{
  "schema": "ferrofinder.endpoint_parent_recovery.v4_variable_cell",
  "status": "complete",
  "input_atom_count": 64,
  "input_formula": "Bi16O40Se8",
  "input_spacegroup": "Aem2",
  "input_pointgroup": "mm2",
  "input_is_polar_point_group": true,
  "input_energy_eV": -352.4973868404428,
  "input_cartesian_polarization_e_A2": [
    -1.7284836296850698e-17,
    4.122099249060131e-18,
    -0.0014417421928463233
  ],
  "input_reduced_polarization": [
    -1.6029378011140913e-15,
    2.67003790131194e-16,
    -0.2788162846186034
  ],
  "input_formal_targets": [
    {
      "orbit_id": 0,
      "representative_formal_class": [
        0.0,
        0.0,
        0.5
      ],
      "target_reduced_polarization": [
        0.0,
        0.0,
        -0.5
      ]
    },
    {
      "orbit_id": 1,
      "representative_formal_class": [
        0.0,
        0.0,
        0.0
      ],
      "target_reduced_polarization": [
        0.0,
        0.0,
        0.0
      ]
    },
    {
      "orbit_id": 2,
      "representative_formal_class": [
        0.5,
        0.0,
        0.5
      ],
      "target_reduced_polarization": [
        -0.5,
        0.0,
        -0.5
      ]
    },
    {
      "orbit_id": 3,
      "representative_formal_class": [
        0.0,
        0.5,
        0.5
      ],
      "target_reduced_polarization": [
        0.0,
        0.5,
        -0.5
      ]
    },
    {
      "orbit_id": 4,
      "representative_formal_class": [
        0.5,
        0.0,
        0.0
      ],
      "target_reduced_polarization": [
        -0.5,
        0.0,
        0.0
      ]
    },
    {
      "orbit_id": 5,
      "representative_formal_class": [
        0.0,
        0.5,
        0.0
      ],
      "target_reduced_polarization": [
        0.0,
        0.5,
        0.0
      ]
    },
    {
      "orbit_id": 6,
      "representative_formal_class": [
        0.5,
        0.5,
        0.5
      ],
      "target_reduced_polarization": [
        -0.5,
        0.5,
        -0.5
      ]
    },
    {
      "orbit_id": 7,
      "representative_formal_class": [
        0.5,
        0.5,
        0.0
      ],
      "target_reduced_polarization": [
        -0.5,
        0.5,
        0.0
      ]
    }
  ],
  "parent_candidates": [
    {
      "candidate_id": "inversion_parent_endpoint_00",
      "source": "same_species_inversion_center_projection_from_endpoint",
      "spacegroup": "Cmme",
      "spacegroup_number": 67,
      "pointgroup": "mmm",
      "has_inversion": true,
      "is_polar_point_group": false,
      "nonpolar_parent_hypothesis": true,
      "symmetry_tolerance_A": null,
      "target_reduced_polarization": [
        0.0,
        0.0,
        0.0
      ],
      "formal_class": [
        0.0,
        0.0,
        0.0
      ],
      "target_residual": 5.011703985351939e-15,
      "parent_symmetrization_rmsd_A": 0.4787782668622278,
      "parent_cell_rmsd_A": 0.0,
      "energy_eV": -334.43678718523915,
      "reduced_polarization": [
        -3.487505781477929e-15,
        -2.663957846769711e-15,
        2.4202910675339478e-15
      ],
      "cartesian_polarization_e_A2": [
        -3.760655371360588e-17,
        -4.1127126451282355e-17,
        1.2515179146748941e-17
      ],
      "ranking_score": 0.47877826686223784
    },
    {
      "candidate_id": "bec_projection_00",
      "source": "MACEField_BEC_backprojection",
      "spacegroup": "Aem2",
      "spacegroup_number": 39,
      "pointgroup": "mm2",
      "has_inversion": false,
      "is_polar_point_group": true,
      "nonpolar_parent_hypothesis": false,
      "symmetry_tolerance_A": null,
      "target_reduced_polarization": [
        0.0,
        0.0,
        -0.5
      ],
      "formal_class": [
        0.0,
        0.0,
        0.5
      ],
      "target_residual": 0.0009794263358408606,
      "parent_symmetrization_rmsd_A": 0.009841438188828653,
      "parent_cell_rmsd_A": 0.00733508804633528,
      "energy_eV": -352.5007679800771,
      "reduced_polarization": [
        -8.289933932708443e-15,
        1.7334126103078185e-15,
        -0.49902057366415914
      ],
      "cartesian_polarization_e_A2": [
        -9.183928914304165e-17,
        2.849024799903405e-17,
        -0.002578306801828229
      ],
      "ranking_score": 0.5136340628720942
    },
    {
      "candidate_id": "inversion_parent_bec_00_00",
      "source": "same_species_inversion_center_projection_after_BEC",
      "spacegroup": "Cmme",
      "spacegroup_number": 67,
      "pointgroup": "mmm",
      "has_inversion": true,
      "is_polar_point_group": false,
      "nonpolar_parent_hypothesis": true,
      "symmetry_tolerance_A": null,
      "target_reduced_polarization": [
        0.0,
        0.0,
        -0.5
      ],
      "formal_class": [
        0.0,
        0.0,
        0.5
      ],
      "target_residual": 0.49999999999999395,
      "parent_symmetrization_rmsd_A": 0.4787801359097722,
      "parent_cell_rmsd_A": 0.00733508804633528,
      "energy_eV": -334.4262219336804,
      "reduced_polarization": [
        -6.295729593474674e-16,
        2.0966122559063956e-15,
        -6.0718286174098014e-15
      ],
      "cartesian_polarization_e_A2": [
        -6.785178327904214e-18,
        3.2316285174166113e-17,
        -3.1371526245606933e-17
      ],
      "ranking_score": 1.4806139079213438
    },
    {
      "candidate_id": "bec_projection_01",
      "source": "MACEField_BEC_backprojection",
      "spacegroup": "Aem2",
      "spacegroup_number": 39,
      "pointgroup": "mm2",
      "has_inversion": false,
      "is_polar_point_group": true,
      "nonpolar_parent_hypothesis": false,
      "symmetry_tolerance_A": null,
      "target_reduced_polarization": [
        0.0,
        0.0,
        0.0
      ],
      "formal_class": [
        0.0,
        0.0,
        0.0
      ],
      "target_residual": 4.904161649218956e-07,
      "parent_symmetrization_rmsd_A": 0.012359785215009977,
      "parent_cell_rmsd_A": 0.009181105032830676,
      "energy_eV": -352.4435474673455,
      "reduced_polarization": [
        9.774526796943916e-16,
        6.066327916671676e-16,
        -4.904161649218956e-07
      ],
      "cartesian_polarization_e_A2": [
        1.0547199344908376e-17,
        9.384298069917752e-18,
        -2.5385011178528744e-09
      ],
      "ranking_score": 0.5146560423055475
    },
    {
      "candidate_id": "bec_projection_02",
      "source": "MACEField_BEC_backprojection",
      "spacegroup": "Cm",
      "spacegroup_number": 8,
      "pointgroup": "m",
      "has_inversion": false,
      "is_polar_point_group": true,
      "nonpolar_parent_hypothesis": false,
      "symmetry_tolerance_A": null,
      "target_reduced_polarization": [
        -0.5,
        0.0,
        -0.5
      ],
      "formal_class": [
        0.5,
        0.0,
        0.5
      ],
      "target_residual": 0.0003773105773901517,
      "parent_symmetrization_rmsd_A": 0.04844346788896739,
      "parent_cell_rmsd_A": 0.054529446310991415,
      "energy_eV": -351.6175867283112,
      "reduced_polarization": [
        -0.49995381360772545,
        -2.4507304419878603e-15,
        -0.4996255269182182
      ],
      "cartesian_polarization_e_A2": [
        -0.005415411441349214,
        -1.978782437019264e-17,
        -0.002638524825664926
      ],
      "ranking_score": 0.5628304506214955
    },
    {
      "candidate_id": "bec_projection_03",
      "source": "MACEField_BEC_backprojection",
      "spacegroup": "Pc",
      "spacegroup_number": 7,
      "pointgroup": "m",
      "has_inversion": false,
      "is_polar_point_group": true,
      "nonpolar_parent_hypothesis": false,
      "symmetry_tolerance_A": null,
      "target_reduced_polarization": [
        0.0,
        0.5,
        -0.5
      ],
      "formal_class": [
        0.0,
        0.5,
        0.5
      ],
      "target_residual": 0.0002258893358407032,
      "parent_symmetrization_rmsd_A": 0.07018576300158423,
      "parent_cell_rmsd_A": 0.0349004427068818,
      "energy_eV": -351.522146593411,
      "reduced_polarization": [
        -4.37612553176271e-15,
        0.4999517654182189,
        -0.4997793205556311
      ],
      "cartesian_polarization_e_A2": [
        -1.2811678898563437e-16,
        0.007715980685867954,
        -0.0026180812166305702
      ],
      "ranking_score": 0.5793626523499861
    },
    {
      "candidate_id": "bec_projection_04",
      "source": "MACEField_BEC_backprojection",
      "spacegroup": "Cm",
      "spacegroup_number": 8,
      "pointgroup": "m",
      "has_inversion": false,
      "is_polar_point_group": true,
      "nonpolar_parent_hypothesis": false,
      "symmetry_tolerance_A": null,
      "target_reduced_polarization": [
        -0.5,
        0.0,
        0.0
      ],
      "formal_class": [
        0.5,
        0.0,
        0.0
      ],
      "target_residual": 5.0666223002306134e-05,
      "parent_symmetrization_rmsd_A": 0.04802771169641122,
      "parent_cell_rmsd_A": 0.05315877129107055,
      "energy_eV": -351.52264937285554,
      "reduced_polarization": [
        -0.5000035709544514,
        1.380889523353372e-15,
        5.05402259356419e-05
      ],
      "cartesian_polarization_e_A2": [
        -0.005395041279225837,
        -3.164716955935569e-17,
        -5.640459117455313e-05
      ],
      "ranking_score": 0.5614187369651835
    },
    {
      "candidate_id": "bec_projection_05",
      "source": "MACEField_BEC_backprojection",
      "spacegroup": "Pc",
      "spacegroup_number": 7,
      "pointgroup": "m",
      "has_inversion": false,
      "is_polar_point_group": true,
      "nonpolar_parent_hypothesis": false,
      "symmetry_tolerance_A": null,
      "target_reduced_polarization": [
        0.0,
        0.5,
        0.0
      ],
      "formal_class": [
        0.0,
        0.5,
        0.0
      ],
      "target_residual": 9.638614967106377e-05,
      "parent_symmetrization_rmsd_A": 0.06982747848556507,
      "parent_cell_rmsd_A": 0.03452977533522648,
      "energy_eV": -351.42527718189365,
      "reduced_polarization": [
        -2.1000592403173092e-15,
        0.49997738284620385,
        9.369500628408233e-05
      ],
      "cartesian_polarization_e_A2": [
        -1.370934705405523e-17,
        0.007732510153770194,
        -3.559346706600285e-05
      ],
      "ranking_score": 0.5786526946187138
    },
    {
      "candidate_id": "bec_projection_06",
      "source": "MACEField_BEC_backprojection",
      "spacegroup": "P1",
      "spacegroup_number": 1,
      "pointgroup": "1",
      "has_inversion": false,
      "is_polar_point_group": true,
      "nonpolar_parent_hypothesis": false,
      "symmetry_tolerance_A": null,
      "target_reduced_polarization": [
        -0.5,
        0.5,
        -0.5
      ],
      "formal_class": [
        0.5,
        0.5,
        0.5
      ],
      "target_residual": 1.6761324670156365e-05,
      "parent_symmetrization_rmsd_A": 0.08564735390970277,
      "parent_cell_rmsd_A": 0.06535234010817832,
      "energy_eV": -350.5287600074477,
      "reduced_polarization": [
        -0.4999979932083992,
        0.4999973032393865,
        -0.4999835792121272
      ],
      "cartesian_polarization_e_A2": [
        -0.005416017071398478,
        0.007714273502499402,
        -0.0026775950311543105
      ],
      "ranking_score": 0.6020189615860877
    },
    {
      "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,
        0.0
      ],
      "formal_class": [
        0.5,
        0.5,
        0.0
      ],
      "target_residual": 0.0006518197965369221,
      "parent_symmetrization_rmsd_A": 0.08477336343560918,
      "parent_cell_rmsd_A": 0.06368347437733735,
      "energy_eV": -350.3895818863999,
      "reduced_polarization": [
        -0.4999704821777565,
        0.4999063958479822,
        0.0006443880880746195
      ],
      "cartesian_polarization_e_A2": [
        -0.005394394038062008,
        0.0077292201133817235,
        -9.069880639192134e-05
      ],
      "ranking_score": 0.6019978716230173
    }
  ],
  "formal_branches": [
    {
      "orbit_id": 0,
      "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": [
              -1.6029378011140913e-15,
              2.67003790131194e-16,
              -0.2788162846186034
            ],
            "branch_aligned_reduced_polarization": [
              -1.6029378011140913e-15,
              2.67003790131194e-16,
              -0.2788162846186034
            ],
            "target_residual": 0.22118371538139658,
            "energy_eV": -352.4973868404428,
            "max_atomic_step_A": 0.008904916486917791,
            "max_log_strain_component": 0.0009413376588588231,
            "step_scale": 1.0,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 3.5040048223629934,
            "cell_principal_stretches": [
              1.000941780856208,
              1.0006654116325209,
              0.9998722416500364
            ],
            "cell_volume_ratio": 1.0014798553983792,
            "cell_rmsd_from_input_A": 0.00733508804633528
          },
          {
            "iteration": 1,
            "reduced_polarization": [
              -8.289933932708443e-15,
              1.7334126103078185e-15,
              -0.49902057366415914
            ],
            "branch_aligned_reduced_polarization": [
              -8.289933932708443e-15,
              1.7334126103078185e-15,
              -0.49902057366415914
            ],
            "target_residual": 0.0009794263358408606,
            "energy_eV": -352.5007679800771
          }
        ],
        "iterations": 1
      },
      "parent": {
        "candidate_id": "bec_projection_00",
        "source": "MACEField_BEC_backprojection",
        "spacegroup": "Aem2",
        "spacegroup_number": 39,
        "pointgroup": "mm2",
        "has_inversion": false,
        "is_polar_point_group": true,
        "nonpolar_parent_hypothesis": false,
        "symmetry_tolerance_A": null,
        "target_reduced_polarization": [
          0.0,
          0.0,
          -0.5
        ],
        "formal_class": [
          0.0,
          0.0,
          0.5
        ],
        "target_residual": 0.0009794263358408606,
        "parent_symmetrization_rmsd_A": 0.009841438188828653,
        "parent_cell_rmsd_A": 0.00733508804633528,
        "energy_eV": -352.5007679800771,
        "reduced_polarization": [
          -8.289933932708443e-15,
          1.7334126103078185e-15,
          -0.49902057366415914
        ],
        "cartesian_polarization_e_A2": [
          -9.183928914304165e-17,
          2.849024799903405e-17,
          -0.002578306801828229
        ],
        "ranking_score": 0.5136340628720942
      },
      "branch_status": "awaiting_branch_sampling"
    },
    {
      "orbit_id": 1,
      "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": [
              -1.6029378011140913e-15,
              2.67003790131194e-16,
              -0.2788162846186034
            ],
            "branch_aligned_reduced_polarization": [
              -1.6029378011140913e-15,
              2.67003790131194e-16,
              -0.2788162846186034
            ],
            "target_residual": 0.2788162846186034,
            "energy_eV": -352.4973868404428,
            "max_atomic_step_A": 0.011225219385794787,
            "max_log_strain_component": 0.0011866166013262771,
            "step_scale": 1.0,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 3.5040048223629934,
            "cell_principal_stretches": [
              1.000161070867776,
              0.9991618362870754,
              0.9988140871497645
            ],
            "cell_volume_ratio": 0.9981376624340679,
            "cell_rmsd_from_input_A": 0.009228397632344697
          },
          {
            "iteration": 1,
            "reduced_polarization": [
              1.306479911984491e-14,
              -3.3963253552173885e-15,
              0.001456634807623038
            ],
            "branch_aligned_reduced_polarization": [
              1.306479911984491e-14,
              -3.3963253552173885e-15,
              0.001456634807623038
            ],
            "target_residual": 0.001456634807623038,
            "energy_eV": -352.44312281149996,
            "max_atomic_step_A": 5.8421477368854314e-05,
            "max_log_strain_component": 6.08759202775246e-06,
            "step_scale": 1.0,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 3.5040048223629934,
            "cell_principal_stretches": [
              1.0001602444742406,
              0.999166134449414,
              0.9988201675409463
            ],
            "cell_volume_ratio": 0.9981472077599166,
            "cell_rmsd_from_input_A": 0.009181105032830676
          },
          {
            "iteration": 2,
            "reduced_polarization": [
              9.774526796943916e-16,
              6.066327916671676e-16,
              -4.904161649218956e-07
            ],
            "branch_aligned_reduced_polarization": [
              9.774526796943916e-16,
              6.066327916671676e-16,
              -4.904161649218956e-07
            ],
            "target_residual": 4.904161649218956e-07,
            "energy_eV": -352.4435474673455
          }
        ],
        "iterations": 2
      },
      "parent": {
        "candidate_id": "inversion_parent_endpoint_00",
        "source": "same_species_inversion_center_projection_from_endpoint",
        "spacegroup": "Cmme",
        "spacegroup_number": 67,
        "pointgroup": "mmm",
        "has_inversion": true,
        "is_polar_point_group": false,
        "nonpolar_parent_hypothesis": true,
        "symmetry_tolerance_A": null,
        "target_reduced_polarization": [
          0.0,
          0.0,
          0.0
        ],
        "formal_class": [
          0.0,
          0.0,
          0.0
        ],
        "target_residual": 5.011703985351939e-15,
        "parent_symmetrization_rmsd_A": 0.4787782668622278,
        "parent_cell_rmsd_A": 0.0,
        "energy_eV": -334.43678718523915,
        "reduced_polarization": [
          -3.487505781477929e-15,
          -2.663957846769711e-15,
          2.4202910675339478e-15
        ],
        "cartesian_polarization_e_A2": [
          -3.760655371360588e-17,
          -4.1127126451282355e-17,
          1.2515179146748941e-17
        ],
        "ranking_score": 0.47877826686223784
      },
      "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": [
          -352.4973868404428,
          -351.4274815275081,
          -349.29001263086354,
          -346.3578403099269,
          -343.00179142865386,
          -339.70170995598403,
          -336.9316771335561,
          -335.08533473355396,
          -334.43678718523915
        ],
        "cartesian_polarizations_e_A2": [
          [
            1.5519162805032688e-18,
            1.4209624059295897e-17,
            -0.0014417421928463149
          ],
          [
            -5.033420362767305e-18,
            1.0786712654406012e-17,
            -0.0012168287603146544
          ],
          [
            1.6187375248513244e-17,
            1.2644750988777002e-17,
            -0.0009062828251845359
          ],
          [
            2.9713102985357574e-18,
            1.573731415149071e-17,
            -0.0005555400397987228
          ],
          [
            1.07406272622805e-17,
            3.9197503744843235e-17,
            -0.00026002850984684474
          ],
          [
            3.308425326664372e-17,
            3.540890885370069e-17,
            -0.00012514368519653236
          ],
          [
            2.229292514090905e-17,
            5.4446782954181344e-17,
            -0.00014952237701111227
          ],
          [
            2.414088874645132e-17,
            1.9858877676463565e-17,
            -0.00014161905680562534
          ],
          [
            -5.7092001288990164e-18,
            1.3121684314342862e-17,
            3.268155925433906e-17
          ]
        ],
        "raw_reduced_polarization": [
          [
            1.4391951578021683e-16,
            9.204105119585539e-16,
            -0.2788162846186018
          ],
          [
            -4.667825387416111e-16,
            6.9869573432498e-16,
            -0.23532062504059373
          ],
          [
            1.5011629408019386e-15,
            8.190478286126709e-16,
            -0.17526462871475224
          ],
          [
            2.755493609870259e-16,
            1.0193647146878773e-15,
            -0.10743502591663502
          ],
          [
            9.960497832150615e-16,
            2.53896896488873e-15,
            -0.05028650986989395
          ],
          [
            3.068122791096264e-15,
            2.2935674997402663e-15,
            -0.024201343016182684
          ],
          [
            2.0673711796900598e-15,
            3.5267218305167105e-15,
            -0.02891590038249238
          ],
          [
            2.238745132415693e-15,
            1.2863338039656651e-15,
            -0.027387489556493973
          ],
          [
            -5.294520898878909e-16,
            8.499405844324136e-16,
            6.320236011715878e-15
          ]
        ],
        "unwrapped_reduced_polarization": [
          [
            1.4391951578021683e-16,
            9.204105119585539e-16,
            -0.2788162846186018
          ],
          [
            -4.667825387416111e-16,
            6.9869573432498e-16,
            -0.23532062504059373
          ],
          [
            1.5011629408019386e-15,
            8.190478286126709e-16,
            -0.17526462871475224
          ],
          [
            2.7554936098702595e-16,
            1.0193647146878773e-15,
            -0.10743502591663502
          ],
          [
            9.960497832150615e-16,
            2.53896896488873e-15,
            -0.05028650986989395
          ],
          [
            3.068122791096264e-15,
            2.2935674997402663e-15,
            -0.024201343016182684
          ],
          [
            2.0673711796900598e-15,
            3.5267218305167105e-15,
            -0.02891590038249238
          ],
          [
            2.238745132415693e-15,
            1.2863338039656651e-15,
            -0.027387489556493973
          ],
          [
            -5.29452089887891e-16,
            8.499405844324136e-16,
            6.321332346459485e-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": [
          [
            1.1102230246251565e-16,
            8.881784197001252e-16,
            -0.2788162846186018
          ],
          [
            -4.440892098500626e-16,
            6.661338147750939e-16,
            -0.2353206250405937
          ],
          [
            1.5543122344752192e-15,
            7.771561172376096e-16,
            -0.17526462871475224
          ],
          [
            2.220446049250313e-16,
            9.992007221626409e-16,
            -0.10743502591663501
          ],
          [
            9.992007221626409e-16,
            2.55351295663786e-15,
            -0.05028650986989397
          ],
          [
            3.1086244689504383e-15,
            2.3314683517128287e-15,
            -0.024201343016182708
          ],
          [
            2.1094237467877974e-15,
            3.552713678800501e-15,
            -0.028915900382492365
          ],
          [
            2.220446049250313e-15,
            1.3322676295501878e-15,
            -0.02738748955649395
          ],
          [
            -5.551115123125783e-16,
            8.881784197001252e-16,
            6.328271240363392e-15
          ]
        ]
      },
      "reflected": {
        "reached": true,
        "construction": "reflect_displacements_about_reconstructed_parent",
        "energies_eV": [
          -334.43678718523915,
          -335.0853347335539,
          -336.93167713355626,
          -339.7017099559839,
          -343.00179142865386,
          -346.3578403099269,
          -349.29001263086377,
          -351.427481527508,
          -352.49738684044297
        ],
        "cartesian_polarizations_e_A2": [
          [
            -5.49197057552538e-18,
            -1.7638246233523697e-19,
            3.092902049480663e-17
          ],
          [
            1.1587986879677899e-17,
            2.516327336080929e-17,
            0.00014161905680565198
          ],
          [
            4.731833561900309e-17,
            4.1022499350440214e-17,
            0.00014952237701116707
          ],
          [
            2.4165232392760568e-17,
            3.793476624989122e-17,
            0.00012514368519663712
          ],
          [
            3.4697469940981607e-17,
            3.665730114621507e-17,
            0.00026002850984689835
          ],
          [
            -1.814290448934751e-17,
            5.9010089672562e-17,
            0.0005555400397987617
          ],
          [
            2.837577809929077e-17,
            3.4697032712867965e-17,
            0.0009062828251846734
          ],
          [
            9.47165415170082e-17,
            3.9410059636053534e-17,
            0.0012168287603146364
          ],
          [
            6.773832463212485e-17,
            6.702892391790189e-17,
            0.0014417421928463526
          ]
        ],
        "raw_reduced_polarization": [
          [
            -5.093069489885712e-16,
            -1.142495197487513e-17,
            5.981315261523884e-15
          ],
          [
            1.0746310748476205e-15,
            1.6299193574670228e-15,
            0.027387489556499126
          ],
          [
            4.3881438936927025e-15,
            2.657180758012894e-15,
            0.02891590038250298
          ],
          [
            2.2410026806050936e-15,
            2.457176733134526e-15,
            0.02420134301620294
          ],
          [
            3.2177270999987963e-15,
            2.3744305390637153e-15,
            0.05028650986990432
          ],
          [
            -1.6825121701196795e-15,
            3.822304279099574e-15,
            0.10743502591664256
          ],
          [
            2.6314745809693228e-15,
            2.247456618797833e-15,
            0.17526462871477883
          ],
          [
            8.783694689435222e-15,
            2.552737005185383e-15,
            0.23532062504059026
          ],
          [
            6.281825252620649e-15,
            4.341714173567239e-15,
            0.2788162846186091
          ]
        ],
        "unwrapped_reduced_polarization": [
          [
            -5.093069489885712e-16,
            -1.142495197487513e-17,
            5.981315261523884e-15
          ],
          [
            1.0746310748476205e-15,
            1.6299193574670228e-15,
            0.027387489556499126
          ],
          [
            4.3881438936927025e-15,
            2.657180758012894e-15,
            0.02891590038250298
          ],
          [
            2.2410026806050936e-15,
            2.457176733134526e-15,
            0.02420134301620294
          ],
          [
            3.2177270999987963e-15,
            2.3744305390637153e-15,
            0.05028650986990432
          ],
          [
            -1.682512170119679e-15,
            3.822304279099574e-15,
            0.10743502591664256
          ],
          [
            2.6314745809693224e-15,
            2.247456618797833e-15,
            0.17526462871477883
          ],
          [
            8.783694689435222e-15,
            2.552737005185383e-15,
            0.23532062504059026
          ],
          [
            6.281825252620649e-15,
            4.341714173567239e-15,
            0.2788162846186091
          ]
        ],
        "gauge_integer_shift": [
          0,
          0,
          0
        ],
        "expected_opposite_endpoint_reduced_polarization": [
          -1.2028236955559986e-15,
          7.794706569062734e-16,
          0.2788162846186144
        ],
        "actual_opposite_endpoint_branch_residual": 9.854366612694664e-15
      },
      "pnp_branch": {
        "construction": "incoming_path_concatenated_with_parent_reflection",
        "reduced_polarization": [
          [
            1.4391951578021683e-16,
            9.204105119585539e-16,
            -0.2788162846186018
          ],
          [
            -4.667825387416111e-16,
            6.9869573432498e-16,
            -0.23532062504059373
          ],
          [
            1.5011629408019386e-15,
            8.190478286126709e-16,
            -0.17526462871475224
          ],
          [
            2.755493609870259e-16,
            1.0193647146878773e-15,
            -0.10743502591663502
          ],
          [
            9.960497832150615e-16,
            2.53896896488873e-15,
            -0.05028650986989395
          ],
          [
            3.068122791096264e-15,
            2.2935674997402663e-15,
            -0.024201343016182684
          ],
          [
            2.0673711796900598e-15,
            3.5267218305167105e-15,
            -0.02891590038249238
          ],
          [
            2.238745132415693e-15,
            1.2863338039656651e-15,
            -0.027387489556493973
          ],
          [
            -5.294520898878909e-16,
            8.499405844324136e-16,
            6.320236011715878e-15
          ],
          [
            1.0746310748476205e-15,
            1.6299193574670228e-15,
            0.027387489556499126
          ],
          [
            4.3881438936927025e-15,
            2.657180758012894e-15,
            0.02891590038250298
          ],
          [
            2.2410026806050936e-15,
            2.457176733134526e-15,
            0.02420134301620294
          ],
          [
            3.2177270999987963e-15,
            2.3744305390637153e-15,
            0.05028650986990432
          ],
          [
            -1.6825121701196795e-15,
            3.822304279099574e-15,
            0.10743502591664256
          ],
          [
            2.6314745809693228e-15,
            2.247456618797833e-15,
            0.17526462871477883
          ],
          [
            8.783694689435222e-15,
            2.552737005185383e-15,
            0.23532062504059026
          ],
          [
            6.281825252620649e-15,
            4.341714173567239e-15,
            0.2788162846186091
          ]
        ],
        "unwrapped_reduced_polarization": [
          [
            1.4391951578021683e-16,
            9.204105119585539e-16,
            -0.2788162846186018
          ],
          [
            -4.667825387416111e-16,
            6.9869573432498e-16,
            -0.23532062504059373
          ],
          [
            1.5011629408019386e-15,
            8.190478286126709e-16,
            -0.17526462871475224
          ],
          [
            2.7554936098702595e-16,
            1.0193647146878773e-15,
            -0.10743502591663502
          ],
          [
            9.960497832150615e-16,
            2.53896896488873e-15,
            -0.05028650986989395
          ],
          [
            3.068122791096264e-15,
            2.2935674997402663e-15,
            -0.024201343016182684
          ],
          [
            2.0673711796900598e-15,
            3.5267218305167105e-15,
            -0.02891590038249238
          ],
          [
            2.238745132415693e-15,
            1.2863338039656651e-15,
            -0.027387489556493973
          ],
          [
            -5.29452089887891e-16,
            8.499405844324136e-16,
            6.321332346459485e-15
          ],
          [
            1.0746310748476205e-15,
            1.6299193574670228e-15,
            0.027387489556499126
          ],
          [
            4.3881438936927025e-15,
            2.657180758012894e-15,
            0.02891590038250298
          ],
          [
            2.2410026806050936e-15,
            2.457176733134526e-15,
            0.02420134301620294
          ],
          [
            3.2177270999987963e-15,
            2.3744305390637153e-15,
            0.05028650986990432
          ],
          [
            -1.682512170119679e-15,
            3.822304279099574e-15,
            0.10743502591664256
          ],
          [
            2.6314745809693224e-15,
            2.247456618797833e-15,
            0.17526462871477883
          ],
          [
            8.783694689435222e-15,
            2.552737005185383e-15,
            0.23532062504059026
          ],
          [
            6.281825252620649e-15,
            4.341714173567239e-15,
            0.2788162846186091
          ]
        ],
        "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": [
          [
            1.1102230246251565e-16,
            8.881784197001252e-16,
            -0.2788162846186018
          ],
          [
            -4.440892098500626e-16,
            6.661338147750939e-16,
            -0.2353206250405937
          ],
          [
            1.5543122344752192e-15,
            7.771561172376096e-16,
            -0.17526462871475224
          ],
          [
            2.220446049250313e-16,
            9.992007221626409e-16,
            -0.10743502591663501
          ],
          [
            9.992007221626409e-16,
            2.55351295663786e-15,
            -0.05028650986989397
          ],
          [
            3.1086244689504383e-15,
            2.3314683517128287e-15,
            -0.024201343016182708
          ],
          [
            2.1094237467877974e-15,
            3.552713678800501e-15,
            -0.028915900382492365
          ],
          [
            2.220446049250313e-15,
            1.3322676295501878e-15,
            -0.02738748955649395
          ],
          [
            -5.551115123125783e-16,
            8.881784197001252e-16,
            6.328271240363392e-15
          ],
          [
            1.1102230246251565e-15,
            1.6653345369377348e-15,
            0.027387489556499167
          ],
          [
            4.440892098500626e-15,
            2.6645352591003757e-15,
            0.028915900382503024
          ],
          [
            2.220446049250313e-15,
            2.4424906541753444e-15,
            0.024201343016202914
          ],
          [
            3.219646771412954e-15,
            2.3314683517128287e-15,
            0.05028650986990435
          ],
          [
            -1.6653345369377348e-15,
            3.774758283725532e-15,
            0.10743502591664256
          ],
          [
            2.6645352591003757e-15,
            2.220446049250313e-15,
            0.17526462871477877
          ],
          [
            8.770761894538737e-15,
            2.55351295663786e-15,
            0.23532062504059026
          ],
          [
            6.328271240363392e-15,
            4.3298697960381105e-15,
            0.2788162846186091
          ]
        ]
      },
      "incoming_structure_ids": [
        "incoming_01_000",
        "incoming_01_001",
        "incoming_01_002",
        "incoming_01_003",
        "incoming_01_004",
        "incoming_01_005",
        "incoming_01_006",
        "incoming_01_007",
        "incoming_01_008"
      ],
      "reflected_structure_ids": [
        "reflected_01_001",
        "reflected_01_002",
        "reflected_01_003",
        "reflected_01_004",
        "reflected_01_005",
        "reflected_01_006",
        "reflected_01_007",
        "reflected_01_008"
      ]
    },
    {
      "orbit_id": 2,
      "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": [
              -1.6029378011140913e-15,
              2.67003790131194e-16,
              -0.2788162846186034
            ],
            "branch_aligned_reduced_polarization": [
              -1.609823385706477e-15,
              2.67003790131194e-16,
              -0.2788162846186034
            ],
            "target_residual": 0.5467378128041969,
            "energy_eV": -352.4973868404428,
            "max_atomic_step_A": 0.04563410081904152,
            "max_log_strain_component": 0.01050340589906462,
            "step_scale": 1.0,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 3.5040048223629934,
            "cell_principal_stretches": [
              1.0113717496954413,
              0.9998722416500531,
              0.9903458539970289
            ],
            "cell_volume_ratio": 1.0014798553983315,
            "cell_rmsd_from_input_A": 0.0534971687447802
          },
          {
            "iteration": 1,
            "reduced_polarization": [
              -0.49459381682407183,
              1.5669900489456064e-15,
              -0.45503780964558976
            ],
            "branch_aligned_reduced_polarization": [
              -0.49459381682407183,
              1.5669900489456064e-15,
              -0.45503780964558976
            ],
            "target_residual": 0.045286039548606036,
            "energy_eV": -351.63669739770205,
            "max_atomic_step_A": 0.001954352945974247,
            "max_log_strain_component": 0.00020058537294248988,
            "step_scale": 1.0,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 3.5040048223629934,
            "cell_principal_stretches": [
              1.0116983730379359,
              0.9998450203122592,
              0.9903650956905733
            ],
            "cell_volume_ratio": 1.0017954740084123,
            "cell_rmsd_from_input_A": 0.054529446310991415
          },
          {
            "iteration": 2,
            "reduced_polarization": [
              -0.49995381360772545,
              -2.4507304419878603e-15,
              -0.4996255269182182
            ],
            "branch_aligned_reduced_polarization": [
              -0.49995381360772545,
              -2.4507304419878603e-15,
              -0.4996255269182182
            ],
            "target_residual": 0.0003773105773901517,
            "energy_eV": -351.6175867283112
          }
        ],
        "iterations": 2
      },
      "parent": {
        "candidate_id": "bec_projection_02",
        "source": "MACEField_BEC_backprojection",
        "spacegroup": "Cm",
        "spacegroup_number": 8,
        "pointgroup": "m",
        "has_inversion": false,
        "is_polar_point_group": true,
        "nonpolar_parent_hypothesis": false,
        "symmetry_tolerance_A": null,
        "target_reduced_polarization": [
          -0.5,
          0.0,
          -0.5
        ],
        "formal_class": [
          0.5,
          0.0,
          0.5
        ],
        "target_residual": 0.0003773105773901517,
        "parent_symmetrization_rmsd_A": 0.04844346788896739,
        "parent_cell_rmsd_A": 0.054529446310991415,
        "energy_eV": -351.6175867283112,
        "reduced_polarization": [
          -0.49995381360772545,
          -2.4507304419878603e-15,
          -0.4996255269182182
        ],
        "cartesian_polarization_e_A2": [
          -0.005415411441349214,
          -1.978782437019264e-17,
          -0.002638524825664926
        ],
        "ranking_score": 0.5628304506214955
      },
      "branch_status": "awaiting_branch_sampling"
    },
    {
      "orbit_id": 3,
      "formal_class": [
        0.0,
        0.5,
        0.5
      ],
      "formal_classes_in_orbit": [
        [
          0.0,
          0.5,
          0.5
        ]
      ],
      "target_reduced_polarization": [
        0.0,
        0.5,
        -0.5
      ],
      "bec_backprojection": {
        "converged_to_target": true,
        "history": [
          {
            "iteration": 0,
            "reduced_polarization": [
              -1.6029378011140913e-15,
              2.67003790131194e-16,
              -0.2788162846186034
            ],
            "branch_aligned_reduced_polarization": [
              -1.6029378011140913e-15,
              2.7755575615628914e-16,
              -0.2788162846186034
            ],
            "target_residual": 0.5467378128041981,
            "energy_eV": -352.4973868404428,
            "max_atomic_step_A": 0.06536388095406163,
            "max_log_strain_component": 0.00463762978739014,
            "step_scale": 1.0,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 3.5040048223629934,
            "cell_principal_stretches": [
              1.0049353977894857,
              1.000941780856176,
              0.9956237689223517
            ],
            "cell_volume_ratio": 1.0014798553983326,
            "cell_rmsd_from_input_A": 0.03416648954901973
          },
          {
            "iteration": 1,
            "reduced_polarization": [
              5.258048052025887e-15,
              0.49445633482024426,
              -0.4613236255499701
            ],
            "branch_aligned_reduced_polarization": [
              5.258048052025887e-15,
              0.49445633482024426,
              -0.4613236255499701
            ],
            "target_residual": 0.03907165422943036,
            "energy_eV": -351.544351065899,
            "max_atomic_step_A": 0.0018923467516828115,
            "max_log_strain_component": 0.00017262141628124407,
            "step_scale": 1.0,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 3.5040048223629934,
            "cell_principal_stretches": [
              1.0050519536337974,
              1.001114579757969,
              0.9956064207966054
            ],
            "cell_volume_ratio": 1.001751467101374,
            "cell_rmsd_from_input_A": 0.0349004427068818
          },
          {
            "iteration": 2,
            "reduced_polarization": [
              -4.37612553176271e-15,
              0.4999517654182189,
              -0.4997793205556311
            ],
            "branch_aligned_reduced_polarization": [
              -4.37612553176271e-15,
              0.4999517654182189,
              -0.4997793205556311
            ],
            "target_residual": 0.0002258893358407032,
            "energy_eV": -351.522146593411
          }
        ],
        "iterations": 2
      },
      "parent": {
        "candidate_id": "bec_projection_03",
        "source": "MACEField_BEC_backprojection",
        "spacegroup": "Pc",
        "spacegroup_number": 7,
        "pointgroup": "m",
        "has_inversion": false,
        "is_polar_point_group": true,
        "nonpolar_parent_hypothesis": false,
        "symmetry_tolerance_A": null,
        "target_reduced_polarization": [
          0.0,
          0.5,
          -0.5
        ],
        "formal_class": [
          0.0,
          0.5,
          0.5
        ],
        "target_residual": 0.0002258893358407032,
        "parent_symmetrization_rmsd_A": 0.07018576300158423,
        "parent_cell_rmsd_A": 0.0349004427068818,
        "energy_eV": -351.522146593411,
        "reduced_polarization": [
          -4.37612553176271e-15,
          0.4999517654182189,
          -0.4997793205556311
        ],
        "cartesian_polarization_e_A2": [
          -1.2811678898563437e-16,
          0.007715980685867954,
          -0.0026180812166305702
        ],
        "ranking_score": 0.5793626523499861
      },
      "branch_status": "awaiting_branch_sampling"
    },
    {
      "orbit_id": 4,
      "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": [
              -1.6029378011140913e-15,
              2.67003790131194e-16,
              -0.2788162846186034
            ],
            "branch_aligned_reduced_polarization": [
              -1.609823385706477e-15,
              2.67003790131194e-16,
              -0.2788162846186034
            ],
            "target_residual": 0.5724845155709632,
            "energy_eV": -352.4973868404428,
            "max_atomic_step_A": 0.04643559246498764,
            "max_log_strain_component": 0.010503405899062356,
            "step_scale": 1.0,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 3.5040048223629934,
            "cell_principal_stretches": [
              1.0095374765977638,
              1.0001610708677924,
              0.9885486577369756
            ],
            "cell_volume_ratio": 0.9981376624340199,
            "cell_rmsd_from_input_A": 0.05335110846332614
          },
          {
            "iteration": 1,
            "reduced_polarization": [
              -0.5013887888383681,
              -1.4408527507425286e-15,
              0.04315639476503253
            ],
            "branch_aligned_reduced_polarization": [
              -0.5013887888383681,
              -1.4408527507425286e-15,
              0.04315639476503253
            ],
            "target_residual": 0.04317873485354687,
            "energy_eV": -351.50130964121877,
            "max_atomic_step_A": 0.0018025631738835147,
            "max_log_strain_component": 0.00018102013487393252,
            "step_scale": 1.0,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 3.5040048223629934,
            "cell_principal_stretches": [
              1.0096920965774192,
              1.0001364975894373,
              0.9887026751131381
            ],
            "cell_volume_ratio": 0.9984215404605588,
            "cell_rmsd_from_input_A": 0.05315877129107055
          },
          {
            "iteration": 2,
            "reduced_polarization": [
              -0.5000035709544514,
              1.380889523353372e-15,
              5.05402259356419e-05
            ],
            "branch_aligned_reduced_polarization": [
              -0.5000035709544514,
              1.380889523353372e-15,
              5.05402259356419e-05
            ],
            "target_residual": 5.0666223002306134e-05,
            "energy_eV": -351.52264937285554
          }
        ],
        "iterations": 2
      },
      "parent": {
        "candidate_id": "bec_projection_04",
        "source": "MACEField_BEC_backprojection",
        "spacegroup": "Cm",
        "spacegroup_number": 8,
        "pointgroup": "m",
        "has_inversion": false,
        "is_polar_point_group": true,
        "nonpolar_parent_hypothesis": false,
        "symmetry_tolerance_A": null,
        "target_reduced_polarization": [
          -0.5,
          0.0,
          0.0
        ],
        "formal_class": [
          0.5,
          0.0,
          0.0
        ],
        "target_residual": 5.0666223002306134e-05,
        "parent_symmetrization_rmsd_A": 0.04802771169641122,
        "parent_cell_rmsd_A": 0.05315877129107055,
        "energy_eV": -351.52264937285554,
        "reduced_polarization": [
          -0.5000035709544514,
          1.380889523353372e-15,
          5.05402259356419e-05
        ],
        "cartesian_polarization_e_A2": [
          -0.005395041279225837,
          -3.164716955935569e-17,
          -5.640459117455313e-05
        ],
        "ranking_score": 0.5614187369651835
      },
      "branch_status": "awaiting_branch_sampling"
    },
    {
      "orbit_id": 5,
      "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": [
              -1.6029378011140913e-15,
              2.67003790131194e-16,
              -0.2788162846186034
            ],
            "branch_aligned_reduced_polarization": [
              -1.6029378011140913e-15,
              2.7755575615628914e-16,
              -0.2788162846186034
            ],
            "target_residual": 0.5724845155709645,
            "energy_eV": -352.4973868404428,
            "max_atomic_step_A": 0.06631382168027049,
            "max_log_strain_component": 0.00463762978738858,
            "step_scale": 1.0,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 3.5040048223629934,
            "cell_principal_stretches": [
              1.0043351234031201,
              0.9988140871497326,
              0.995009284117181
            ],
            "cell_volume_ratio": 0.9981376624340211,
            "cell_rmsd_from_input_A": 0.03462199375688278
          },
          {
            "iteration": 1,
            "reduced_polarization": [
              2.2262726747628086e-14,
              0.49743610730880544,
              0.036397840348372526
            ],
            "branch_aligned_reduced_polarization": [
              2.2262726747628086e-14,
              0.49743610730880544,
              0.036397840348372526
            ],
            "target_residual": 0.03648802992431321,
            "energy_eV": -351.42179560222627,
            "max_atomic_step_A": 0.0015955318454104522,
            "max_log_strain_component": 0.00015513441621370328,
            "step_scale": 1.0,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 3.5040048223629934,
            "cell_principal_stretches": [
              1.004402943598112,
              0.9989690496097433,
              0.9950302227129446
            ],
            "cell_volume_ratio": 0.9983809412080173,
            "cell_rmsd_from_input_A": 0.03452977533522648
          },
          {
            "iteration": 2,
            "reduced_polarization": [
              -2.1000592403173092e-15,
              0.49997738284620385,
              9.369500628408233e-05
            ],
            "branch_aligned_reduced_polarization": [
              -2.1000592403173092e-15,
              0.49997738284620385,
              9.369500628408233e-05
            ],
            "target_residual": 9.638614967106377e-05,
            "energy_eV": -351.42527718189365
          }
        ],
        "iterations": 2
      },
      "parent": {
        "candidate_id": "bec_projection_05",
        "source": "MACEField_BEC_backprojection",
        "spacegroup": "Pc",
        "spacegroup_number": 7,
        "pointgroup": "m",
        "has_inversion": false,
        "is_polar_point_group": true,
        "nonpolar_parent_hypothesis": false,
        "symmetry_tolerance_A": null,
        "target_reduced_polarization": [
          0.0,
          0.5,
          0.0
        ],
        "formal_class": [
          0.0,
          0.5,
          0.0
        ],
        "target_residual": 9.638614967106377e-05,
        "parent_symmetrization_rmsd_A": 0.06982747848556507,
        "parent_cell_rmsd_A": 0.03452977533522648,
        "energy_eV": -351.42527718189365,
        "reduced_polarization": [
          -2.1000592403173092e-15,
          0.49997738284620385,
          9.369500628408233e-05
        ],
        "cartesian_polarization_e_A2": [
          -1.370934705405523e-17,
          0.007732510153770194,
          -3.559346706600285e-05
        ],
        "ranking_score": 0.5786526946187138
      },
      "branch_status": "awaiting_branch_sampling"
    },
    {
      "orbit_id": 6,
      "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": [
              -1.6029378011140913e-15,
              2.67003790131194e-16,
              -0.2788162846186034
            ],
            "branch_aligned_reduced_polarization": [
              -1.609823385706477e-15,
              2.7755575615628914e-16,
              -0.2788162846186034
            ],
            "target_residual": 0.7408928640160578,
            "energy_eV": -352.4973868404428,
            "max_atomic_step_A": 0.08092372821140277,
            "max_log_strain_component": 0.01050340589906666,
            "step_scale": 1.0,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 3.5040048223629934,
            "cell_principal_stretches": [
              1.0122790776181247,
              1.0000473901951508,
              0.9892848913541687
            ],
            "cell_volume_ratio": 1.0014798553982844,
            "cell_rmsd_from_input_A": 0.0630577977710383
          },
          {
            "iteration": 1,
            "reduced_polarization": [
              -0.48879052614393237,
              0.48993998194540767,
              -0.41912707233493174
            ],
            "branch_aligned_reduced_polarization": [
              -0.48879052614393237,
              0.48993998194540767,
              -0.41912707233493174
            ],
            "target_residual": 0.08226351984025453,
            "energy_eV": -350.61281304222666,
            "max_atomic_step_A": 0.004063649851073673,
            "max_log_strain_component": 0.00037229850723593573,
            "step_scale": 1.0,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 3.5040048223629934,
            "cell_principal_stretches": [
              1.0129162884897902,
              1.0000647931913016,
              0.9892237197521182
            ],
            "cell_volume_ratio": 1.00206574152811,
            "cell_rmsd_from_input_A": 0.0653160629649788
          },
          {
            "iteration": 2,
            "reduced_polarization": [
              -0.49983364129300617,
              0.49981320036097066,
              -0.498812088466833
            ],
            "branch_aligned_reduced_polarization": [
              -0.49983364129300617,
              0.49981320036097066,
              -0.498812088466833
            ],
            "target_residual": 0.001213961751936739,
            "energy_eV": -350.5302115570646,
            "max_atomic_step_A": 6.277056044858157e-05,
            "max_log_strain_component": 5.548826023864841e-06,
            "step_scale": 1.0,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 3.5040048223629934,
            "cell_principal_stretches": [
              1.0129260226483783,
              1.0000650785723988,
              0.9892225538391498
            ],
            "cell_volume_ratio": 1.0020744763069867,
            "cell_rmsd_from_input_A": 0.06535234010817832
          },
          {
            "iteration": 3,
            "reduced_polarization": [
              -0.4999979932083992,
              0.4999973032393865,
              -0.4999835792121272
            ],
            "branch_aligned_reduced_polarization": [
              -0.4999979932083992,
              0.4999973032393865,
              -0.4999835792121272
            ],
            "target_residual": 1.6761324670156365e-05,
            "energy_eV": -350.5287600074477
          }
        ],
        "iterations": 3
      },
      "parent": {
        "candidate_id": "bec_projection_06",
        "source": "MACEField_BEC_backprojection",
        "spacegroup": "P1",
        "spacegroup_number": 1,
        "pointgroup": "1",
        "has_inversion": false,
        "is_polar_point_group": true,
        "nonpolar_parent_hypothesis": false,
        "symmetry_tolerance_A": null,
        "target_reduced_polarization": [
          -0.5,
          0.5,
          -0.5
        ],
        "formal_class": [
          0.5,
          0.5,
          0.5
        ],
        "target_residual": 1.6761324670156365e-05,
        "parent_symmetrization_rmsd_A": 0.08564735390970277,
        "parent_cell_rmsd_A": 0.06535234010817832,
        "energy_eV": -350.5287600074477,
        "reduced_polarization": [
          -0.4999979932083992,
          0.4999973032393865,
          -0.4999835792121272
        ],
        "cartesian_polarization_e_A2": [
          -0.005416017071398478,
          0.007714273502499402,
          -0.0026775950311543105
        ],
        "ranking_score": 0.6020189615860877
      },
      "branch_status": "awaiting_branch_sampling"
    },
    {
      "orbit_id": 7,
      "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": [
              -1.6029378011140913e-15,
              2.67003790131194e-16,
              -0.2788162846186034
            ],
            "branch_aligned_reduced_polarization": [
              -1.609823385706477e-15,
              2.7755575615628914e-16,
              -0.2788162846186034
            ],
            "target_residual": 0.7600911264897915,
            "energy_eV": -352.4973868404428,
            "max_atomic_step_A": 0.08111716040983355,
            "max_log_strain_component": 0.010503405899064396,
            "step_scale": 1.0,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 3.5040048223629934,
            "cell_principal_stretches": [
              1.0106470997890893,
              0.9999397181138626,
              0.9876818880601937
            ],
            "cell_volume_ratio": 0.9981376624339731,
            "cell_rmsd_from_input_A": 0.06293369195052621
          },
          {
            "iteration": 1,
            "reduced_polarization": [
              -0.49502731792672267,
              0.4927805502305387,
              0.0757945066829823
            ],
            "branch_aligned_reduced_polarization": [
              -0.49502731792672267,
              0.4927805502305387,
              0.0757945066829823
            ],
            "target_residual": 0.07629977238034408,
            "energy_eV": -350.406985496675,
            "max_atomic_step_A": 0.0035646692030328673,
            "max_log_strain_component": 0.00033074057036406055,
            "step_scale": 1.0,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 3.5040048223629934,
            "cell_principal_stretches": [
              1.0110832517677564,
              0.9999565180960392,
              0.9877523127158571
            ],
            "cell_volume_ratio": 0.9986563949121992,
            "cell_rmsd_from_input_A": 0.06368347437733735
          },
          {
            "iteration": 2,
            "reduced_polarization": [
              -0.4999704821777565,
              0.4999063958479822,
              0.0006443880880746195
            ],
            "branch_aligned_reduced_polarization": [
              -0.4999704821777565,
              0.4999063958479822,
              0.0006443880880746195
            ],
            "target_residual": 0.0006518197965369221,
            "energy_eV": -350.3895818863999
          }
        ],
        "iterations": 2
      },
      "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,
          0.0
        ],
        "formal_class": [
          0.5,
          0.5,
          0.0
        ],
        "target_residual": 0.0006518197965369221,
        "parent_symmetrization_rmsd_A": 0.08477336343560918,
        "parent_cell_rmsd_A": 0.06368347437733735,
        "energy_eV": -350.3895818863999,
        "reduced_polarization": [
          -0.4999704821777565,
          0.4999063958479822,
          0.0006443880880746195
        ],
        "cartesian_polarization_e_A2": [
          -0.005394394038062008,
          0.0077292201133817235,
          -9.069880639192134e-05
        ],
        "ranking_score": 0.6019978716230173
      },
      "branch_status": "awaiting_branch_sampling"
    }
  ],
  "sampled_polarization_branches": [
    {
      "orbit_id": 1,
      "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,
          56,
          57,
          58,
          59,
          60,
          61,
          62,
          63
        ],
        "endpoint_rmsd_A": 0.4787782668622278,
        "minimum_distance_A_by_image": [
          1.7208264139247806,
          1.6808029479950772,
          1.6453286052841543,
          1.6147032405347108,
          1.5892072101742833,
          1.5690905725917157,
          1.554562176103647,
          1.545779596190107,
          1.5428409596821158
        ],
        "minimum_distance_A": 1.5428409596821158,
        "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": [
          1077.8056469832316,
          1077.8056469832316,
          1077.8056469832316,
          1077.8056469832316,
          1077.8056469832316,
          1077.8056469832316,
          1077.8056469832316,
          1077.8056469832316,
          1077.8056469832316
        ],
        "cell_deformation_log_strain_norm": 0.0
      },
      "parent_reduced_polarization": [
        -5.294520898878909e-16,
        8.499405844324136e-16,
        6.320236011715878e-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": [
          -352.4973868404428,
          -351.4274815275081,
          -349.29001263086354,
          -346.3578403099269,
          -343.00179142865386,
          -339.70170995598403,
          -336.9316771335561,
          -335.08533473355396,
          -334.43678718523915
        ],
        "cartesian_polarizations_e_A2": [
          [
            1.5519162805032688e-18,
            1.4209624059295897e-17,
            -0.0014417421928463149
          ],
          [
            -5.033420362767305e-18,
            1.0786712654406012e-17,
            -0.0012168287603146544
          ],
          [
            1.6187375248513244e-17,
            1.2644750988777002e-17,
            -0.0009062828251845359
          ],
          [
            2.9713102985357574e-18,
            1.573731415149071e-17,
            -0.0005555400397987228
          ],
          [
            1.07406272622805e-17,
            3.9197503744843235e-17,
            -0.00026002850984684474
          ],
          [
            3.308425326664372e-17,
            3.540890885370069e-17,
            -0.00012514368519653236
          ],
          [
            2.229292514090905e-17,
            5.4446782954181344e-17,
            -0.00014952237701111227
          ],
          [
            2.414088874645132e-17,
            1.9858877676463565e-17,
            -0.00014161905680562534
          ],
          [
            -5.7092001288990164e-18,
            1.3121684314342862e-17,
            3.268155925433906e-17
          ]
        ],
        "raw_reduced_polarization": [
          [
            1.4391951578021683e-16,
            9.204105119585539e-16,
            -0.2788162846186018
          ],
          [
            -4.667825387416111e-16,
            6.9869573432498e-16,
            -0.23532062504059373
          ],
          [
            1.5011629408019386e-15,
            8.190478286126709e-16,
            -0.17526462871475224
          ],
          [
            2.755493609870259e-16,
            1.0193647146878773e-15,
            -0.10743502591663502
          ],
          [
            9.960497832150615e-16,
            2.53896896488873e-15,
            -0.05028650986989395
          ],
          [
            3.068122791096264e-15,
            2.2935674997402663e-15,
            -0.024201343016182684
          ],
          [
            2.0673711796900598e-15,
            3.5267218305167105e-15,
            -0.02891590038249238
          ],
          [
            2.238745132415693e-15,
            1.2863338039656651e-15,
            -0.027387489556493973
          ],
          [
            -5.294520898878909e-16,
            8.499405844324136e-16,
            6.320236011715878e-15
          ]
        ],
        "unwrapped_reduced_polarization": [
          [
            1.4391951578021683e-16,
            9.204105119585539e-16,
            -0.2788162846186018
          ],
          [
            -4.667825387416111e-16,
            6.9869573432498e-16,
            -0.23532062504059373
          ],
          [
            1.5011629408019386e-15,
            8.190478286126709e-16,
            -0.17526462871475224
          ],
          [
            2.7554936098702595e-16,
            1.0193647146878773e-15,
            -0.10743502591663502
          ],
          [
            9.960497832150615e-16,
            2.53896896488873e-15,
            -0.05028650986989395
          ],
          [
            3.068122791096264e-15,
            2.2935674997402663e-15,
            -0.024201343016182684
          ],
          [
            2.0673711796900598e-15,
            3.5267218305167105e-15,
            -0.02891590038249238
          ],
          [
            2.238745132415693e-15,
            1.2863338039656651e-15,
            -0.027387489556493973
          ],
          [
            -5.29452089887891e-16,
            8.499405844324136e-16,
            6.321332346459485e-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": [
          [
            1.1102230246251565e-16,
            8.881784197001252e-16,
            -0.2788162846186018
          ],
          [
            -4.440892098500626e-16,
            6.661338147750939e-16,
            -0.2353206250405937
          ],
          [
            1.5543122344752192e-15,
            7.771561172376096e-16,
            -0.17526462871475224
          ],
          [
            2.220446049250313e-16,
            9.992007221626409e-16,
            -0.10743502591663501
          ],
          [
            9.992007221626409e-16,
            2.55351295663786e-15,
            -0.05028650986989397
          ],
          [
            3.1086244689504383e-15,
            2.3314683517128287e-15,
            -0.024201343016182708
          ],
          [
            2.1094237467877974e-15,
            3.552713678800501e-15,
            -0.028915900382492365
          ],
          [
            2.220446049250313e-15,
            1.3322676295501878e-15,
            -0.02738748955649395
          ],
          [
            -5.551115123125783e-16,
            8.881784197001252e-16,
            6.328271240363392e-15
          ]
        ]
      },
      "reflected": {
        "reached": true,
        "construction": "reflect_displacements_about_reconstructed_parent",
        "energies_eV": [
          -334.43678718523915,
          -335.0853347335539,
          -336.93167713355626,
          -339.7017099559839,
          -343.00179142865386,
          -346.3578403099269,
          -349.29001263086377,
          -351.427481527508,
          -352.49738684044297
        ],
        "cartesian_polarizations_e_A2": [
          [
            -5.49197057552538e-18,
            -1.7638246233523697e-19,
            3.092902049480663e-17
          ],
          [
            1.1587986879677899e-17,
            2.516327336080929e-17,
            0.00014161905680565198
          ],
          [
            4.731833561900309e-17,
            4.1022499350440214e-17,
            0.00014952237701116707
          ],
          [
            2.4165232392760568e-17,
            3.793476624989122e-17,
            0.00012514368519663712
          ],
          [
            3.4697469940981607e-17,
            3.665730114621507e-17,
            0.00026002850984689835
          ],
          [
            -1.814290448934751e-17,
            5.9010089672562e-17,
            0.0005555400397987617
          ],
          [
            2.837577809929077e-17,
            3.4697032712867965e-17,
            0.0009062828251846734
          ],
          [
            9.47165415170082e-17,
            3.9410059636053534e-17,
            0.0012168287603146364
          ],
          [
            6.773832463212485e-17,
            6.702892391790189e-17,
            0.0014417421928463526
          ]
        ],
        "raw_reduced_polarization": [
          [
            -5.093069489885712e-16,
            -1.142495197487513e-17,
            5.981315261523884e-15
          ],
          [
            1.0746310748476205e-15,
            1.6299193574670228e-15,
            0.027387489556499126
          ],
          [
            4.3881438936927025e-15,
            2.657180758012894e-15,
            0.02891590038250298
          ],
          [
            2.2410026806050936e-15,
            2.457176733134526e-15,
            0.02420134301620294
          ],
          [
            3.2177270999987963e-15,
            2.3744305390637153e-15,
            0.05028650986990432
          ],
          [
            -1.6825121701196795e-15,
            3.822304279099574e-15,
            0.10743502591664256
          ],
          [
            2.6314745809693228e-15,
            2.247456618797833e-15,
            0.17526462871477883
          ],
          [
            8.783694689435222e-15,
            2.552737005185383e-15,
            0.23532062504059026
          ],
          [
            6.281825252620649e-15,
            4.341714173567239e-15,
            0.2788162846186091
          ]
        ],
        "unwrapped_reduced_polarization": [
          [
            -5.093069489885712e-16,
            -1.142495197487513e-17,
            5.981315261523884e-15
          ],
          [
            1.0746310748476205e-15,
            1.6299193574670228e-15,
            0.027387489556499126
          ],
          [
            4.3881438936927025e-15,
            2.657180758012894e-15,
            0.02891590038250298
          ],
          [
            2.2410026806050936e-15,
            2.457176733134526e-15,
            0.02420134301620294
          ],
          [
            3.2177270999987963e-15,
            2.3744305390637153e-15,
            0.05028650986990432
          ],
          [
            -1.682512170119679e-15,
            3.822304279099574e-15,
            0.10743502591664256
          ],
          [
            2.6314745809693224e-15,
            2.247456618797833e-15,
            0.17526462871477883
          ],
          [
            8.783694689435222e-15,
            2.552737005185383e-15,
            0.23532062504059026
          ],
          [
            6.281825252620649e-15,
            4.341714173567239e-15,
            0.2788162846186091
          ]
        ],
        "gauge_integer_shift": [
          0,
          0,
          0
        ],
        "expected_opposite_endpoint_reduced_polarization": [
          -1.2028236955559986e-15,
          7.794706569062734e-16,
          0.2788162846186144
        ],
        "actual_opposite_endpoint_branch_residual": 9.854366612694664e-15
      },
      "pnp_branch": {
        "construction": "incoming_path_concatenated_with_parent_reflection",
        "reduced_polarization": [
          [
            1.4391951578021683e-16,
            9.204105119585539e-16,
            -0.2788162846186018
          ],
          [
            -4.667825387416111e-16,
            6.9869573432498e-16,
            -0.23532062504059373
          ],
          [
            1.5011629408019386e-15,
            8.190478286126709e-16,
            -0.17526462871475224
          ],
          [
            2.755493609870259e-16,
            1.0193647146878773e-15,
            -0.10743502591663502
          ],
          [
            9.960497832150615e-16,
            2.53896896488873e-15,
            -0.05028650986989395
          ],
          [
            3.068122791096264e-15,
            2.2935674997402663e-15,
            -0.024201343016182684
          ],
          [
            2.0673711796900598e-15,
            3.5267218305167105e-15,
            -0.02891590038249238
          ],
          [
            2.238745132415693e-15,
            1.2863338039656651e-15,
            -0.027387489556493973
          ],
          [
            -5.294520898878909e-16,
            8.499405844324136e-16,
            6.320236011715878e-15
          ],
          [
            1.0746310748476205e-15,
            1.6299193574670228e-15,
            0.027387489556499126
          ],
          [
            4.3881438936927025e-15,
            2.657180758012894e-15,
            0.02891590038250298
          ],
          [
            2.2410026806050936e-15,
            2.457176733134526e-15,
            0.02420134301620294
          ],
          [
            3.2177270999987963e-15,
            2.3744305390637153e-15,
            0.05028650986990432
          ],
          [
            -1.6825121701196795e-15,
            3.822304279099574e-15,
            0.10743502591664256
          ],
          [
            2.6314745809693228e-15,
            2.247456618797833e-15,
            0.17526462871477883
          ],
          [
            8.783694689435222e-15,
            2.552737005185383e-15,
            0.23532062504059026
          ],
          [
            6.281825252620649e-15,
            4.341714173567239e-15,
            0.2788162846186091
          ]
        ],
        "unwrapped_reduced_polarization": [
          [
            1.4391951578021683e-16,
            9.204105119585539e-16,
            -0.2788162846186018
          ],
          [
            -4.667825387416111e-16,
            6.9869573432498e-16,
            -0.23532062504059373
          ],
          [
            1.5011629408019386e-15,
            8.190478286126709e-16,
            -0.17526462871475224
          ],
          [
            2.7554936098702595e-16,
            1.0193647146878773e-15,
            -0.10743502591663502
          ],
          [
            9.960497832150615e-16,
            2.53896896488873e-15,
            -0.05028650986989395
          ],
          [
            3.068122791096264e-15,
            2.2935674997402663e-15,
            -0.024201343016182684
          ],
          [
            2.0673711796900598e-15,
            3.5267218305167105e-15,
            -0.02891590038249238
          ],
          [
            2.238745132415693e-15,
            1.2863338039656651e-15,
            -0.027387489556493973
          ],
          [
            -5.29452089887891e-16,
            8.499405844324136e-16,
            6.321332346459485e-15
          ],
          [
            1.0746310748476205e-15,
            1.6299193574670228e-15,
            0.027387489556499126
          ],
          [
            4.3881438936927025e-15,
            2.657180758012894e-15,
            0.02891590038250298
          ],
          [
            2.2410026806050936e-15,
            2.457176733134526e-15,
            0.02420134301620294
          ],
          [
            3.2177270999987963e-15,
            2.3744305390637153e-15,
            0.05028650986990432
          ],
          [
            -1.682512170119679e-15,
            3.822304279099574e-15,
            0.10743502591664256
          ],
          [
            2.6314745809693224e-15,
            2.247456618797833e-15,
            0.17526462871477883
          ],
          [
            8.783694689435222e-15,
            2.552737005185383e-15,
            0.23532062504059026
          ],
          [
            6.281825252620649e-15,
            4.341714173567239e-15,
            0.2788162846186091
          ]
        ],
        "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": [
          [
            1.1102230246251565e-16,
            8.881784197001252e-16,
            -0.2788162846186018
          ],
          [
            -4.440892098500626e-16,
            6.661338147750939e-16,
            -0.2353206250405937
          ],
          [
            1.5543122344752192e-15,
            7.771561172376096e-16,
            -0.17526462871475224
          ],
          [
            2.220446049250313e-16,
            9.992007221626409e-16,
            -0.10743502591663501
          ],
          [
            9.992007221626409e-16,
            2.55351295663786e-15,
            -0.05028650986989397
          ],
          [
            3.1086244689504383e-15,
            2.3314683517128287e-15,
            -0.024201343016182708
          ],
          [
            2.1094237467877974e-15,
            3.552713678800501e-15,
            -0.028915900382492365
          ],
          [
            2.220446049250313e-15,
            1.3322676295501878e-15,
            -0.02738748955649395
          ],
          [
            -5.551115123125783e-16,
            8.881784197001252e-16,
            6.328271240363392e-15
          ],
          [
            1.1102230246251565e-15,
            1.6653345369377348e-15,
            0.027387489556499167
          ],
          [
            4.440892098500626e-15,
            2.6645352591003757e-15,
            0.028915900382503024
          ],
          [
            2.220446049250313e-15,
            2.4424906541753444e-15,
            0.024201343016202914
          ],
          [
            3.219646771412954e-15,
            2.3314683517128287e-15,
            0.05028650986990435
          ],
          [
            -1.6653345369377348e-15,
            3.774758283725532e-15,
            0.10743502591664256
          ],
          [
            2.6645352591003757e-15,
            2.220446049250313e-15,
            0.17526462871477877
          ],
          [
            8.770761894538737e-15,
            2.55351295663786e-15,
            0.23532062504059026
          ],
          [
            6.328271240363392e-15,
            4.3298697960381105e-15,
            0.2788162846186091
          ]
        ]
      },
      "incoming_structure_ids": [
        "incoming_01_000",
        "incoming_01_001",
        "incoming_01_002",
        "incoming_01_003",
        "incoming_01_004",
        "incoming_01_005",
        "incoming_01_006",
        "incoming_01_007",
        "incoming_01_008"
      ],
      "reflected_structure_ids": [
        "reflected_01_001",
        "reflected_01_002",
        "reflected_01_003",
        "reflected_01_004",
        "reflected_01_005",
        "reflected_01_006",
        "reflected_01_007",
        "reflected_01_008"
      ],
      "positive_extension_structure_ids": [
        "extension_plus_01_000",
        "extension_plus_01_001",
        "extension_plus_01_002",
        "extension_plus_01_003"
      ],
      "negative_extension_structure_ids": [
        "extension_minus_01_000",
        "extension_minus_01_001",
        "extension_minus_01_002",
        "extension_minus_01_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": "Cmme",
        "spacegroup_number": 67,
        "pointgroup": "mmm",
        "has_inversion": true,
        "is_polar_point_group": false,
        "nonpolar_parent_hypothesis": true,
        "symmetry_tolerance_A": null,
        "target_reduced_polarization": [
          0.0,
          0.0,
          0.0
        ],
        "formal_class": [
          0.0,
          0.0,
          0.0
        ],
        "target_residual": 5.011703985351939e-15,
        "parent_symmetrization_rmsd_A": 0.4787782668622278,
        "parent_cell_rmsd_A": 0.0,
        "energy_eV": -334.43678718523915,
        "reduced_polarization": [
          -3.487505781477929e-15,
          -2.663957846769711e-15,
          2.4202910675339478e-15
        ],
        "cartesian_polarization_e_A2": [
          -3.760655371360588e-17,
          -4.1127126451282355e-17,
          1.2515179146748941e-17
        ],
        "ranking_score": 0.47877826686223784
      }
    }
  ],
  "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": 49,
      "full_response": 17,
      "energy_polarization": 32
    },
    "model_evaluations_for_recovery_and_path_properties": {
      "total": 74,
      "full_response": 42,
      "energy_polarization": 32
    },
    "elapsed_seconds": 1405.647257723962
  }
}
