{
  "schema": "ferrofinder.endpoint_parent_recovery.v4_variable_cell",
  "status": "complete",
  "input_atom_count": 32,
  "input_formula": "B8O16Tl8",
  "input_spacegroup": "P4_1",
  "input_pointgroup": "4",
  "input_is_polar_point_group": true,
  "input_energy_eV": -202.00728618593232,
  "input_cartesian_polarization_e_A2": [
    1.1067089580436911e-17,
    -1.7510819028807406e-17,
    -0.0007167641654606777
  ],
  "input_reduced_polarization": [
    7.99376516851991e-16,
    -1.2648074654800998e-15,
    -0.041680943272863306
  ],
  "input_formal_targets": [
    {
      "orbit_id": 0,
      "representative_formal_class": [
        0.0,
        0.0,
        0.0
      ],
      "target_reduced_polarization": [
        0.0,
        0.0,
        0.0
      ]
    },
    {
      "orbit_id": 1,
      "representative_formal_class": [
        0.0,
        0.0,
        0.5
      ],
      "target_reduced_polarization": [
        0.0,
        0.0,
        -0.5
      ]
    },
    {
      "orbit_id": 2,
      "representative_formal_class": [
        0.0,
        0.5,
        0.0
      ],
      "target_reduced_polarization": [
        0.0,
        -0.5,
        0.0
      ]
    },
    {
      "orbit_id": 3,
      "representative_formal_class": [
        0.0,
        0.5,
        0.5
      ],
      "target_reduced_polarization": [
        0.0,
        -0.5,
        -0.5
      ]
    },
    {
      "orbit_id": 4,
      "representative_formal_class": [
        0.5,
        0.5,
        0.0
      ],
      "target_reduced_polarization": [
        0.5,
        -0.5,
        0.0
      ]
    },
    {
      "orbit_id": 5,
      "representative_formal_class": [
        0.5,
        0.5,
        0.5
      ],
      "target_reduced_polarization": [
        0.5,
        -0.5,
        -0.5
      ]
    }
  ],
  "parent_candidates": [
    {
      "candidate_id": "inversion_parent_endpoint_00",
      "source": "same_species_inversion_center_projection_from_endpoint",
      "spacegroup": "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": 2.0092596845488425e-15,
      "parent_symmetrization_rmsd_A": 0.7382141880490553,
      "parent_cell_rmsd_A": 0.0,
      "energy_eV": "Infinity",
      "reduced_polarization": [
        7.245344923658484e-16,
        -1.5068497574352843e-15,
        1.1142612161619468e-15
      ],
      "cartesian_polarization_e_A2": [
        1.0030927806969711e-17,
        -2.0861810296190694e-17,
        1.9161334845017598e-17
      ],
      "ranking_score": 0.7382141880490593
    },
    {
      "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": 3.2564733452746735e-15,
      "parent_symmetrization_rmsd_A": 0.7382141880490554,
      "parent_cell_rmsd_A": 0.0,
      "energy_eV": "Infinity",
      "reduced_polarization": [
        3.1119723251380873e-15,
        7.156626414389198e-16,
        6.388066058735915e-16
      ],
      "cartesian_polarization_e_A2": [
        4.308417343778513e-17,
        9.90810011953743e-18,
        1.0985204455482056e-17
      ],
      "ranking_score": 0.7382141880490619
    },
    {
      "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": 1.7440090865482422e-15,
      "parent_symmetrization_rmsd_A": 0.7883750603525528,
      "parent_cell_rmsd_A": 0.0,
      "energy_eV": "Infinity",
      "reduced_polarization": [
        7.771968895346692e-16,
        1.5605358297110583e-15,
        -4.7545904644751814e-17
      ],
      "cartesian_polarization_e_A2": [
        1.0760020361856206e-17,
        2.1605075276550145e-17,
        -8.176206675715041e-19
      ],
      "ranking_score": 0.7883750603525562
    },
    {
      "candidate_id": "bec_projection_00",
      "source": "MACEField_BEC_backprojection",
      "spacegroup": "P4_1",
      "spacegroup_number": 76,
      "pointgroup": "4",
      "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": 0.00017968464563869523,
      "parent_symmetrization_rmsd_A": 0.006721081583797575,
      "parent_cell_rmsd_A": 0.00606060393489319,
      "energy_eV": -201.98680503666503,
      "reduced_polarization": [
        -5.4324040841452405e-15,
        3.810984938482209e-15,
        -0.00017968464563869523
      ],
      "cartesian_polarization_e_A2": [
        -7.519520862526129e-17,
        5.2750993407843225e-17,
        -3.0928014970731554e-06
      ],
      "ranking_score": 0.5085956018587983
    },
    {
      "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": 0.00033118314777322587,
      "parent_symmetrization_rmsd_A": 0.7382156988968143,
      "parent_cell_rmsd_A": 0.00606060393489319,
      "energy_eV": 2.6248059873317914e+18,
      "reduced_polarization": [
        -0.0003009943334624756,
        -2.317695257989649e-06,
        0.00013812790044431114
      ],
      "cartesian_polarization_e_A2": [
        -4.166074959774957e-06,
        -3.207931549472363e-08,
        2.3775107537053667e-06
      ],
      "ranking_score": 0.7403932161760841
    },
    {
      "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": 8.349694472459678e-06,
      "parent_symmetrization_rmsd_A": 0.7382156988968156,
      "parent_cell_rmsd_A": 0.00606060393489319,
      "energy_eV": 8.865650613211934e+18,
      "reduced_polarization": [
        -4.566788727636932e-06,
        -6.954013646026713e-06,
        7.096003885471101e-07
      ],
      "cartesian_polarization_e_A2": [
        -6.320911076990083e-08,
        -9.625078913423088e-08,
        1.2213915864770875e-08
      ],
      "ranking_score": 0.7397475492694838
    },
    {
      "candidate_id": "bec_projection_01",
      "source": "MACEField_BEC_backprojection",
      "spacegroup": "P4_1",
      "spacegroup_number": 76,
      "pointgroup": "4",
      "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": 6.543560160454653e-05,
      "parent_symmetrization_rmsd_A": 0.07138087290050257,
      "parent_cell_rmsd_A": 0.06374616355257044,
      "energy_eV": -199.21047912792142,
      "reduced_polarization": [
        2.698074277676801e-15,
        4.70654181372452e-16,
        -0.5000654356016045
      ],
      "cartesian_polarization_e_A2": [
        1.8753741904970365e-16,
        -8.000054528486872e-17,
        -0.008515562255674246
      ],
      "ranking_score": 0.5874482849918543
    },
    {
      "candidate_id": "bec_projection_02",
      "source": "MACEField_BEC_backprojection",
      "spacegroup": "P1",
      "spacegroup_number": 1,
      "pointgroup": "1",
      "has_inversion": false,
      "is_polar_point_group": true,
      "nonpolar_parent_hypothesis": false,
      "symmetry_tolerance_A": null,
      "target_reduced_polarization": [
        0.0,
        -0.5,
        0.0
      ],
      "formal_class": [
        0.0,
        0.5,
        0.0
      ],
      "target_residual": 9.326106014038128e-05,
      "parent_symmetrization_rmsd_A": 0.07279938790367797,
      "parent_cell_rmsd_A": 0.047593372912715946,
      "energy_eV": -199.27322426195224,
      "reduced_polarization": [
        5.759788904307211e-05,
        -0.4999524385903304,
        5.5839240920071096e-05
      ],
      "cartesian_polarization_e_A2": [
        8.363171404083874e-07,
        -0.006920724437461645,
        -3.5853149929951975e-05
      ],
      "ranking_score": 0.5848842532521377
    },
    {
      "candidate_id": "bec_projection_03",
      "source": "MACEField_BEC_backprojection",
      "spacegroup": "P1",
      "spacegroup_number": 1,
      "pointgroup": "1",
      "has_inversion": false,
      "is_polar_point_group": true,
      "nonpolar_parent_hypothesis": false,
      "symmetry_tolerance_A": null,
      "target_reduced_polarization": [
        0.0,
        -0.5,
        -0.5
      ],
      "formal_class": [
        0.0,
        0.5,
        0.5
      ],
      "target_residual": 3.454970076870021e-05,
      "parent_symmetrization_rmsd_A": 0.1065257925736373,
      "parent_cell_rmsd_A": 0.0839901277312475,
      "energy_eV": -196.29555862434344,
      "reduced_polarization": [
        5.714089422775663e-06,
        -0.49998074012861093,
        -0.4999718914895565
      ],
      "cartesian_polarization_e_A2": [
        2.120387050532857e-05,
        -0.006992025898262938,
        -0.008551242198698577
      ],
      "ranking_score": 0.6275924239079866
    },
    {
      "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": 1.0812440663114994e-05,
      "parent_symmetrization_rmsd_A": 0.10340316133748213,
      "parent_cell_rmsd_A": 0.06810513471851186,
      "energy_eV": -196.47187808221062,
      "reduced_polarization": [
        0.49999986264859014,
        -0.49999395727997925,
        8.965240790655354e-06
      ],
      "cartesian_polarization_e_A2": [
        0.006922493636180693,
        -0.006922246611714287,
        -7.470100102154524e-05
      ],
      "ranking_score": 0.6204510698984363
    },
    {
      "candidate_id": "bec_projection_05",
      "source": "MACEField_BEC_backprojection",
      "spacegroup": "P1",
      "spacegroup_number": 1,
      "pointgroup": "1",
      "has_inversion": false,
      "is_polar_point_group": true,
      "nonpolar_parent_hypothesis": false,
      "symmetry_tolerance_A": null,
      "target_reduced_polarization": [
        0.5,
        -0.5,
        -0.5
      ],
      "formal_class": [
        0.5,
        0.5,
        0.5
      ],
      "target_residual": 0.00020199981485646658,
      "parent_symmetrization_rmsd_A": 0.13391461124253226,
      "parent_cell_rmsd_A": 0.10226186355982532,
      "energy_eV": -193.1524895229373,
      "reduced_polarization": [
        0.499893371661637,
        -0.49992678027968074,
        -0.49984484460945117
      ],
      "cartesian_polarization_e_A2": [
        0.007014774322068724,
        -0.006971909587452242,
        -0.008586475853301056
      ],
      "ranking_score": 0.6598840767622015
    }
  ],
  "formal_branches": [
    {
      "orbit_id": 0,
      "formal_class": [
        0.0,
        0.0,
        0.0
      ],
      "formal_classes_in_orbit": [
        [
          0.0,
          0.0,
          0.0
        ]
      ],
      "target_reduced_polarization": [
        0.0,
        0.0,
        0.0
      ],
      "bec_backprojection": {
        "converged_to_target": true,
        "history": [
          {
            "iteration": 0,
            "reduced_polarization": [
              7.99376516851991e-16,
              -1.2648074654800998e-15,
              -0.041680943272863306
            ],
            "branch_aligned_reduced_polarization": [
              7.99376516851991e-16,
              -1.2648074654800998e-15,
              -0.041680943272863306
            ],
            "target_residual": 0.041680943272863306,
            "energy_eV": -202.00728618593232,
            "max_atomic_step_A": 0.007808657406882046,
            "max_log_strain_component": 0.0007240383334186501,
            "step_scale": 1.0,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 1.2242439913613525,
            "cell_principal_stretches": [
              1.0007243005124447,
              0.9995369036439351,
              0.9995369036333059
            ],
            "cell_volume_ratio": 0.9997976515613941,
            "cell_rmsd_from_input_A": 0.00606060393489319
          },
          {
            "iteration": 1,
            "reduced_polarization": [
              -5.4324040841452405e-15,
              3.810984938482209e-15,
              -0.00017968464563869523
            ],
            "branch_aligned_reduced_polarization": [
              -5.4324040841452405e-15,
              3.810984938482209e-15,
              -0.00017968464563869523
            ],
            "target_residual": 0.00017968464563869523,
            "energy_eV": -201.98680503666503
          }
        ],
        "iterations": 1
      },
      "parent": {
        "candidate_id": "bec_projection_00",
        "source": "MACEField_BEC_backprojection",
        "spacegroup": "P4_1",
        "spacegroup_number": 76,
        "pointgroup": "4",
        "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": 0.00017968464563869523,
        "parent_symmetrization_rmsd_A": 0.006721081583797575,
        "parent_cell_rmsd_A": 0.00606060393489319,
        "energy_eV": -201.98680503666503,
        "reduced_polarization": [
          -5.4324040841452405e-15,
          3.810984938482209e-15,
          -0.00017968464563869523
        ],
        "cartesian_polarization_e_A2": [
          -7.519520862526129e-17,
          5.2750993407843225e-17,
          -3.0928014970731554e-06
        ],
        "ranking_score": 0.5085956018587983
      },
      "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": [
          -202.0072861859323,
          -202.00694845454245,
          -202.00596884572101,
          -202.00435087068115,
          -202.00209799290576,
          -201.99921362693513,
          -201.9957011395894,
          -201.99156385133287,
          -201.986805036665
        ],
        "cartesian_polarizations_e_A2": [
          [
            5.3099354105340446e-18,
            -2.740632143681332e-17,
            -0.0007167641654606914
          ],
          [
            -5.168341893117799e-18,
            -2.0156848333914636e-19,
            -0.0006273365068456419
          ],
          [
            -1.2324334805495404e-17,
            2.0043973090256262e-17,
            -0.0005379708577587757
          ],
          [
            -1.2608116587932526e-17,
            -7.149743855759889e-19,
            -0.00044866744768929447
          ],
          [
            -6.431782500334088e-18,
            8.787792936303676e-18,
            -0.000359426517091979
          ],
          [
            -2.568368323849385e-17,
            2.5910470728458476e-17,
            -0.00027024831772774874
          ],
          [
            4.957951932058813e-18,
            -8.2559034395973e-18,
            -0.0001811331130084525
          ],
          [
            -1.1132049146690882e-17,
            -3.058636027571264e-18,
            -9.20811783445453e-05
          ],
          [
            -6.862102235736634e-17,
            7.547871450169183e-17,
            -3.0928014970480806e-06
          ]
        ],
        "raw_reduced_polarization": [
          [
            3.835369400718432e-16,
            -1.979560173490616e-15,
            -0.041680943272864104
          ],
          [
            -3.640078444593433e-16,
            -2.0047781453507886e-17,
            -0.036476362561839
          ],
          [
            -8.742718006783247e-16,
            1.4384596836237394e-15,
            -0.0312765917272664
          ],
          [
            -8.90791859798504e-16,
            -6.342167852578294e-17,
            -0.02608164264808406
          ],
          [
            -4.4328589514130274e-16,
            6.222499463386776e-16,
            -0.020891527834743098
          ],
          [
            -1.8353780502928802e-15,
            1.8600010807317648e-15,
            -0.015706260448633384
          ],
          [
            3.7431537796863823e-16,
            -6.059464967035105e-16,
            -0.010525854321740954
          ],
          [
            -7.946846754841057e-16,
            -2.2661322550540243e-16,
            -0.0053503239764595995
          ],
          [
            -4.9574263574280425e-15,
            5.453037788663034e-15,
            -0.00017968464563723847
          ]
        ],
        "unwrapped_reduced_polarization": [
          [
            3.835369400718432e-16,
            -1.979560173490616e-15,
            -0.041680943272864104
          ],
          [
            -3.640078444593433e-16,
            -2.0047781453507778e-17,
            -0.036476362561839
          ],
          [
            -8.742718006783247e-16,
            1.4384596836237394e-15,
            -0.0312765917272664
          ],
          [
            -8.90791859798504e-16,
            -6.34216785257829e-17,
            -0.02608164264808406
          ],
          [
            -4.4328589514130274e-16,
            6.222499463386776e-16,
            -0.020891527834743098
          ],
          [
            -1.8353780502928802e-15,
            1.8600010807317648e-15,
            -0.015706260448633384
          ],
          [
            3.743153779686384e-16,
            -6.059464967035106e-16,
            -0.010525854321740954
          ],
          [
            -7.946846754841057e-16,
            -2.2661322550540243e-16,
            -0.0053503239764595995
          ],
          [
            -4.9574263574280425e-15,
            5.453037788663034e-15,
            -0.00017968464563723838
          ]
        ],
        "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": [
          [
            3.3306690738754696e-16,
            -1.9984014443252818e-15,
            -0.04168094327286409
          ],
          [
            -3.885780586188048e-16,
            0.0,
            -0.036476362561839004
          ],
          [
            -8.881784197001252e-16,
            1.4432899320127035e-15,
            -0.03127659172726638
          ],
          [
            -8.881784197001252e-16,
            -5.551115123125783e-17,
            -0.026081642648084047
          ],
          [
            -4.440892098500626e-16,
            6.661338147750939e-16,
            -0.020891527834743073
          ],
          [
            -1.8318679906315083e-15,
            1.887379141862766e-15,
            -0.01570626044863338
          ],
          [
            3.3306690738754696e-16,
            -6.106226635438361e-16,
            -0.010525854321740968
          ],
          [
            -7.771561172376096e-16,
            -2.220446049250313e-16,
            -0.0053503239764596255
          ],
          [
            -4.9404924595819466e-15,
            5.440092820663267e-15,
            -0.00017968464563722364
          ]
        ]
      },
      "reflected": {
        "reached": true,
        "construction": "reflect_displacements_about_reconstructed_parent",
        "energies_eV": [
          -201.986805036665,
          -201.9811765883839,
          -201.97498434257366,
          -201.9682304582859,
          -201.9609170595723,
          -201.9530462359761,
          -201.9446200431539,
          -201.93564050317113,
          -201.92610960466146
        ],
        "cartesian_polarizations_e_A2": [
          [
            -6.279340156407183e-17,
            7.093947041350946e-17,
            -3.092801497022628e-06
          ],
          [
            -7.130937424527113e-17,
            1.630432551875269e-17,
            8.199488823285894e-05
          ],
          [
            -4.627841790712076e-17,
            3.9323425616151344e-17,
            0.0001669801981519086
          ],
          [
            1.3232420074186003e-17,
            5.10397845470388e-17,
            0.0002518631530866051
          ],
          [
            -4.56650258030576e-17,
            9.027173675787216e-18,
            0.00033664377171430826
          ],
          [
            -5.734913485712602e-17,
            -2.2866581670844402e-17,
            0.0004213220656481153
          ],
          [
            -1.0779147313653839e-16,
            3.407223458365686e-17,
            0.00050589803798748
          ],
          [
            -8.148090988229774e-17,
            2.8081009335184824e-17,
            0.0005903716830376955
          ],
          [
            -6.838352762095238e-17,
            1.9696521979525453e-17,
            0.0006747429860166421
          ]
        ],
        "raw_reduced_polarization": [
          [
            -4.536387165072337e-15,
            5.125082396129411e-15,
            -0.00017968464563575975
          ],
          [
            -5.160375302261061e-15,
            1.1829510234344024e-15,
            0.0047642658830655375
          ],
          [
            -3.3582184367420106e-15,
            2.849651727325352e-15,
            0.009703412099368104
          ],
          [
            9.372405496202155e-16,
            3.698222408696527e-15,
            0.014637753578090308
          ],
          [
            -3.3188075138403264e-15,
            6.638968218292559e-16,
            0.019567289536855718
          ],
          [
            -4.161500834659685e-15,
            -1.6407596852072737e-15,
            0.024492018782687714
          ],
          [
            -7.801313361913626e-15,
            2.4700508766853428e-15,
            0.02941193962750747
          ],
          [
            -5.894327847342369e-15,
            2.0335236829875355e-15,
            0.03432704987153687
          ],
          [
            -4.93934613272831e-15,
            1.4226809153080112e-15,
            0.03923734678594917
          ]
        ],
        "unwrapped_reduced_polarization": [
          [
            -4.536387165072337e-15,
            5.125082396129411e-15,
            -0.00017968464563575975
          ],
          [
            -5.160375302261061e-15,
            1.182951023434402e-15,
            0.0047642658830655375
          ],
          [
            -3.3582184367420106e-15,
            2.849651727325352e-15,
            0.009703412099368104
          ],
          [
            9.372405496202157e-16,
            3.698222408696527e-15,
            0.014637753578090308
          ],
          [
            -3.3188075138403268e-15,
            6.638968218292558e-16,
            0.019567289536855718
          ],
          [
            -4.161500834659685e-15,
            -1.6407596852072735e-15,
            0.024492018782687714
          ],
          [
            -7.801313361913626e-15,
            2.4700508766853428e-15,
            0.02941193962750747
          ],
          [
            -5.894327847342369e-15,
            2.0335236829875355e-15,
            0.03432704987153687
          ],
          [
            -4.93934613272831e-15,
            1.4226809153080112e-15,
            0.03923734678594917
          ]
        ],
        "gauge_integer_shift": [
          0,
          0,
          0
        ],
        "expected_opposite_endpoint_reduced_polarization": [
          -1.0296537722466984e-14,
          1.2883223951812778e-14,
          0.0413212409050153
        ],
        "actual_opposite_endpoint_branch_residual": 0.002083894119066128
      },
      "pnp_branch": {
        "construction": "incoming_path_concatenated_with_parent_reflection",
        "reduced_polarization": [
          [
            3.835369400718432e-16,
            -1.979560173490616e-15,
            -0.041680943272864104
          ],
          [
            -3.640078444593433e-16,
            -2.0047781453507886e-17,
            -0.036476362561839
          ],
          [
            -8.742718006783247e-16,
            1.4384596836237394e-15,
            -0.0312765917272664
          ],
          [
            -8.90791859798504e-16,
            -6.342167852578294e-17,
            -0.02608164264808406
          ],
          [
            -4.4328589514130274e-16,
            6.222499463386776e-16,
            -0.020891527834743098
          ],
          [
            -1.8353780502928802e-15,
            1.8600010807317648e-15,
            -0.015706260448633384
          ],
          [
            3.7431537796863823e-16,
            -6.059464967035105e-16,
            -0.010525854321740954
          ],
          [
            -7.946846754841057e-16,
            -2.2661322550540243e-16,
            -0.0053503239764595995
          ],
          [
            -4.9574263574280425e-15,
            5.453037788663034e-15,
            -0.00017968464563723847
          ],
          [
            -5.160375302261061e-15,
            1.1829510234344024e-15,
            0.0047642658830655375
          ],
          [
            -3.3582184367420106e-15,
            2.849651727325352e-15,
            0.009703412099368104
          ],
          [
            9.372405496202155e-16,
            3.698222408696527e-15,
            0.014637753578090308
          ],
          [
            -3.3188075138403264e-15,
            6.638968218292559e-16,
            0.019567289536855718
          ],
          [
            -4.161500834659685e-15,
            -1.6407596852072737e-15,
            0.024492018782687714
          ],
          [
            -7.801313361913626e-15,
            2.4700508766853428e-15,
            0.02941193962750747
          ],
          [
            -5.894327847342369e-15,
            2.0335236829875355e-15,
            0.03432704987153687
          ],
          [
            -4.93934613272831e-15,
            1.4226809153080112e-15,
            0.03923734678594917
          ]
        ],
        "unwrapped_reduced_polarization": [
          [
            3.835369400718432e-16,
            -1.979560173490616e-15,
            -0.041680943272864104
          ],
          [
            -3.640078444593433e-16,
            -2.0047781453507778e-17,
            -0.036476362561839
          ],
          [
            -8.742718006783247e-16,
            1.4384596836237394e-15,
            -0.0312765917272664
          ],
          [
            -8.90791859798504e-16,
            -6.34216785257829e-17,
            -0.02608164264808406
          ],
          [
            -4.4328589514130274e-16,
            6.222499463386776e-16,
            -0.020891527834743098
          ],
          [
            -1.8353780502928802e-15,
            1.8600010807317648e-15,
            -0.015706260448633384
          ],
          [
            3.743153779686384e-16,
            -6.059464967035106e-16,
            -0.010525854321740954
          ],
          [
            -7.946846754841057e-16,
            -2.2661322550540243e-16,
            -0.0053503239764595995
          ],
          [
            -4.9574263574280425e-15,
            5.453037788663034e-15,
            -0.00017968464563723838
          ],
          [
            -5.160375302261061e-15,
            1.182951023434402e-15,
            0.0047642658830655375
          ],
          [
            -3.3582184367420106e-15,
            2.849651727325352e-15,
            0.009703412099368104
          ],
          [
            9.372405496202157e-16,
            3.698222408696527e-15,
            0.014637753578090308
          ],
          [
            -3.3188075138403268e-15,
            6.638968218292558e-16,
            0.019567289536855718
          ],
          [
            -4.161500834659685e-15,
            -1.6407596852072735e-15,
            0.024492018782687714
          ],
          [
            -7.801313361913626e-15,
            2.4700508766853428e-15,
            0.02941193962750747
          ],
          [
            -5.894327847342369e-15,
            2.0335236829875355e-15,
            0.03432704987153687
          ],
          [
            -4.93934613272831e-15,
            1.4226809153080112e-15,
            0.03923734678594917
          ]
        ],
        "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": [
          [
            3.3306690738754696e-16,
            -1.9984014443252818e-15,
            -0.04168094327286409
          ],
          [
            -3.885780586188048e-16,
            0.0,
            -0.036476362561839004
          ],
          [
            -8.881784197001252e-16,
            1.4432899320127035e-15,
            -0.03127659172726638
          ],
          [
            -8.881784197001252e-16,
            -5.551115123125783e-17,
            -0.026081642648084047
          ],
          [
            -4.440892098500626e-16,
            6.661338147750939e-16,
            -0.020891527834743073
          ],
          [
            -1.8318679906315083e-15,
            1.887379141862766e-15,
            -0.01570626044863338
          ],
          [
            3.3306690738754696e-16,
            -6.106226635438361e-16,
            -0.010525854321740968
          ],
          [
            -7.771561172376096e-16,
            -2.220446049250313e-16,
            -0.0053503239764596255
          ],
          [
            -4.9404924595819466e-15,
            5.440092820663267e-15,
            -0.00017968464563722364
          ],
          [
            -5.162537064506978e-15,
            1.2212453270876722e-15,
            0.004764265883065555
          ],
          [
            -3.3306690738754696e-15,
            2.886579864025407e-15,
            0.009703412099368092
          ],
          [
            8.881784197001252e-16,
            3.6637359812630166e-15,
            0.014637753578090273
          ],
          [
            -3.3306690738754696e-15,
            6.661338147750939e-16,
            0.019567289536855714
          ],
          [
            -4.163336342344337e-15,
            -1.6653345369377348e-15,
            0.024492018782687697
          ],
          [
            -7.827072323607354e-15,
            2.4424906541753444e-15,
            0.029411939627507433
          ],
          [
            -5.88418203051333e-15,
            1.9984014443252818e-15,
            0.0343270498715369
          ],
          [
            -4.9404924595819466e-15,
            1.4432899320127035e-15,
            0.039237346785949145
          ]
        ]
      },
      "incoming_structure_ids": [
        "incoming_00_000",
        "incoming_00_001",
        "incoming_00_002",
        "incoming_00_003",
        "incoming_00_004",
        "incoming_00_005",
        "incoming_00_006",
        "incoming_00_007",
        "incoming_00_008"
      ],
      "reflected_structure_ids": [
        "reflected_00_001",
        "reflected_00_002",
        "reflected_00_003",
        "reflected_00_004",
        "reflected_00_005",
        "reflected_00_006",
        "reflected_00_007",
        "reflected_00_008"
      ]
    },
    {
      "orbit_id": 1,
      "formal_class": [
        0.0,
        0.0,
        0.5
      ],
      "formal_classes_in_orbit": [
        [
          0.0,
          0.0,
          0.5
        ]
      ],
      "target_reduced_polarization": [
        0.0,
        0.0,
        -0.5
      ],
      "bec_backprojection": {
        "converged_to_target": true,
        "history": [
          {
            "iteration": 0,
            "reduced_polarization": [
              7.99376516851991e-16,
              -1.2648074654800998e-15,
              -0.041680943272863306
            ],
            "branch_aligned_reduced_polarization": [
              7.99376516851991e-16,
              -1.2648074654800998e-15,
              -0.04168094327286331
            ],
            "target_residual": 0.4583190567271367,
            "energy_eV": -202.00728618593232,
            "max_atomic_step_A": 0.08586313590838653,
            "max_log_strain_component": 0.007961445685965823,
            "step_scale": 1.0,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 1.2242439913613525,
            "cell_principal_stretches": [
              1.0051063291195712,
              1.0051063290020432,
              0.9920701626843421
            ],
            "cell_volume_ratio": 1.002227703917661,
            "cell_rmsd_from_input_A": 0.06630936481418352
          },
          {
            "iteration": 1,
            "reduced_polarization": [
              -2.411827785431799e-14,
              8.16042063030019e-15,
              -0.5213889919259133
            ],
            "branch_aligned_reduced_polarization": [
              -2.411827785431799e-14,
              8.16042063030019e-15,
              -0.5213889919259133
            ],
            "target_residual": 0.02138899192591326,
            "energy_eV": -198.91695327430577,
            "max_atomic_step_A": 0.003801746784820532,
            "max_log_strain_component": 0.0003090999504381983,
            "step_scale": 1.0,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 1.2242439913613525,
            "cell_principal_stretches": [
              1.0049075922718997,
              1.0049075921589572,
              0.992376858919913
            ],
            "cell_volume_ratio": 1.0021411216772327,
            "cell_rmsd_from_input_A": 0.06374616355257044
          },
          {
            "iteration": 2,
            "reduced_polarization": [
              2.698074277676801e-15,
              4.70654181372452e-16,
              -0.5000654356016045
            ],
            "branch_aligned_reduced_polarization": [
              2.698074277676801e-15,
              4.70654181372452e-16,
              -0.5000654356016045
            ],
            "target_residual": 6.543560160454653e-05,
            "energy_eV": -199.21047912792142
          }
        ],
        "iterations": 2
      },
      "parent": {
        "candidate_id": "bec_projection_01",
        "source": "MACEField_BEC_backprojection",
        "spacegroup": "P4_1",
        "spacegroup_number": 76,
        "pointgroup": "4",
        "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": 6.543560160454653e-05,
        "parent_symmetrization_rmsd_A": 0.07138087290050257,
        "parent_cell_rmsd_A": 0.06374616355257044,
        "energy_eV": -199.21047912792142,
        "reduced_polarization": [
          2.698074277676801e-15,
          4.70654181372452e-16,
          -0.5000654356016045
        ],
        "cartesian_polarization_e_A2": [
          1.8753741904970365e-16,
          -8.000054528486872e-17,
          -0.008515562255674246
        ],
        "ranking_score": 0.5874482849918543
      },
      "branch_status": "awaiting_branch_sampling"
    },
    {
      "orbit_id": 2,
      "formal_class": [
        0.0,
        0.5,
        0.0
      ],
      "formal_classes_in_orbit": [
        [
          0.0,
          0.5,
          0.0
        ],
        [
          0.5,
          0.0,
          0.0
        ]
      ],
      "target_reduced_polarization": [
        0.0,
        -0.5,
        0.0
      ],
      "bec_backprojection": {
        "converged_to_target": true,
        "history": [
          {
            "iteration": 0,
            "reduced_polarization": [
              7.99376516851991e-16,
              -1.2648074654800998e-15,
              -0.041680943272863306
            ],
            "branch_aligned_reduced_polarization": [
              7.99376516851991e-16,
              -1.27675647831893e-15,
              -0.041680943272863306
            ],
            "target_residual": 0.5017342932590062,
            "energy_eV": -202.00728618593232,
            "max_atomic_step_A": 0.12,
            "max_log_strain_component": 0.005161460277558003,
            "step_scale": 0.9968007243660724,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 1.2242439913613525,
            "cell_principal_stretches": [
              1.0057847954573367,
              0.9995383848738408,
              0.9945070143672851
            ],
            "cell_volume_ratio": 0.9997982988644871,
            "cell_rmsd_from_input_A": 0.04650289880879233
          },
          {
            "iteration": 1,
            "reduced_polarization": [
              0.0009444563502256605,
              -0.4882323405277491,
              0.016305925582879882
            ],
            "branch_aligned_reduced_polarization": [
              0.0009444563502256605,
              -0.4882323405277491,
              0.016305925582879882
            ],
            "target_residual": 0.0201308970581729,
            "energy_eV": -199.37960060030187,
            "max_atomic_step_A": 0.004366420832866998,
            "max_log_strain_component": 0.0003062783368278343,
            "step_scale": 1.0,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 1.2242439913613525,
            "cell_principal_stretches": [
              1.0058757419301774,
              0.9997342552195145,
              0.9943073811259221
            ],
            "cell_volume_ratio": 0.9998838901409343,
            "cell_rmsd_from_input_A": 0.047593372912715946
          },
          {
            "iteration": 2,
            "reduced_polarization": [
              5.759788904307211e-05,
              -0.4999524385903304,
              5.5839240920071096e-05
            ],
            "branch_aligned_reduced_polarization": [
              5.759788904307211e-05,
              -0.4999524385903304,
              5.5839240920071096e-05
            ],
            "target_residual": 9.326106014038128e-05,
            "energy_eV": -199.27322426195224
          }
        ],
        "iterations": 2
      },
      "parent": {
        "candidate_id": "bec_projection_02",
        "source": "MACEField_BEC_backprojection",
        "spacegroup": "P1",
        "spacegroup_number": 1,
        "pointgroup": "1",
        "has_inversion": false,
        "is_polar_point_group": true,
        "nonpolar_parent_hypothesis": false,
        "symmetry_tolerance_A": null,
        "target_reduced_polarization": [
          0.0,
          -0.5,
          0.0
        ],
        "formal_class": [
          0.0,
          0.5,
          0.0
        ],
        "target_residual": 9.326106014038128e-05,
        "parent_symmetrization_rmsd_A": 0.07279938790367797,
        "parent_cell_rmsd_A": 0.047593372912715946,
        "energy_eV": -199.27322426195224,
        "reduced_polarization": [
          5.759788904307211e-05,
          -0.4999524385903304,
          5.5839240920071096e-05
        ],
        "cartesian_polarization_e_A2": [
          8.363171404083874e-07,
          -0.006920724437461645,
          -3.5853149929951975e-05
        ],
        "ranking_score": 0.5848842532521377
      },
      "branch_status": "awaiting_branch_sampling"
    },
    {
      "orbit_id": 3,
      "formal_class": [
        0.0,
        0.5,
        0.5
      ],
      "formal_classes_in_orbit": [
        [
          0.0,
          0.5,
          0.5
        ],
        [
          0.5,
          0.0,
          0.5
        ]
      ],
      "target_reduced_polarization": [
        0.0,
        -0.5,
        -0.5
      ],
      "bec_backprojection": {
        "converged_to_target": true,
        "history": [
          {
            "iteration": 0,
            "reduced_polarization": [
              7.99376516851991e-16,
              -1.2648074654800998e-15,
              -0.041680943272863306
            ],
            "branch_aligned_reduced_polarization": [
              7.99376516851991e-16,
              -1.27675647831893e-15,
              -0.04168094327286331
            ],
            "target_residual": 0.67827454453138,
            "energy_eV": -202.00728618593232,
            "max_atomic_step_A": 0.12,
            "max_log_strain_component": 0.005867087072698146,
            "step_scale": 0.7369373985713483,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 1.2242439913613525,
            "cell_principal_stretches": [
              1.0053071843678658,
              1.003760522817449,
              0.9926205943407845
            ],
            "cell_volume_ratio": 1.0016411977476791,
            "cell_rmsd_from_input_A": 0.05951142144140814
          },
          {
            "iteration": 1,
            "reduced_polarization": [
              3.510690721999311e-05,
              -0.3473791845959895,
              -0.38109462053696125
            ],
            "branch_aligned_reduced_polarization": [
              3.510690721999311e-05,
              -0.3473791845959895,
              -0.38109462053696125
            ],
            "target_residual": 0.19347248846368112,
            "energy_eV": -199.2944346407246,
            "max_atomic_step_A": 0.04287204449662891,
            "max_log_strain_component": 0.0020563609582107635,
            "step_scale": 1.0,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 1.2242439913613525,
            "cell_principal_stretches": [
              1.0076314139420344,
              1.0050818961749406,
              0.9895976198995896
            ],
            "cell_volume_ratio": 1.002217059960055,
            "cell_rmsd_from_input_A": 0.08350757993702035
          },
          {
            "iteration": 2,
            "reduced_polarization": [
              0.0010642809896995518,
              -0.4952674841926927,
              -0.4991906802125444
            ],
            "branch_aligned_reduced_polarization": [
              0.0010642809896995518,
              -0.4952674841926927,
              -0.4991906802125444
            ],
            "target_residual": 0.00491776355773808,
            "energy_eV": -196.36892193181194,
            "max_atomic_step_A": 0.0013261627575568602,
            "max_log_strain_component": 6.6789633669298e-05,
            "step_scale": 1.0,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 1.2242439913613525,
            "cell_principal_stretches": [
              1.0076874337419757,
              1.0050966935803978,
              0.9895344021073117
            ],
            "cell_volume_ratio": 1.0022235063406246,
            "cell_rmsd_from_input_A": 0.0839901277312475
          },
          {
            "iteration": 3,
            "reduced_polarization": [
              5.714089422775663e-06,
              -0.49998074012861093,
              -0.4999718914895565
            ],
            "branch_aligned_reduced_polarization": [
              5.714089422775663e-06,
              -0.49998074012861093,
              -0.4999718914895565
            ],
            "target_residual": 3.454970076870021e-05,
            "energy_eV": -196.29555862434344
          }
        ],
        "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,
          -0.5,
          -0.5
        ],
        "formal_class": [
          0.0,
          0.5,
          0.5
        ],
        "target_residual": 3.454970076870021e-05,
        "parent_symmetrization_rmsd_A": 0.1065257925736373,
        "parent_cell_rmsd_A": 0.0839901277312475,
        "energy_eV": -196.29555862434344,
        "reduced_polarization": [
          5.714089422775663e-06,
          -0.49998074012861093,
          -0.4999718914895565
        ],
        "cartesian_polarization_e_A2": [
          2.120387050532857e-05,
          -0.006992025898262938,
          -0.008551242198698577
        ],
        "ranking_score": 0.6275924239079866
      },
      "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": [
              7.99376516851991e-16,
              -1.2648074654800998e-15,
              -0.041680943272863306
            ],
            "branch_aligned_reduced_polarization": [
              7.771561172376096e-16,
              -1.27675647831893e-15,
              -0.041680943272863306
            ],
            "target_residual": 0.7083341732770724,
            "energy_eV": -202.00728618593232,
            "max_atomic_step_A": 0.12000000000000001,
            "max_log_strain_component": 0.006482844450063574,
            "step_scale": 0.8789801423118043,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 1.2242439913613525,
            "cell_principal_stretches": [
              1.0071517562931573,
              0.9995929360886722,
              0.9931266947228239
            ],
            "cell_volume_ratio": 0.9998221375627399,
            "cell_rmsd_from_input_A": 0.05774315756257617
          },
          {
            "iteration": 1,
            "reduced_polarization": [
              0.43245224245188174,
              -0.42706864727944044,
              0.020564873115926013
            ],
            "branch_aligned_reduced_polarization": [
              0.43245224245188174,
              -0.42706864727944044,
              0.020564873115926013
            ],
            "target_residual": 0.1015115548383738,
            "energy_eV": -198.00491954365634,
            "max_atomic_step_A": 0.023581570722831974,
            "max_log_strain_component": 0.0011678323334550521,
            "step_scale": 1.0,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 1.2242439913613525,
            "cell_principal_stretches": [
              1.0083211785600186,
              0.9999551106089142,
              0.9917725619839595
            ],
            "cell_volume_ratio": 0.9999803880373299,
            "cell_rmsd_from_input_A": 0.0680046765733483
          },
          {
            "iteration": 2,
            "reduced_polarization": [
              0.49958818389702403,
              -0.49931923428108477,
              0.0012602834507986008
            ],
            "branch_aligned_reduced_polarization": [
              0.49958818389702403,
              -0.49931923428108477,
              0.0012602834507986008
            ],
            "target_residual": 0.0014904190159405904,
            "energy_eV": -196.4823404954409,
            "max_atomic_step_A": 0.0003455630281297412,
            "max_log_strain_component": 2.4137176163750775e-05,
            "step_scale": 1.0,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 1.2242439913613525,
            "cell_principal_stretches": [
              1.0083293659399324,
              0.9999705517966632,
              0.9917558852753049
            ],
            "cell_volume_ratio": 0.9999871342751689,
            "cell_rmsd_from_input_A": 0.06810513471851186
          },
          {
            "iteration": 3,
            "reduced_polarization": [
              0.49999986264859014,
              -0.49999395727997925,
              8.965240790655354e-06
            ],
            "branch_aligned_reduced_polarization": [
              0.49999986264859014,
              -0.49999395727997925,
              8.965240790655354e-06
            ],
            "target_residual": 1.0812440663114994e-05,
            "energy_eV": -196.47187808221062
          }
        ],
        "iterations": 3
      },
      "parent": {
        "candidate_id": "bec_projection_04",
        "source": "MACEField_BEC_backprojection",
        "spacegroup": "P1",
        "spacegroup_number": 1,
        "pointgroup": "1",
        "has_inversion": false,
        "is_polar_point_group": true,
        "nonpolar_parent_hypothesis": false,
        "symmetry_tolerance_A": null,
        "target_reduced_polarization": [
          0.5,
          -0.5,
          0.0
        ],
        "formal_class": [
          0.5,
          0.5,
          0.0
        ],
        "target_residual": 1.0812440663114994e-05,
        "parent_symmetrization_rmsd_A": 0.10340316133748213,
        "parent_cell_rmsd_A": 0.06810513471851186,
        "energy_eV": -196.47187808221062,
        "reduced_polarization": [
          0.49999986264859014,
          -0.49999395727997925,
          8.965240790655354e-06
        ],
        "cartesian_polarization_e_A2": [
          0.006922493636180693,
          -0.006922246611714287,
          -7.470100102154524e-05
        ],
        "ranking_score": 0.6204510698984363
      },
      "branch_status": "awaiting_branch_sampling"
    },
    {
      "orbit_id": 5,
      "formal_class": [
        0.5,
        0.5,
        0.5
      ],
      "formal_classes_in_orbit": [
        [
          0.5,
          0.5,
          0.5
        ]
      ],
      "target_reduced_polarization": [
        0.5,
        -0.5,
        -0.5
      ],
      "bec_backprojection": {
        "converged_to_target": true,
        "history": [
          {
            "iteration": 0,
            "reduced_polarization": [
              7.99376516851991e-16,
              -1.2648074654800998e-15,
              -0.041680943272863306
            ],
            "branch_aligned_reduced_polarization": [
              7.771561172376096e-16,
              -1.27675647831893e-15,
              -0.04168094327286331
            ],
            "target_residual": 0.8426484188315138,
            "energy_eV": -202.00728618593232,
            "max_atomic_step_A": 0.12000000000000001,
            "max_log_strain_component": 0.005075218667455341,
            "step_scale": 0.6374745074750233,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 1.2242439913613525,
            "cell_principal_stretches": [
              1.0056615197317458,
              1.0032521486186181,
              0.9925539597757489
            ],
            "cell_volume_ratio": 1.001419531599341,
            "cell_rmsd_from_input_A": 0.059273047963036875
          },
          {
            "iteration": 1,
            "reduced_polarization": [
              0.30381873652880853,
              -0.30138720236123623,
              -0.3278065513769346
            ],
            "branch_aligned_reduced_polarization": [
              0.30381873652880853,
              -0.30138720236123623,
              -0.3278065513769346
            ],
            "target_residual": 0.328001090351471,
            "energy_eV": -199.14021058140577,
            "max_atomic_step_A": 0.0747053499478858,
            "max_log_strain_component": 0.0035678901580130443,
            "step_scale": 1.0,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 1.2242439913613525,
            "cell_principal_stretches": [
              1.0097758892385325,
              1.005308086252269,
              0.9873708781162351
            ],
            "cell_volume_ratio": 1.0023155921642535,
            "cell_rmsd_from_input_A": 0.10029954789647282
          },
          {
            "iteration": 2,
            "reduced_polarization": [
              0.4887628065348978,
              -0.4903545917916838,
              -0.49593626863389245
            ],
            "branch_aligned_reduced_polarization": [
              0.4887628065348978,
              -0.4903545917916838,
              -0.49593626863389245
            ],
            "target_residual": 0.01535650771149079,
            "energy_eV": -193.51012828502402,
            "max_atomic_step_A": 0.0036972669850557495,
            "max_log_strain_component": 0.00021616889990500176,
            "step_scale": 1.0,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 1.2242439913613525,
            "cell_principal_stretches": [
              1.0099921517304835,
              1.0053799157623788,
              0.987119743841275
            ],
            "cell_volume_ratio": 1.0023468796986468,
            "cell_rmsd_from_input_A": 0.10226186355982532
          },
          {
            "iteration": 3,
            "reduced_polarization": [
              0.499893371661637,
              -0.49992678027968074,
              -0.49984484460945117
            ],
            "branch_aligned_reduced_polarization": [
              0.499893371661637,
              -0.49992678027968074,
              -0.49984484460945117
            ],
            "target_residual": 0.00020199981485646658,
            "energy_eV": -193.1524895229373
          }
        ],
        "iterations": 3
      },
      "parent": {
        "candidate_id": "bec_projection_05",
        "source": "MACEField_BEC_backprojection",
        "spacegroup": "P1",
        "spacegroup_number": 1,
        "pointgroup": "1",
        "has_inversion": false,
        "is_polar_point_group": true,
        "nonpolar_parent_hypothesis": false,
        "symmetry_tolerance_A": null,
        "target_reduced_polarization": [
          0.5,
          -0.5,
          -0.5
        ],
        "formal_class": [
          0.5,
          0.5,
          0.5
        ],
        "target_residual": 0.00020199981485646658,
        "parent_symmetrization_rmsd_A": 0.13391461124253226,
        "parent_cell_rmsd_A": 0.10226186355982532,
        "energy_eV": -193.1524895229373,
        "reduced_polarization": [
          0.499893371661637,
          -0.49992678027968074,
          -0.49984484460945117
        ],
        "cartesian_polarization_e_A2": [
          0.007014774322068724,
          -0.006971909587452242,
          -0.008586475853301056
        ],
        "ranking_score": 0.6598840767622015
      },
      "branch_status": "awaiting_branch_sampling"
    }
  ],
  "sampled_polarization_branches": [
    {
      "orbit_id": 0,
      "candidate_id": "bec_projection_00",
      "formal_class": [
        0.0,
        0.0,
        0.0
      ],
      "construction": "MACEField-BEC-parent plus variable-cell P-N-P path and symmetric log-strain continuation beyond both polar endpoints",
      "geometry_diagnostics": {
        "collision_aware": false,
        "permutations_tested": 1,
        "selected_order": [
          0,
          1,
          2,
          3,
          4,
          5,
          6,
          7,
          8,
          9,
          10,
          11,
          12,
          13,
          14,
          15,
          16,
          17,
          18,
          19,
          20,
          21,
          22,
          23,
          24,
          25,
          26,
          27,
          28,
          29,
          30,
          31
        ],
        "endpoint_rmsd_A": 0.006721081583797575,
        "minimum_distance_A_by_image": [
          1.3554960554617888,
          1.3548586279010186,
          1.3542226672731505,
          1.3535881763345181,
          1.3529551578421457,
          1.3523236145537343,
          1.3516935492276205,
          1.3510649646227586,
          1.3504378634986847
        ],
        "minimum_distance_A": 1.3504378634986847,
        "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": [
          550.8059052271486,
          550.7919721542804,
          550.7780394338604,
          550.7641070658797,
          550.7501750503286,
          550.7362433871996,
          550.722312076483,
          550.7083811181694,
          550.6944505122511
        ],
        "cell_deformation_log_strain_norm": 0.0009763947470782931
      },
      "parent_reduced_polarization": [
        -4.9574263574280425e-15,
        5.453037788663034e-15,
        -0.00017968464563723847
      ],
      "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": [
          -202.0072861859323,
          -202.00694845454245,
          -202.00596884572101,
          -202.00435087068115,
          -202.00209799290576,
          -201.99921362693513,
          -201.9957011395894,
          -201.99156385133287,
          -201.986805036665
        ],
        "cartesian_polarizations_e_A2": [
          [
            5.3099354105340446e-18,
            -2.740632143681332e-17,
            -0.0007167641654606914
          ],
          [
            -5.168341893117799e-18,
            -2.0156848333914636e-19,
            -0.0006273365068456419
          ],
          [
            -1.2324334805495404e-17,
            2.0043973090256262e-17,
            -0.0005379708577587757
          ],
          [
            -1.2608116587932526e-17,
            -7.149743855759889e-19,
            -0.00044866744768929447
          ],
          [
            -6.431782500334088e-18,
            8.787792936303676e-18,
            -0.000359426517091979
          ],
          [
            -2.568368323849385e-17,
            2.5910470728458476e-17,
            -0.00027024831772774874
          ],
          [
            4.957951932058813e-18,
            -8.2559034395973e-18,
            -0.0001811331130084525
          ],
          [
            -1.1132049146690882e-17,
            -3.058636027571264e-18,
            -9.20811783445453e-05
          ],
          [
            -6.862102235736634e-17,
            7.547871450169183e-17,
            -3.0928014970480806e-06
          ]
        ],
        "raw_reduced_polarization": [
          [
            3.835369400718432e-16,
            -1.979560173490616e-15,
            -0.041680943272864104
          ],
          [
            -3.640078444593433e-16,
            -2.0047781453507886e-17,
            -0.036476362561839
          ],
          [
            -8.742718006783247e-16,
            1.4384596836237394e-15,
            -0.0312765917272664
          ],
          [
            -8.90791859798504e-16,
            -6.342167852578294e-17,
            -0.02608164264808406
          ],
          [
            -4.4328589514130274e-16,
            6.222499463386776e-16,
            -0.020891527834743098
          ],
          [
            -1.8353780502928802e-15,
            1.8600010807317648e-15,
            -0.015706260448633384
          ],
          [
            3.7431537796863823e-16,
            -6.059464967035105e-16,
            -0.010525854321740954
          ],
          [
            -7.946846754841057e-16,
            -2.2661322550540243e-16,
            -0.0053503239764595995
          ],
          [
            -4.9574263574280425e-15,
            5.453037788663034e-15,
            -0.00017968464563723847
          ]
        ],
        "unwrapped_reduced_polarization": [
          [
            3.835369400718432e-16,
            -1.979560173490616e-15,
            -0.041680943272864104
          ],
          [
            -3.640078444593433e-16,
            -2.0047781453507778e-17,
            -0.036476362561839
          ],
          [
            -8.742718006783247e-16,
            1.4384596836237394e-15,
            -0.0312765917272664
          ],
          [
            -8.90791859798504e-16,
            -6.34216785257829e-17,
            -0.02608164264808406
          ],
          [
            -4.4328589514130274e-16,
            6.222499463386776e-16,
            -0.020891527834743098
          ],
          [
            -1.8353780502928802e-15,
            1.8600010807317648e-15,
            -0.015706260448633384
          ],
          [
            3.743153779686384e-16,
            -6.059464967035106e-16,
            -0.010525854321740954
          ],
          [
            -7.946846754841057e-16,
            -2.2661322550540243e-16,
            -0.0053503239764595995
          ],
          [
            -4.9574263574280425e-15,
            5.453037788663034e-15,
            -0.00017968464563723838
          ]
        ],
        "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": [
          [
            3.3306690738754696e-16,
            -1.9984014443252818e-15,
            -0.04168094327286409
          ],
          [
            -3.885780586188048e-16,
            0.0,
            -0.036476362561839004
          ],
          [
            -8.881784197001252e-16,
            1.4432899320127035e-15,
            -0.03127659172726638
          ],
          [
            -8.881784197001252e-16,
            -5.551115123125783e-17,
            -0.026081642648084047
          ],
          [
            -4.440892098500626e-16,
            6.661338147750939e-16,
            -0.020891527834743073
          ],
          [
            -1.8318679906315083e-15,
            1.887379141862766e-15,
            -0.01570626044863338
          ],
          [
            3.3306690738754696e-16,
            -6.106226635438361e-16,
            -0.010525854321740968
          ],
          [
            -7.771561172376096e-16,
            -2.220446049250313e-16,
            -0.0053503239764596255
          ],
          [
            -4.9404924595819466e-15,
            5.440092820663267e-15,
            -0.00017968464563722364
          ]
        ]
      },
      "reflected": {
        "reached": true,
        "construction": "reflect_displacements_about_reconstructed_parent",
        "energies_eV": [
          -201.986805036665,
          -201.9811765883839,
          -201.97498434257366,
          -201.9682304582859,
          -201.9609170595723,
          -201.9530462359761,
          -201.9446200431539,
          -201.93564050317113,
          -201.92610960466146
        ],
        "cartesian_polarizations_e_A2": [
          [
            -6.279340156407183e-17,
            7.093947041350946e-17,
            -3.092801497022628e-06
          ],
          [
            -7.130937424527113e-17,
            1.630432551875269e-17,
            8.199488823285894e-05
          ],
          [
            -4.627841790712076e-17,
            3.9323425616151344e-17,
            0.0001669801981519086
          ],
          [
            1.3232420074186003e-17,
            5.10397845470388e-17,
            0.0002518631530866051
          ],
          [
            -4.56650258030576e-17,
            9.027173675787216e-18,
            0.00033664377171430826
          ],
          [
            -5.734913485712602e-17,
            -2.2866581670844402e-17,
            0.0004213220656481153
          ],
          [
            -1.0779147313653839e-16,
            3.407223458365686e-17,
            0.00050589803798748
          ],
          [
            -8.148090988229774e-17,
            2.8081009335184824e-17,
            0.0005903716830376955
          ],
          [
            -6.838352762095238e-17,
            1.9696521979525453e-17,
            0.0006747429860166421
          ]
        ],
        "raw_reduced_polarization": [
          [
            -4.536387165072337e-15,
            5.125082396129411e-15,
            -0.00017968464563575975
          ],
          [
            -5.160375302261061e-15,
            1.1829510234344024e-15,
            0.0047642658830655375
          ],
          [
            -3.3582184367420106e-15,
            2.849651727325352e-15,
            0.009703412099368104
          ],
          [
            9.372405496202155e-16,
            3.698222408696527e-15,
            0.014637753578090308
          ],
          [
            -3.3188075138403264e-15,
            6.638968218292559e-16,
            0.019567289536855718
          ],
          [
            -4.161500834659685e-15,
            -1.6407596852072737e-15,
            0.024492018782687714
          ],
          [
            -7.801313361913626e-15,
            2.4700508766853428e-15,
            0.02941193962750747
          ],
          [
            -5.894327847342369e-15,
            2.0335236829875355e-15,
            0.03432704987153687
          ],
          [
            -4.93934613272831e-15,
            1.4226809153080112e-15,
            0.03923734678594917
          ]
        ],
        "unwrapped_reduced_polarization": [
          [
            -4.536387165072337e-15,
            5.125082396129411e-15,
            -0.00017968464563575975
          ],
          [
            -5.160375302261061e-15,
            1.182951023434402e-15,
            0.0047642658830655375
          ],
          [
            -3.3582184367420106e-15,
            2.849651727325352e-15,
            0.009703412099368104
          ],
          [
            9.372405496202157e-16,
            3.698222408696527e-15,
            0.014637753578090308
          ],
          [
            -3.3188075138403268e-15,
            6.638968218292558e-16,
            0.019567289536855718
          ],
          [
            -4.161500834659685e-15,
            -1.6407596852072735e-15,
            0.024492018782687714
          ],
          [
            -7.801313361913626e-15,
            2.4700508766853428e-15,
            0.02941193962750747
          ],
          [
            -5.894327847342369e-15,
            2.0335236829875355e-15,
            0.03432704987153687
          ],
          [
            -4.93934613272831e-15,
            1.4226809153080112e-15,
            0.03923734678594917
          ]
        ],
        "gauge_integer_shift": [
          0,
          0,
          0
        ],
        "expected_opposite_endpoint_reduced_polarization": [
          -1.0296537722466984e-14,
          1.2883223951812778e-14,
          0.0413212409050153
        ],
        "actual_opposite_endpoint_branch_residual": 0.002083894119066128
      },
      "pnp_branch": {
        "construction": "incoming_path_concatenated_with_parent_reflection",
        "reduced_polarization": [
          [
            3.835369400718432e-16,
            -1.979560173490616e-15,
            -0.041680943272864104
          ],
          [
            -3.640078444593433e-16,
            -2.0047781453507886e-17,
            -0.036476362561839
          ],
          [
            -8.742718006783247e-16,
            1.4384596836237394e-15,
            -0.0312765917272664
          ],
          [
            -8.90791859798504e-16,
            -6.342167852578294e-17,
            -0.02608164264808406
          ],
          [
            -4.4328589514130274e-16,
            6.222499463386776e-16,
            -0.020891527834743098
          ],
          [
            -1.8353780502928802e-15,
            1.8600010807317648e-15,
            -0.015706260448633384
          ],
          [
            3.7431537796863823e-16,
            -6.059464967035105e-16,
            -0.010525854321740954
          ],
          [
            -7.946846754841057e-16,
            -2.2661322550540243e-16,
            -0.0053503239764595995
          ],
          [
            -4.9574263574280425e-15,
            5.453037788663034e-15,
            -0.00017968464563723847
          ],
          [
            -5.160375302261061e-15,
            1.1829510234344024e-15,
            0.0047642658830655375
          ],
          [
            -3.3582184367420106e-15,
            2.849651727325352e-15,
            0.009703412099368104
          ],
          [
            9.372405496202155e-16,
            3.698222408696527e-15,
            0.014637753578090308
          ],
          [
            -3.3188075138403264e-15,
            6.638968218292559e-16,
            0.019567289536855718
          ],
          [
            -4.161500834659685e-15,
            -1.6407596852072737e-15,
            0.024492018782687714
          ],
          [
            -7.801313361913626e-15,
            2.4700508766853428e-15,
            0.02941193962750747
          ],
          [
            -5.894327847342369e-15,
            2.0335236829875355e-15,
            0.03432704987153687
          ],
          [
            -4.93934613272831e-15,
            1.4226809153080112e-15,
            0.03923734678594917
          ]
        ],
        "unwrapped_reduced_polarization": [
          [
            3.835369400718432e-16,
            -1.979560173490616e-15,
            -0.041680943272864104
          ],
          [
            -3.640078444593433e-16,
            -2.0047781453507778e-17,
            -0.036476362561839
          ],
          [
            -8.742718006783247e-16,
            1.4384596836237394e-15,
            -0.0312765917272664
          ],
          [
            -8.90791859798504e-16,
            -6.34216785257829e-17,
            -0.02608164264808406
          ],
          [
            -4.4328589514130274e-16,
            6.222499463386776e-16,
            -0.020891527834743098
          ],
          [
            -1.8353780502928802e-15,
            1.8600010807317648e-15,
            -0.015706260448633384
          ],
          [
            3.743153779686384e-16,
            -6.059464967035106e-16,
            -0.010525854321740954
          ],
          [
            -7.946846754841057e-16,
            -2.2661322550540243e-16,
            -0.0053503239764595995
          ],
          [
            -4.9574263574280425e-15,
            5.453037788663034e-15,
            -0.00017968464563723838
          ],
          [
            -5.160375302261061e-15,
            1.182951023434402e-15,
            0.0047642658830655375
          ],
          [
            -3.3582184367420106e-15,
            2.849651727325352e-15,
            0.009703412099368104
          ],
          [
            9.372405496202157e-16,
            3.698222408696527e-15,
            0.014637753578090308
          ],
          [
            -3.3188075138403268e-15,
            6.638968218292558e-16,
            0.019567289536855718
          ],
          [
            -4.161500834659685e-15,
            -1.6407596852072735e-15,
            0.024492018782687714
          ],
          [
            -7.801313361913626e-15,
            2.4700508766853428e-15,
            0.02941193962750747
          ],
          [
            -5.894327847342369e-15,
            2.0335236829875355e-15,
            0.03432704987153687
          ],
          [
            -4.93934613272831e-15,
            1.4226809153080112e-15,
            0.03923734678594917
          ]
        ],
        "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": [
          [
            3.3306690738754696e-16,
            -1.9984014443252818e-15,
            -0.04168094327286409
          ],
          [
            -3.885780586188048e-16,
            0.0,
            -0.036476362561839004
          ],
          [
            -8.881784197001252e-16,
            1.4432899320127035e-15,
            -0.03127659172726638
          ],
          [
            -8.881784197001252e-16,
            -5.551115123125783e-17,
            -0.026081642648084047
          ],
          [
            -4.440892098500626e-16,
            6.661338147750939e-16,
            -0.020891527834743073
          ],
          [
            -1.8318679906315083e-15,
            1.887379141862766e-15,
            -0.01570626044863338
          ],
          [
            3.3306690738754696e-16,
            -6.106226635438361e-16,
            -0.010525854321740968
          ],
          [
            -7.771561172376096e-16,
            -2.220446049250313e-16,
            -0.0053503239764596255
          ],
          [
            -4.9404924595819466e-15,
            5.440092820663267e-15,
            -0.00017968464563722364
          ],
          [
            -5.162537064506978e-15,
            1.2212453270876722e-15,
            0.004764265883065555
          ],
          [
            -3.3306690738754696e-15,
            2.886579864025407e-15,
            0.009703412099368092
          ],
          [
            8.881784197001252e-16,
            3.6637359812630166e-15,
            0.014637753578090273
          ],
          [
            -3.3306690738754696e-15,
            6.661338147750939e-16,
            0.019567289536855714
          ],
          [
            -4.163336342344337e-15,
            -1.6653345369377348e-15,
            0.024492018782687697
          ],
          [
            -7.827072323607354e-15,
            2.4424906541753444e-15,
            0.029411939627507433
          ],
          [
            -5.88418203051333e-15,
            1.9984014443252818e-15,
            0.0343270498715369
          ],
          [
            -4.9404924595819466e-15,
            1.4432899320127035e-15,
            0.039237346785949145
          ]
        ]
      },
      "incoming_structure_ids": [
        "incoming_00_000",
        "incoming_00_001",
        "incoming_00_002",
        "incoming_00_003",
        "incoming_00_004",
        "incoming_00_005",
        "incoming_00_006",
        "incoming_00_007",
        "incoming_00_008"
      ],
      "reflected_structure_ids": [
        "reflected_00_001",
        "reflected_00_002",
        "reflected_00_003",
        "reflected_00_004",
        "reflected_00_005",
        "reflected_00_006",
        "reflected_00_007",
        "reflected_00_008"
      ],
      "positive_extension_structure_ids": [
        "extension_plus_00_000",
        "extension_plus_00_001",
        "extension_plus_00_002",
        "extension_plus_00_003"
      ],
      "negative_extension_structure_ids": [
        "extension_minus_00_000",
        "extension_minus_00_001",
        "extension_minus_00_002",
        "extension_minus_00_003"
      ],
      "extension": {
        "enabled": true,
        "fraction_beyond_polar_endpoint": 0.35,
        "images_per_side": 4,
        "construction": "continue fractional atomic displacements and symmetric log strain beyond +P; reflect these structures about N for the -P side",
        "positive_path_coordinates": [
          1.35,
          1.2625,
          1.175,
          1.0875
        ],
        "negative_path_coordinates": [
          -1.0875,
          -1.175,
          -1.2625,
          -1.35
        ]
      },
      "branch_coordinates": [
        1.35,
        1.2625,
        1.175,
        1.0875,
        1.0,
        0.875,
        0.75,
        0.625,
        0.5,
        0.375,
        0.25,
        0.125,
        0.0,
        -0.125,
        -0.25,
        -0.375,
        -0.5,
        -0.625,
        -0.75,
        -0.875,
        -1.0,
        -1.0875,
        -1.175,
        -1.2625,
        -1.35
      ],
      "parent": {
        "candidate_id": "bec_projection_00",
        "source": "MACEField_BEC_backprojection",
        "spacegroup": "P4_1",
        "spacegroup_number": 76,
        "pointgroup": "4",
        "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": 0.00017968464563869523,
        "parent_symmetrization_rmsd_A": 0.006721081583797575,
        "parent_cell_rmsd_A": 0.00606060393489319,
        "energy_eV": -201.98680503666503,
        "reduced_polarization": [
          -5.4324040841452405e-15,
          3.810984938482209e-15,
          -0.00017968464563869523
        ],
        "cartesian_polarization_e_A2": [
          -7.519520862526129e-17,
          5.2750993407843225e-17,
          -3.0928014970731554e-06
        ],
        "ranking_score": 0.5085956018587983
      }
    }
  ],
  "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": 50,
      "full_response": 15,
      "energy_polarization": 35
    },
    "model_evaluations_for_recovery_and_path_properties": {
      "total": 75,
      "full_response": 40,
      "energy_polarization": 35
    },
    "elapsed_seconds": 427.3264183520223
  }
}