{
  "schema": "ferrofinder.endpoint_parent_recovery.v4_variable_cell",
  "status": "complete",
  "input_atom_count": 20,
  "input_formula": "Br12Ge4Rb4",
  "input_spacegroup": "Pna2_1",
  "input_pointgroup": "mm2",
  "input_is_polar_point_group": true,
  "input_energy_eV": -63.1994507889346,
  "input_cartesian_polarization_e_A2": [
    4.513919888372915e-17,
    -2.6605223183125126e-17,
    -0.006090243506090867
  ],
  "input_reduced_polarization": [
    4.006761362331097e-15,
    -2.5392506845499547e-15,
    -0.3966276683525275
  ],
  "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": "Pnma",
      "spacegroup_number": 62,
      "pointgroup": "mmm",
      "has_inversion": true,
      "is_polar_point_group": false,
      "nonpolar_parent_hypothesis": true,
      "symmetry_tolerance_A": null,
      "target_reduced_polarization": [
        0.0,
        0.0,
        0.0
      ],
      "formal_class": [
        0.0,
        0.0,
        0.0
      ],
      "target_residual": 1.130345762600744e-15,
      "parent_symmetrization_rmsd_A": 0.20906010232059521,
      "parent_cell_rmsd_A": 0.0,
      "energy_eV": -62.238962623759996,
      "reduced_polarization": [
        -6.583958033300684e-16,
        -8.577103786998092e-16,
        -3.2943802976802943e-16
      ],
      "cartesian_polarization_e_A2": [
        -7.417326968890924e-18,
        -8.986736201603362e-18,
        -5.058542259010624e-18
      ],
      "ranking_score": 0.20906010232059746
    },
    {
      "candidate_id": "bec_projection_00",
      "source": "MACEField_BEC_backprojection",
      "spacegroup": "Pna2_1",
      "spacegroup_number": 33,
      "pointgroup": "mm2",
      "has_inversion": false,
      "is_polar_point_group": true,
      "nonpolar_parent_hypothesis": false,
      "symmetry_tolerance_A": null,
      "target_reduced_polarization": [
        0.0,
        0.0,
        -0.5
      ],
      "formal_class": [
        0.0,
        0.0,
        0.5
      ],
      "target_residual": 0.00011414028192374692,
      "parent_symmetrization_rmsd_A": 0.030410746110512754,
      "parent_cell_rmsd_A": 0.09656256065727122,
      "energy_eV": -63.252572805867516,
      "reduced_polarization": [
        -3.885647378195166e-15,
        2.952636520072984e-15,
        -0.49988585971807625
      ],
      "cartesian_polarization_e_A2": [
        -3.381789368788934e-16,
        -1.2250128676509179e-17,
        -0.007662104909373379
      ],
      "ranking_score": 0.5547796668386781
    },
    {
      "candidate_id": "inversion_parent_bec_00_00",
      "source": "same_species_inversion_center_projection_after_BEC",
      "spacegroup": "Pnma",
      "spacegroup_number": 62,
      "pointgroup": "mmm",
      "has_inversion": true,
      "is_polar_point_group": false,
      "nonpolar_parent_hypothesis": true,
      "symmetry_tolerance_A": null,
      "target_reduced_polarization": [
        0.0,
        0.0,
        -0.5
      ],
      "formal_class": [
        0.0,
        0.0,
        0.5
      ],
      "target_residual": 0.49999999999999994,
      "parent_symmetrization_rmsd_A": 0.20909103591078343,
      "parent_cell_rmsd_A": 0.09656256065727122,
      "energy_eV": -62.3416034300149,
      "reduced_polarization": [
        -7.131165854997823e-16,
        -2.815706822247964e-15,
        -3.719421789152856e-17
      ],
      "cartesian_polarization_e_A2": [
        -8.113354454211079e-18,
        -2.9777235859822314e-17,
        -5.701021422529271e-19
      ],
      "ranking_score": 1.2332316760751012
    },
    {
      "candidate_id": "bec_projection_01",
      "source": "MACEField_BEC_backprojection",
      "spacegroup": "Pna2_1",
      "spacegroup_number": 33,
      "pointgroup": "mm2",
      "has_inversion": false,
      "is_polar_point_group": true,
      "nonpolar_parent_hypothesis": false,
      "symmetry_tolerance_A": null,
      "target_reduced_polarization": [
        0.0,
        0.0,
        0.0
      ],
      "formal_class": [
        0.0,
        0.0,
        0.0
      ],
      "target_residual": 0.00040798262422558077,
      "parent_symmetrization_rmsd_A": 0.10344604692197899,
      "parent_cell_rmsd_A": 0.3510687116379058,
      "energy_eV": -62.57088147002476,
      "reduced_polarization": [
        -1.7155742040593142e-15,
        4.2763481935016526e-16,
        -0.00040798262422558077
      ],
      "cartesian_polarization_e_A2": [
        -1.783899421212705e-17,
        4.4597485530317626e-18,
        -6.303477330709555e-06
      ],
      "ranking_score": 0.6920291900799066
    },
    {
      "candidate_id": "bec_projection_02",
      "source": "MACEField_BEC_backprojection",
      "spacegroup": "Pc",
      "spacegroup_number": 7,
      "pointgroup": "m",
      "has_inversion": false,
      "is_polar_point_group": true,
      "nonpolar_parent_hypothesis": false,
      "symmetry_tolerance_A": null,
      "target_reduced_polarization": [
        0.5,
        0.0,
        -0.5
      ],
      "formal_class": [
        0.5,
        0.0,
        0.5
      ],
      "target_residual": 0.00012577738972490834,
      "parent_symmetrization_rmsd_A": 0.1443893945306966,
      "parent_cell_rmsd_A": 0.18653668629432443,
      "energy_eV": -62.846476427592606,
      "reduced_polarization": [
        0.49987755345092916,
        -1.3111744250646516e-15,
        -0.49997124596747144
      ],
      "cartesian_polarization_e_A2": [
        0.005592045677159222,
        -3.2015381598487883e-16,
        -0.007577346419915142
      ],
      "ranking_score": 0.6912751208837276
    },
    {
      "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": 2.441491171324116e-05,
      "parent_symmetrization_rmsd_A": 0.1353304662687817,
      "parent_cell_rmsd_A": 0.09904932293474611,
      "energy_eV": -62.900029626031035,
      "reduced_polarization": [
        2.7455193718934407e-15,
        -0.4999796763042359,
        -0.4999864709459143
      ],
      "cartesian_polarization_e_A2": [
        -2.6995350649436844e-16,
        -0.005257086053196212,
        -0.0076444785234853554
      ],
      "ranking_score": 0.6601416268258947
    },
    {
      "candidate_id": "bec_projection_04",
      "source": "MACEField_BEC_backprojection",
      "spacegroup": "Pc",
      "spacegroup_number": 7,
      "pointgroup": "m",
      "has_inversion": false,
      "is_polar_point_group": true,
      "nonpolar_parent_hypothesis": false,
      "symmetry_tolerance_A": null,
      "target_reduced_polarization": [
        0.5,
        0.0,
        0.0
      ],
      "formal_class": [
        0.5,
        0.0,
        0.0
      ],
      "target_residual": 0.000876383475656722,
      "parent_symmetrization_rmsd_A": 0.1730338842544026,
      "parent_cell_rmsd_A": 0.3985806169684423,
      "energy_eV": -62.07187327272956,
      "reduced_polarization": [
        0.49998392468829816,
        -4.598189051635025e-15,
        -0.0008762360302782835
      ],
      "cartesian_polarization_e_A2": [
        0.005433884299753871,
        -1.5261574523144903e-16,
        6.552311268511564e-05
      ],
      "ranking_score": 0.7744318054478266
    },
    {
      "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": 0.0007699737454353256,
      "parent_symmetrization_rmsd_A": 0.1786226122286941,
      "parent_cell_rmsd_A": 0.3842127900871302,
      "energy_eV": -62.044339431525586,
      "reduced_polarization": [
        5.4857095807986284e-15,
        -0.49994636301806095,
        -0.0007681032761472726
      ],
      "cartesian_polarization_e_A2": [
        -3.190502855520819e-16,
        -0.005058141018690511,
        9.368400668202884e-06
      ],
      "ranking_score": 0.7762157572413473
    },
    {
      "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": 1.171283930817288e-05,
      "parent_symmetrization_rmsd_A": 0.20562737240781448,
      "parent_cell_rmsd_A": 0.19336374216069288,
      "energy_eV": -62.84418589454948,
      "reduced_polarization": [
        0.49999241253705623,
        -0.49999116118050085,
        -0.49999877677451077
      ],
      "cartesian_polarization_e_A2": [
        0.005578442374851817,
        -0.005266125950260644,
        -0.0075502838164652
      ],
      "ranking_score": 0.753991733626604
    },
    {
      "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": 6.595629070249473e-06,
      "parent_symmetrization_rmsd_A": 0.22652250559766554,
      "parent_cell_rmsd_A": 0.4229879612319614,
      "energy_eV": -62.016527215762785,
      "reduced_polarization": [
        0.4999992261656645,
        -0.5000017315067342,
        -6.317071131694728e-06
      ],
      "cartesian_polarization_e_A2": [
        0.005423445010889588,
        -0.005054502600680677,
        0.00010279788750652914
      ],
      "ranking_score": 0.8322826871637964
    }
  ],
  "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": [
              4.006761362331097e-15,
              -2.5392506845499547e-15,
              -0.3966276683525275
            ],
            "branch_aligned_reduced_polarization": [
              4.006761362331097e-15,
              -2.5392506845499547e-15,
              -0.3966276683525275
            ],
            "target_residual": 0.1033723316474725,
            "energy_eV": -63.1994507889346,
            "max_atomic_step_A": 0.03475949990105544,
            "max_log_strain_component": 0.00970435433974727,
            "step_scale": 1.0,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 2.0969912693991226,
            "cell_principal_stretches": [
              1.001087798714353,
              1.0005665259360192,
              0.9903425809585382
            ],
            "cell_volume_ratio": 0.9919815394171762,
            "cell_rmsd_from_input_A": 0.0896135888649868
          },
          {
            "iteration": 1,
            "reduced_polarization": [
              -1.5120488857042156e-14,
              -6.727189462288288e-16,
              -0.49371079110238913
            ],
            "branch_aligned_reduced_polarization": [
              -1.5120488857042156e-14,
              -6.727189462288288e-16,
              -0.49371079110238913
            ],
            "target_residual": 0.006289208897610865,
            "energy_eV": -63.252320765566274,
            "max_atomic_step_A": 0.0022506250830834347,
            "max_log_strain_component": 0.0007604005271715748,
            "step_scale": 1.0,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 2.0969912693991226,
            "cell_principal_stretches": [
              1.0011730849343548,
              1.0006109305578896,
              0.989589810177818
            ],
            "cell_volume_ratio": 0.9913559629428691,
            "cell_rmsd_from_input_A": 0.09656256065727122
          },
          {
            "iteration": 2,
            "reduced_polarization": [
              -3.885647378195166e-15,
              2.952636520072984e-15,
              -0.49988585971807625
            ],
            "branch_aligned_reduced_polarization": [
              -3.885647378195166e-15,
              2.952636520072984e-15,
              -0.49988585971807625
            ],
            "target_residual": 0.00011414028192374692,
            "energy_eV": -63.252572805867516
          }
        ],
        "iterations": 2
      },
      "parent": {
        "candidate_id": "bec_projection_00",
        "source": "MACEField_BEC_backprojection",
        "spacegroup": "Pna2_1",
        "spacegroup_number": 33,
        "pointgroup": "mm2",
        "has_inversion": false,
        "is_polar_point_group": true,
        "nonpolar_parent_hypothesis": false,
        "symmetry_tolerance_A": null,
        "target_reduced_polarization": [
          0.0,
          0.0,
          -0.5
        ],
        "formal_class": [
          0.0,
          0.0,
          0.5
        ],
        "target_residual": 0.00011414028192374692,
        "parent_symmetrization_rmsd_A": 0.030410746110512754,
        "parent_cell_rmsd_A": 0.09656256065727122,
        "energy_eV": -63.252572805867516,
        "reduced_polarization": [
          -3.885647378195166e-15,
          2.952636520072984e-15,
          -0.49988585971807625
        ],
        "cartesian_polarization_e_A2": [
          -3.381789368788934e-16,
          -1.2250128676509179e-17,
          -0.007662104909373379
        ],
        "ranking_score": 0.5547796668386781
      },
      "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": [
              4.006761362331097e-15,
              -2.5392506845499547e-15,
              -0.3966276683525275
            ],
            "branch_aligned_reduced_polarization": [
              4.006761362331097e-15,
              -2.5392506845499547e-15,
              -0.3966276683525275
            ],
            "target_residual": 0.3966276683525275,
            "energy_eV": -63.1994507889346,
            "max_atomic_step_A": 0.07163691407822273,
            "max_log_strain_component": 0.02,
            "step_scale": 0.5371364880334516,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 2.0969912693991226,
            "cell_principal_stretches": [
              1.0202013400267558,
              0.9988334409744382,
              0.9977618493089307
            ],
            "cell_volume_ratio": 1.0167305142907193,
            "cell_rmsd_from_input_A": 0.19023849717560062
          },
          {
            "iteration": 1,
            "reduced_polarization": [
              6.304834538929056e-14,
              -4.00112795497971e-15,
              -0.17308049584754623
            ],
            "branch_aligned_reduced_polarization": [
              6.304834538929056e-14,
              -4.00112795497971e-15,
              -0.17308049584754623
            ],
            "target_residual": 0.17308049584754623,
            "energy_eV": -62.90105437369918,
            "max_atomic_step_A": 0.05558805612235653,
            "max_log_strain_component": 0.014014365939664267,
            "step_scale": 1.0,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 2.0969912693991226,
            "cell_principal_stretches": [
              1.034599469614915,
              0.9980168227001492,
              0.9961965216988591
            ],
            "cell_volume_ratio": 1.0286204027539365,
            "cell_rmsd_from_input_A": 0.32812866085182957
          },
          {
            "iteration": 2,
            "reduced_polarization": [
              5.04090773967001e-14,
              8.503715560725189e-15,
              -0.019437609717413765
            ],
            "branch_aligned_reduced_polarization": [
              5.04090773967001e-14,
              8.503715560725189e-15,
              -0.019437609717413765
            ],
            "target_residual": 0.019437609717413765,
            "energy_eV": -62.61500058567111,
            "max_atomic_step_A": 0.00683627416976461,
            "max_log_strain_component": 0.0019964884251048756,
            "step_scale": 1.0,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 2.0969912693991226,
            "cell_principal_stretches": [
              1.0366670987926894,
              0.9979005414967294,
              0.995973724852771
            ],
            "cell_volume_ratio": 1.0303255152057413,
            "cell_rmsd_from_input_A": 0.3480875560160235
          },
          {
            "iteration": 3,
            "reduced_polarization": [
              1.4908091916792728e-14,
              3.4326361446737567e-15,
              -0.002772980629862257
            ],
            "branch_aligned_reduced_polarization": [
              1.4908091916792728e-14,
              3.4326361446737567e-15,
              -0.002772980629862257
            ],
            "target_residual": 0.002772980629862257,
            "energy_eV": -62.57653275953872,
            "max_atomic_step_A": 0.000991198372758045,
            "max_log_strain_component": 0.0002975247664224117,
            "step_scale": 1.0,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 2.0969912693991226,
            "cell_principal_stretches": [
              1.0369755788170638,
              0.9978832139622628,
              0.9959405270335157
            ],
            "cell_volume_ratio": 1.0305798598294018,
            "cell_rmsd_from_input_A": 0.3510687116379058
          },
          {
            "iteration": 4,
            "reduced_polarization": [
              -1.7155742040593142e-15,
              4.2763481935016526e-16,
              -0.00040798262422558077
            ],
            "branch_aligned_reduced_polarization": [
              -1.7155742040593142e-15,
              4.2763481935016526e-16,
              -0.00040798262422558077
            ],
            "target_residual": 0.00040798262422558077,
            "energy_eV": -62.57088147002476
          }
        ],
        "iterations": 4
      },
      "parent": {
        "candidate_id": "inversion_parent_endpoint_00",
        "source": "same_species_inversion_center_projection_from_endpoint",
        "spacegroup": "Pnma",
        "spacegroup_number": 62,
        "pointgroup": "mmm",
        "has_inversion": true,
        "is_polar_point_group": false,
        "nonpolar_parent_hypothesis": true,
        "symmetry_tolerance_A": null,
        "target_reduced_polarization": [
          0.0,
          0.0,
          0.0
        ],
        "formal_class": [
          0.0,
          0.0,
          0.0
        ],
        "target_residual": 1.130345762600744e-15,
        "parent_symmetrization_rmsd_A": 0.20906010232059521,
        "parent_cell_rmsd_A": 0.0,
        "energy_eV": -62.238962623759996,
        "reduced_polarization": [
          -6.583958033300684e-16,
          -8.577103786998092e-16,
          -3.2943802976802943e-16
        ],
        "cartesian_polarization_e_A2": [
          -7.417326968890924e-18,
          -8.986736201603362e-18,
          -5.058542259010624e-18
        ],
        "ranking_score": 0.20906010232059746
      },
      "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": [
          -63.1994507889346,
          -63.10208860612396,
          -62.975761892547034,
          -62.827163549020355,
          -62.665123550909584,
          -62.504690208087894,
          -62.36656056437451,
          -62.27245017170043,
          -62.23896262376
        ],
        "cartesian_polarizations_e_A2": [
          [
            4.386872474296194e-17,
            -2.653048941013882e-17,
            -0.006090243506090864
          ],
          [
            2.7277827140001886e-17,
            -7.809679277069034e-18,
            -0.005470717919301803
          ],
          [
            3.744162026613958e-17,
            4.596127038657852e-18,
            -0.004770880407544779
          ],
          [
            4.2897185694139954e-17,
            3.960889968274247e-18,
            -0.0040164285172556305
          ],
          [
            -3.6432714330824436e-17,
            -1.5301740018946265e-17,
            -0.003228972137291115
          ],
          [
            -3.3181795205920104e-17,
            2.9800091978289734e-18,
            -0.002425033585782295
          ],
          [
            -3.4489636233180467e-17,
            -3.024849461620757e-17,
            -0.0016158289491220725
          ],
          [
            -2.2027779587713853e-17,
            -7.870400467620407e-19,
            -0.0008071508370948823
          ],
          [
            -1.886093595741911e-17,
            5.9693601172812345e-18,
            8.295448801480026e-18
          ]
        ],
        "raw_reduced_polarization": [
          [
            3.893988277629724e-15,
            -2.5321179579079608e-15,
            -0.3966276683525274
          ],
          [
            2.421304465647103e-15,
            -7.453699340883998e-16,
            -0.3562810075454298
          ],
          [
            3.3234891432580784e-15,
            4.386626884826467e-16,
            -0.31070402523984225
          ],
          [
            3.807750036387499e-15,
            3.7803451202569553e-16,
            -0.2615702765103744
          ],
          [
            -3.233934046583459e-15,
            -1.460425779948324e-15,
            -0.21028710735592454
          ],
          [
            -2.9453676239652433e-15,
            2.8441747484952094e-16,
            -0.15793053526406078
          ],
          [
            -3.061457564099008e-15,
            -2.886971108347175e-15,
            -0.10523100889247768
          ],
          [
            -1.9552862773958457e-15,
            -7.5116527448502e-17,
            -0.052565772486036534
          ],
          [
            -1.6741827795005138e-15,
            5.697265405292912e-16,
            5.402418659907852e-16
          ]
        ],
        "unwrapped_reduced_polarization": [
          [
            3.893988277629724e-15,
            -2.5321179579079608e-15,
            -0.3966276683525274
          ],
          [
            2.421304465647103e-15,
            -7.453699340884e-16,
            -0.3562810075454298
          ],
          [
            3.3234891432580784e-15,
            4.386626884826468e-16,
            -0.31070402523984225
          ],
          [
            3.807750036387499e-15,
            3.7803451202569553e-16,
            -0.2615702765103744
          ],
          [
            -3.2339340465834593e-15,
            -1.4604257799483242e-15,
            -0.21028710735592454
          ],
          [
            -2.9453676239652433e-15,
            2.844174748495209e-16,
            -0.15793053526406078
          ],
          [
            -3.061457564099008e-15,
            -2.886971108347175e-15,
            -0.10523100889247768
          ],
          [
            -1.9552862773958457e-15,
            -7.511652744850213e-17,
            -0.052565772486036534
          ],
          [
            -1.6741827795005138e-15,
            5.697265405292912e-16,
            5.412337245047638e-16
          ]
        ],
        "berry_integer_shifts": [
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ]
        ],
        "folded_reduced_polarization": [
          [
            3.885780586188048e-15,
            -2.55351295663786e-15,
            -0.3966276683525274
          ],
          [
            2.4424906541753444e-15,
            -7.216449660063518e-16,
            -0.3562810075454298
          ],
          [
            3.3306690738754696e-15,
            4.440892098500626e-16,
            -0.31070402523984225
          ],
          [
            3.774758283725532e-15,
            3.3306690738754696e-16,
            -0.2615702765103744
          ],
          [
            -3.219646771412954e-15,
            -1.4432899320127035e-15,
            -0.21028710735592454
          ],
          [
            -2.942091015256665e-15,
            3.3306690738754696e-16,
            -0.15793053526406076
          ],
          [
            -3.0531133177191805e-15,
            -2.886579864025407e-15,
            -0.10523100889247766
          ],
          [
            -1.942890293094024e-15,
            -5.551115123125783e-17,
            -0.052565772486036555
          ],
          [
            -1.6653345369377348e-15,
            5.551115123125783e-16,
            5.551115123125783e-16
          ]
        ]
      },
      "reflected": {
        "reached": true,
        "construction": "reflect_displacements_about_reconstructed_parent",
        "energies_eV": [
          -62.238962623759996,
          -62.272450171700456,
          -62.366560564374495,
          -62.50469020808791,
          -62.665123550909556,
          -62.8271635490204,
          -62.97576189254705,
          -63.102088606124006,
          -63.19945078893464
        ],
        "cartesian_polarizations_e_A2": [
          [
            -1.759980353827519e-17,
            -1.1102636149278165e-17,
            -2.008470149006988e-17
          ],
          [
            -1.589260391161925e-17,
            -5.119263449561998e-18,
            0.0008071508370948863
          ],
          [
            -3.181790384892001e-17,
            -1.2966309613124185e-17,
            0.0016158289491220688
          ],
          [
            -6.464471363315515e-18,
            2.0402320025261684e-17,
            0.002425033585782293
          ],
          [
            1.705798368412447e-17,
            -5.0968433176661056e-17,
            0.0032289721372910757
          ],
          [
            -1.2517906975206345e-17,
            9.341721623288317e-18,
            0.0040164285172556505
          ],
          [
            -1.2630007634685805e-17,
            -7.099708433699121e-19,
            0.00477088040754473
          ],
          [
            -1.8384508154631407e-17,
            1.3788381115973557e-17,
            0.005470717919301916
          ],
          [
            -2.4512677539508544e-17,
            -1.3825748002466709e-18,
            0.006090243506090729
          ]
        ],
        "raw_reduced_polarization": [
          [
            -1.5622389086572403e-15,
            -1.0596557017512715e-15,
            -1.3080180313966083e-15
          ],
          [
            -1.410700076089772e-15,
            -4.885917749766065e-16,
            0.0525657724860368
          ],
          [
            -2.824302400682888e-15,
            -1.2375280723860035e-15,
            0.10523100889247744
          ],
          [
            -5.738159898040394e-16,
            1.9472343732644317e-15,
            0.15793053526406065
          ],
          [
            1.5141445048875376e-15,
            -4.864519569840082e-15,
            0.21028710735592196
          ],
          [
            -1.1111465698517527e-15,
            8.915908302492818e-16,
            0.26157027651037573
          ],
          [
            -1.1210971361489325e-15,
            -6.776090309894543e-17,
            0.31070402523983903
          ],
          [
            -1.6318928727374992e-15,
            1.3159880654479403e-15,
            0.3562810075454371
          ],
          [
            -2.1758571636499994e-15,
            -1.3195544287689372e-16,
            0.3966276683525185
          ]
        ],
        "unwrapped_reduced_polarization": [
          [
            -1.5622389086572403e-15,
            -1.0596557017512715e-15,
            -1.3080180313966083e-15
          ],
          [
            -1.410700076089772e-15,
            -4.885917749766065e-16,
            0.0525657724860368
          ],
          [
            -2.824302400682888e-15,
            -1.2375280723860035e-15,
            0.10523100889247744
          ],
          [
            -5.738159898040393e-16,
            1.9472343732644317e-15,
            0.15793053526406065
          ],
          [
            1.5141445048875374e-15,
            -4.864519569840082e-15,
            0.21028710735592196
          ],
          [
            -1.1111465698517527e-15,
            8.915908302492822e-16,
            0.26157027651037573
          ],
          [
            -1.1210971361489325e-15,
            -6.776090309894538e-17,
            0.31070402523983903
          ],
          [
            -1.6318928727374992e-15,
            1.3159880654479403e-15,
            0.3562810075454371
          ],
          [
            -2.1758571636499994e-15,
            -1.319554428768938e-16,
            0.3966276683525185
          ]
        ],
        "gauge_integer_shift": [
          0,
          0,
          0
        ],
        "expected_opposite_endpoint_reduced_polarization": [
          -7.242353836630753e-15,
          3.671571038966543e-15,
          0.3966276683525284
        ],
        "actual_opposite_endpoint_branch_residual": 1.173754936978557e-14
      },
      "pnp_branch": {
        "construction": "incoming_path_concatenated_with_parent_reflection",
        "reduced_polarization": [
          [
            3.893988277629724e-15,
            -2.5321179579079608e-15,
            -0.3966276683525274
          ],
          [
            2.421304465647103e-15,
            -7.453699340883998e-16,
            -0.3562810075454298
          ],
          [
            3.3234891432580784e-15,
            4.386626884826467e-16,
            -0.31070402523984225
          ],
          [
            3.807750036387499e-15,
            3.7803451202569553e-16,
            -0.2615702765103744
          ],
          [
            -3.233934046583459e-15,
            -1.460425779948324e-15,
            -0.21028710735592454
          ],
          [
            -2.9453676239652433e-15,
            2.8441747484952094e-16,
            -0.15793053526406078
          ],
          [
            -3.061457564099008e-15,
            -2.886971108347175e-15,
            -0.10523100889247768
          ],
          [
            -1.9552862773958457e-15,
            -7.5116527448502e-17,
            -0.052565772486036534
          ],
          [
            -1.6741827795005138e-15,
            5.697265405292912e-16,
            5.402418659907852e-16
          ],
          [
            -1.410700076089772e-15,
            -4.885917749766065e-16,
            0.0525657724860368
          ],
          [
            -2.824302400682888e-15,
            -1.2375280723860035e-15,
            0.10523100889247744
          ],
          [
            -5.738159898040394e-16,
            1.9472343732644317e-15,
            0.15793053526406065
          ],
          [
            1.5141445048875376e-15,
            -4.864519569840082e-15,
            0.21028710735592196
          ],
          [
            -1.1111465698517527e-15,
            8.915908302492818e-16,
            0.26157027651037573
          ],
          [
            -1.1210971361489325e-15,
            -6.776090309894543e-17,
            0.31070402523983903
          ],
          [
            -1.6318928727374992e-15,
            1.3159880654479403e-15,
            0.3562810075454371
          ],
          [
            -2.1758571636499994e-15,
            -1.3195544287689372e-16,
            0.3966276683525185
          ]
        ],
        "unwrapped_reduced_polarization": [
          [
            3.893988277629724e-15,
            -2.5321179579079608e-15,
            -0.3966276683525274
          ],
          [
            2.421304465647103e-15,
            -7.453699340884e-16,
            -0.3562810075454298
          ],
          [
            3.3234891432580784e-15,
            4.386626884826468e-16,
            -0.31070402523984225
          ],
          [
            3.807750036387499e-15,
            3.7803451202569553e-16,
            -0.2615702765103744
          ],
          [
            -3.2339340465834593e-15,
            -1.4604257799483242e-15,
            -0.21028710735592454
          ],
          [
            -2.9453676239652433e-15,
            2.844174748495209e-16,
            -0.15793053526406078
          ],
          [
            -3.061457564099008e-15,
            -2.886971108347175e-15,
            -0.10523100889247768
          ],
          [
            -1.9552862773958457e-15,
            -7.511652744850213e-17,
            -0.052565772486036534
          ],
          [
            -1.6741827795005138e-15,
            5.697265405292912e-16,
            5.412337245047638e-16
          ],
          [
            -1.410700076089772e-15,
            -4.885917749766066e-16,
            0.0525657724860368
          ],
          [
            -2.824302400682888e-15,
            -1.2375280723860035e-15,
            0.10523100889247744
          ],
          [
            -5.738159898040393e-16,
            1.9472343732644317e-15,
            0.15793053526406065
          ],
          [
            1.5141445048875374e-15,
            -4.864519569840082e-15,
            0.21028710735592196
          ],
          [
            -1.1111465698517527e-15,
            8.915908302492822e-16,
            0.26157027651037573
          ],
          [
            -1.1210971361489325e-15,
            -6.776090309894538e-17,
            0.31070402523983903
          ],
          [
            -1.6318928727374992e-15,
            1.3159880654479403e-15,
            0.3562810075454371
          ],
          [
            -2.1758571636499994e-15,
            -1.319554428768938e-16,
            0.3966276683525185
          ]
        ],
        "berry_integer_shifts": [
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ]
        ],
        "folded_reduced_polarization": [
          [
            3.885780586188048e-15,
            -2.55351295663786e-15,
            -0.3966276683525274
          ],
          [
            2.4424906541753444e-15,
            -7.216449660063518e-16,
            -0.3562810075454298
          ],
          [
            3.3306690738754696e-15,
            4.440892098500626e-16,
            -0.31070402523984225
          ],
          [
            3.774758283725532e-15,
            3.3306690738754696e-16,
            -0.2615702765103744
          ],
          [
            -3.219646771412954e-15,
            -1.4432899320127035e-15,
            -0.21028710735592454
          ],
          [
            -2.942091015256665e-15,
            3.3306690738754696e-16,
            -0.15793053526406076
          ],
          [
            -3.0531133177191805e-15,
            -2.886579864025407e-15,
            -0.10523100889247766
          ],
          [
            -1.942890293094024e-15,
            -5.551115123125783e-17,
            -0.052565772486036555
          ],
          [
            -1.6653345369377348e-15,
            5.551115123125783e-16,
            5.551115123125783e-16
          ],
          [
            -1.3877787807814457e-15,
            -4.996003610813204e-16,
            0.05256577248603678
          ],
          [
            -2.831068712794149e-15,
            -1.2212453270876722e-15,
            0.1052310088924775
          ],
          [
            -5.551115123125783e-16,
            1.9984014443252818e-15,
            0.15793053526406065
          ],
          [
            1.5543122344752192e-15,
            -4.884981308350689e-15,
            0.21028710735592193
          ],
          [
            -1.1102230246251565e-15,
            8.881784197001252e-16,
            0.2615702765103758
          ],
          [
            -1.1102230246251565e-15,
            -5.551115123125783e-17,
            0.310704025239839
          ],
          [
            -1.609823385706477e-15,
            1.3322676295501878e-15,
            0.3562810075454371
          ],
          [
            -2.1649348980190553e-15,
            -1.1102230246251565e-16,
            0.3966276683525185
          ]
        ]
      },
      "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": [
              4.006761362331097e-15,
              -2.5392506845499547e-15,
              -0.3966276683525275
            ],
            "branch_aligned_reduced_polarization": [
              3.9968028886505635e-15,
              -2.5392506845499547e-15,
              -0.3966276683525275
            ],
            "target_residual": 0.5105740288638182,
            "energy_eV": -63.1994507889346,
            "max_atomic_step_A": 0.12,
            "max_log_strain_component": 0.009719200323028487,
            "step_scale": 0.7322492526388805,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 2.0969912693991226,
            "cell_principal_stretches": [
              1.0073636310312013,
              1.000414806737869,
              0.9864461408555552
            ],
            "cell_volume_ratio": 0.9941221638584641,
            "cell_rmsd_from_input_A": 0.11363037671427138
          },
          {
            "iteration": 1,
            "reduced_polarization": [
              0.345793392779886,
              7.80559938395014e-15,
              -0.45530483513450115
            ],
            "branch_aligned_reduced_polarization": [
              0.345793392779886,
              7.80559938395014e-15,
              -0.45530483513450115
            ],
            "target_residual": 0.1605532169490622,
            "energy_eV": -63.03094675232853,
            "max_atomic_step_A": 0.07274903085884629,
            "max_log_strain_component": 0.006249652577461734,
            "step_scale": 1.0,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 2.0969912693991226,
            "cell_principal_stretches": [
              1.010378286645852,
              1.0007797668086318,
              0.9780600726681572
            ],
            "cell_volume_ratio": 0.9889812343321321,
            "cell_rmsd_from_input_A": 0.18353030374641058
          },
          {
            "iteration": 2,
            "reduced_polarization": [
              0.4951240570547422,
              2.0512700323931054e-14,
              -0.4979594147887995
            ],
            "branch_aligned_reduced_polarization": [
              0.4951240570547422,
              2.0512700323931054e-14,
              -0.4979594147887995
            ],
            "target_residual": 0.005285717322140796,
            "energy_eV": -62.8522725749576,
            "max_atomic_step_A": 0.002466023828640066,
            "max_log_strain_component": 0.0003117525830966725,
            "step_scale": 1.0,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 2.0969912693991226,
            "cell_principal_stretches": [
              1.0104681732377796,
              1.000797975665776,
              0.9777023780279539
            ],
            "cell_volume_ratio": 0.9887254856899013,
            "cell_rmsd_from_input_A": 0.18653668629432443
          },
          {
            "iteration": 3,
            "reduced_polarization": [
              0.49987755345092916,
              -1.3111744250646516e-15,
              -0.49997124596747144
            ],
            "branch_aligned_reduced_polarization": [
              0.49987755345092916,
              -1.3111744250646516e-15,
              -0.49997124596747144
            ],
            "target_residual": 0.00012577738972490834,
            "energy_eV": -62.846476427592606
          }
        ],
        "iterations": 3
      },
      "parent": {
        "candidate_id": "bec_projection_02",
        "source": "MACEField_BEC_backprojection",
        "spacegroup": "Pc",
        "spacegroup_number": 7,
        "pointgroup": "m",
        "has_inversion": false,
        "is_polar_point_group": true,
        "nonpolar_parent_hypothesis": false,
        "symmetry_tolerance_A": null,
        "target_reduced_polarization": [
          0.5,
          0.0,
          -0.5
        ],
        "formal_class": [
          0.5,
          0.0,
          0.5
        ],
        "target_residual": 0.00012577738972490834,
        "parent_symmetrization_rmsd_A": 0.1443893945306966,
        "parent_cell_rmsd_A": 0.18653668629432443,
        "energy_eV": -62.846476427592606,
        "reduced_polarization": [
          0.49987755345092916,
          -1.3111744250646516e-15,
          -0.49997124596747144
        ],
        "cartesian_polarization_e_A2": [
          0.005592045677159222,
          -3.2015381598487883e-16,
          -0.007577346419915142
        ],
        "ranking_score": 0.6912751208837276
      },
      "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": [
              4.006761362331097e-15,
              -2.5392506845499547e-15,
              -0.3966276683525275
            ],
            "branch_aligned_reduced_polarization": [
              4.006761362331097e-15,
              -2.55351295663786e-15,
              -0.3966276683525275
            ],
            "target_residual": 0.5105740288638196,
            "energy_eV": -63.1994507889346,
            "max_atomic_step_A": 0.12,
            "max_log_strain_component": 0.00803691888761418,
            "step_scale": 0.8281765696342531,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 2.0969912693991226,
            "cell_principal_stretches": [
              1.001362789593348,
              1.000900805251082,
              0.9911100215559807
            ],
            "cell_volume_ratio": 0.9933547097856508,
            "cell_rmsd_from_input_A": 0.07862035388346189
          },
          {
            "iteration": 1,
            "reduced_polarization": [
              1.359175615351832e-15,
              -0.3999191772479841,
              -0.47873452393032345
            ],
            "branch_aligned_reduced_polarization": [
              1.359175615351832e-15,
              -0.3999191772479841,
              -0.47873452393032345
            ],
            "target_residual": 0.10231515799328275,
            "energy_eV": -63.01478903893411,
            "max_atomic_step_A": 0.032270710786366376,
            "max_log_strain_component": 0.001973087917559336,
            "step_scale": 1.0,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 2.0969912693991226,
            "cell_principal_stretches": [
              1.0017595272967508,
              1.0011220796996685,
              0.988878522085506
            ],
            "cell_volume_ratio": 0.9917300337257509,
            "cell_rmsd_from_input_A": 0.09802447429401663
          },
          {
            "iteration": 2,
            "reduced_polarization": [
              6.8795187322708935e-15,
              -0.49729987242591867,
              -0.4990331810324835
            ],
            "branch_aligned_reduced_polarization": [
              6.8795187322708935e-15,
              -0.49729987242591867,
              -0.4990331810324835
            ],
            "target_residual": 0.0028680006681073155,
            "energy_eV": -62.90301748413947,
            "max_atomic_step_A": 0.0009416383401775093,
            "max_log_strain_component": 0.00011087842026131413,
            "step_scale": 1.0,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 2.0969912693991226,
            "cell_principal_stretches": [
              1.0017694622806428,
              1.0011345157524572,
              0.9887654751900836
            ],
            "cell_volume_ratio": 0.9916388133396385,
            "cell_rmsd_from_input_A": 0.09904932293474611
          },
          {
            "iteration": 3,
            "reduced_polarization": [
              2.7455193718934407e-15,
              -0.4999796763042359,
              -0.4999864709459143
            ],
            "branch_aligned_reduced_polarization": [
              2.7455193718934407e-15,
              -0.4999796763042359,
              -0.4999864709459143
            ],
            "target_residual": 2.441491171324116e-05,
            "energy_eV": -62.900029626031035
          }
        ],
        "iterations": 3
      },
      "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": 2.441491171324116e-05,
        "parent_symmetrization_rmsd_A": 0.1353304662687817,
        "parent_cell_rmsd_A": 0.09904932293474611,
        "energy_eV": -62.900029626031035,
        "reduced_polarization": [
          2.7455193718934407e-15,
          -0.4999796763042359,
          -0.4999864709459143
        ],
        "cartesian_polarization_e_A2": [
          -2.6995350649436844e-16,
          -0.005257086053196212,
          -0.0076444785234853554
        ],
        "ranking_score": 0.6601416268258947
      },
      "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": [
              4.006761362331097e-15,
              -2.5392506845499547e-15,
              -0.3966276683525275
            ],
            "branch_aligned_reduced_polarization": [
              3.9968028886505635e-15,
              -2.5392506845499547e-15,
              -0.3966276683525275
            ],
            "target_residual": 0.638211177669867,
            "energy_eV": -63.1994507889346,
            "max_atomic_step_A": 0.11170206186916905,
            "max_log_strain_component": 0.02,
            "step_scale": 0.5371364880337264,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 2.0969912693991226,
            "cell_principal_stretches": [
              1.0223349404924404,
              0.998833440974454,
              0.9956795325827692
            ],
            "cell_volume_ratio": 1.0167305142907366,
            "cell_rmsd_from_input_A": 0.20317040520012308
          },
          {
            "iteration": 1,
            "reduced_polarization": [
              0.2605621693015418,
              -2.390389261415256e-15,
              -0.17104412719112314
            ],
            "branch_aligned_reduced_polarization": [
              0.2605621693015418,
              -2.390389261415256e-15,
              -0.17104412719112314
            ],
            "target_residual": 0.29425595697650136,
            "energy_eV": -62.78037410323581,
            "max_atomic_step_A": 0.11405665815474289,
            "max_log_strain_component": 0.014542695689300287,
            "step_scale": 1.0,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 2.0969912693991226,
            "cell_principal_stretches": [
              1.0397409088998404,
              0.9979860499441983,
              0.9917355591912971
            ],
            "cell_volume_ratio": 1.029071351065865,
            "cell_rmsd_from_input_A": 0.36216747664145893
          },
          {
            "iteration": 2,
            "reduced_polarization": [
              0.48784364477715464,
              1.515865643678195e-14,
              -0.026768989573546936
            ],
            "branch_aligned_reduced_polarization": [
              0.48784364477715464,
              1.515865643678195e-14,
              -0.026768989573546936
            ],
            "target_residual": 0.029399928147746623,
            "energy_eV": -62.16382456446716,
            "max_atomic_step_A": 0.012235212234859235,
            "max_log_strain_component": 0.003112395008293929,
            "step_scale": 1.0,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 2.0969912693991226,
            "cell_principal_stretches": [
              1.042921092177745,
              0.9978047866375269,
              0.9914477415584201
            ],
            "cell_volume_ratio": 1.0317319069796815,
            "cell_rmsd_from_input_A": 0.3930287784769303
          },
          {
            "iteration": 3,
            "reduced_polarization": [
              0.49967746349816167,
              2.838667060333579e-15,
              -0.004802453960107495
            ],
            "branch_aligned_reduced_polarization": [
              0.49967746349816167,
              2.838667060333579e-15,
              -0.004802453960107495
            ],
            "target_residual": 0.004813272673968334,
            "energy_eV": -62.08404840967153,
            "max_atomic_step_A": 0.0019304841500881501,
            "max_log_strain_component": 0.0005785158305925919,
            "step_scale": 1.0,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 2.0969912693991226,
            "cell_principal_stretches": [
              1.0434816219797765,
              0.9977710979835108,
              0.9914243297883569
            ],
            "cell_volume_ratio": 1.0322271948770065,
            "cell_rmsd_from_input_A": 0.3985806169684423
          },
          {
            "iteration": 4,
            "reduced_polarization": [
              0.49998392468829816,
              -4.598189051635025e-15,
              -0.0008762360302782835
            ],
            "branch_aligned_reduced_polarization": [
              0.49998392468829816,
              -4.598189051635025e-15,
              -0.0008762360302782835
            ],
            "target_residual": 0.000876383475656722,
            "energy_eV": -62.07187327272956
          }
        ],
        "iterations": 4
      },
      "parent": {
        "candidate_id": "bec_projection_04",
        "source": "MACEField_BEC_backprojection",
        "spacegroup": "Pc",
        "spacegroup_number": 7,
        "pointgroup": "m",
        "has_inversion": false,
        "is_polar_point_group": true,
        "nonpolar_parent_hypothesis": false,
        "symmetry_tolerance_A": null,
        "target_reduced_polarization": [
          0.5,
          0.0,
          0.0
        ],
        "formal_class": [
          0.5,
          0.0,
          0.0
        ],
        "target_residual": 0.000876383475656722,
        "parent_symmetrization_rmsd_A": 0.1730338842544026,
        "parent_cell_rmsd_A": 0.3985806169684423,
        "energy_eV": -62.07187327272956,
        "reduced_polarization": [
          0.49998392468829816,
          -4.598189051635025e-15,
          -0.0008762360302782835
        ],
        "cartesian_polarization_e_A2": [
          0.005433884299753871,
          -1.5261574523144903e-16,
          6.552311268511564e-05
        ],
        "ranking_score": 0.7744318054478266
      },
      "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": [
              4.006761362331097e-15,
              -2.5392506845499547e-15,
              -0.3966276683525275
            ],
            "branch_aligned_reduced_polarization": [
              4.006761362331097e-15,
              -2.55351295663786e-15,
              -0.3966276683525275
            ],
            "target_residual": 0.6382111776698681,
            "energy_eV": -63.1994507889346,
            "max_atomic_step_A": 0.1011864870811573,
            "max_log_strain_component": 0.02,
            "step_scale": 0.5371364880335737,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 2.0969912693991226,
            "cell_principal_stretches": [
              1.0203701625725987,
              0.9986681817277961,
              0.9977618493088859
            ],
            "cell_volume_ratio": 1.0167305142906897,
            "cell_rmsd_from_input_A": 0.19104659904554366
          },
          {
            "iteration": 1,
            "reduced_polarization": [
              6.855196731466752e-14,
              -0.24887293297331134,
              -0.17564660086086265
            ],
            "branch_aligned_reduced_polarization": [
              6.855196731466752e-14,
              -0.24887293297331137,
              -0.17564660086086265
            ],
            "target_residual": 0.30645804311096514,
            "energy_eV": -62.78689523868711,
            "max_atomic_step_A": 0.0997474342747865,
            "max_log_strain_component": 0.015968792843769702,
            "step_scale": 1.0,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 2.0969912693991226,
            "cell_principal_stretches": [
              1.037055200291889,
              0.9974875850086715,
              0.9959784181672884
            ],
            "cell_volume_ratio": 1.0302895631907025,
            "cell_rmsd_from_input_A": 0.3498025011291104
          },
          {
            "iteration": 2,
            "reduced_polarization": [
              1.2242630085996254e-13,
              -0.49098999932498794,
              -0.025931893047403495
            ],
            "branch_aligned_reduced_polarization": [
              1.2242630085996254e-13,
              -0.49098999932498794,
              -0.025931893047403495
            ],
            "target_residual": 0.02745256252493912,
            "energy_eV": -62.12733353971426,
            "max_atomic_step_A": 0.010112000186364892,
            "max_log_strain_component": 0.002916410863849727,
            "step_scale": 1.0,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 2.0969912693991226,
            "cell_principal_stretches": [
              1.0400732509568953,
              0.9973282167753428,
              0.9956530511862852
            ],
            "cell_volume_ratio": 1.03278533502801,
            "cell_rmsd_from_input_A": 0.37906112467562164
          },
          {
            "iteration": 3,
            "reduced_polarization": [
              2.1805773989254302e-14,
              -0.4997321493263566,
              -0.0044137610949428014
            ],
            "branch_aligned_reduced_polarization": [
              2.1805773989254302e-14,
              -0.4997321493263566,
              -0.0044137610949428014
            ],
            "target_residual": 0.004421880933110014,
            "energy_eV": -62.05509111425856,
            "max_atomic_step_A": 0.0017513705870311747,
            "max_log_strain_component": 0.0005128217343449404,
            "step_scale": 1.0,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 2.0969912693991226,
            "cell_principal_stretches": [
              1.0406027104059954,
              0.9973022488712178,
              0.9955958496403347
            ],
            "cell_volume_ratio": 1.0332248161827322,
            "cell_rmsd_from_input_A": 0.3842127900871302
          },
          {
            "iteration": 4,
            "reduced_polarization": [
              5.4857095807986284e-15,
              -0.49994636301806095,
              -0.0007681032761472726
            ],
            "branch_aligned_reduced_polarization": [
              5.4857095807986284e-15,
              -0.49994636301806095,
              -0.0007681032761472726
            ],
            "target_residual": 0.0007699737454353256,
            "energy_eV": -62.044339431525586
          }
        ],
        "iterations": 4
      },
      "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": 0.0007699737454353256,
        "parent_symmetrization_rmsd_A": 0.1786226122286941,
        "parent_cell_rmsd_A": 0.3842127900871302,
        "energy_eV": -62.044339431525586,
        "reduced_polarization": [
          5.4857095807986284e-15,
          -0.49994636301806095,
          -0.0007681032761472726
        ],
        "cartesian_polarization_e_A2": [
          -3.190502855520819e-16,
          -0.005058141018690511,
          9.368400668202884e-06
        ],
        "ranking_score": 0.7762157572413473
      },
      "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": [
              4.006761362331097e-15,
              -2.5392506845499547e-15,
              -0.3966276683525275
            ],
            "branch_aligned_reduced_polarization": [
              3.9968028886505635e-15,
              -2.55351295663786e-15,
              -0.3966276683525275
            ],
            "target_residual": 0.7146228648386703,
            "energy_eV": -63.1994507889346,
            "max_atomic_step_A": 0.12000000000000001,
            "max_log_strain_component": 0.006656016350160125,
            "step_scale": 0.5014674907375806,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 2.0969912693991226,
            "cell_principal_stretches": [
              1.0052380393167246,
              1.0003005785383987,
              0.9904834645839066
            ],
            "cell_volume_ratio": 0.9959709334450216,
            "cell_rmsd_from_input_A": 0.07962248992840378
          },
          {
            "iteration": 1,
            "reduced_polarization": [
              0.23142461159431396,
              -0.24198122441416334,
              -0.44104073210566064
            ],
            "branch_aligned_reduced_polarization": [
              0.23142461159431393,
              -0.24198122441416337,
              -0.44104073210566064
            ],
            "target_residual": 0.3770711114401578,
            "energy_eV": -63.03879892829659,
            "max_atomic_step_A": 0.12,
            "max_log_strain_component": 0.005702915778382559,
            "step_scale": 0.6798166619314345,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 2.0969912693991226,
            "cell_principal_stretches": [
              1.0096458014535765,
              1.000577262497423,
              0.9822079136176478
            ],
            "cell_volume_ratio": 0.992254557022001,
            "cell_rmsd_from_input_A": 0.14847119188297533
          },
          {
            "iteration": 2,
            "reduced_polarization": [
              0.4030367335838612,
              -0.40515664268363794,
              -0.4782687205679794
            ],
            "branch_aligned_reduced_polarization": [
              0.4030367335838612,
              -0.40515664268363794,
              -0.4782687205679794
            ],
            "target_residual": 0.13736588356239984,
            "energy_eV": -62.86357038726632,
            "max_atomic_step_A": 0.07308152253016131,
            "max_log_strain_component": 0.0035338179716193803,
            "step_scale": 1.0,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 2.0969912693991226,
            "cell_principal_stretches": [
              1.0123005535669882,
              1.000778459450438,
              0.9767989016749475
            ],
            "cell_volume_ratio": 0.9895838205458288,
            "cell_rmsd_from_input_A": 0.19320174413311614
          },
          {
            "iteration": 3,
            "reduced_polarization": [
              0.5000404837109305,
              -0.49873871825521865,
              -0.4998315438530852
            ],
            "branch_aligned_reduced_polarization": [
              0.5000404837109305,
              -0.49873871825521865,
              -0.4998315438530852
            ],
            "target_residual": 0.0012731253056956998,
            "energy_eV": -62.844325850152536,
            "max_atomic_step_A": 0.0005095331883735003,
            "max_log_strain_component": 2.0895818471222572e-05,
            "step_scale": 1.0,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 2.0969912693991226,
            "cell_principal_stretches": [
              1.0123023890847953,
              1.0007799290342883,
              0.9767787632892158
            ],
            "cell_volume_ratio": 0.9895666659854241,
            "cell_rmsd_from_input_A": 0.19336374216069288
          },
          {
            "iteration": 4,
            "reduced_polarization": [
              0.49999241253705623,
              -0.49999116118050085,
              -0.49999877677451077
            ],
            "branch_aligned_reduced_polarization": [
              0.49999241253705623,
              -0.49999116118050085,
              -0.49999877677451077
            ],
            "target_residual": 1.171283930817288e-05,
            "energy_eV": -62.84418589454948
          }
        ],
        "iterations": 4
      },
      "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": 1.171283930817288e-05,
        "parent_symmetrization_rmsd_A": 0.20562737240781448,
        "parent_cell_rmsd_A": 0.19336374216069288,
        "energy_eV": -62.84418589454948,
        "reduced_polarization": [
          0.49999241253705623,
          -0.49999116118050085,
          -0.49999877677451077
        ],
        "cartesian_polarization_e_A2": [
          0.005578442374851817,
          -0.005266125950260644,
          -0.0075502838164652
        ],
        "ranking_score": 0.753991733626604
      },
      "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": [
              4.006761362331097e-15,
              -2.5392506845499547e-15,
              -0.3966276683525275
            ],
            "branch_aligned_reduced_polarization": [
              3.9968028886505635e-15,
              -2.55351295663786e-15,
              -0.3966276683525275
            ],
            "target_residual": 0.8107487325323154,
            "energy_eV": -63.1994507889346,
            "max_atomic_step_A": 0.12,
            "max_log_strain_component": 0.01639482269380771,
            "step_scale": 0.4403128741844756,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 2.0969912693991226,
            "cell_principal_stretches": [
              1.0183883728531518,
              0.9990028359001335,
              0.9963840913112123
            ],
            "cell_volume_ratio": 1.01369414511851,
            "cell_rmsd_from_input_A": 0.16650322596589712
          },
          {
            "iteration": 1,
            "reduced_polarization": [
              0.2082561881075422,
              -0.20410457520769665,
              -0.21239356654388658
            ],
            "branch_aligned_reduced_polarization": [
              0.2082561881075422,
              -0.20410457520769665,
              -0.21239356654388658
            ],
            "target_residual": 0.46666859900768104,
            "energy_eV": -62.80132807134072,
            "max_atomic_step_A": 0.11999999999999998,
            "max_log_strain_component": 0.011586540125977218,
            "step_scale": 0.6170659032689915,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 2.0969912693991226,
            "cell_principal_stretches": [
              1.032139639087137,
              0.9982846984965608,
              0.9933187067666992
            ],
            "cell_volume_ratio": 1.0234850095924841,
            "cell_rmsd_from_input_A": 0.29137392994469546
          },
          {
            "iteration": 2,
            "reduced_polarization": [
              0.3784597555649493,
              -0.3807302946701969,
              -0.09367372794654406
            ],
            "branch_aligned_reduced_polarization": [
              0.3784597555649493,
              -0.3807302946701969,
              -0.09367372794654406
            ],
            "target_residual": 0.19435035614629853,
            "energy_eV": -62.3220727281614,
            "max_atomic_step_A": 0.09082214695127282,
            "max_log_strain_component": 0.010173646096030312,
            "step_scale": 1.0,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 2.0969912693991226,
            "cell_principal_stretches": [
              1.043998568805422,
              0.997658115442384,
              0.9909810176316881
            ],
            "cell_volume_ratio": 1.0321598907219527,
            "cell_rmsd_from_input_A": 0.4013557368948424
          },
          {
            "iteration": 3,
            "reduced_polarization": [
              0.4962374471834156,
              -0.5012678142936098,
              -0.01786666916224058
            ],
            "branch_aligned_reduced_polarization": [
              0.4962374471834156,
              -0.5012678142936098,
              -0.01786666916224058
            ],
            "target_residual": 0.01830251413696017,
            "energy_eV": -62.06140935966047,
            "max_atomic_step_A": 0.007306638524630116,
            "max_log_strain_component": 0.0021505513089157776,
            "step_scale": 1.0,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 2.0969912693991226,
            "cell_principal_stretches": [
              1.0461032051933687,
              0.9975313015062346,
              0.9908792681210865
            ],
            "cell_volume_ratio": 1.0340030193465024,
            "cell_rmsd_from_input_A": 0.4221748062436959
          },
          {
            "iteration": 4,
            "reduced_polarization": [
              0.5000123943326901,
              -0.5000162083848974,
              -0.003411587816695042
            ],
            "branch_aligned_reduced_polarization": [
              0.5000123943326901,
              -0.5000162083848974,
              -0.003411587816695042
            ],
            "target_residual": 0.0034116488333716085,
            "energy_eV": -62.02017846726521,
            "max_atomic_step_A": 0.001835682997033041,
            "max_log_strain_component": 0.0001165958049962018,
            "step_scale": 1.0,
            "strain_jacobian_refreshed": true,
            "strain_jacobian_frobenius_norm": 3.005977478174224,
            "cell_principal_stretches": [
              1.0461599410048619,
              0.9974868018081091,
              0.9908740921541629
            ],
            "cell_volume_ratio": 1.0340075684223564,
            "cell_rmsd_from_input_A": 0.4229879612319614
          },
          {
            "iteration": 5,
            "reduced_polarization": [
              0.4999992261656645,
              -0.5000017315067342,
              -6.317071131694728e-06
            ],
            "branch_aligned_reduced_polarization": [
              0.4999992261656645,
              -0.5000017315067342,
              -6.317071131694728e-06
            ],
            "target_residual": 6.595629070249473e-06,
            "energy_eV": -62.016527215762785
          }
        ],
        "iterations": 5
      },
      "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": 6.595629070249473e-06,
        "parent_symmetrization_rmsd_A": 0.22652250559766554,
        "parent_cell_rmsd_A": 0.4229879612319614,
        "energy_eV": -62.016527215762785,
        "reduced_polarization": [
          0.4999992261656645,
          -0.5000017315067342,
          -6.317071131694728e-06
        ],
        "cartesian_polarization_e_A2": [
          0.005423445010889588,
          -0.005054502600680677,
          0.00010279788750652914
        ],
        "ranking_score": 0.8322826871637964
      },
      "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
        ],
        "endpoint_rmsd_A": 0.20906010232059521,
        "minimum_distance_A_by_image": [
          2.5681682891278323,
          2.613554036976698,
          2.653921537640513,
          2.6947800404380597,
          2.736107548940775,
          2.7778831305571927,
          2.820086872657283,
          2.862699838661018,
          2.905704024473567
        ],
        "minimum_distance_A": 2.5681682891278323,
        "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": [
          742.7853434006223,
          742.7853434006223,
          742.7853434006223,
          742.7853434006223,
          742.7853434006223,
          742.7853434006223,
          742.7853434006223,
          742.7853434006223,
          742.7853434006223
        ],
        "cell_deformation_log_strain_norm": 0.0
      },
      "parent_reduced_polarization": [
        -1.6741827795005138e-15,
        5.697265405292912e-16,
        5.402418659907852e-16
      ],
      "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": [
          -63.1994507889346,
          -63.10208860612396,
          -62.975761892547034,
          -62.827163549020355,
          -62.665123550909584,
          -62.504690208087894,
          -62.36656056437451,
          -62.27245017170043,
          -62.23896262376
        ],
        "cartesian_polarizations_e_A2": [
          [
            4.386872474296194e-17,
            -2.653048941013882e-17,
            -0.006090243506090864
          ],
          [
            2.7277827140001886e-17,
            -7.809679277069034e-18,
            -0.005470717919301803
          ],
          [
            3.744162026613958e-17,
            4.596127038657852e-18,
            -0.004770880407544779
          ],
          [
            4.2897185694139954e-17,
            3.960889968274247e-18,
            -0.0040164285172556305
          ],
          [
            -3.6432714330824436e-17,
            -1.5301740018946265e-17,
            -0.003228972137291115
          ],
          [
            -3.3181795205920104e-17,
            2.9800091978289734e-18,
            -0.002425033585782295
          ],
          [
            -3.4489636233180467e-17,
            -3.024849461620757e-17,
            -0.0016158289491220725
          ],
          [
            -2.2027779587713853e-17,
            -7.870400467620407e-19,
            -0.0008071508370948823
          ],
          [
            -1.886093595741911e-17,
            5.9693601172812345e-18,
            8.295448801480026e-18
          ]
        ],
        "raw_reduced_polarization": [
          [
            3.893988277629724e-15,
            -2.5321179579079608e-15,
            -0.3966276683525274
          ],
          [
            2.421304465647103e-15,
            -7.453699340883998e-16,
            -0.3562810075454298
          ],
          [
            3.3234891432580784e-15,
            4.386626884826467e-16,
            -0.31070402523984225
          ],
          [
            3.807750036387499e-15,
            3.7803451202569553e-16,
            -0.2615702765103744
          ],
          [
            -3.233934046583459e-15,
            -1.460425779948324e-15,
            -0.21028710735592454
          ],
          [
            -2.9453676239652433e-15,
            2.8441747484952094e-16,
            -0.15793053526406078
          ],
          [
            -3.061457564099008e-15,
            -2.886971108347175e-15,
            -0.10523100889247768
          ],
          [
            -1.9552862773958457e-15,
            -7.5116527448502e-17,
            -0.052565772486036534
          ],
          [
            -1.6741827795005138e-15,
            5.697265405292912e-16,
            5.402418659907852e-16
          ]
        ],
        "unwrapped_reduced_polarization": [
          [
            3.893988277629724e-15,
            -2.5321179579079608e-15,
            -0.3966276683525274
          ],
          [
            2.421304465647103e-15,
            -7.453699340884e-16,
            -0.3562810075454298
          ],
          [
            3.3234891432580784e-15,
            4.386626884826468e-16,
            -0.31070402523984225
          ],
          [
            3.807750036387499e-15,
            3.7803451202569553e-16,
            -0.2615702765103744
          ],
          [
            -3.2339340465834593e-15,
            -1.4604257799483242e-15,
            -0.21028710735592454
          ],
          [
            -2.9453676239652433e-15,
            2.844174748495209e-16,
            -0.15793053526406078
          ],
          [
            -3.061457564099008e-15,
            -2.886971108347175e-15,
            -0.10523100889247768
          ],
          [
            -1.9552862773958457e-15,
            -7.511652744850213e-17,
            -0.052565772486036534
          ],
          [
            -1.6741827795005138e-15,
            5.697265405292912e-16,
            5.412337245047638e-16
          ]
        ],
        "berry_integer_shifts": [
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ]
        ],
        "folded_reduced_polarization": [
          [
            3.885780586188048e-15,
            -2.55351295663786e-15,
            -0.3966276683525274
          ],
          [
            2.4424906541753444e-15,
            -7.216449660063518e-16,
            -0.3562810075454298
          ],
          [
            3.3306690738754696e-15,
            4.440892098500626e-16,
            -0.31070402523984225
          ],
          [
            3.774758283725532e-15,
            3.3306690738754696e-16,
            -0.2615702765103744
          ],
          [
            -3.219646771412954e-15,
            -1.4432899320127035e-15,
            -0.21028710735592454
          ],
          [
            -2.942091015256665e-15,
            3.3306690738754696e-16,
            -0.15793053526406076
          ],
          [
            -3.0531133177191805e-15,
            -2.886579864025407e-15,
            -0.10523100889247766
          ],
          [
            -1.942890293094024e-15,
            -5.551115123125783e-17,
            -0.052565772486036555
          ],
          [
            -1.6653345369377348e-15,
            5.551115123125783e-16,
            5.551115123125783e-16
          ]
        ]
      },
      "reflected": {
        "reached": true,
        "construction": "reflect_displacements_about_reconstructed_parent",
        "energies_eV": [
          -62.238962623759996,
          -62.272450171700456,
          -62.366560564374495,
          -62.50469020808791,
          -62.665123550909556,
          -62.8271635490204,
          -62.97576189254705,
          -63.102088606124006,
          -63.19945078893464
        ],
        "cartesian_polarizations_e_A2": [
          [
            -1.759980353827519e-17,
            -1.1102636149278165e-17,
            -2.008470149006988e-17
          ],
          [
            -1.589260391161925e-17,
            -5.119263449561998e-18,
            0.0008071508370948863
          ],
          [
            -3.181790384892001e-17,
            -1.2966309613124185e-17,
            0.0016158289491220688
          ],
          [
            -6.464471363315515e-18,
            2.0402320025261684e-17,
            0.002425033585782293
          ],
          [
            1.705798368412447e-17,
            -5.0968433176661056e-17,
            0.0032289721372910757
          ],
          [
            -1.2517906975206345e-17,
            9.341721623288317e-18,
            0.0040164285172556505
          ],
          [
            -1.2630007634685805e-17,
            -7.099708433699121e-19,
            0.00477088040754473
          ],
          [
            -1.8384508154631407e-17,
            1.3788381115973557e-17,
            0.005470717919301916
          ],
          [
            -2.4512677539508544e-17,
            -1.3825748002466709e-18,
            0.006090243506090729
          ]
        ],
        "raw_reduced_polarization": [
          [
            -1.5622389086572403e-15,
            -1.0596557017512715e-15,
            -1.3080180313966083e-15
          ],
          [
            -1.410700076089772e-15,
            -4.885917749766065e-16,
            0.0525657724860368
          ],
          [
            -2.824302400682888e-15,
            -1.2375280723860035e-15,
            0.10523100889247744
          ],
          [
            -5.738159898040394e-16,
            1.9472343732644317e-15,
            0.15793053526406065
          ],
          [
            1.5141445048875376e-15,
            -4.864519569840082e-15,
            0.21028710735592196
          ],
          [
            -1.1111465698517527e-15,
            8.915908302492818e-16,
            0.26157027651037573
          ],
          [
            -1.1210971361489325e-15,
            -6.776090309894543e-17,
            0.31070402523983903
          ],
          [
            -1.6318928727374992e-15,
            1.3159880654479403e-15,
            0.3562810075454371
          ],
          [
            -2.1758571636499994e-15,
            -1.3195544287689372e-16,
            0.3966276683525185
          ]
        ],
        "unwrapped_reduced_polarization": [
          [
            -1.5622389086572403e-15,
            -1.0596557017512715e-15,
            -1.3080180313966083e-15
          ],
          [
            -1.410700076089772e-15,
            -4.885917749766065e-16,
            0.0525657724860368
          ],
          [
            -2.824302400682888e-15,
            -1.2375280723860035e-15,
            0.10523100889247744
          ],
          [
            -5.738159898040393e-16,
            1.9472343732644317e-15,
            0.15793053526406065
          ],
          [
            1.5141445048875374e-15,
            -4.864519569840082e-15,
            0.21028710735592196
          ],
          [
            -1.1111465698517527e-15,
            8.915908302492822e-16,
            0.26157027651037573
          ],
          [
            -1.1210971361489325e-15,
            -6.776090309894538e-17,
            0.31070402523983903
          ],
          [
            -1.6318928727374992e-15,
            1.3159880654479403e-15,
            0.3562810075454371
          ],
          [
            -2.1758571636499994e-15,
            -1.319554428768938e-16,
            0.3966276683525185
          ]
        ],
        "gauge_integer_shift": [
          0,
          0,
          0
        ],
        "expected_opposite_endpoint_reduced_polarization": [
          -7.242353836630753e-15,
          3.671571038966543e-15,
          0.3966276683525284
        ],
        "actual_opposite_endpoint_branch_residual": 1.173754936978557e-14
      },
      "pnp_branch": {
        "construction": "incoming_path_concatenated_with_parent_reflection",
        "reduced_polarization": [
          [
            3.893988277629724e-15,
            -2.5321179579079608e-15,
            -0.3966276683525274
          ],
          [
            2.421304465647103e-15,
            -7.453699340883998e-16,
            -0.3562810075454298
          ],
          [
            3.3234891432580784e-15,
            4.386626884826467e-16,
            -0.31070402523984225
          ],
          [
            3.807750036387499e-15,
            3.7803451202569553e-16,
            -0.2615702765103744
          ],
          [
            -3.233934046583459e-15,
            -1.460425779948324e-15,
            -0.21028710735592454
          ],
          [
            -2.9453676239652433e-15,
            2.8441747484952094e-16,
            -0.15793053526406078
          ],
          [
            -3.061457564099008e-15,
            -2.886971108347175e-15,
            -0.10523100889247768
          ],
          [
            -1.9552862773958457e-15,
            -7.5116527448502e-17,
            -0.052565772486036534
          ],
          [
            -1.6741827795005138e-15,
            5.697265405292912e-16,
            5.402418659907852e-16
          ],
          [
            -1.410700076089772e-15,
            -4.885917749766065e-16,
            0.0525657724860368
          ],
          [
            -2.824302400682888e-15,
            -1.2375280723860035e-15,
            0.10523100889247744
          ],
          [
            -5.738159898040394e-16,
            1.9472343732644317e-15,
            0.15793053526406065
          ],
          [
            1.5141445048875376e-15,
            -4.864519569840082e-15,
            0.21028710735592196
          ],
          [
            -1.1111465698517527e-15,
            8.915908302492818e-16,
            0.26157027651037573
          ],
          [
            -1.1210971361489325e-15,
            -6.776090309894543e-17,
            0.31070402523983903
          ],
          [
            -1.6318928727374992e-15,
            1.3159880654479403e-15,
            0.3562810075454371
          ],
          [
            -2.1758571636499994e-15,
            -1.3195544287689372e-16,
            0.3966276683525185
          ]
        ],
        "unwrapped_reduced_polarization": [
          [
            3.893988277629724e-15,
            -2.5321179579079608e-15,
            -0.3966276683525274
          ],
          [
            2.421304465647103e-15,
            -7.453699340884e-16,
            -0.3562810075454298
          ],
          [
            3.3234891432580784e-15,
            4.386626884826468e-16,
            -0.31070402523984225
          ],
          [
            3.807750036387499e-15,
            3.7803451202569553e-16,
            -0.2615702765103744
          ],
          [
            -3.2339340465834593e-15,
            -1.4604257799483242e-15,
            -0.21028710735592454
          ],
          [
            -2.9453676239652433e-15,
            2.844174748495209e-16,
            -0.15793053526406078
          ],
          [
            -3.061457564099008e-15,
            -2.886971108347175e-15,
            -0.10523100889247768
          ],
          [
            -1.9552862773958457e-15,
            -7.511652744850213e-17,
            -0.052565772486036534
          ],
          [
            -1.6741827795005138e-15,
            5.697265405292912e-16,
            5.412337245047638e-16
          ],
          [
            -1.410700076089772e-15,
            -4.885917749766066e-16,
            0.0525657724860368
          ],
          [
            -2.824302400682888e-15,
            -1.2375280723860035e-15,
            0.10523100889247744
          ],
          [
            -5.738159898040393e-16,
            1.9472343732644317e-15,
            0.15793053526406065
          ],
          [
            1.5141445048875374e-15,
            -4.864519569840082e-15,
            0.21028710735592196
          ],
          [
            -1.1111465698517527e-15,
            8.915908302492822e-16,
            0.26157027651037573
          ],
          [
            -1.1210971361489325e-15,
            -6.776090309894538e-17,
            0.31070402523983903
          ],
          [
            -1.6318928727374992e-15,
            1.3159880654479403e-15,
            0.3562810075454371
          ],
          [
            -2.1758571636499994e-15,
            -1.319554428768938e-16,
            0.3966276683525185
          ]
        ],
        "berry_integer_shifts": [
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ]
        ],
        "folded_reduced_polarization": [
          [
            3.885780586188048e-15,
            -2.55351295663786e-15,
            -0.3966276683525274
          ],
          [
            2.4424906541753444e-15,
            -7.216449660063518e-16,
            -0.3562810075454298
          ],
          [
            3.3306690738754696e-15,
            4.440892098500626e-16,
            -0.31070402523984225
          ],
          [
            3.774758283725532e-15,
            3.3306690738754696e-16,
            -0.2615702765103744
          ],
          [
            -3.219646771412954e-15,
            -1.4432899320127035e-15,
            -0.21028710735592454
          ],
          [
            -2.942091015256665e-15,
            3.3306690738754696e-16,
            -0.15793053526406076
          ],
          [
            -3.0531133177191805e-15,
            -2.886579864025407e-15,
            -0.10523100889247766
          ],
          [
            -1.942890293094024e-15,
            -5.551115123125783e-17,
            -0.052565772486036555
          ],
          [
            -1.6653345369377348e-15,
            5.551115123125783e-16,
            5.551115123125783e-16
          ],
          [
            -1.3877787807814457e-15,
            -4.996003610813204e-16,
            0.05256577248603678
          ],
          [
            -2.831068712794149e-15,
            -1.2212453270876722e-15,
            0.1052310088924775
          ],
          [
            -5.551115123125783e-16,
            1.9984014443252818e-15,
            0.15793053526406065
          ],
          [
            1.5543122344752192e-15,
            -4.884981308350689e-15,
            0.21028710735592193
          ],
          [
            -1.1102230246251565e-15,
            8.881784197001252e-16,
            0.2615702765103758
          ],
          [
            -1.1102230246251565e-15,
            -5.551115123125783e-17,
            0.310704025239839
          ],
          [
            -1.609823385706477e-15,
            1.3322676295501878e-15,
            0.3562810075454371
          ],
          [
            -2.1649348980190553e-15,
            -1.1102230246251565e-16,
            0.3966276683525185
          ]
        ]
      },
      "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": "Pnma",
        "spacegroup_number": 62,
        "pointgroup": "mmm",
        "has_inversion": true,
        "is_polar_point_group": false,
        "nonpolar_parent_hypothesis": true,
        "symmetry_tolerance_A": null,
        "target_reduced_polarization": [
          0.0,
          0.0,
          0.0
        ],
        "formal_class": [
          0.0,
          0.0,
          0.0
        ],
        "target_residual": 1.130345762600744e-15,
        "parent_symmetrization_rmsd_A": 0.20906010232059521,
        "parent_cell_rmsd_A": 0.0,
        "energy_eV": -62.238962623759996,
        "reduced_polarization": [
          -6.583958033300684e-16,
          -8.577103786998092e-16,
          -3.2943802976802943e-16
        ],
        "cartesian_polarization_e_A2": [
          -7.417326968890924e-18,
          -8.986736201603362e-18,
          -5.058542259010624e-18
        ],
        "ranking_score": 0.20906010232059746
      }
    }
  ],
  "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": 74,
      "full_response": 30,
      "energy_polarization": 44
    },
    "model_evaluations_for_recovery_and_path_properties": {
      "total": 99,
      "full_response": 55,
      "energy_polarization": 44
    },
    "elapsed_seconds": 175.27191274496727
  }
}
