851,
            "max_log_strain_component": 0.0003357313481892345,
            "step_scale": 1.0,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 2.1391672092387974,
            "cell_principal_stretches": [
              1.001594832808938,
              1.0000265750837576,
              0.9981986215421701
            ],
            "cell_volume_ratio": 0.9998171509720847,
            "cell_rmsd_from_input_A": 0.007176600898691593
          },
          {
            "iteration": 2,
            "reduced_polarization": [
              -0.00017607383354022621,
              -0.000646579555199185,
              -0.49896046420913975
            ],
            "branch_aligned_reduced_polarization": [
              -0.00017607383354022621,
              -0.000646579555199185,
              -0.49896046420913975
            ],
            "target_residual": 0.0012368111321210548,
            "energy_eV": -115.35904205382967,
            "max_atomic_step_A": 0.0003796949679817896,
            "max_log_strain_component": 7.959902456873238e-06,
            "step_scale": 1.0,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 2.1391672092387974,
            "cell_principal_stretches": [
              1.0016025301890947,
              1.0000269231898933,
              0.9981883821922306
            ],
            "cell_volume_ratio": 0.9998149266915227,
            "cell_rmsd_from_input_A": 0.007214420142497463
          },
          {
            "iteration": 3,
            "reduced_polarization": [
              -1.4575144817902764e-06,
              4.5373220597489107e-07,
              -0.4999995148584215
            ],
            "branch_aligned_reduced_polarization": [
              -1.4575144817902764e-06,
              4.5373220597489107e-07,
              -0.4999995148584215
            ],
            "target_residual": 1.601743965363147e-06,
            "energy_eV": -115.33991822750367
          }
        ],
        "iterations": 3
      },
      "parent": {
        "candidate_id": "bec_projection_03",
        "source": "MACEField_BEC_backprojection",
        "spacegroup": "P1",
        "spacegroup_number": 1,
        "pointgroup": "1",
        "has_inversion": false,
        "is_polar_point_group": true,
        "nonpolar_parent_hypothesis": false,
        "symmetry_tolerance_A": null,
        "target_reduced_polarization": [
          0.0,
          0.0,
          -0.5
        ],
        "formal_class": [
          0.0,
          0.0,
          0.5
        ],
        "target_residual": 1.601743965363147e-06,
        "parent_symmetrization_rmsd_A": 0.10079601475579975,
        "parent_cell_rmsd_A": 0.007214420142497463,
        "energy_eV": -115.33991822750367,
        "reduced_polarization": [
          -1.4575144817902764e-06,
          4.5373220597489107e-07,
          -0.4999995148584215
        ],
        "cartesian_polarization_e_A2": [
          0.0010173811129768685,
          -1.7401106652214755e-06,
          -0.016898037511846938
        ],
        "ranking_score": 0.6026028232793549
      },
      "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": [
              5.406203805838582e-09,
              -0.05162436938372586,
              -2.510672541994593e-09
            ],
            "branch_aligned_reduced_polarization": [
              5.4062038179480965e-09,
              -0.05162436938372583,
              -2.510672541994593e-09
            ],
            "target_residual": 0.6715956378091937,
            "energy_eV": -119.22742062566527,
            "max_atomic_step_A": 0.12000000000000001,
            "max_log_strain_component": 0.008808110426778471,
            "step_scale": 0.8943901545851931,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 2.1391672092387974,
            "cell_principal_stretches": [
              1.0104677810132232,
              0.9996516914937037,
              0.9912417219714387
            ],
            "cell_volume_ratio": 1.001268951240311,
            "cell_rmsd_from_input_A": 0.04116652476989903
          },
          {
            "iteration": 1,
            "reduced_polarization": [
              0.4560544142208921,
              -0.4533926682947331,
              -0.000562619639845466
            ],
            "branch_aligned_reduced_polarization": [
              0.4560544142208921,
              -0.4533926682947331,
              -0.000562619639845466
            ],
            "target_residual": 0.06406070885506064,
            "energy_eV": -115.76087094722956,
            "max_atomic_step_A": 0.012733837125390878,
            "max_log_strain_component": 0.0008062599322900665,
            "step_scale": 1.0,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 2.1391672092387974,
            "cell_principal_stretches": [
              1.0115026839050396,
              0.9996108811144554,
              0.9904213439192746
            ],
            "cell_volume_ratio": 1.0014240228832925,
            "cell_rmsd_from_input_A": 0.045134328676004615
          },
          {
            "iteration": 2,
            "reduced_polarization": [
              0.5000640076880359,
              -0.4998122229361498,
              -9.117542013676291e-05
            ],
            "branch_aligned_reduced_polarization": [
              0.5000640076880359,
              -0.4998122229361498,
              -9.117542013676291e-05
            ],
            "target_residual": 0.00021833498820167252,
            "energy_eV": -114.92281359800158
          }
        ],
        "iterations": 2
      },
      "parent": {
        "candidate_id": "bec_projection_04",
        "source": "MACEField_BEC_backprojection",
        "spacegroup": "P1",
        "spacegroup_number": 1,
        "pointgroup": "1",
        "has_inversion": false,
        "is_polar_point_group": true,
        "nonpolar_parent_hypothesis": false,
        "symmetry_tolerance_A": null,
        "target_reduced_polarization": [
          0.5,
          -0.5,
          0.0
        ],
        "formal_class": [
          0.5,
          0.5,
          0.0
        ],
        "target_residual": 0.00021833498820167252,
        "parent_symmetrization_rmsd_A": 0.09416309208094531,
        "parent_cell_rmsd_A": 0.045134328676004615,
        "energy_eV": -114.92281359800158,
        "reduced_polarization": [
          0.5000640076880359,
          -0.4998122229361498,
          -9.117542013676291e-05
        ],
        "cartesian_polarization_e_A2": [
          0.012242409218107177,
          -0.009846875399956758,
          -6.411817149824642e-06
        ],
        "ranking_score": 0.6058833442263498
      },
      "branch_status": "awaiting_branch_sampling"
    },
    {
      "orbit_id": 5,
      "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": [
              5.406203805838582e-09,
              -0.05162436938372586,
              -2.510672541994593e-09
            ],
            "branch_aligned_reduced_polarization": [
              5.406203805838582e-09,
              -0.05162436938372583,
              -2.510672558742044e-09
            ],
            "target_residual": 0.671595639964904,
            "energy_eV": -119.22742062566527,
            "max_atomic_step_A": 0.12,
            "max_log_strain_component": 0.003530610246680842,
            "step_scale": 0.6959354865085804,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 2.1391672092387974,
            "cell_principal_stretches": [
              1.0037468155199283,
              0.9998726051886362,
              0.9973777931865886
            ],
            "cell_volume_ratio": 1.0009872469522985,
            "cell_rmsd_from_input_A": 0.013349677904135056
          },
          {
            "iteration": 1,
            "reduced_polarization": [
              0.0022691484212868274,
              -0.356227189339799,
              -0.3454434824178043
            ],
            "branch_aligned_reduced_polarization": [
              0.0022691484212868274,
              -0.356227189339799,
              -0.3454434824178043
            ],
            "target_residual": 0.21110065667076308,
            "energy_eV": -116.92553887622832,
            "max_atomic_step_A": 0.058284634297263445,
            "max_log_strain_component": 0.0018356067748678594,
            "step_scale": 1.0,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 2.1391672092387974,
            "cell_principal_stretches": [
              1.0056560018032172,
              0.9998074852757579,
              0.9960600369958328
            ],
            "cell_volume_ratio": 1.0015009135642978,
            "cell_rmsd_from_input_A": 0.020107802475254823
          },
          {
            "iteration": 2,
            "reduced_polarization": [
              0.00036545197413466793,
              -0.4958786436049287,
              -0.49806421407624846
            ],
            "branch_aligned_reduced_polarization": [
              0.00036545197413466793,
              -0.4958786436049287,
              -0.49806421407624846
            ],
            "target_residual": 0.0045679755716497026,
            "energy_eV": -113.80183214539251,
            "max_atomic_step_A": 0.0010948994658443274,
            "max_log_strain_component": 5.690840024465096e-05,
            "step_scale": 1.0,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 2.1391672092387974,
            "cell_principal_stretches": [
              1.0057106206527247,
              0.999805564686917,
              0.9960236973397174
            ],
            "cell_volume_ratio": 1.001516842725677,
            "cell_rmsd_from_input_A": 0.02029786398428768
          },
          {
            "iteration": 3,
            "reduced_polarization": [
              8.297178142949762e-06,
              -0.49998556160796886,
              -0.49999781187688597
            ],
            "branch_aligned_reduced_polarization": [
              8.297178142949762e-06,
              -0.49998556160796886,
              -0.49999781187688597
            ],
            "target_residual": 1.67957795991362e-05,
            "energy_eV": -113.73610774439489
          }
        ],
        "iterations": 3
      },
      "parent": {
        "candidate_id": "bec_projection_05",
        "source": "MACEField_BEC_backprojection",
        "spacegroup": "P1",
        "spacegroup_number": 1,
        "pointgroup": "1",
        "has_inversion": false,
        "is_polar_point_group": true,
        "nonpolar_parent_hypothesis": false,
        "symmetry_tolerance_A": null,
        "target_reduced_polarization": [
          0.0,
          -0.5,
          -0.5
        ],
        "formal_class": [
          0.0,
          0.5,
          0.5
        ],
        "target_residual": 1.67957795991362e-05,
        "parent_symmetrization_rmsd_A": 0.11495135108043489,
        "parent_cell_rmsd_A": 0.02029786398428768,
        "energy_eV": -113.73610774439489,
        "reduced_polarization": [
          8.297178142949762e-06,
          -0.49998556160796886,
          -0.49999781187688597
        ],
        "cartesian_polarization_e_A2": [
          0.0010104088814515291,
          -0.009973202886030628,
          -0.01686531485163681
        ],
        "ranking_score": 0.6200594086357051
      },
      "branch_status": "awaiting_branch_sampling"
    },
    {
      "orbit_id": 6,
      "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": [
              5.406203805838582e-09,
              -0.05162436938372586,
              -2.510672541994593e-09
            ],
            "branch_aligned_reduced_polarization": [
              5.4062038179480965e-09,
              -0.05162436938372586,
              -2.510672558742044e-09
            ],
            "target_residual": 0.7089887640840234,
            "energy_eV": -119.22742062566527,
            "max_atomic_step_A": 0.12000000000000001,
            "max_log_strain_component": 0.007276735459574209,
            "step_scale": 0.6348191296099429,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 2.1391672092387974,
            "cell_principal_stretches": [
              1.0072472620816033,
              1.000028081819328,
              0.9926741229960269
            ],
            "cell_volume_ratio": 0.9998963706477471,
            "cell_rmsd_from_input_A": 0.03117103632077552
          },
          {
            "iteration": 1,
            "reduced_polarization": [
              0.3147211256259212,
              -0.026983321060336126,
              -0.3155198599560104
            ],
            "branch_aligned_reduced_polarization": [
              0.3147211256259212,
              -0.026983321060336126,
              -0.3155198599560104
            ],
            "target_residual": 0.2628484030299991,
            "energy_eV": -116.46300787348389,
            "max_atomic_step_A": 0.07600848355662886,
            "max_log_strain_component": 0.0044561664591098405,
            "step_scale": 1.0,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 2.1391672092387974,
            "cell_principal_stretches": [
              1.0116730706307784,
              1.0000667080771064,
              0.9881522592809326
            ],
            "cell_volume_ratio": 0.9997537175969878,
            "cell_rmsd_from_input_A": 0.05031233712083297
          },
          {
            "iteration": 2,
            "reduced_polarization": [
              0.49479433956626806,
              -0.006738906378787067,
              -0.49669816803058486
            ],
            "branch_aligned_reduced_polarization": [
              0.49479433956626806,
              -0.006738906378787067,
              -0.49669816803058486
            ],
            "target_residual": 0.009133118530251925,
            "energy_eV": -111.28156697835728,
            "max_atomic_step_A": 0.0021754783522892,
            "max_log_strain_component": 0.0001391327987620183,
            "step_scale": 1.0,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 2.1391672092387974,
            "cell_principal_stretches": [
              1.0118020832452224,
              1.0000737617947633,
              0.9879935704055975
            ],
            "cell_volume_ratio": 0.9997276890389672,
            "cell_rmsd_from_input_A": 0.050927862093357305
          },
          {
            "iteration": 3,
            "reduced_polarization": [
              0.4999725975485993,
              -1.8510928040338043e-05,
              -0.4999937136271133
            ],
            "branch_aligned_reduced_polarization": [
              0.4999725975485993,
              -1.8510928040338043e-05,
              -0.4999937136271133
            ],
            "target_residual": 3.366106480420695e-05,
            "energy_eV": -111.1329108240389
          }
        ],
        "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,
          0.0,
          -0.5
        ],
        "formal_class": [
          0.5,
          0.0,
          0.5
        ],
        "target_residual": 3.366106480420695e-05,
        "parent_symmetrization_rmsd_A": 0.13494247137252197,
        "parent_cell_rmsd_A": 0.050927862093357305,
        "energy_eV": -111.1329108240389,
        "reduced_polarization": [
          0.4999725975485993,
          -1.8510928040338043e-05,
          -0.4999937136271133
        ],
        "cartesian_polarization_e_A2": [
          0.013422794169444934,
          0.00016521719856877164,
          -0.016897973524688453
        ],
        "ranking_score": 0.6477417590254697
      },
      "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": [
              5.406203805838582e-09,
              -0.05162436938372586,
              -2.510672541994593e-09
            ],
            "branch_aligned_reduced_polarization": [
              5.4062038179480965e-09,
              -0.05162436938372583,
              -2.510672558742044e-09
            ],
            "target_residual": 0.8372817316851391,
            "energy_eV": -119.22742062566527,
            "max_atomic_step_A": 0.11999999999999998,
            "max_log_strain_component": 0.00674937924561626,
            "step_scale": 0.5888128114004441,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 2.1391672092387974,
            "cell_principal_stretches": [
              1.0077553985741354,
              0.9997874236815995,
              0.9933442389804421
            ],
            "cell_volume_ratio": 1.0008352203725344,
            "cell_rmsd_from_input_A": 0.030770011577962726
          },
          {
            "iteration": 1,
            "reduced_polarization": [
              0.2988249184313498,
              -0.31375476991355816,
              -0.29201022101292917
            ],
            "branch_aligned_reduced_polarization": [
              0.2988249184313498,
              -0.31375476991355816,
              -0.29201022101292917
            ],
            "target_residual": 0.3441198153800436,
            "energy_eV": -116.26982683453504,
            "max_atomic_step_A": 0.08977975665366046,
            "max_log_strain_component": 0.004550471768607588,
            "step_scale": 1.0,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 2.1391672092387974,
            "cell_principal_stretches": [
              1.013124830155997,
              0.9996312939997838,
              0.9888530875160446
            ],
            "cell_volume_ratio": 1.0014622350107751,
            "cell_rmsd_from_input_A": 0.05181746216267531
          },
          {
            "iteration": 2,
            "reduced_polarization": [
              0.4983173796932595,
              -0.49854184479314223,
              -0.496106911705442
            ],
            "branch_aligned_reduced_polarization": [
              0.4983173796932595,
              -0.49854184479314223,
              -0.496106911705442
            ],
            "target_residual": 0.004484814842684839,
            "energy_eV": -108.9266141871041,
            "max_atomic_step_A": 0.0014191616080851852,
            "max_log_strain_component": 4.84576749785535e-05,
            "step_scale": 1.0,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 2.1391672092387974,
            "cell_principal_stretches": [
              1.0131796262745447,
              0.9996300941547984,
              0.9888059817236606
            ],
            "cell_volume_ratio": 1.0014674892609168,
            "cell_rmsd_from_input_A": 0.0520345270207427
          },
          {
            "iteration": 3,
            "reduced_polarization": [
              0.500000922276586,
              -0.49999741068198356,
              -0.4999998152760002
            ],
            "branch_aligned_reduced_polarization": [
              0.500000922276586,
              -0.49999741068198356,
              -0.4999998152760002
            ],
            "target_residual": 2.75486566776967e-06,
            "energy_eV": -108.77352802140646
          }
        ],
        "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": 2.75486566776967e-06,
        "parent_symmetrization_rmsd_A": 0.1441639491673684,
        "parent_cell_rmsd_A": 0.0520345270207427,
        "energy_eV": -108.77352802140646,
        "reduced_polarization": [
          0.500000922276586,
          -0.49999741068198356,
          -0.4999998152760002
        ],
        "cartesian_polarization_e_A2": [
          0.013247607831439372,
          -0.009812914285873293,
          -0.016869926033925363
        ],
        "ranking_score": 0.6571780906538897
      },
      "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
        ],
        "endpoint_rmsd_A": 0.39809216009749443,
        "minimum_distance_A_by_image": [
          1.5885618842015554,
          1.5599274624425012,
          1.5346788608319586,
          1.5129855958813778,
          1.4877867377061946,
          1.461872979967566,
          1.4430782788737582,
          1.431683032339364,
          1.4278644081119225
        ],
        "minimum_distance_A": 1.4278644081119225,
        "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": [
          245.15434864045403,
          245.15434864045403,
          245.15434864045403,
          245.15434864045403,
          245.15434864045403,
          245.15434864045403,
          245.15434864045403,
          245.15434864045403,
          245.15434864045403
        ],
        "cell_deformation_log_strain_norm": 0.0
      },
      "parent_reduced_polarization": [
        2.203309619287723e-15,
        6.013849154519932e-16,
        1.5513937184051124e-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": [
          -119.22742062566527,
          -118.86939100055557,
          -118.03934265475783,
          -116.92998439864097,
          -115.7202317496577,
          -114.57366546439566,
          -113.61993922830808,
          -112.97942651748109,
          -112.75464902921549
        ],
        "cartesian_polarizations_e_A2": [
          [
            1.3912509417534038e-10,
            -0.0010255477608689598,
            -8.483198495607407e-11
          ],
          [
            1.2045605724520739e-10,
            -0.004218580221489486,
            -7.605196266989055e-11
          ],
          [
            1.0141727460193136e-10,
            -0.007252414005550464,
            -6.612175673048407e-11
          ],
          [
            8.224963079048165e-11,
            -0.009977125891292255,
            -5.5452354803868836e-11
          ],
          [
            6.318966818258619e-11,
            -0.012062981205879416,
            -4.4560101692413606e-11
          ],
          [
            4.4774929490086095e-11,
            -0.012842533665229416,
            -3.386265733844104e-11
          ],
          [
            2.7625468000182623e-11,
            -0.011297819914398769,
            -2.3403231928891053e-11
          ],
          [
            1.2737696523697504e-11,
            -0.006772422706961249,
            -1.2319500896379838e-11
          ],
          [
            5.1457007339504694e-17,
            1.1946856897715041e-17,
            5.2419349610980575e-17
          ]
        ],
        "raw_reduced_polarization": [
          [
            5.406203887548531e-09,
            -0.051624369383726346,
            -2.510672291003047e-09
          ],
          [
            4.674420755060886e-09,
            -0.2123563152675856,
            -2.250820317956272e-09
          ],
          [
            3.9305184715183345e-09,
            -0.36507446442963565,
            -1.956927714724941e-09
          ],
          [
            3.1832152450390983e-09,
            -0.5022319311229269,
            -1.6411579989438251e-09
          ],
          [
            2.4407979204625817e-09,
            -0.6072304200767878,
            -1.3187928192573832e-09
          ],
          [
            1.7239360584191464e-09,
            -0.6464717949313119,
            -1.002193164799541e-09
          ],
          [
            1.0575383439773287e-09,
            -0.5687134726885391,
            -6.926378765533935e-10
          ],
          [
            4.838982627050095e-10,
            -0.3409125004092098,
            -3.6460575047894624e-10
          ],
          [
            2.203309619287723e-15,
            6.013849154519932e-16,
            1.5513937184051124e-15
          ]
        ],
        "unwrapped_reduced_polarization": [
          [
            5.406203887548531e-09,
            -0.051624369383726346,
            -2.510672291003047e-09
          ],
          [
            4.674420755060886e-09,
            -0.21235631526758558,
            -2.250820317956272e-09
          ],
          [
            3.9305184715183345e-09,
            -0.36507446442963565,
            -1.956927714724941e-09
          ],
          [
            3.1832152450390983e-09,
            -0.5022319311229269,
            -1.6411579989438251e-09
          ],
          [
            2.4407979204625817e-09,
            -0.6072304200767878,
            -1.3187928192573832e-09
          ],
          [
            1.7239360584191464e-09,
            -0.6464717949313119,
            -1.002193164799541e-09
          ],
          [
            1.0575383439773287e-09,
            -0.5687134726885391,
            -6.926378765533935e-10
          ],
          [
            4.838982627050095e-10,
            -0.3409125004092098,
            -3.6460575047894624e-10
          ],
          [
            2.203309619298305e-15,
            6.106226635438361e-16,
            1.5513937184006558e-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": [
          [
            5.406203928970399e-09,
            -0.05162436938372633,
            -2.510672281186288e-09
          ],
          [
            4.674420739370078e-09,
            -0.21235631526758558,
            -2.2508203079141254e-09
          ],
          [
            3.930518466255251e-09,
            -0.36507446442963565,
            -1.9569277309727795e-09
          ],
          [
            3.1832152469490893e-09,
            0.49776806887707314,
            -1.64115798728659e-09
          ],
          [
            2.4407978971296984e-09,
            0.39276957992321215,
            -1.318792797189161e-09
          ],
          [
            1.7239361049803392e-09,
            0.3535282050686881,
            -1.0021931617920643e-09
          ],
          [
            1.057538390192292e-09,
            0.4312865273114609,
            -6.926378914862141e-10
          ],
          [
            4.838982547994419e-10,
            -0.3409125004092098,
            -3.646057344930398e-10
          ],
          [
            2.220446049250313e-15,
            6.661338147750939e-16,
            1.5543122344752192e-15
          ]
        ]
      },
      "reflected": {
        "reached": true,
        "construction": "reflect_displacements_about_reconstructed_parent",
        "energies_eV": [
          -112.75464902921547,
          -112.97942651748109,
          -113.61993922830807,
          -114.57366546439565,
          -115.7202317496577,
          -116.92998439864098,
          -118.03934265475786,
          -118.86939100055555,
          -119.22742062566529
        ],
        "cartesian_polarizations_e_A2": [
          [
            5.4287425785022004e-17,
            -1.6629960824843986e-18,
            6.328815644176705e-17
          ],
          [
            -1.2737664766402546e-11,
            0.006772422706961232,
            1.2319515954205967e-11
          ],
          [
            -2.7625412240939247e-11,
            0.011297819914398752,
            2.340333337108814e-11
          ],
          [
            -4.477494098158499e-11,
            0.01284253366522942,
            3.386268134038946e-11
          ],
          [
            -6.318959340293085e-11,
            0.012062981205879375,
            4.4560104862482265e-11
          ],
          [
            -8.22496143174463e-11,
            0.009977125891292292,
            5.5452363408340915e-11
          ],
          [
            -1.0141729212222154e-10,
            0.007252414005550508,
            6.61217626743628e-11
          ],
          [
            -1.20455972021308e-10,
            0.00421858022148948,
            7.605200574885929e-11
          ],
          [
            -1.391250588587942e-10,
            0.0010255477608689708,
            8.48320612393892e-11
          ]
        ],
        "raw_reduced_polarization": [
          [
            2.343921799777614e-15,
            -8.371245818246601e-17,
            1.8730649861521763e-15
          ],
          [
            -4.838969449585724e-10,
            0.3409125004092089,
            3.6460619612768173e-10
          ],
          [
            -1.057535847902249e-09,
            0.5687134726885382,
            6.926408788185592e-10
          ],
          [
            -1.7239364636362522e-09,
            0.6464717949313121,
            1.0021938751569238e-09
          ],
          [
            -2.4407948960451876e-09,
            0.6072304200767858,
            1.3187929130781695e-09
          ],
          [
            -3.1832145595720873e-09,
            0.5022319311229287,
            1.6411582536002457e-09
          ],
          [
            -3.9305191638561044e-09,
            0.36507446442963787,
            1.9569278906389156e-09
          ],
          [
            -4.67441721226358e-09,
            0.2123563152675853,
            2.2508215929137447e-09
          ],
          [
            -5.406202277336748e-09,
            0.0516243693837269,
            2.5106745486704314e-09
          ]
        ],
        "unwrapped_reduced_polarization": [
          [
            2.343921799777614e-15,
            -8.371245818246601e-17,
            1.8730649861521763e-15
          ],
          [
            -4.838969449585724e-10,
            0.3409125004092089,
            3.6460619612768173e-10
          ],
          [
            -1.057535847902249e-09,
            0.5687134726885382,
            6.926408788185592e-10
          ],
          [
            -1.7239364636362522e-09,
            0.6464717949313121,
            1.0021938751569238e-09
          ],
          [
            -2.4407948960451876e-09,
            0.6072304200767858,
            1.3187929130781695e-09
          ],
          [
            -3.1832145595720873e-09,
            0.5022319311229287,
            1.6411582536002457e-09
          ],
          [
            -3.9305191638561044e-09,
            0.36507446442963787,
            1.9569278906389156e-09
          ],
          [
            -4.67441721226358e-09,
            0.2123563152675853,
            2.2508215929137447e-09
          ],
          [
            -5.406202277336748e-09,
            0.05162436938372689,
            2.5106745486704314e-09
          ]
        ],
        "gauge_integer_shift": [
          0,
          0,
          0
        ],
        "expected_opposite_endpoint_reduced_polarization": [
          -5.406199480929292e-09,
          0.051624369383727546,
          2.5106753937904842e-09
        ],
        "actual_opposite_endpoint_branch_residual": 2.9947721964455615e-15
      },
      "pnp_branch": {
        "construction": "incoming_path_concatenated_with_parent_reflection",
        "reduced_polarization": [
          [
            5.406203887548531e-09,
            -0.051624369383726346,
            -2.510672291003047e-09
          ],
          [
            4.674420755060886e-09,
            -0.2123563152675856,
            -2.250820317956272e-09
          ],
          [
            3.9305184715183345e-09,
            -0.36507446442963565,
            -1.956927714724941e-09
          ],
          [
            3.1832152450390983e-09,
            -0.5022319311229269,
            -1.6411579989438251e-09
          ],
          [
            2.4407979204625817e-09,
            -0.6072304200767878,
            -1.3187928192573832e-09
          ],
          [
            1.7239360584191464e-09,
            -0.6464717949313119,
            -1.002193164799541e-09
          ],
          [
            1.0575383439773287e-09,
            -0.5687134726885391,
            -6.926378765533935e-10
          ],
          [
            4.838982627050095e-10,
            -0.3409125004092098,
            -3.6460575047894624e-10
          ],
          [
            2.203309619287723e-15,
            6.013849154519932e-16,
            1.5513937184051124e-15
          ],
          [
            -4.838969449585724e-10,
            0.3409125004092089,
            3.6460619612768173e-10
          ],
          [
            -1.057535847902249e-09,
            0.5687134726885382,
            6.926408788185592e-10
          ],
          [
            -1.7239364636362522e-09,
            0.6464717949313121,
            1.0021938751569238e-09
          ],
          [
            -2.4407948960451876e-09,
            0.6072304200767858,
            1.3187929130781695e-09
          ],
          [
            -3.1832145595720873e-09,
            0.5022319311229287,
            1.6411582536002457e-09
          ],
          [
            -3.9305191638561044e-09,
            0.36507446442963787,
            1.9569278906389156e-09
          ],
          [
            -4.67441721226358e-09,
            0.2123563152675853,
            2.2508215929137447e-09
          ],
          [
            -5.406202277336748e-09,
            0.0516243693837269,
            2.5106745486704314e-09
          ]
        ],
        "unwrapped_reduced_polarization": [
          [
            5.406203887548531e-09,
            -0.051624369383726346,
            -2.510672291003047e-09
          ],
          [
            4.674420755060886e-09,
            -0.21235631526758558,
            -2.250820317956272e-09
          ],
          [
            3.9305184715183345e-09,
            -0.36507446442963565,
            -1.956927714724941e-09
          ],
          [
            3.1832152450390983e-09,
            -0.5022319311229269,
            -1.6411579989438251e-09
          ],
          [
            2.4407979204625817e-09,
            -0.6072304200767878,
            -1.3187928192573832e-09
          ],
          [
            1.7239360584191464e-09,
            -0.6464717949313119,
            -1.002193164799541e-09
          ],
          [
            1.0575383439773287e-09,
            -0.5687134726885391,
            -6.926378765533935e-10
          ],
          [
            4.838982627050095e-10,
            -0.3409125004092098,
            -3.6460575047894624e-10
          ],
          [
            2.203309619298305e-15,
            6.106226635438361e-16,
            1.5513937184006558e-15
          ],
          [
            -4.838969449585724e-10,
            0.3409125004092089,
            3.6460619612768173e-10
          ],
          [
            -1.057535847902249e-09,
            0.5687134726885382,
            6.926408788185592e-10
          ],
          [
            -1.7239364636362522e-09,
            0.6464717949313121,
            1.0021938751569238e-09
          ],
          [
            -2.4407948960451876e-09,
            0.6072304200767858,
            1.3187929130781695e-09
          ],
          [
            -3.1832145595720873e-09,
            0.5022319311229287,
            1.6411582536002457e-09
          ],
          [
            -3.9305191638561044e-09,
            0.36507446442963787,
            1.9569278906389156e-09
          ],
          [
            -4.67441721226358e-09,
            0.2123563152675853,
            2.2508215929137447e-09
          ],
          [
            -5.406202277336748e-09,
            0.05162436938372689,
            2.5106745486704314e-09
          ]
        ],
        "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": [
          [
            5.406203928970399e-09,
            -0.05162436938372633,
            -2.510672281186288e-09
          ],
          [
            4.674420739370078e-09,
            -0.21235631526758558,
            -2.2508203079141254e-09
          ],
          [
            3.930518466255251e-09,
            -0.36507446442963565,
            -1.9569277309727795e-09
          ],
          [
            3.1832152469490893e-09,
            0.49776806887707314,
            -1.64115798728659e-09
          ],
          [
            2.4407978971296984e-09,
            0.39276957992321215,
            -1.318792797189161e-09
          ],
          [
            1.7239361049803392e-09,
            0.3535282050686881,
            -1.0021931617920643e-09
          ],
          [
            1.057538390192292e-09,
            0.4312865273114609,
            -6.926378914862141e-10
          ],
          [
            4.838982547994419e-10,
            -0.3409125004092098,
            -3.646057344930398e-10
          ],
          [
            2.220446049250313e-15,
            6.661338147750939e-16,
            1.5543122344752192e-15
          ],
          [
            -4.838969225318124e-10,
            0.34091250040920884,
            3.6460623409340087e-10
          ],
          [
            -1.0575358366793353e-09,
            -0.43128652731146166,
            6.926408335772294e-10
          ],
          [
            -1.7239364380472466e-09,
            -0.3535282050686879,
            1.0021938834370303e-09
          ],
          [
            -2.440794899527532e-09,
            -0.39276957992321426,
            1.3187929637226148e-09
          ],
          [
            -3.1832145808152745e-09,
            -0.49776806887707137,
            1.641158209331195e-09
          ],
          [
            -3.930519187900217e-09,
            0.36507446442963787,
            1.956927841995082e-09
          ],
          [
            -4.674417186656399e-09,
            0.21235631526758536,
            2.250821640181755e-09
          ],
          [
            -5.406202263635862e-09,
            0.05162436938372683,
            2.5106745571434885e-09
          ]
        ]
      },
      "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": "P2_1/m",
        "spacegroup_number": 11,
        "pointgroup": "2/m",
        "has_inversion": true,
        "is_polar_point_group": false,
        "nonpolar_parent_hypothesis": true,
        "symmetry_tolerance_A": null,
        "target_reduced_polarization": [
          0.0,
          0.0,
          0.0
        ],
        "formal_class": [
          0.0,
          0.0,
          0.0
        ],
        "target_residual": 7.462475374655307e-16,
        "parent_symmetrization_rmsd_A": 0.39809216009749443,
        "parent_cell_rmsd_A": 0.0,
        "energy_eV": -112.75464902921549,
        "reduced_polarization": [
          -9.216221085842965e-17,
          -5.516760619322125e-18,
          7.40514064292721e-16
        ],
        "cartesian_polarization_e_A2": [
          -3.792760716993195e-18,
          -1.0959361960127595e-19,
          2.5020899058373018e-17
        ],
        "ranking_score": 0.39809216009749593
      }
    }
  ],
  "path_sampling": {
    "num_images": 17,
    "images_per_leg_including_parent": 9,
    "extension_fraction_beyond_polar_endpoint": 0.35,
    "extension_images_per_side": 4,
    "total_images_per_sampled_branch": 25,
    "construction": "linear polar-to-parent interpolation plus parent-reflected second leg and symmetric log-strain continuation beyond both polar endpoints"
  },
  "branch_folding": "componentwise integer unwrap with per-image shifts, then reduced-coordinate fold [-0.5, 0.5)",
  "bec_backprojection_settings": {
    "variable_cell": true,
    "max_strain_step_log_component": 0.02,
    "strain_response_refresh_iterations": 4,
    "cell_principal_stretch_bounds": [
      0.85,
      1.15
    ],
    "cell_volume_ratio_bounds": [
      0.7,
      1.3
    ],
    "strain_jacobian": "branch-matched finite differences of reduced polarization in six symmetric log-strain coordinates at fixed fractional positions"
  },
  "model_input_contract": "one polar endpoint structure; no reference parent or path frame",
  "run": {
    "model_file": "MACEField-MH-0-omat-dielectric.model",
    "model_sha256": "f92e043aaf2cd8879919db8452503553fe7b608cb749d8d169dd96d4aa094aa2",
    "model_head": "mp-ferroelectric",
    "device": "cpu",
    "dtype": "float64",
    "num_images": 17,
    "compute_becs_for_every_image": true,
    "compute_polarizability_for_every_image": true,
    "initial_structure_relaxation": {
      "enabled": false
    },
    "model_evaluations_for_recovery": {
      "total": 55,
      "full_response": 20,
      "energy_polarization": 35
    },
    "model_evaluations_for_recovery_and_path_properties": {
      "total": 80,
      "full_response": 45,
      "energy_polarization": 35
    },
    "elapsed_seconds": 257.60893461300293
  }
}