{
  "schema": "ferrofinder.endpoint_parent_recovery.v4_variable_cell",
  "status": "complete",
  "input_atom_count": 56,
  "input_formula": "Mo8N24Na24",
  "input_spacegroup": "Cc",
  "input_pointgroup": "m",
  "input_is_polar_point_group": true,
  "input_energy_eV": -328.95207304724465,
  "input_cartesian_polarization_e_A2": [
    0.002228068530576507,
    -1.564182363636577e-11,
    0.0005490906689836025
  ],
  "input_reduced_polarization": [
    0.15657645795624495,
    -1.2410708084422061e-09,
    0.08361512268393877
  ],
  "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": [
        0.5,
        0.0,
        0.0
      ],
      "target_reduced_polarization": [
        0.5,
        0.0,
        0.0
      ]
    },
    {
      "orbit_id": 2,
      "representative_formal_class": [
        0.0,
        0.0,
        0.5
      ],
      "target_reduced_polarization": [
        0.0,
        0.0,
        0.5
      ]
    },
    {
      "orbit_id": 3,
      "representative_formal_class": [
        0.0,
        0.5,
        0.0
      ],
      "target_reduced_polarization": [
        0.0,
        -0.5,
        0.0
      ]
    },
    {
      "orbit_id": 4,
      "representative_formal_class": [
        0.5,
        0.0,
        0.5
      ],
      "target_reduced_polarization": [
        0.5,
        0.0,
        0.5
      ]
    },
    {
      "orbit_id": 5,
      "representative_formal_class": [
        0.5,
        0.5,
        0.0
      ],
      "target_reduced_polarization": [
        0.5,
        -0.5,
        0.0
      ]
    },
    {
      "orbit_id": 6,
      "representative_formal_class": [
        0.0,
        0.5,
        0.5
      ],
      "target_reduced_polarization": [
        0.0,
        -0.5,
        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": "C2/c",
      "spacegroup_number": 15,
      "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": 1.5591041438553887e-15,
      "parent_symmetrization_rmsd_A": 0.37346744167352186,
      "parent_cell_rmsd_A": 0.0,
      "energy_eV": -326.91972917493104,
      "reduced_polarization": [
        -1.2869464548963208e-15,
        8.788198430963645e-16,
        -4.743666300361159e-17
      ],
      "cartesian_polarization_e_A2": [
        -2.046502339708837e-17,
        1.1076197184193225e-17,
        -3.1151098254629533e-19
      ],
      "ranking_score": 0.37346744167352497
    },
    {
      "candidate_id": "inversion_parent_endpoint_01",
      "source": "same_species_inversion_center_projection_from_endpoint",
      "spacegroup": "C2/c",
      "spacegroup_number": 15,
      "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": 3.8917407905797144e-15,
      "parent_symmetrization_rmsd_A": 0.39664488032859396,
      "parent_cell_rmsd_A": 0.0,
      "energy_eV": -325.79991352606487,
      "reduced_polarization": [
        2.5410528666685134e-15,
        7.69011989323141e-16,
        2.8455785475250935e-15
      ],
      "cartesian_polarization_e_A2": [
        3.1152356880881444e-17,
        9.69223498725417e-18,
        1.868657939081241e-17
      ],
      "ranking_score": 0.39664488032860173
    },
    {
      "candidate_id": "bec_projection_00",
      "source": "MACEField_BEC_backprojection",
      "spacegroup": "Cc",
      "spacegroup_number": 9,
      "pointgroup": "m",
      "has_inversion": false,
      "is_polar_point_group": true,
      "nonpolar_parent_hypothesis": false,
      "symmetry_tolerance_A": null,
      "target_reduced_polarization": [
        0.0,
        0.0,
        0.0
      ],
      "formal_class": [
        0.0,
        0.0,
        0.0
      ],
      "target_residual": 1.9747955361319182e-06,
      "parent_symmetrization_rmsd_A": 0.009849018727964332,
      "parent_cell_rmsd_A": 0.040904674653548224,
      "energy_eV": -328.79421482671967,
      "reduced_polarization": [
        1.8510452792742324e-06,
        -5.499563298348036e-14,
        -6.880761466604746e-07
      ],
      "cartesian_polarization_e_A2": [
        3.198691308542717e-08,
        -6.953369832316011e-16,
        -4.707711376780984e-09
      ],
      "ranking_score": 0.5200791369824237
    },
    {
      "candidate_id": "inversion_parent_bec_00_00",
      "source": "same_species_inversion_center_projection_after_BEC",
      "spacegroup": "C2/c",
      "spacegroup_number": 15,
      "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": 4.726138849071566e-15,
      "parent_symmetrization_rmsd_A": 0.37346895224226,
      "parent_cell_rmsd_A": 0.040904674653548224,
      "energy_eV": -326.8786859160699,
      "reduced_polarization": [
        -2.503313719491185e-15,
        1.6546276828638616e-15,
        -3.651303339029953e-15
      ],
      "cartesian_polarization_e_A2": [
        -2.7686343475545463e-17,
        2.0885796626131897e-17,
        -2.3861904477440984e-17
      ],
      "ranking_score": 0.3836951209056565
    },
    {
      "candidate_id": "inversion_parent_bec_00_01",
      "source": "same_species_inversion_center_projection_after_BEC",
      "spacegroup": "C2/c",
      "spacegroup_number": 15,
      "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": 2.282430385014599e-15,
      "parent_symmetrization_rmsd_A": 0.39664664747355505,
      "parent_cell_rmsd_A": 0.040904674653548224,
      "energy_eV": -325.73743146521133,
      "reduced_polarization": [
        1.4461523650547631e-15,
        1.731295374685003e-15,
        -3.474883092691332e-16
      ],
      "cartesian_polarization_e_A2": [
        2.4344163159708032e-17,
        2.1853546550966354e-17,
        -2.4239151128904223e-18
      ],
      "ranking_score": 0.40687281613694665
    },
    {
      "candidate_id": "bec_projection_01",
      "source": "MACEField_BEC_backprojection",
      "spacegroup": "Cc",
      "spacegroup_number": 9,
      "pointgroup": "m",
      "has_inversion": false,
      "is_polar_point_group": true,
      "nonpolar_parent_hypothesis": false,
      "symmetry_tolerance_A": null,
      "target_reduced_polarization": [
        0.5,
        0.0,
        0.0
      ],
      "formal_class": [
        0.5,
        0.0,
        0.0
      ],
      "target_residual": 0.00045356095845893357,
      "parent_symmetrization_rmsd_A": 0.028313326414842466,
      "parent_cell_rmsd_A": 0.11973002618214393,
      "energy_eV": -328.1093745184469,
      "reduced_polarization": [
        0.49954694000526917,
        -1.76628065844633e-12,
        -2.131159807911489e-05
      ],
      "cartesian_polarization_e_A2": [
        0.008001620186833716,
        -7.018609892128896e-14,
        0.00013920280490896687
      ],
      "ranking_score": 0.5591529548772963
    },
    {
      "candidate_id": "bec_projection_02",
      "source": "MACEField_BEC_backprojection",
      "spacegroup": "Cc",
      "spacegroup_number": 9,
      "pointgroup": "m",
      "has_inversion": false,
      "is_polar_point_group": true,
      "nonpolar_parent_hypothesis": false,
      "symmetry_tolerance_A": null,
      "target_reduced_polarization": [
        0.0,
        0.0,
        0.5
      ],
      "formal_class": [
        0.0,
        0.0,
        0.5
      ],
      "target_residual": 0.00017575066953044027,
      "parent_symmetrization_rmsd_A": 0.025982271293415824,
      "parent_cell_rmsd_A": 0.11213023316665387,
      "energy_eV": -328.0616585747727,
      "reduced_polarization": [
        7.343159412683061e-05,
        4.047524748433473e-13,
        0.5001596749787048
      ],
      "cartesian_polarization_e_A2": [
        -0.0017314295627375942,
        -1.400098291533136e-13,
        0.0032959809775284133
      ],
      "ranking_score": 0.5543663309241402
    },
    {
      "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,
        0.0
      ],
      "formal_class": [
        0.0,
        0.5,
        0.0
      ],
      "target_residual": 3.512630058705842e-05,
      "parent_symmetrization_rmsd_A": 0.05089168403914328,
      "parent_cell_rmsd_A": 0.13550725712062853,
      "energy_eV": -326.32302064856265,
      "reduced_polarization": [
        -3.162306051704104e-05,
        -0.4999861012480832,
        -6.376812026606024e-06
      ],
      "cartesian_polarization_e_A2": [
        -6.066364707382947e-05,
        -0.00631119321077702,
        3.967991541489899e-06
      ],
      "ranking_score": 0.5848387509204745
    },
    {
      "candidate_id": "bec_projection_04",
      "source": "MACEField_BEC_backprojection",
      "spacegroup": "Cc",
      "spacegroup_number": 9,
      "pointgroup": "m",
      "has_inversion": false,
      "is_polar_point_group": true,
      "nonpolar_parent_hypothesis": false,
      "symmetry_tolerance_A": null,
      "target_reduced_polarization": [
        0.5,
        0.0,
        0.5
      ],
      "formal_class": [
        0.5,
        0.0,
        0.5
      ],
      "target_residual": 0.0006070473333015721,
      "parent_symmetrization_rmsd_A": 0.022527105068925968,
      "parent_cell_rmsd_A": 0.09558792550226994,
      "energy_eV": -328.6288198363407,
      "reduced_polarization": [
        0.4996485047139743,
        -3.6640324261712075e-13,
        0.49950506815744966
      ],
      "cartesian_polarization_e_A2": [
        0.006379554750444828,
        1.0624645479395667e-13,
        0.003317981661330917
      ],
      "ranking_score": 0.5476381811110966
    },
    {
      "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,
        0.0
      ],
      "formal_class": [
        0.5,
        0.5,
        0.0
      ],
      "target_residual": 3.2444897783903965e-05,
      "parent_symmetrization_rmsd_A": 0.05894812699212401,
      "parent_cell_rmsd_A": 0.18002306580547833,
      "energy_eV": -325.22509172769793,
      "reduced_polarization": [
        0.4999705181601158,
        -0.4999869439817532,
        -3.6101103568402523e-06
      ],
      "cartesian_polarization_e_A2": [
        0.00794847858973806,
        -0.006201614380281772,
        0.00014639571346856757
      ],
      "ranking_score": 0.6040187832390614
    },
    {
      "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": [
        0.0,
        -0.5,
        0.5
      ],
      "formal_class": [
        0.0,
        0.5,
        0.5
      ],
      "target_residual": 0.00027394257047132377,
      "parent_symmetrization_rmsd_A": 0.05651707244368118,
      "parent_cell_rmsd_A": 0.17451150216132408,
      "energy_eV": -325.54552293258286,
      "reduced_polarization": [
        0.00019768451602076057,
        -0.5000789305474118,
        0.5001724393595655
      ],
      "cartesian_polarization_e_A2": [
        -0.0017908979241411142,
        -0.006329480191287158,
        0.003299783542429876
      ],
      "ranking_score": 0.6006928331249548
    },
    {
      "candidate_id": "bec_projection_07",
      "source": "MACEField_BEC_backprojection",
      "spacegroup": "P1",
      "spacegroup_number": 1,
      "pointgroup": "1",
      "has_inversion": false,
      "is_polar_point_group": true,
      "nonpolar_parent_hypothesis": false,
      "symmetry_tolerance_A": null,
      "target_reduced_polarization": [
        0.5,
        -0.5,
        0.5
      ],
      "formal_class": [
        0.5,
        0.5,
        0.5
      ],
      "target_residual": 3.5002414935659875e-05,
      "parent_symmetrization_rmsd_A": 0.05648677943755225,
      "parent_cell_rmsd_A": 0.16708053313288337,
      "energy_eV": -325.79168635306,
      "reduced_polarization": [
        0.49997683998242926,
        -0.49999062231434954,
        0.49997548792849855
      ],
      "cartesian_polarization_e_A2": [
        0.006324222690325606,
        -0.006217628964670932,
        0.00332589667259688
      ],
      "ranking_score": 0.5983269175506444
    }
  ],
  "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": [
              0.15657645795624495,
              -1.2410708084422061e-09,
              0.08361512268393877
            ],
            "branch_aligned_reduced_polarization": [
              0.15657645795624495,
              -1.2410708084422061e-09,
              0.08361512268393877
            ],
            "target_residual": 0.17750401665194473,
            "energy_eV": -328.95207304724465,
            "max_atomic_step_A": 0.020476342231783868,
            "max_log_strain_component": 0.005695076019218281,
            "step_scale": 1.0,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 6.613441357848438,
            "cell_principal_stretches": [
              1.0050609617801516,
              1.0001765833580702,
              0.9934382877283334
            ],
            "cell_volume_ratio": 0.9986423534198935,
            "cell_rmsd_from_input_A": 0.04121275679003986
          },
          {
            "iteration": 1,
            "reduced_polarization": [
              -0.0015440533527186068,
              9.375388393400575e-12,
              -0.0024978889046698544
            ],
            "branch_aligned_reduced_polarization": [
              -0.0015440533527186068,
              9.375388393400575e-12,
              -0.0024978889046698544
            ],
            "target_residual": 0.002936588111416774,
            "energy_eV": -328.79232242658105,
            "max_atomic_step_A": 0.00022274093013026401,
            "max_log_strain_component": 3.4135298359067674e-05,
            "step_scale": 1.0,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 6.613441357848438,
            "cell_principal_stretches": [
              1.0050342488080595,
              1.000176958720495,
              0.9934801723719212
            ],
            "cell_volume_ratio": 0.9986582887716671,
            "cell_rmsd_from_input_A": 0.040904674653548224
          },
          {
            "iteration": 2,
            "reduced_polarization": [
              1.8510452792742324e-06,
              -5.499563298348036e-14,
              -6.880761466604746e-07
            ],
            "branch_aligned_reduced_polarization": [
              1.8510452792742324e-06,
              -5.499563298348036e-14,
              -6.880761466604746e-07
            ],
            "target_residual": 1.9747955361319182e-06,
            "energy_eV": -328.79421482671967
          }
        ],
        "iterations": 2
      },
      "parent": {
        "candidate_id": "inversion_parent_endpoint_00",
        "source": "same_species_inversion_center_projection_from_endpoint",
        "spacegroup": "C2/c",
        "spacegroup_number": 15,
        "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": 1.5591041438553887e-15,
        "parent_symmetrization_rmsd_A": 0.37346744167352186,
        "parent_cell_rmsd_A": 0.0,
        "energy_eV": -326.91972917493104,
        "reduced_polarization": [
          -1.2869464548963208e-15,
          8.788198430963645e-16,
          -4.743666300361159e-17
        ],
        "cartesian_polarization_e_A2": [
          -2.046502339708837e-17,
          1.1076197184193225e-17,
          -3.1151098254629533e-19
        ],
        "ranking_score": 0.37346744167352497
      },
      "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": [
          -328.9520730472446,
          -328.8518264321061,
          -328.58027632501705,
          -328.2151407779967,
          -327.82400022686704,
          -327.4635953976018,
          -327.17454927939093,
          -326.9858249813361,
          -326.919729174931
        ],
        "cartesian_polarizations_e_A2": [
          [
            0.002228068530576508,
            -1.5641826872916897e-11,
            0.000549090668983602
          ],
          [
            0.0022945623354899323,
            -1.2430272455128825e-11,
            0.0008292254612611509
          ],
          [
            0.002306754535817516,
            -9.317127242313462e-12,
            0.0010417829711251796
          ],
          [
            0.00224156763572027,
            -6.484548053833746e-12,
            0.0011383564579845106
          ],
          [
            0.002074052867553156,
            -4.2481065060030256e-12,
            0.001087527082808434
          ],
          [
            0.0017743735357228286,
            -2.8184498547233914e-12,
            0.0009024858952596622
          ],
          [
            0.0013188953885650092,
            -1.8789575074724436e-12,
            0.0006292711525236873
          ],
          [
            0.0007104945480377624,
            -1.0081534378682653e-12,
            0.0003181860772521631
          ],
          [
            -1.9623192000038768e-17,
            -1.1267992806430336e-17,
            -7.503734509890689e-18
          ]
        ],
        "raw_reduced_polarization": [
          [
            0.156576457956245,
            -1.2410710652402124e-09,
            0.08361512268393871
          ],
          [
            0.1696781350371012,
            -9.86256375450855e-10,
            0.12627384254105295
          ],
          [
            0.17723182659551126,
            -7.392497772506195e-10,
            0.1586419436008873
          ],
          [
            0.17625054367370246,
            -5.145041577404979e-10,
            0.17334808305633642
          ],
          [
            0.16417343179455493,
            -3.3705794786589965e-10,
            0.16560782323884074
          ],
          [
            0.13956027908751142,
            -2.2362455434052452e-10,
            0.13742988747622387
          ],
          [
            0.1024076294342686,
            -1.4908231719259926e-10,
            0.0958249476668906
          ],
          [
            0.05450253978118933,
            -7.999002106506678e-11,
            0.04845314150941317
          ],
          [
            -1.4642663702229633e-15,
            -8.940375027170808e-16,
            -1.142663164889717e-15
          ]
        ],
        "unwrapped_reduced_polarization": [
          [
            0.156576457956245,
            -1.2410710652402124e-09,
            0.08361512268393871
          ],
          [
            0.1696781350371012,
            -9.86256375450855e-10,
            0.12627384254105295
          ],
          [
            0.17723182659551126,
            -7.392497772506195e-10,
            0.1586419436008873
          ],
          [
            0.17625054367370246,
            -5.145041577404979e-10,
            0.17334808305633642
          ],
          [
            0.16417343179455493,
            -3.3705794786589965e-10,
            0.16560782323884074
          ],
          [
            0.13956027908751142,
            -2.2362455434052452e-10,
            0.13742988747622387
          ],
          [
            0.1024076294342686,
            -1.4908231719259926e-10,
            0.0958249476668906
          ],
          [
            0.05450253978118933,
            -7.999002106506678e-11,
            0.04845314150941317
          ],
          [
            -1.4641066137244252e-15,
            -8.940375027136992e-16,
            -1.1449174941446927e-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": [
          [
            0.15657645795624497,
            -1.2410710792387647e-09,
            0.08361512268393867
          ],
          [
            0.16967813503710116,
            -9.8625635436278e-10,
            0.126273842541053
          ],
          [
            0.1772318265955113,
            -7.392497725078329e-10,
            0.15864194360088724
          ],
          [
            0.17625054367370252,
            -5.145041614973422e-10,
            0.17334808305633642
          ],
          [
            0.1641734317945549,
            -3.370579371164695e-10,
            0.1656078232388407
          ],
          [
            0.13956027908751145,
            -2.2362456331137537e-10,
            0.13742988747622387
          ],
          [
            0.10240762943426862,
            -1.490823020589005e-10,
            0.09582494766689065
          ],
          [
            0.05450253978118935,
            -7.999001461200805e-11,
            0.048453141509413156
          ],
          [
            -1.4432899320127035e-15,
            -8.881784197001252e-16,
            -1.1657341758564144e-15
          ]
        ]
      },
      "reflected": {
        "reached": true,
        "construction": "reflect_displacements_about_reconstructed_parent",
        "energies_eV": [
          -326.91972917493104,
          -326.98582498133607,
          -327.17454927939093,
          -327.46359539760175,
          -327.82400022686704,
          -328.2151407779966,
          -328.580276325017,
          -328.85182643210607,
          -328.95207304724465
        ],
        "cartesian_polarizations_e_A2": [
          [
            -3.4810285383054644e-17,
            -2.431009511855396e-17,
            -1.3261765951305893e-17
          ],
          [
            -0.0007104945480377138,
            1.0082314187716731e-12,
            -0.0003181860772521533
          ],
          [
            -0.0013188953885649693,
            1.8789947477890946e-12,
            -0.0006292711525236366
          ],
          [
            -0.0017743735357227941,
            2.8184818766008205e-12,
            -0.0009024858952596372
          ],
          [
            -0.0020740528675531416,
            4.2481239514131655e-12,
            -0.0010875270828083978
          ],
          [
            -0.0022415676357202363,
            6.484529501603037e-12,
            -0.0011383564579845623
          ],
          [
            -0.002306754535817516,
            9.317178054168258e-12,
            -0.001041782971125185
          ],
          [
            -0.0022945623354899496,
            1.243034093815319e-11,
            -0.0008292254612611321
          ],
          [
            -0.0022280685305765035,
            1.564180014140205e-11,
            -0.0005490906689835547
          ]
        ],
        "raw_reduced_polarization": [
          [
            -2.5959366951768495e-15,
            -1.9288383569257873e-15,
            -2.0194919521701777e-15
          ],
          [
            -0.05450253978118599,
            7.99962083118409e-11,
            -0.04845314150941168
          ],
          [
            -0.10240762943426449,
            1.4908527195484228e-10,
            -0.09582494766688289
          ],
          [
            -0.13956027908750845,
            2.2362709505561202e-10,
            -0.13742988747622006
          ],
          [
            -0.16417343179455288,
            3.3705933203885606e-10,
            -0.16560782323883522
          ],
          [
            -0.17625054367370202,
            5.145026857489642e-10,
            -0.17334808305634428
          ],
          [
            -0.17723182659551145,
            7.39253808820798e-10,
            -0.15864194360088812
          ],
          [
            -0.16967813503710166,
            9.862618091064434e-10,
            -0.1262738425410501
          ],
          [
            -0.1565764579562432,
            1.241068944278903e-09,
            -0.0836151226839315
          ]
        ],
        "unwrapped_reduced_polarization": [
          [
            -2.5959366951768495e-15,
            -1.9288383569257873e-15,
            -2.0194919521701777e-15
          ],
          [
            -0.05450253978118599,
            7.99962083118409e-11,
            -0.04845314150941168
          ],
          [
            -0.10240762943426449,
            1.4908527195484228e-10,
            -0.09582494766688289
          ],
          [
            -0.13956027908750845,
            2.2362709505561202e-10,
            -0.13742988747622006
          ],
          [
            -0.16417343179455288,
            3.3705933203885606e-10,
            -0.16560782323883522
          ],
          [
            -0.17625054367370202,
            5.145026857489642e-10,
            -0.17334808305634428
          ],
          [
            -0.17723182659551145,
            7.39253808820798e-10,
            -0.15864194360088812
          ],
          [
            -0.16967813503710166,
            9.862618091064434e-10,
            -0.1262738425410501
          ],
          [
            -0.1565764579562432,
            1.241068944278903e-09,
            -0.0836151226839315
          ]
        ],
        "gauge_integer_shift": [
          0,
          0,
          0
        ],
        "expected_opposite_endpoint_reduced_polarization": [
          -0.15657645795624794,
          1.241069277165207e-09,
          -0.08361512268394099
        ],
        "actual_opposite_endpoint_branch_residual": 1.0618052942941058e-14
      },
      "pnp_branch": {
        "construction": "incoming_path_concatenated_with_parent_reflection",
        "reduced_polarization": [
          [
            0.156576457956245,
            -1.2410710652402124e-09,
            0.08361512268393871
          ],
          [
            0.1696781350371012,
            -9.86256375450855e-10,
            0.12627384254105295
          ],
          [
            0.17723182659551126,
            -7.392497772506195e-10,
            0.1586419436008873
          ],
          [
            0.17625054367370246,
            -5.145041577404979e-10,
            0.17334808305633642
          ],
          [
            0.16417343179455493,
            -3.3705794786589965e-10,
            0.16560782323884074
          ],
          [
            0.13956027908751142,
            -2.2362455434052452e-10,
            0.13742988747622387
          ],
          [
            0.1024076294342686,
            -1.4908231719259926e-10,
            0.0958249476668906
          ],
          [
            0.05450253978118933,
            -7.999002106506678e-11,
            0.04845314150941317
          ],
          [
            -1.4642663702229633e-15,
            -8.940375027170808e-16,
            -1.142663164889717e-15
          ],
          [
            -0.05450253978118599,
            7.99962083118409e-11,
            -0.04845314150941168
          ],
          [
            -0.10240762943426449,
            1.4908527195484228e-10,
            -0.09582494766688289
          ],
          [
            -0.13956027908750845,
            2.2362709505561202e-10,
            -0.13742988747622006
          ],
          [
            -0.16417343179455288,
            3.3705933203885606e-10,
            -0.16560782323883522
          ],
          [
            -0.17625054367370202,
            5.145026857489642e-10,
            -0.17334808305634428
          ],
          [
            -0.17723182659551145,
            7.39253808820798e-10,
            -0.15864194360088812
          ],
          [
            -0.16967813503710166,
            9.862618091064434e-10,
            -0.1262738425410501
          ],
          [
            -0.1565764579562432,
            1.241068944278903e-09,
            -0.0836151226839315
          ]
        ],
        "unwrapped_reduced_polarization": [
          [
            0.156576457956245,
            -1.2410710652402124e-09,
            0.08361512268393871
          ],
          [
            0.1696781350371012,
            -9.86256375450855e-10,
            0.12627384254105295
          ],
          [
            0.17723182659551126,
            -7.392497772506195e-10,
            0.1586419436008873
          ],
          [
            0.17625054367370246,
            -5.145041577404979e-10,
            0.17334808305633642
          ],
          [
            0.16417343179455493,
            -3.3705794786589965e-10,
            0.16560782323884074
          ],
          [
            0.13956027908751142,
            -2.2362455434052452e-10,
            0.13742988747622387
          ],
          [
            0.1024076294342686,
            -1.4908231719259926e-10,
            0.0958249476668906
          ],
          [
            0.05450253978118933,
            -7.999002106506678e-11,
            0.04845314150941317
          ],
          [
            -1.4641066137244252e-15,
            -8.940375027136992e-16,
            -1.1449174941446927e-15
          ],
          [
            -0.05450253978118599,
            7.99962083118409e-11,
            -0.04845314150941168
          ],
          [
            -0.10240762943426449,
            1.4908527195484228e-10,
            -0.09582494766688289
          ],
          [
            -0.13956027908750845,
            2.2362709505561202e-10,
            -0.13742988747622006
          ],
          [
            -0.16417343179455288,
            3.3705933203885606e-10,
            -0.16560782323883522
          ],
          [
            -0.17625054367370202,
            5.145026857489642e-10,
            -0.17334808305634428
          ],
          [
            -0.17723182659551145,
            7.39253808820798e-10,
            -0.15864194360088812
          ],
          [
            -0.16967813503710166,
            9.862618091064434e-10,
            -0.1262738425410501
          ],
          [
            -0.1565764579562432,
            1.241068944278903e-09,
            -0.0836151226839315
          ]
        ],
        "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": [
          [
            0.15657645795624497,
            -1.2410710792387647e-09,
            0.08361512268393867
          ],
          [
            0.16967813503710116,
            -9.8625635436278e-10,
            0.126273842541053
          ],
          [
            0.1772318265955113,
            -7.392497725078329e-10,
            0.15864194360088724
          ],
          [
            0.17625054367370252,
            -5.145041614973422e-10,
            0.17334808305633642
          ],
          [
            0.1641734317945549,
            -3.370579371164695e-10,
            0.1656078232388407
          ],
          [
            0.13956027908751145,
            -2.2362456331137537e-10,
            0.13742988747622387
          ],
          [
            0.10240762943426862,
            -1.490823020589005e-10,
            0.09582494766689065
          ],
          [
            0.05450253978118935,
            -7.999001461200805e-11,
            0.048453141509413156
          ],
          [
            -1.4432899320127035e-15,
            -8.881784197001252e-16,
            -1.1657341758564144e-15
          ],
          [
            -0.054502539781185966,
            7.999623186094595e-11,
            -0.04845314150941166
          ],
          [
            -0.10240762943426451,
            1.4908529966106698e-10,
            -0.09582494766688288
          ],
          [
            -0.13956027908750845,
            2.23627116824332e-10,
            -0.1374298874762201
          ],
          [
            -0.1641734317945529,
            3.370593804064015e-10,
            -0.16560782323883522
          ],
          [
            -0.17625054367370202,
            5.14502662696259e-10,
            -0.1733480830563443
          ],
          [
            -0.17723182659551145,
            7.392537693107215e-10,
            -0.15864194360088812
          ],
          [
            -0.16967813503710166,
            9.86261849966752e-10,
            -0.12627384254105012
          ],
          [
            -0.1565764579562432,
            1.2410689143038667e-09,
            -0.08361512268393151
          ]
        ]
      },
      "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": [
        0.5,
        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": [
              0.15657645795624495,
              -1.2410708084422061e-09,
              0.08361512268393877
            ],
            "branch_aligned_reduced_polarization": [
              0.15657645795624497,
              -1.2410708084422061e-09,
              0.08361512268393877
            ],
            "target_residual": 0.3534561047306,
            "energy_eV": -328.95207304724465,
            "max_atomic_step_A": 0.05602027545485026,
            "max_log_strain_component": 0.016576018090717813,
            "step_scale": 1.0,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 6.613441357848438,
            "cell_principal_stretches": [
              1.018352727341348,
              0.9992730605300927,
              0.9851450915099706
            ],
            "cell_volume_ratio": 1.0024959067777472,
            "cell_rmsd_from_input_A": 0.11399881561384655
          },
          {
            "iteration": 1,
            "reduced_polarization": [
              0.48088372788791833,
              -7.305292923016258e-11,
              -0.011253235479147843
            ],
            "branch_aligned_reduced_polarization": [
              0.48088372788791833,
              -7.305292923016258e-11,
              -0.011253235479147843
            ],
            "target_residual": 0.022182587049582453,
            "energy_eV": -328.18100393308947,
            "max_atomic_step_A": 0.0025423826911532216,
            "max_log_strain_component": 0.0008485290765921225,
            "step_scale": 1.0,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 6.613441357848438,
            "cell_principal_stretches": [
              1.0193405625248948,
              0.9992482609219102,
              0.9844241105144882
            ],
            "cell_volume_ratio": 1.0027090839037174,
            "cell_rmsd_from_input_A": 0.11973002618214393
          },
          {
            "iteration": 2,
            "reduced_polarization": [
              0.49954694000526917,
              -1.76628065844633e-12,
              -2.131159807911489e-05
            ],
            "branch_aligned_reduced_polarization": [
              0.49954694000526917,
              -1.76628065844633e-12,
              -2.131159807911489e-05
            ],
            "target_residual": 0.00045356095845893357,
            "energy_eV": -328.1093745184469
          }
        ],
        "iterations": 2
      },
      "parent": {
        "candidate_id": "bec_projection_01",
        "source": "MACEField_BEC_backprojection",
        "spacegroup": "Cc",
        "spacegroup_number": 9,
        "pointgroup": "m",
        "has_inversion": false,
        "is_polar_point_group": true,
        "nonpolar_parent_hypothesis": false,
        "symmetry_tolerance_A": null,
        "target_reduced_polarization": [
          0.5,
          0.0,
          0.0
        ],
        "formal_class": [
          0.5,
          0.0,
          0.0
        ],
        "target_residual": 0.00045356095845893357,
        "parent_symmetrization_rmsd_A": 0.028313326414842466,
        "parent_cell_rmsd_A": 0.11973002618214393,
        "energy_eV": -328.1093745184469,
        "reduced_polarization": [
          0.49954694000526917,
          -1.76628065844633e-12,
          -2.131159807911489e-05
        ],
        "cartesian_polarization_e_A2": [
          0.008001620186833716,
          -7.018609892128896e-14,
          0.00013920280490896687
        ],
        "ranking_score": 0.5591529548772963
      },
      "branch_status": "awaiting_branch_sampling"
    },
    {
      "orbit_id": 2,
      "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": [
              0.15657645795624495,
              -1.2410708084422061e-09,
              0.08361512268393877
            ],
            "branch_aligned_reduced_polarization": [
              0.15657645795624495,
              -1.2410708084422061e-09,
              0.08361512268393878
            ],
            "target_residual": 0.4448511585279228,
            "energy_eV": -328.95207304724465,
            "max_atomic_step_A": 0.04170369743767523,
            "max_log_strain_component": 0.013344302623267735,
            "step_scale": 1.0,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 6.613441357848438,
            "cell_principal_stretches": [
              1.0132442551263614,
              1.0008134515881646,
              0.9856863528114262
            ],
            "cell_volume_ratio": 0.9995534618231839,
            "cell_rmsd_from_input_A": 0.1106811316443704
          },
          {
            "iteration": 1,
            "reduced_polarization": [
              0.00725508499048156,
              -6.329149856498842e-11,
              0.5031636573208517
            ],
            "branch_aligned_reduced_polarization": [
              0.00725508499048156,
              -6.329149856498842e-11,
              0.5031636573208517
            ],
            "target_residual": 0.007914858549771383,
            "energy_eV": -328.0834477914118,
            "max_atomic_step_A": 0.0009912103246345085,
            "max_log_strain_component": 0.000291102116499484,
            "step_scale": 1.0,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 6.613441357848438,
            "cell_principal_stretches": [
              1.0134822239727668,
              1.0008235047734826,
              0.9853834671309923
            ],
            "cell_volume_ratio": 0.9994910361159802,
            "cell_rmsd_from_input_A": 0.11213023316665387
          },
          {
            "iteration": 2,
            "reduced_polarization": [
              7.343159412683061e-05,
              4.047524748433473e-13,
              0.5001596749787048
            ],
            "branch_aligned_reduced_polarization": [
              7.343159412683061e-05,
              4.047524748433473e-13,
              0.5001596749787048
            ],
            "target_residual": 0.00017575066953044027,
            "energy_eV": -328.0616585747727
          }
        ],
        "iterations": 2
      },
      "parent": {
        "candidate_id": "bec_projection_02",
        "source": "MACEField_BEC_backprojection",
        "spacegroup": "Cc",
        "spacegroup_number": 9,
        "pointgroup": "m",
        "has_inversion": false,
        "is_polar_point_group": true,
        "nonpolar_parent_hypothesis": false,
        "symmetry_tolerance_A": null,
        "target_reduced_polarization": [
          0.0,
          0.0,
          0.5
        ],
        "formal_class": [
          0.0,
          0.0,
          0.5
        ],
        "target_residual": 0.00017575066953044027,
        "parent_symmetrization_rmsd_A": 0.025982271293415824,
        "parent_cell_rmsd_A": 0.11213023316665387,
        "energy_eV": -328.0616585747727,
        "reduced_polarization": [
          7.343159412683061e-05,
          4.047524748433473e-13,
          0.5001596749787048
        ],
        "cartesian_polarization_e_A2": [
          -0.0017314295627375942,
          -1.400098291533136e-13,
          0.0032959809775284133
        ],
        "ranking_score": 0.5543663309241402
      },
      "branch_status": "awaiting_branch_sampling"
    },
    {
      "orbit_id": 3,
      "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": [
              0.15657645795624495,
              -1.2410708084422061e-09,
              0.08361512268393877
            ],
            "branch_aligned_reduced_polarization": [
              0.15657645795624495,
              -1.2410708016830085e-09,
              0.08361512268393877
            ],
            "target_residual": 0.5305729682960705,
            "energy_eV": -328.95207304724465,
            "max_atomic_step_A": 0.06960798063290836,
            "max_log_strain_component": 0.009480363199229886,
            "step_scale": 1.0,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 6.613441357848438,
            "cell_principal_stretches": [
              1.0106195876812682,
              0.9998131267084842,
              0.9883333157351049
            ],
            "cell_volume_ratio": 0.9986423535754784,
            "cell_rmsd_from_input_A": 0.13493062218071106
          },
          {
            "iteration": 1,
            "reduced_polarization": [
              -0.005128845629987716,
              -0.49697483652951463,
              -0.011476901502093902
            ],
            "branch_aligned_reduced_polarization": [
              -0.005128845629987716,
              -0.49697483652951463,
              -0.011476901502093902
            ],
            "target_residual": 0.012929653499153348,
            "energy_eV": -326.3497107654195,
            "max_atomic_step_A": 0.0009783370043395367,
            "max_log_strain_component": 0.0001503900177226386,
            "step_scale": 1.0,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 6.613441357848438,
            "cell_principal_stretches": [
              1.010700428908475,
              0.9997467790973812,
              0.988380375994886
            ],
            "cell_volume_ratio": 0.9987035132837554,
            "cell_rmsd_from_input_A": 0.13550725712062853
          },
          {
            "iteration": 2,
            "reduced_polarization": [
              -3.162306051704104e-05,
              -0.4999861012480832,
              -6.376812026606024e-06
            ],
            "branch_aligned_reduced_polarization": [
              -3.162306051704104e-05,
              -0.4999861012480832,
              -6.376812026606024e-06
            ],
            "target_residual": 3.512630058705842e-05,
            "energy_eV": -326.32302064856265
          }
        ],
        "iterations": 2
      },
      "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,
          0.0
        ],
        "formal_class": [
          0.0,
          0.5,
          0.0
        ],
        "target_residual": 3.512630058705842e-05,
        "parent_symmetrization_rmsd_A": 0.05089168403914328,
        "parent_cell_rmsd_A": 0.13550725712062853,
        "energy_eV": -326.32302064856265,
        "reduced_polarization": [
          -3.162306051704104e-05,
          -0.4999861012480832,
          -6.376812026606024e-06
        ],
        "cartesian_polarization_e_A2": [
          -6.066364707382947e-05,
          -0.00631119321077702,
          3.967991541489899e-06
        ],
        "ranking_score": 0.5848387509204745
      },
      "branch_status": "awaiting_branch_sampling"
    },
    {
      "orbit_id": 4,
      "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": [
              0.15657645795624495,
              -1.2410708084422061e-09,
              0.08361512268393877
            ],
            "branch_aligned_reduced_polarization": [
              0.15657645795624497,
              -1.2410708084422061e-09,
              0.08361512268393878
            ],
            "target_residual": 0.5397370612505594,
            "energy_eV": -328.95207304724465,
            "max_atomic_step_A": 0.04352823048849324,
            "max_log_strain_component": 0.008926791486668362,
            "step_scale": 1.0,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 6.613441357848438,
            "cell_principal_stretches": [
              1.0119300437989187,
              0.9999093534367947,
              0.9916708186205024
            ],
            "cell_volume_ratio": 1.0034105309590684,
            "cell_rmsd_from_input_A": 0.08986929936367835
          },
          {
            "iteration": 1,
            "reduced_polarization": [
              0.48238408663811905,
              -1.0388532873553745e-11,
              0.47846356906107956
            ],
            "branch_aligned_reduced_polarization": [
              0.48238408663811905,
              -1.0388532873553745e-11,
              0.47846356906107956
            ],
            "target_residual": 0.027823340222916895,
            "energy_eV": -328.670276445795,
            "max_atomic_step_A": 0.0024203926341398977,
            "max_log_strain_component": 0.0005575851292013645,
            "step_scale": 1.0,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 6.613441357848438,
            "cell_principal_stretches": [
              1.012681671782198,
              0.9999038601528065,
              0.9911521348438344
            ],
            "cell_volume_ratio": 1.0036251032628134,
            "cell_rmsd_from_input_A": 0.09558792550226994
          },
          {
            "iteration": 2,
            "reduced_polarization": [
              0.4996485047139743,
              -3.6640324261712075e-13,
              0.49950506815744966
            ],
            "branch_aligned_reduced_polarization": [
              0.4996485047139743,
              -3.6640324261712075e-13,
              0.49950506815744966
            ],
            "target_residual": 0.0006070473333015721,
            "energy_eV": -328.6288198363407
          }
        ],
        "iterations": 2
      },
      "parent": {
        "candidate_id": "bec_projection_04",
        "source": "MACEField_BEC_backprojection",
        "spacegroup": "Cc",
        "spacegroup_number": 9,
        "pointgroup": "m",
        "has_inversion": false,
        "is_polar_point_group": true,
        "nonpolar_parent_hypothesis": false,
        "symmetry_tolerance_A": null,
        "target_reduced_polarization": [
          0.5,
          0.0,
          0.5
        ],
        "formal_class": [
          0.5,
          0.0,
          0.5
        ],
        "target_residual": 0.0006070473333015721,
        "parent_symmetrization_rmsd_A": 0.022527105068925968,
        "parent_cell_rmsd_A": 0.09558792550226994,
        "energy_eV": -328.6288198363407,
        "reduced_polarization": [
          0.4996485047139743,
          -3.6640324261712075e-13,
          0.49950506815744966
        ],
        "cartesian_polarization_e_A2": [
          0.006379554750444828,
          1.0624645479395667e-13,
          0.003317981661330917
        ],
        "ranking_score": 0.5476381811110966
      },
      "branch_status": "awaiting_branch_sampling"
    },
    {
      "orbit_id": 5,
      "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": [
              0.15657645795624495,
              -1.2410708084422061e-09,
              0.08361512268393877
            ],
            "branch_aligned_reduced_polarization": [
              0.15657645795624497,
              -1.2410708016830085e-09,
              0.08361512268393877
            ],
            "target_residual": 0.6123162718156836,
            "energy_eV": -328.95207304724465,
            "max_atomic_step_A": 0.08222896362826207,
            "max_log_strain_component": 0.01657601805906574,
            "step_scale": 1.0,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 6.613441357848438,
            "cell_principal_stretches": [
              1.0204256501489184,
              1.0003501913673627,
              0.9820852349921788
            ],
            "cell_volume_ratio": 1.0024959069339325,
            "cell_rmsd_from_input_A": 0.17167668655471324
          },
          {
            "iteration": 1,
            "reduced_polarization": [
              0.4713760057086021,
              -0.4896615869069434,
              -0.01931082922678457
            ],
            "branch_aligned_reduced_polarization": [
              0.4713760057086021,
              -0.4896615869069434,
              -0.01931082922678457
            ],
            "target_residual": 0.03604336221695613,
            "energy_eV": -325.46081782760047,
            "max_atomic_step_A": 0.0038424248176704813,
            "max_log_strain_component": 0.0012575847655512903,
            "step_scale": 1.0,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 6.613441357848438,
            "cell_principal_stretches": [
              1.0218897616586573,
              1.000246969830146,
              0.9811109067259294
            ],
            "cell_volume_ratio": 1.0028347994230467,
            "cell_rmsd_from_input_A": 0.17970293190230016
          },
          {
            "iteration": 2,
            "reduced_polarization": [
              0.49902444197342527,
              -0.49964484033064105,
              -0.00019605868029499288
            ],
            "branch_aligned_reduced_polarization": [
              0.49902444197342527,
              -0.49964484033064105,
              -0.00019605868029499288
            ],
            "target_residual": 0.0010565466672478574,
            "energy_eV": -325.2341907424835,
            "max_atomic_step_A": 0.0001505856836419434,
            "max_log_strain_component": 5.2050943236552197e-05,
            "step_scale": 1.0,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 6.613441357848438,
            "cell_principal_stretches": [
              1.0219477628855418,
              1.0002435639048315,
              0.9810693446167994
            ],
            "cell_volume_ratio": 1.0028458195327594,
            "cell_rmsd_from_input_A": 0.18002306580547833
          },
          {
            "iteration": 3,
            "reduced_polarization": [
              0.4999705181601158,
              -0.4999869439817532,
              -3.6101103568402523e-06
            ],
            "branch_aligned_reduced_polarization": [
              0.4999705181601158,
              -0.4999869439817532,
              -3.6101103568402523e-06
            ],
            "target_residual": 3.2444897783903965e-05,
            "energy_eV": -325.22509172769793
          }
        ],
        "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,
          0.0
        ],
        "formal_class": [
          0.5,
          0.5,
          0.0
        ],
        "target_residual": 3.2444897783903965e-05,
        "parent_symmetrization_rmsd_A": 0.05894812699212401,
        "parent_cell_rmsd_A": 0.18002306580547833,
        "energy_eV": -325.22509172769793,
        "reduced_polarization": [
          0.4999705181601158,
          -0.4999869439817532,
          -3.6101103568402523e-06
        ],
        "cartesian_polarization_e_A2": [
          0.00794847858973806,
          -0.006201614380281772,
          0.00014639571346856757
        ],
        "ranking_score": 0.6040187832390614
      },
      "branch_status": "awaiting_branch_sampling"
    },
    {
      "orbit_id": 6,
      "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": [
              0.15657645795624495,
              -1.2410708084422061e-09,
              0.08361512268393877
            ],
            "branch_aligned_reduced_polarization": [
              0.15657645795624495,
              -1.2410708016830085e-09,
              0.08361512268393878
            ],
            "target_residual": 0.6692477508386295,
            "energy_eV": -328.95207304724465,
            "max_atomic_step_A": 0.0875978424998845,
            "max_log_strain_component": 0.013344302654919808,
            "step_scale": 1.0,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 6.613441357848438,
            "cell_principal_stretches": [
              1.017312207978602,
              0.9986935166907772,
              0.9838288210959041
            ],
            "cell_volume_ratio": 0.9995534619789107,
            "cell_rmsd_from_input_A": 0.17077294450787736
          },
          {
            "iteration": 1,
            "reduced_polarization": [
              0.0031647906061880744,
              -0.4956240827018239,
              0.4823478640149115
            ],
            "branch_aligned_reduced_polarization": [
              0.0031647906061880744,
              -0.4956240827018239,
              0.4823478640149115
            ],
            "target_residual": 0.018459752344426247,
            "energy_eV": -325.64326869579463,
            "max_atomic_step_A": 0.001885266920932607,
            "max_log_strain_component": 0.0004582531648863884,
            "step_scale": 1.0,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 6.613441357848438,
            "cell_principal_stretches": [
              1.017765440162076,
              0.9987139199533475,
              0.9833735406153398
            ],
            "cell_volume_ratio": 0.9995564394186616,
            "cell_rmsd_from_input_A": 0.17451150216132408
          },
          {
            "iteration": 2,
            "reduced_polarization": [
              0.00019768451602076057,
              -0.5000789305474118,
              0.5001724393595655
            ],
            "branch_aligned_reduced_polarization": [
              0.00019768451602076057,
              -0.5000789305474118,
              0.5001724393595655
            ],
            "target_residual": 0.00027394257047132377,
            "energy_eV": -325.54552293258286
          }
        ],
        "iterations": 2
      },
      "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": [
          0.0,
          -0.5,
          0.5
        ],
        "formal_class": [
          0.0,
          0.5,
          0.5
        ],
        "target_residual": 0.00027394257047132377,
        "parent_symmetrization_rmsd_A": 0.05651707244368118,
        "parent_cell_rmsd_A": 0.17451150216132408,
        "energy_eV": -325.54552293258286,
        "reduced_polarization": [
          0.00019768451602076057,
          -0.5000789305474118,
          0.5001724393595655
        ],
        "cartesian_polarization_e_A2": [
          -0.0017908979241411142,
          -0.006329480191287158,
          0.003299783542429876
        ],
        "ranking_score": 0.6006928331249548
      },
      "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": [
              0.15657645795624495,
              -1.2410708084422061e-09,
              0.08361512268393877
            ],
            "branch_aligned_reduced_polarization": [
              0.15657645795624497,
              -1.2410708016830085e-09,
              0.08361512268393878
            ],
            "target_residual": 0.7357418664493134,
            "energy_eV": -328.95207304724465,
            "max_atomic_step_A": 0.07702338370599435,
            "max_log_strain_component": 0.009480363253681281,
            "step_scale": 1.0,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 6.613441357848438,
            "cell_principal_stretches": [
              1.0160977915973695,
              0.9990627011663353,
              0.9884402045686718
            ],
            "cell_volume_ratio": 1.003410531115396,
            "cell_rmsd_from_input_A": 0.15792643558953445
          },
          {
            "iteration": 1,
            "reduced_polarization": [
              0.4720662307739721,
              -0.48693671705886465,
              0.46368810842795644
            ],
            "branch_aligned_reduced_polarization": [
              0.4720662307739721,
              -0.48693671705886465,
              0.46368810842795644
            ],
            "target_residual": 0.04763925160949729,
            "energy_eV": -326.0167528139749,
            "max_atomic_step_A": 0.004133459280585863,
            "max_log_strain_component": 0.0008846064896449641,
            "step_scale": 1.0,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 6.613441357848438,
            "cell_principal_stretches": [
              1.0172684798984368,
              0.9990169678396408,
              0.9877044978703011
            ],
            "cell_volume_ratio": 1.0037729411018723,
            "cell_rmsd_from_input_A": 0.16683086092612368
          },
          {
            "iteration": 2,
            "reduced_polarization": [
              0.4991181764944984,
              -0.49971779016708423,
              0.4991620470277891
            ],
            "branch_aligned_reduced_polarization": [
              0.4991181764944984,
              -0.49971779016708423,
              0.4991620470277891
            ],
            "target_residual": 0.0012487674996918103,
            "energy_eV": -325.7973389952694,
            "max_atomic_step_A": 0.00011460834400037754,
            "max_log_strain_component": 3.347556297221924e-05,
            "step_scale": 1.0,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 6.613441357848438,
            "cell_principal_stretches": [
              1.0173055826656325,
              0.9990176541136635,
              0.9876785863757122
            ],
            "cell_volume_ratio": 1.0037839071998906,
            "cell_rmsd_from_input_A": 0.16708053313288337
          },
          {
            "iteration": 3,
            "reduced_polarization": [
              0.49997683998242926,
              -0.49999062231434954,
              0.49997548792849855
            ],
            "branch_aligned_reduced_polarization": [
              0.49997683998242926,
              -0.49999062231434954,
              0.49997548792849855
            ],
            "target_residual": 3.5002414935659875e-05,
            "energy_eV": -325.79168635306
          }
        ],
        "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": 3.5002414935659875e-05,
        "parent_symmetrization_rmsd_A": 0.05648677943755225,
        "parent_cell_rmsd_A": 0.16708053313288337,
        "energy_eV": -325.79168635306,
        "reduced_polarization": [
          0.49997683998242926,
          -0.49999062231434954,
          0.49997548792849855
        ],
        "cartesian_polarization_e_A2": [
          0.006324222690325606,
          -0.006217628964670932,
          0.00332589667259688
        ],
        "ranking_score": 0.5983269175506444
      },
      "branch_status": "awaiting_branch_sampling"
    }
  ],
  "sampled_polarization_branches": [
    {
      "orbit_id": 0,
      "candidate_id": "inversion_parent_endpoint_00",
      "formal_class": [
        0.0,
        0.0,
        0.0
      ],
      "construction": "MACEField-BEC-parent plus variable-cell P-N-P path and symmetric log-strain continuation beyond both polar endpoints",
      "geometry_diagnostics": {
        "collision_aware": false,
        "permutations_tested": 1,
        "selected_order": [
          0,
          1,
          2,
          3,
          4,
          5,
          6,
          7,
          8,
          9,
          10,
          11,
          12,
          13,
          14,
          15,
          16,
          17,
          18,
          19,
          20,
          21,
          22,
          23,
          24,
          25,
          26,
          27,
          28,
          29,
          30,
          31,
          32,
          33,
          34,
          35,
          36,
          37,
          38,
          39,
          40,
          41,
          42,
          43,
          44,
          45,
          46,
          47,
          48,
          49,
          50,
          51,
          52,
          53,
          54,
          55
        ],
        "endpoint_rmsd_A": 0.37346744167352186,
        "minimum_distance_A_by_image": [
          1.8087733320584676,
          1.798921536602156,
          1.7903737687653527,
          1.7831487817514997,
          1.7772627078705872,
          1.7727288841387865,
          1.7695577044785014,
          1.7677565022494792,
          1.7673294661602381
        ],
        "minimum_distance_A": 1.7673294661602381,
        "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": [
          868.2860002294129,
          868.2860002294129,
          868.2860002294129,
          868.2860002294129,
          868.2860002294129,
          868.2860002294129,
          868.2860002294129,
          868.2860002294129,
          868.2860002294129
        ],
        "cell_deformation_log_strain_norm": 0.0
      },
      "parent_reduced_polarization": [
        -1.4642663702229633e-15,
        -8.940375027170808e-16,
        -1.142663164889717e-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": [
          -328.9520730472446,
          -328.8518264321061,
          -328.58027632501705,
          -328.2151407779967,
          -327.82400022686704,
          -327.4635953976018,
          -327.17454927939093,
          -326.9858249813361,
          -326.919729174931
        ],
        "cartesian_polarizations_e_A2": [
          [
            0.002228068530576508,
            -1.5641826872916897e-11,
            0.000549090668983602
          ],
          [
            0.0022945623354899323,
            -1.2430272455128825e-11,
            0.0008292254612611509
          ],
          [
            0.002306754535817516,
            -9.317127242313462e-12,
            0.0010417829711251796
          ],
          [
            0.00224156763572027,
            -6.484548053833746e-12,
            0.0011383564579845106
          ],
          [
            0.002074052867553156,
            -4.2481065060030256e-12,
            0.001087527082808434
          ],
          [
            0.0017743735357228286,
            -2.8184498547233914e-12,
            0.0009024858952596622
          ],
          [
            0.0013188953885650092,
            -1.8789575074724436e-12,
            0.0006292711525236873
          ],
          [
            0.0007104945480377624,
            -1.0081534378682653e-12,
            0.0003181860772521631
          ],
          [
            -1.9623192000038768e-17,
            -1.1267992806430336e-17,
            -7.503734509890689e-18
          ]
        ],
        "raw_reduced_polarization": [
          [
            0.156576457956245,
            -1.2410710652402124e-09,
            0.08361512268393871
          ],
          [
            0.1696781350371012,
            -9.86256375450855e-10,
            0.12627384254105295
          ],
          [
            0.17723182659551126,
            -7.392497772506195e-10,
            0.1586419436008873
          ],
          [
            0.17625054367370246,
            -5.145041577404979e-10,
            0.17334808305633642
          ],
          [
            0.16417343179455493,
            -3.3705794786589965e-10,
            0.16560782323884074
          ],
          [
            0.13956027908751142,
            -2.2362455434052452e-10,
            0.13742988747622387
          ],
          [
            0.1024076294342686,
            -1.4908231719259926e-10,
            0.0958249476668906
          ],
          [
            0.05450253978118933,
            -7.999002106506678e-11,
            0.04845314150941317
          ],
          [
            -1.4642663702229633e-15,
            -8.940375027170808e-16,
            -1.142663164889717e-15
          ]
        ],
        "unwrapped_reduced_polarization": [
          [
            0.156576457956245,
            -1.2410710652402124e-09,
            0.08361512268393871
          ],
          [
            0.1696781350371012,
            -9.86256375450855e-10,
            0.12627384254105295
          ],
          [
            0.17723182659551126,
            -7.392497772506195e-10,
            0.1586419436008873
          ],
          [
            0.17625054367370246,
            -5.145041577404979e-10,
            0.17334808305633642
          ],
          [
            0.16417343179455493,
            -3.3705794786589965e-10,
            0.16560782323884074
          ],
          [
            0.13956027908751142,
            -2.2362455434052452e-10,
            0.13742988747622387
          ],
          [
            0.1024076294342686,
            -1.4908231719259926e-10,
            0.0958249476668906
          ],
          [
            0.05450253978118933,
            -7.999002106506678e-11,
            0.04845314150941317
          ],
          [
            -1.4641066137244252e-15,
            -8.940375027136992e-16,
            -1.1449174941446927e-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": [
          [
            0.15657645795624497,
            -1.2410710792387647e-09,
            0.08361512268393867
          ],
          [
            0.16967813503710116,
            -9.8625635436278e-10,
            0.126273842541053
          ],
          [
            0.1772318265955113,
            -7.392497725078329e-10,
            0.15864194360088724
          ],
          [
            0.17625054367370252,
            -5.145041614973422e-10,
            0.17334808305633642
          ],
          [
            0.1641734317945549,
            -3.370579371164695e-10,
            0.1656078232388407
          ],
          [
            0.13956027908751145,
            -2.2362456331137537e-10,
            0.13742988747622387
          ],
          [
            0.10240762943426862,
            -1.490823020589005e-10,
            0.09582494766689065
          ],
          [
            0.05450253978118935,
            -7.999001461200805e-11,
            0.048453141509413156
          ],
          [
            -1.4432899320127035e-15,
            -8.881784197001252e-16,
            -1.1657341758564144e-15
          ]
        ]
      },
      "reflected": {
        "reached": true,
        "construction": "reflect_displacements_about_reconstructed_parent",
        "energies_eV": [
          -326.91972917493104,
          -326.98582498133607,
          -327.17454927939093,
          -327.46359539760175,
          -327.82400022686704,
          -328.2151407779966,
          -328.580276325017,
          -328.85182643210607,
          -328.95207304724465
        ],
        "cartesian_polarizations_e_A2": [
          [
            -3.4810285383054644e-17,
            -2.431009511855396e-17,
            -1.3261765951305893e-17
          ],
          [
            -0.0007104945480377138,
            1.0082314187716731e-12,
            -0.0003181860772521533
          ],
          [
            -0.0013188953885649693,
            1.8789947477890946e-12,
            -0.0006292711525236366
          ],
          [
            -0.0017743735357227941,
            2.8184818766008205e-12,
            -0.0009024858952596372
          ],
          [
            -0.0020740528675531416,
            4.2481239514131655e-12,
            -0.0010875270828083978
          ],
          [
            -0.0022415676357202363,
            6.484529501603037e-12,
            -0.0011383564579845623
          ],
          [
            -0.002306754535817516,
            9.317178054168258e-12,
            -0.001041782971125185
          ],
          [
            -0.0022945623354899496,
            1.243034093815319e-11,
            -0.0008292254612611321
          ],
          [
            -0.0022280685305765035,
            1.564180014140205e-11,
            -0.0005490906689835547
          ]
        ],
        "raw_reduced_polarization": [
          [
            -2.5959366951768495e-15,
            -1.9288383569257873e-15,
            -2.0194919521701777e-15
          ],
          [
            -0.05450253978118599,
            7.99962083118409e-11,
            -0.04845314150941168
          ],
          [
            -0.10240762943426449,
            1.4908527195484228e-10,
            -0.09582494766688289
          ],
          [
            -0.13956027908750845,
            2.2362709505561202e-10,
            -0.13742988747622006
          ],
          [
            -0.16417343179455288,
            3.3705933203885606e-10,
            -0.16560782323883522
          ],
          [
            -0.17625054367370202,
            5.145026857489642e-10,
            -0.17334808305634428
          ],
          [
            -0.17723182659551145,
            7.39253808820798e-10,
            -0.15864194360088812
          ],
          [
            -0.16967813503710166,
            9.862618091064434e-10,
            -0.1262738425410501
          ],
          [
            -0.1565764579562432,
            1.241068944278903e-09,
            -0.0836151226839315
          ]
        ],
        "unwrapped_reduced_polarization": [
          [
            -2.5959366951768495e-15,
            -1.9288383569257873e-15,
            -2.0194919521701777e-15
          ],
          [
            -0.05450253978118599,
            7.99962083118409e-11,
            -0.04845314150941168
          ],
          [
            -0.10240762943426449,
            1.4908527195484228e-10,
            -0.09582494766688289
          ],
          [
            -0.13956027908750845,
            2.2362709505561202e-10,
            -0.13742988747622006
          ],
          [
            -0.16417343179455288,
            3.3705933203885606e-10,
            -0.16560782323883522
          ],
          [
            -0.17625054367370202,
            5.145026857489642e-10,
            -0.17334808305634428
          ],
          [
            -0.17723182659551145,
            7.39253808820798e-10,
            -0.15864194360088812
          ],
          [
            -0.16967813503710166,
            9.862618091064434e-10,
            -0.1262738425410501
          ],
          [
            -0.1565764579562432,
            1.241068944278903e-09,
            -0.0836151226839315
          ]
        ],
        "gauge_integer_shift": [
          0,
          0,
          0
        ],
        "expected_opposite_endpoint_reduced_polarization": [
          -0.15657645795624794,
          1.241069277165207e-09,
          -0.08361512268394099
        ],
        "actual_opposite_endpoint_branch_residual": 1.0618052942941058e-14
      },
      "pnp_branch": {
        "construction": "incoming_path_concatenated_with_parent_reflection",
        "reduced_polarization": [
          [
            0.156576457956245,
            -1.2410710652402124e-09,
            0.08361512268393871
          ],
          [
            0.1696781350371012,
            -9.86256375450855e-10,
            0.12627384254105295
          ],
          [
            0.17723182659551126,
            -7.392497772506195e-10,
            0.1586419436008873
          ],
          [
            0.17625054367370246,
            -5.145041577404979e-10,
            0.17334808305633642
          ],
          [
            0.16417343179455493,
            -3.3705794786589965e-10,
            0.16560782323884074
          ],
          [
            0.13956027908751142,
            -2.2362455434052452e-10,
            0.13742988747622387
          ],
          [
            0.1024076294342686,
            -1.4908231719259926e-10,
            0.0958249476668906
          ],
          [
            0.05450253978118933,
            -7.999002106506678e-11,
            0.04845314150941317
          ],
          [
            -1.4642663702229633e-15,
            -8.940375027170808e-16,
            -1.142663164889717e-15
          ],
          [
            -0.05450253978118599,
            7.99962083118409e-11,
            -0.04845314150941168
          ],
          [
            -0.10240762943426449,
            1.4908527195484228e-10,
            -0.09582494766688289
          ],
          [
            -0.13956027908750845,
            2.2362709505561202e-10,
            -0.13742988747622006
          ],
          [
            -0.16417343179455288,
            3.3705933203885606e-10,
            -0.16560782323883522
          ],
          [
            -0.17625054367370202,
            5.145026857489642e-10,
            -0.17334808305634428
          ],
          [
            -0.17723182659551145,
            7.39253808820798e-10,
            -0.15864194360088812
          ],
          [
            -0.16967813503710166,
            9.862618091064434e-10,
            -0.1262738425410501
          ],
          [
            -0.1565764579562432,
            1.241068944278903e-09,
            -0.0836151226839315
          ]
        ],
        "unwrapped_reduced_polarization": [
          [
            0.156576457956245,
            -1.2410710652402124e-09,
            0.08361512268393871
          ],
          [
            0.1696781350371012,
            -9.86256375450855e-10,
            0.12627384254105295
          ],
          [
            0.17723182659551126,
            -7.392497772506195e-10,
            0.1586419436008873
          ],
          [
            0.17625054367370246,
            -5.145041577404979e-10,
            0.17334808305633642
          ],
          [
            0.16417343179455493,
            -3.3705794786589965e-10,
            0.16560782323884074
          ],
          [
            0.13956027908751142,
            -2.2362455434052452e-10,
            0.13742988747622387
          ],
          [
            0.1024076294342686,
            -1.4908231719259926e-10,
            0.0958249476668906
          ],
          [
            0.05450253978118933,
            -7.999002106506678e-11,
            0.04845314150941317
          ],
          [
            -1.4641066137244252e-15,
            -8.940375027136992e-16,
            -1.1449174941446927e-15
          ],
          [
            -0.05450253978118599,
            7.99962083118409e-11,
            -0.04845314150941168
          ],
          [
            -0.10240762943426449,
            1.4908527195484228e-10,
            -0.09582494766688289
          ],
          [
            -0.13956027908750845,
            2.2362709505561202e-10,
            -0.13742988747622006
          ],
          [
            -0.16417343179455288,
            3.3705933203885606e-10,
            -0.16560782323883522
          ],
          [
            -0.17625054367370202,
            5.145026857489642e-10,
            -0.17334808305634428
          ],
          [
            -0.17723182659551145,
            7.39253808820798e-10,
            -0.15864194360088812
          ],
          [
            -0.16967813503710166,
            9.862618091064434e-10,
            -0.1262738425410501
          ],
          [
            -0.1565764579562432,
            1.241068944278903e-09,
            -0.0836151226839315
          ]
        ],
        "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": [
          [
            0.15657645795624497,
            -1.2410710792387647e-09,
            0.08361512268393867
          ],
          [
            0.16967813503710116,
            -9.8625635436278e-10,
            0.126273842541053
          ],
          [
            0.1772318265955113,
            -7.392497725078329e-10,
            0.15864194360088724
          ],
          [
            0.17625054367370252,
            -5.145041614973422e-10,
            0.17334808305633642
          ],
          [
            0.1641734317945549,
            -3.370579371164695e-10,
            0.1656078232388407
          ],
          [
            0.13956027908751145,
            -2.2362456331137537e-10,
            0.13742988747622387
          ],
          [
            0.10240762943426862,
            -1.490823020589005e-10,
            0.09582494766689065
          ],
          [
            0.05450253978118935,
            -7.999001461200805e-11,
            0.048453141509413156
          ],
          [
            -1.4432899320127035e-15,
            -8.881784197001252e-16,
            -1.1657341758564144e-15
          ],
          [
            -0.054502539781185966,
            7.999623186094595e-11,
            -0.04845314150941166
          ],
          [
            -0.10240762943426451,
            1.4908529966106698e-10,
            -0.09582494766688288
          ],
          [
            -0.13956027908750845,
            2.23627116824332e-10,
            -0.1374298874762201
          ],
          [
            -0.1641734317945529,
            3.370593804064015e-10,
            -0.16560782323883522
          ],
          [
            -0.17625054367370202,
            5.14502662696259e-10,
            -0.1733480830563443
          ],
          [
            -0.17723182659551145,
            7.392537693107215e-10,
            -0.15864194360088812
          ],
          [
            -0.16967813503710166,
            9.86261849966752e-10,
            -0.12627384254105012
          ],
          [
            -0.1565764579562432,
            1.2410689143038667e-09,
            -0.08361512268393151
          ]
        ]
      },
      "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": "C2/c",
        "spacegroup_number": 15,
        "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": 1.5591041438553887e-15,
        "parent_symmetrization_rmsd_A": 0.37346744167352186,
        "parent_cell_rmsd_A": 0.0,
        "energy_eV": -326.91972917493104,
        "reduced_polarization": [
          -1.2869464548963208e-15,
          8.788198430963645e-16,
          -4.743666300361159e-17
        ],
        "cartesian_polarization_e_A2": [
          -2.046502339708837e-17,
          1.1076197184193225e-17,
          -3.1151098254629533e-19
        ],
        "ranking_score": 0.37346744167352497
      }
    }
  ],
  "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": 53,
      "full_response": 19,
      "energy_polarization": 34
    },
    "model_evaluations_for_recovery_and_path_properties": {
      "total": 78,
      "full_response": 44,
      "energy_polarization": 34
    },
    "elapsed_seconds": 1264.4775357579929
  }
}