{
  "schema": "ferrofinder.endpoint_parent_recovery.v4_variable_cell",
  "status": "complete",
  "input_atom_count": 48,
  "input_formula": "Ag18O24P6",
  "input_spacegroup": "R3c",
  "input_pointgroup": "3m",
  "input_is_polar_point_group": true,
  "input_energy_eV": -247.56934685966073,
  "input_cartesian_polarization_e_A2": [
    -2.1727160429287753e-07,
    1.259282308810915e-07,
    6.737246186233797e-05
  ],
  "input_reduced_polarization": [
    -1.1433529682789355e-05,
    1.1500157957619056e-05,
    0.004330921366717734
  ],
  "input_formal_targets": [
    {
      "orbit_id": 0,
      "representative_formal_class": [
        0.0,
        0.0,
        0.0
      ],
      "target_reduced_polarization": [
        0.0,
        0.0,
        0.0
      ]
    },
    {
      "orbit_id": 1,
      "representative_formal_class": [
        0.0,
        0.0,
        0.5
      ],
      "target_reduced_polarization": [
        0.0,
        0.0,
        0.5
      ]
    },
    {
      "orbit_id": 2,
      "representative_formal_class": [
        0.0,
        0.5,
        0.0
      ],
      "target_reduced_polarization": [
        0.0,
        0.5,
        0.0
      ]
    },
    {
      "orbit_id": 3,
      "representative_formal_class": [
        0.5,
        0.0,
        0.0
      ],
      "target_reduced_polarization": [
        -0.5,
        0.0,
        0.0
      ]
    },
    {
      "orbit_id": 4,
      "representative_formal_class": [
        0.0,
        0.5,
        0.5
      ],
      "target_reduced_polarization": [
        0.0,
        0.5,
        0.5
      ]
    },
    {
      "orbit_id": 5,
      "representative_formal_class": [
        0.5,
        0.0,
        0.5
      ],
      "target_reduced_polarization": [
        -0.5,
        0.0,
        0.5
      ]
    },
    {
      "orbit_id": 6,
      "representative_formal_class": [
        0.5,
        0.5,
        0.0
      ],
      "target_reduced_polarization": [
        -0.5,
        0.5,
        0.0
      ]
    },
    {
      "orbit_id": 7,
      "representative_formal_class": [
        0.5,
        0.5,
        0.5
      ],
      "target_reduced_polarization": [
        -0.5,
        0.5,
        0.5
      ]
    }
  ],
  "parent_candidates": [
    {
      "candidate_id": "inversion_parent_endpoint_00",
      "source": "same_species_inversion_center_projection_from_endpoint",
      "spacegroup": "C2/c",
      "spacegroup_number": 15,
      "pointgroup": "2/m",
      "has_inversion": true,
      "is_polar_point_group": false,
      "nonpolar_parent_hypothesis": true,
      "symmetry_tolerance_A": null,
      "target_reduced_polarization": [
        0.0,
        0.0,
        0.0
      ],
      "formal_class": [
        0.0,
        0.0,
        0.0
      ],
      "target_residual": 4.903852345147087e-15,
      "parent_symmetrization_rmsd_A": 0.6624956131071844,
      "parent_cell_rmsd_A": 0.0,
      "energy_eV": -154.48895389981277,
      "reduced_polarization": [
        1.796865491437787e-15,
        4.2928110370502245e-15,
        1.5462262540987978e-15
      ],
      "cartesian_polarization_e_A2": [
        -4.419620688949682e-18,
        4.7006841244681414e-17,
        2.4053327344007254e-17
      ],
      "ranking_score": 0.6624956131071942
    },
    {
      "candidate_id": "inversion_parent_endpoint_01",
      "source": "same_species_inversion_center_projection_from_endpoint",
      "spacegroup": "C2/c",
      "spacegroup_number": 15,
      "pointgroup": "2/m",
      "has_inversion": true,
      "is_polar_point_group": false,
      "nonpolar_parent_hypothesis": true,
      "symmetry_tolerance_A": null,
      "target_reduced_polarization": [
        0.0,
        0.0,
        0.0
      ],
      "formal_class": [
        0.0,
        0.0,
        0.0
      ],
      "target_residual": 3.3653263097916146e-15,
      "parent_symmetrization_rmsd_A": 0.6770130906851064,
      "parent_cell_rmsd_A": 0.0,
      "energy_eV": -188.76260986470564,
      "reduced_polarization": [
        2.6509874963078992e-15,
        -3.840838297880725e-16,
        -2.0371956404553168e-15
      ],
      "cartesian_polarization_e_A2": [
        3.5947606064498566e-17,
        -4.205768074968246e-18,
        -3.169092070048712e-17
      ],
      "ranking_score": 0.6770130906851132
    },
    {
      "candidate_id": "inversion_parent_endpoint_02",
      "source": "same_species_inversion_center_projection_from_endpoint",
      "spacegroup": "C2/c",
      "spacegroup_number": 15,
      "pointgroup": "2/m",
      "has_inversion": true,
      "is_polar_point_group": false,
      "nonpolar_parent_hypothesis": true,
      "symmetry_tolerance_A": null,
      "target_reduced_polarization": [
        0.0,
        0.0,
        0.0
      ],
      "formal_class": [
        0.0,
        0.0,
        0.0
      ],
      "target_residual": 2.8095551080574244e-15,
      "parent_symmetrization_rmsd_A": 0.6770130960839769,
      "parent_cell_rmsd_A": 0.0,
      "energy_eV": -188.76260604045794,
      "reduced_polarization": [
        -1.086228395585418e-15,
        -1.1963234382195885e-15,
        -2.2983729046875655e-15
      ],
      "cartesian_polarization_e_A2": [
        -6.1711754320357314e-18,
        -1.3099897818078986e-17,
        -3.575383336591205e-17
      ],
      "ranking_score": 0.6770130960839825
    },
    {
      "candidate_id": "bec_projection_00",
      "source": "MACEField_BEC_backprojection",
      "spacegroup": "R3c",
      "spacegroup_number": 161,
      "pointgroup": "3m",
      "has_inversion": false,
      "is_polar_point_group": true,
      "nonpolar_parent_hypothesis": false,
      "symmetry_tolerance_A": null,
      "target_reduced_polarization": [
        0.0,
        0.0,
        0.0
      ],
      "formal_class": [
        0.0,
        0.0,
        0.0
      ],
      "target_residual": 1.2230583002344048e-06,
      "parent_symmetrization_rmsd_A": 0.00040085439201025956,
      "parent_cell_rmsd_A": 0.0023038509277992386,
      "energy_eV": -247.56885025998784,
      "reduced_polarization": [
        -8.012771198741645e-10,
        1.904667405414541e-09,
        -1.2230565546896527e-06
      ],
      "cartesian_polarization_e_A2": [
        -2.216732947027708e-11,
        2.085403509094177e-11,
        -1.9022965306770204e-08
      ],
      "ranking_score": 0.5009792632405605
    },
    {
      "candidate_id": "inversion_parent_bec_00_00",
      "source": "same_species_inversion_center_projection_after_BEC",
      "spacegroup": "C2/c",
      "spacegroup_number": 15,
      "pointgroup": "2/m",
      "has_inversion": true,
      "is_polar_point_group": false,
      "nonpolar_parent_hypothesis": true,
      "symmetry_tolerance_A": null,
      "target_reduced_polarization": [
        0.0,
        0.0,
        0.0
      ],
      "formal_class": [
        0.0,
        0.0,
        0.0
      ],
      "target_residual": 6.308325984016281e-15,
      "parent_symmetrization_rmsd_A": 0.6770130919437435,
      "parent_cell_rmsd_A": 0.0023038509277992386,
      "energy_eV": -188.8010125920588,
      "reduced_polarization": [
        -4.012536482664252e-15,
        -4.520294442221559e-15,
        1.805952892941634e-15
      ],
      "cartesian_polarization_e_A2": [
        -2.2161678244870785e-17,
        -4.9507315233601515e-17,
        2.808911240779119e-17
      ],
      "ranking_score": 0.677589054675706
    },
    {
      "candidate_id": "inversion_parent_bec_00_01",
      "source": "same_species_inversion_center_projection_after_BEC",
      "spacegroup": "C2/c",
      "spacegroup_number": 15,
      "pointgroup": "2/m",
      "has_inversion": true,
      "is_polar_point_group": false,
      "nonpolar_parent_hypothesis": true,
      "symmetry_tolerance_A": null,
      "target_reduced_polarization": [
        0.0,
        0.0,
        0.0
      ],
      "formal_class": [
        0.0,
        0.0,
        0.0
      ],
      "target_residual": 3.4351459059867267e-15,
      "parent_symmetrization_rmsd_A": 0.6770130973432512,
      "parent_cell_rmsd_A": 0.0023038509277992386,
      "energy_eV": -188.80093053050717,
      "reduced_polarization": [
        -7.80953670546785e-16,
        -1.829276691529599e-15,
        2.8007294667110205e-15
      ],
      "cartesian_polarization_e_A2": [
        1.6906427337539295e-18,
        -2.0034661305615508e-17,
        4.356149360036609e-17
      ],
      "ranking_score": 0.6775890600752079
    },
    {
      "candidate_id": "bec_projection_01",
      "source": "MACEField_BEC_backprojection",
      "spacegroup": "R3c",
      "spacegroup_number": 161,
      "pointgroup": "3m",
      "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": 0.000995770548818129,
      "parent_symmetrization_rmsd_A": 0.04756785804183332,
      "parent_cell_rmsd_A": 0.29448634485190034,
      "energy_eV": -245.46557913312094,
      "reduced_polarization": [
        4.4143119184231023e-10,
        9.163963261754935e-10,
        0.4990042294511824
      ],
      "cartesian_polarization_e_A2": [
        -3.6659962030761813e-09,
        2.0009777501702763e-09,
        0.007920354949904928
      ],
      "ranking_score": 0.6231809853524447
    },
    {
      "candidate_id": "bec_projection_02",
      "source": "MACEField_BEC_backprojection",
      "spacegroup": "P1",
      "spacegroup_number": 1,
      "pointgroup": "1",
      "has_inversion": false,
      "is_polar_point_group": true,
      "nonpolar_parent_hypothesis": false,
      "symmetry_tolerance_A": null,
      "target_reduced_polarization": [
        0.0,
        0.5,
        0.0
      ],
      "formal_class": [
        0.0,
        0.5,
        0.0
      ],
      "target_residual": 0.0001565960714783967,
      "parent_symmetrization_rmsd_A": 0.04103351885062665,
      "parent_cell_rmsd_A": 0.211675732287877,
      "energy_eV": -245.26749289483698,
      "reduced_polarization": [
        -7.65711930143842e-05,
        0.4998850290265055,
        7.376216683739838e-05
      ],
      "cartesian_polarization_e_A2": [
        -0.0030635473231651993,
        0.005504890061130843,
        -0.00010307542381953337
      ],
      "ranking_score": 0.5942656440655527
    },
    {
      "candidate_id": "bec_projection_03",
      "source": "MACEField_BEC_backprojection",
      "spacegroup": "P1",
      "spacegroup_number": 1,
      "pointgroup": "1",
      "has_inversion": false,
      "is_polar_point_group": true,
      "nonpolar_parent_hypothesis": false,
      "symmetry_tolerance_A": null,
      "target_reduced_polarization": [
        -0.5,
        0.0,
        0.0
      ],
      "formal_class": [
        0.5,
        0.0,
        0.0
      ],
      "target_residual": 5.8969312505579984e-05,
      "parent_symmetrization_rmsd_A": 0.03776809087441365,
      "parent_cell_rmsd_A": 0.24203002181598376,
      "energy_eV": -245.17040814530466,
      "reduced_polarization": [
        -0.49995164291869404,
        2.8381511524597028e-05,
        1.8260950373094252e-05
      ],
      "cartesian_polarization_e_A2": [
        -0.006329075666472781,
        -0.00015135610589655396,
        -9.662508982790814e-05
      ],
      "ranking_score": 0.5983935349534207
    },
    {
      "candidate_id": "bec_projection_04",
      "source": "MACEField_BEC_backprojection",
      "spacegroup": "P1",
      "spacegroup_number": 1,
      "pointgroup": "1",
      "has_inversion": false,
      "is_polar_point_group": true,
      "nonpolar_parent_hypothesis": false,
      "symmetry_tolerance_A": null,
      "target_reduced_polarization": [
        0.0,
        0.5,
        0.5
      ],
      "formal_class": [
        0.0,
        0.5,
        0.5
      ],
      "target_residual": 0.00011219538014789882,
      "parent_symmetrization_rmsd_A": 0.06367659203550156,
      "parent_cell_rmsd_A": 0.3899076042223225,
      "energy_eV": -242.39428154229904,
      "reduced_polarization": [
        1.4382343905923721e-06,
        0.49999864001742095,
        0.49988782208213844
      ],
      "cartesian_polarization_e_A2": [
        -0.002929396934393759,
        0.005257499773150536,
        0.007832879889209741
      ],
      "ranking_score": 0.661377883851378
    },
    {
      "candidate_id": "bec_projection_05",
      "source": "MACEField_BEC_backprojection",
      "spacegroup": "P1",
      "spacegroup_number": 1,
      "pointgroup": "1",
      "has_inversion": false,
      "is_polar_point_group": true,
      "nonpolar_parent_hypothesis": false,
      "symmetry_tolerance_A": null,
      "target_reduced_polarization": [
        -0.5,
        0.0,
        0.5
      ],
      "formal_class": [
        0.5,
        0.0,
        0.5
      ],
      "target_residual": 0.00012119700942320248,
      "parent_symmetrization_rmsd_A": 0.06177613527628021,
      "parent_cell_rmsd_A": 0.4127426905041598,
      "energy_eV": -242.20589436929384,
      "reduced_polarization": [
        -0.4999955948136586,
        7.364925848248722e-07,
        0.4998788853146596
      ],
      "cartesian_polarization_e_A2": [
        -0.00605561019330837,
        -0.00014556344075629518,
        0.007840156513639207
      ],
      "ranking_score": 0.6652042019211666
    },
    {
      "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,
        0.0
      ],
      "formal_class": [
        0.5,
        0.5,
        0.0
      ],
      "target_residual": 0.0006943026554292374,
      "parent_symmetrization_rmsd_A": 0.0697036327773138,
      "parent_cell_rmsd_A": 0.4263833574074132,
      "energy_eV": -238.0290615367193,
      "reduced_polarization": [
        -0.49936869808965695,
        0.5002073729843567,
        0.0002012722551478557
      ],
      "cartesian_polarization_e_A2": [
        -0.009183897779343513,
        0.005203371953236484,
        -0.000293309745173332
      ],
      "ranking_score": 0.6776880774400256
    },
    {
      "candidate_id": "bec_projection_07",
      "source": "MACEField_BEC_backprojection",
      "spacegroup": "P1",
      "spacegroup_number": 1,
      "pointgroup": "1",
      "has_inversion": false,
      "is_polar_point_group": true,
      "nonpolar_parent_hypothesis": false,
      "symmetry_tolerance_A": null,
      "target_reduced_polarization": [
        -0.5,
        0.5,
        0.5
      ],
      "formal_class": [
        0.5,
        0.5,
        0.5
      ],
      "target_residual": 0.00045910561796354103,
      "parent_symmetrization_rmsd_A": 0.08864738379978339,
      "parent_cell_rmsd_A": 0.5795193507445275,
      "energy_eV": -232.31134247875863,
      "reduced_polarization": [
        -0.49988559157487056,
        0.5000261292440213,
        0.49955614648439833
      ],
      "cartesian_polarization_e_A2": [
        -0.008763308527015306,
        0.004945536863986719,
        0.007634316489225644
      ],
      "ranking_score": 0.7344454327218424
    }
  ],
  "formal_branches": [
    {
      "orbit_id": 0,
      "formal_class": [
        0.0,
        0.0,
        0.0
      ],
      "formal_classes_in_orbit": [
        [
          0.0,
          0.0,
          0.0
        ]
      ],
      "target_reduced_polarization": [
        0.0,
        0.0,
        0.0
      ],
      "bec_backprojection": {
        "converged_to_target": true,
        "history": [
          {
            "iteration": 0,
            "reduced_polarization": [
              -1.1433529682789355e-05,
              1.1500157957619056e-05,
              0.004330921366717734
            ],
            "branch_aligned_reduced_polarization": [
              -1.1433529682789355e-05,
              1.1500157957619056e-05,
              0.004330921366717734
            ],
            "target_residual": 0.004330951727268068,
            "energy_eV": -247.56934685966073,
            "max_atomic_step_A": 0.0005611884012307855,
            "max_log_strain_component": 0.00027384097533659216,
            "step_scale": 1.0,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 8.51374711949435,
            "cell_principal_stretches": [
              1.000081952907746,
              1.0000802529291866,
              0.9997261954519987
            ],
            "cell_volume_ratio": 0.9998883634513954,
            "cell_rmsd_from_input_A": 0.0023038509277992386
          },
          {
            "iteration": 1,
            "reduced_polarization": [
              -8.012771198741645e-10,
              1.904667405414541e-09,
              -1.2230565546896527e-06
            ],
            "branch_aligned_reduced_polarization": [
              -8.012771198741645e-10,
              1.904667405414541e-09,
              -1.2230565546896527e-06
            ],
            "target_residual": 1.2230583002344048e-06,
            "energy_eV": -247.56885025998784
          }
        ],
        "iterations": 1
      },
      "parent": {
        "candidate_id": "bec_projection_00",
        "source": "MACEField_BEC_backprojection",
        "spacegroup": "R3c",
        "spacegroup_number": 161,
        "pointgroup": "3m",
        "has_inversion": false,
        "is_polar_point_group": true,
        "nonpolar_parent_hypothesis": false,
        "symmetry_tolerance_A": null,
        "target_reduced_polarization": [
          0.0,
          0.0,
          0.0
        ],
        "formal_class": [
          0.0,
          0.0,
          0.0
        ],
        "target_residual": 1.2230583002344048e-06,
        "parent_symmetrization_rmsd_A": 0.00040085439201025956,
        "parent_cell_rmsd_A": 0.0023038509277992386,
        "energy_eV": -247.56885025998784,
        "reduced_polarization": [
          -8.012771198741645e-10,
          1.904667405414541e-09,
          -1.2230565546896527e-06
        ],
        "cartesian_polarization_e_A2": [
          -2.216732947027708e-11,
          2.085403509094177e-11,
          -1.9022965306770204e-08
        ],
        "ranking_score": 0.5009792632405605
      },
      "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": [
          -247.56934685966078,
          -247.5693055004472,
          -247.56925823279954,
          -247.56920505154912,
          -247.5691459515222,
          -247.5690809275397,
          -247.56900997441707,
          -247.56893308696485,
          -247.5688502599878
        ],
        "cartesian_polarizations_e_A2": [
          [
            -2.1727160428140587e-07,
            1.2592823086919723e-07,
            6.737246186233976e-05
          ],
          [
            -1.901248721491128e-07,
            1.10195059564023e-07,
            5.8948125998341e-05
          ],
          [
            -1.629754378285502e-07,
            9.446038595392808e-08,
            5.052390131789988e-05
          ],
          [
            -1.3582330275594567e-07,
            7.872421111747367e-08,
            4.209978941039949e-05
          ],
          [
            -1.086684683687581e-07,
            6.298653609742487e-08,
            3.3675791864388756e-05
          ],
          [
            -8.151093616334316e-08,
            4.724736181983496e-08,
            2.52519102674458e-05
          ],
          [
            -5.4350707665967516e-08,
            3.150668938043008e-08,
            1.68281462062039e-05
          ],
          [
            -2.7187784141854036e-08,
            1.576451984802055e-08,
            8.404501266870771e-06
          ],
          [
            -2.216726829905467e-11,
            2.085407294708057e-11,
            -1.9022965326100564e-08
          ]
        ],
        "raw_reduced_polarization": [
          [
            -1.143352968242519e-05,
            1.1500157956532835e-05,
            0.0043309213667178485
          ],
          [
            -1.0004515555917484e-05,
            1.006288717207093e-05,
            0.0037894544370219636
          ],
          [
            -8.575479302892984e-06,
            8.625613078890528e-06,
            0.0032479726969246625
          ],
          [
            -7.146420994300568e-06,
            7.188335781257812e-06,
            0.0027064762483698427
          ],
          [
            -5.717340702793873e-06,
            5.751055380136176e-06,
            0.0021649651932560596
          ],
          [
            -4.288238510985561e-06,
            4.313771965798082e-06,
            0.0016234396334277438
          ],
          [
            -2.8591144960790743e-06,
            2.8764856439760712e-06,
            0.00108189967067685
          ],
          [
            -1.429968715837185e-06,
            1.4391965179108995e-06,
            0.0005403454067762502
          ],
          [
            -8.012705546481341e-10,
            1.904670861894687e-09,
            -1.2230565559324713e-06
          ]
        ],
        "unwrapped_reduced_polarization": [
          [
            -1.143352968242519e-05,
            1.1500157956532835e-05,
            0.0043309213667178485
          ],
          [
            -1.0004515555917484e-05,
            1.006288717207093e-05,
            0.0037894544370219636
          ],
          [
            -8.575479302892984e-06,
            8.625613078890528e-06,
            0.0032479726969246625
          ],
          [
            -7.146420994300568e-06,
            7.188335781257812e-06,
            0.0027064762483698427
          ],
          [
            -5.717340702793873e-06,
            5.751055380136176e-06,
            0.0021649651932560596
          ],
          [
            -4.288238510985561e-06,
            4.313771965798082e-06,
            0.0016234396334277438
          ],
          [
            -2.8591144960790743e-06,
            2.8764856439760712e-06,
            0.00108189967067685
          ],
          [
            -1.429968715837185e-06,
            1.4391965179108995e-06,
            0.0005403454067762502
          ],
          [
            -8.012705546481936e-10,
            1.9046708618947063e-09,
            -1.223056555932421e-06
          ]
        ],
        "berry_integer_shifts": [
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ]
        ],
        "folded_reduced_polarization": [
          [
            -1.1433529682414179e-05,
            1.1500157956478851e-05,
            0.004330921366717866
          ],
          [
            -1.0004515555939175e-05,
            1.0062887172090917e-05,
            0.003789454437021944
          ],
          [
            -8.575479302885824e-06,
            8.625613078905303e-06,
            0.0032479726969246725
          ],
          [
            -7.1464209943084e-06,
            7.188335781282973e-06,
            0.002706476248369838
          ],
          [
            -5.717340702815488e-06,
            5.7510553801432e-06,
            0.002164965193256041
          ],
          [
            -4.28823851100768e-06,
            4.313771965747115e-06,
            0.0016234396334277035
          ],
          [
            -2.8591144961009896e-06,
            2.876485644009996e-06,
            0.0010818996706768447
          ],
          [
            -1.4299687158270125e-06,
            1.4391965179605393e-06,
            0.000540345406776277
          ],
          [
            -8.012705499105266e-10,
            1.904670865471303e-09,
            -1.2230565559212536e-06
          ]
        ]
      },
      "reflected": {
        "reached": true,
        "construction": "reflect_displacements_about_reconstructed_parent",
        "energies_eV": [
          -247.56885025998778,
          -247.56857989425302,
          -247.56830728521714,
          -247.56803243196478,
          -247.56775533358064,
          -247.56747598914816,
          -247.5671943977509,
          -247.56691055847142,
          -247.56662447039187
        ],
        "cartesian_polarizations_e_A2": [
          [
            -2.21672937172571e-11,
            2.085404133409837e-11,
            -1.9022965350543592e-08
          ],
          [
            1.1495122463830964e-08,
            -9.204605716584576e-09,
            -3.649146745620589e-06
          ],
          [
            2.301000995120482e-08,
            -1.8428600365721716e-08,
            -7.279863593982786e-06
          ],
          [
            3.452249591512468e-08,
            -2.765113035996144e-08,
            -1.0911173446938333e-05
          ],
          [
            4.603258132574767e-08,
            -3.687219631447914e-08,
            -1.4543076239958687e-05
          ],
          [
            5.7540266917865525e-08,
            -4.609179852244378e-08,
            -1.8175571907792118e-05
          ],
          [
            6.904555347223155e-08,
            -5.530993756282647e-08,
            -2.1808660384320956e-05
          ],
          [
            8.054844195759581e-08,
            -6.452661397929163e-08,
            -2.5442341602415203e-05
          ],
          [
            9.204893311002357e-08,
            -7.374182821926165e-08,
            -2.9076615494108314e-05
          ]
        ],
        "raw_reduced_polarization": [
          [
            -8.012740077620152e-10,
            1.9046679754532743e-09,
            -1.2230565575040041e-06
          ],
          [
            4.886666684573585e-07,
            -8.403535515166546e-07,
            -0.00023461233685860105
          ],
          [
            9.780584903623264e-07,
            -1.6825464048999195e-06,
            -0.0004680302825577404
          ],
          [
            1.4673742278072837e-06,
            -2.524673932322749e-06,
            -0.000701476887541224
          ],
          [
            1.9566139272003367e-06,
            -3.3667361886644697e-06,
            -0.0009349521456295711
          ],
          [
            2.4457776310421363e-06,
            -4.208733199404042e-06,
            -0.0011684560505972347
          ],
          [
            2.9348653724217638e-06,
            -5.050665016120771e-06,
            -0.0014019885961634227
          ],
          [
            3.423877200910632e-06,
            -5.892531687173504e-06,
            -0.0016355497759826998
          ],
          [
            3.912813152075901e-06,
            -6.734333252135407e-06,
            -0.0018691395836562892
          ]
        ],
        "unwrapped_reduced_polarization": [
          [
            -8.012740077620152e-10,
            1.9046679754532743e-09,
            -1.2230565575040041e-06
          ],
          [
            4.886666684573585e-07,
            -8.403535515166546e-07,
            -0.00023461233685860105
          ],
          [
            9.780584903623264e-07,
            -1.6825464048999195e-06,
            -0.0004680302825577404
          ],
          [
            1.4673742278072837e-06,
            -2.524673932322749e-06,
            -0.000701476887541224
          ],
          [
            1.9566139272003367e-06,
            -3.3667361886644697e-06,
            -0.0009349521456295711
          ],
          [
            2.4457776310421363e-06,
            -4.208733199404042e-06,
            -0.0011684560505972347
          ],
          [
            2.9348653724217638e-06,
            -5.050665016120771e-06,
            -0.0014019885961634227
          ],
          [
            3.423877200910632e-06,
            -5.892531687173504e-06,
            -0.0016355497759826998
          ],
          [
            3.912813152075901e-06,
            -6.734333252135407e-06,
            -0.0018691395836562892
          ]
        ],
        "gauge_integer_shift": [
          0,
          0,
          0
        ],
        "expected_opposite_endpoint_reduced_polarization": [
          1.143192780475487e-05,
          -1.1496349038845779e-05,
          -0.004333367083104389
        ],
        "actual_opposite_endpoint_branch_residual": 0.0024642435721567275
      },
      "pnp_branch": {
        "construction": "incoming_path_concatenated_with_parent_reflection",
        "reduced_polarization": [
          [
            -1.143352968242519e-05,
            1.1500157956532835e-05,
            0.0043309213667178485
          ],
          [
            -1.0004515555917484e-05,
            1.006288717207093e-05,
            0.0037894544370219636
          ],
          [
            -8.575479302892984e-06,
            8.625613078890528e-06,
            0.0032479726969246625
          ],
          [
            -7.146420994300568e-06,
            7.188335781257812e-06,
            0.0027064762483698427
          ],
          [
            -5.717340702793873e-06,
            5.751055380136176e-06,
            0.0021649651932560596
          ],
          [
            -4.288238510985561e-06,
            4.313771965798082e-06,
            0.0016234396334277438
          ],
          [
            -2.8591144960790743e-06,
            2.8764856439760712e-06,
            0.00108189967067685
          ],
          [
            -1.429968715837185e-06,
            1.4391965179108995e-06,
            0.0005403454067762502
          ],
          [
            -8.012705546481341e-10,
            1.904670861894687e-09,
            -1.2230565559324713e-06
          ],
          [
            4.886666684573585e-07,
            -8.403535515166546e-07,
            -0.00023461233685860105
          ],
          [
            9.780584903623264e-07,
            -1.6825464048999195e-06,
            -0.0004680302825577404
          ],
          [
            1.4673742278072837e-06,
            -2.524673932322749e-06,
            -0.000701476887541224
          ],
          [
            1.9566139272003367e-06,
            -3.3667361886644697e-06,
            -0.0009349521456295711
          ],
          [
            2.4457776310421363e-06,
            -4.208733199404042e-06,
            -0.0011684560505972347
          ],
          [
            2.9348653724217638e-06,
            -5.050665016120771e-06,
            -0.0014019885961634227
          ],
          [
            3.423877200910632e-06,
            -5.892531687173504e-06,
            -0.0016355497759826998
          ],
          [
            3.912813152075901e-06,
            -6.734333252135407e-06,
            -0.0018691395836562892
          ]
        ],
        "unwrapped_reduced_polarization": [
          [
            -1.143352968242519e-05,
            1.1500157956532835e-05,
            0.0043309213667178485
          ],
          [
            -1.0004515555917484e-05,
            1.006288717207093e-05,
            0.0037894544370219636
          ],
          [
            -8.575479302892984e-06,
            8.625613078890528e-06,
            0.0032479726969246625
          ],
          [
            -7.146420994300568e-06,
            7.188335781257812e-06,
            0.0027064762483698427
          ],
          [
            -5.717340702793873e-06,
            5.751055380136176e-06,
            0.0021649651932560596
          ],
          [
            -4.288238510985561e-06,
            4.313771965798082e-06,
            0.0016234396334277438
          ],
          [
            -2.8591144960790743e-06,
            2.8764856439760712e-06,
            0.00108189967067685
          ],
          [
            -1.429968715837185e-06,
            1.4391965179108995e-06,
            0.0005403454067762502
          ],
          [
            -8.012705546481936e-10,
            1.9046708618947063e-09,
            -1.223056555932421e-06
          ],
          [
            4.886666684573585e-07,
            -8.403535515166546e-07,
            -0.00023461233685860105
          ],
          [
            9.780584903623264e-07,
            -1.6825464048999195e-06,
            -0.0004680302825577404
          ],
          [
            1.4673742278072837e-06,
            -2.524673932322749e-06,
            -0.000701476887541224
          ],
          [
            1.9566139272003367e-06,
            -3.3667361886644697e-06,
            -0.0009349521456295711
          ],
          [
            2.4457776310421363e-06,
            -4.208733199404042e-06,
            -0.0011684560505972347
          ],
          [
            2.9348653724217638e-06,
            -5.050665016120771e-06,
            -0.0014019885961634227
          ],
          [
            3.423877200910632e-06,
            -5.892531687173504e-06,
            -0.0016355497759826998
          ],
          [
            3.912813152075901e-06,
            -6.734333252135407e-06,
            -0.0018691395836562892
          ]
        ],
        "berry_integer_shifts": [
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ]
        ],
        "folded_reduced_polarization": [
          [
            -1.1433529682414179e-05,
            1.1500157956478851e-05,
            0.004330921366717866
          ],
          [
            -1.0004515555939175e-05,
            1.0062887172090917e-05,
            0.003789454437021944
          ],
          [
            -8.575479302885824e-06,
            8.625613078905303e-06,
            0.0032479726969246725
          ],
          [
            -7.1464209943084e-06,
            7.188335781282973e-06,
            0.002706476248369838
          ],
          [
            -5.717340702815488e-06,
            5.7510553801432e-06,
            0.002164965193256041
          ],
          [
            -4.28823851100768e-06,
            4.313771965747115e-06,
            0.0016234396334277035
          ],
          [
            -2.8591144961009896e-06,
            2.876485644009996e-06,
            0.0010818996706768447
          ],
          [
            -1.4299687158270125e-06,
            1.4391965179605393e-06,
            0.000540345406776277
          ],
          [
            -8.012705499105266e-10,
            1.904670865471303e-09,
            -1.2230565559212536e-06
          ],
          [
            4.886666684633667e-07,
            -8.403535515233429e-07,
            -0.00023461233685861949
          ],
          [
            9.780584903085199e-07,
            -1.6825464049241567e-06,
            -0.00046803028255776313
          ],
          [
            1.4673742277926394e-06,
            -2.5246739323026013e-06,
            -0.0007014768875412414
          ],
          [
            1.9566139272120253e-06,
            -3.3667361886702274e-06,
            -0.0009349521456295529
          ],
          [
            2.4457776310882196e-06,
            -4.208733199395631e-06,
            -0.001168456050597233
          ],
          [
            2.934865372394846e-06,
            -5.050665016104183e-06,
            -0.001401988596163417
          ],
          [
            3.423877200869896e-06,
            -5.8925316871460964e-06,
            -0.001635549775982681
          ],
          [
            3.912813152040506e-06,
            -6.734333252156333e-06,
            -0.0018691395836563096
          ]
        ]
      },
      "incoming_structure_ids": [
        "incoming_00_000",
        "incoming_00_001",
        "incoming_00_002",
        "incoming_00_003",
        "incoming_00_004",
        "incoming_00_005",
        "incoming_00_006",
        "incoming_00_007",
        "incoming_00_008"
      ],
      "reflected_structure_ids": [
        "reflected_00_001",
        "reflected_00_002",
        "reflected_00_003",
        "reflected_00_004",
        "reflected_00_005",
        "reflected_00_006",
        "reflected_00_007",
        "reflected_00_008"
      ]
    },
    {
      "orbit_id": 1,
      "formal_class": [
        0.0,
        0.0,
        0.5
      ],
      "formal_classes_in_orbit": [
        [
          0.0,
          0.0,
          0.5
        ]
      ],
      "target_reduced_polarization": [
        0.0,
        0.0,
        0.5
      ],
      "bec_backprojection": {
        "converged_to_target": true,
        "history": [
          {
            "iteration": 0,
            "reduced_polarization": [
              -1.1433529682789355e-05,
              1.1500157957619056e-05,
              0.004330921366717734
            ],
            "branch_aligned_reduced_polarization": [
              -1.1433529682789355e-05,
              1.1500157957619056e-05,
              0.004330921366717755
            ],
            "target_residual": 0.49566907889855927,
            "energy_eV": -247.56934685966073,
            "max_atomic_step_A": 0.04098613929532979,
            "max_log_strain_component": 0.02,
            "step_scale": 0.6381459714851191,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 8.51374711949435,
            "cell_principal_stretches": [
              1.0202013400316778,
              0.9940949481120045,
              0.9940939059584484
            ],
            "cell_volume_ratio": 1.008187173456543,
            "cell_rmsd_from_input_A": 0.17120891245667097
          },
          {
            "iteration": 1,
            "reduced_polarization": [
              -4.0912298471266664e-06,
              4.086617726140629e-06,
              0.3105283506122559
            ],
            "branch_aligned_reduced_polarization": [
              -4.0912298471266664e-06,
              4.086617726140629e-06,
              0.3105283506122559
            ],
            "target_residual": 0.1894716494759858,
            "energy_eV": -246.74960300653584,
            "max_atomic_step_A": 0.024447406884343756,
            "max_log_strain_component": 0.012945651296309492,
            "step_scale": 1.0,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 8.51374711949435,
            "cell_principal_stretches": [
              1.033494368642828,
              0.9902912590366051,
              0.9902896586432933
            ],
            "cell_volume_ratio": 1.0135222892976214,
            "cell_rmsd_from_input_A": 0.28534166718543696
          },
          {
            "iteration": 2,
            "reduced_polarization": [
              5.400068394599247e-09,
              -1.374987701757477e-08,
              0.48649285883113536
            ],
            "branch_aligned_reduced_polarization": [
              5.400068394599247e-09,
              -1.374987701757477e-08,
              0.48649285883113536
            ],
            "target_residual": 0.013507141168872723,
            "energy_eV": -245.57023266207185,
            "max_atomic_step_A": 0.00172476551673476,
            "max_log_strain_component": 0.001024308913743022,
            "step_scale": 1.0,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 8.51374711949435,
            "cell_principal_stretches": [
              1.034553528497478,
              0.9899908944900796,
              0.9899892988053451
            ],
            "cell_volume_ratio": 1.0139456271960396,
            "cell_rmsd_from_input_A": 0.29448634485190034
          },
          {
            "iteration": 3,
            "reduced_polarization": [
              4.4143119184231023e-10,
              9.163963261754935e-10,
              0.4990042294511824
            ],
            "branch_aligned_reduced_polarization": [
              4.4143119184231023e-10,
              9.163963261754935e-10,
              0.4990042294511824
            ],
            "target_residual": 0.000995770548818129,
            "energy_eV": -245.46557913312094
          }
        ],
        "iterations": 3
      },
      "parent": {
        "candidate_id": "bec_projection_01",
        "source": "MACEField_BEC_backprojection",
        "spacegroup": "R3c",
        "spacegroup_number": 161,
        "pointgroup": "3m",
        "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": 0.000995770548818129,
        "parent_symmetrization_rmsd_A": 0.04756785804183332,
        "parent_cell_rmsd_A": 0.29448634485190034,
        "energy_eV": -245.46557913312094,
        "reduced_polarization": [
          4.4143119184231023e-10,
          9.163963261754935e-10,
          0.4990042294511824
        ],
        "cartesian_polarization_e_A2": [
          -3.6659962030761813e-09,
          2.0009777501702763e-09,
          0.007920354949904928
        ],
        "ranking_score": 0.6231809853524447
      },
      "branch_status": "awaiting_branch_sampling"
    },
    {
      "orbit_id": 2,
      "formal_class": [
        0.0,
        0.5,
        0.0
      ],
      "formal_classes_in_orbit": [
        [
          0.0,
          0.5,
          0.0
        ]
      ],
      "target_reduced_polarization": [
        0.0,
        0.5,
        0.0
      ],
      "bec_backprojection": {
        "converged_to_target": true,
        "history": [
          {
            "iteration": 0,
            "reduced_polarization": [
              -1.1433529682789355e-05,
              1.1500157957619056e-05,
              0.004330921366717734
            ],
            "branch_aligned_reduced_polarization": [
              -1.1433529682789355e-05,
              1.1500157957644586e-05,
              0.004330921366717734
            ],
            "target_residual": 0.5000072569322432,
            "energy_eV": -247.56934685966073,
            "max_atomic_step_A": 0.057564192109222964,
            "max_log_strain_component": 0.014495888453716103,
            "step_scale": 1.0,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 8.51374711949435,
            "cell_principal_stretches": [
              1.0225337656909563,
              1.0014435349207231,
              0.9764441017774587
            ],
            "cell_volume_ratio": 0.9998883575811502,
            "cell_rmsd_from_input_A": 0.21085351699208024
          },
          {
            "iteration": 1,
            "reduced_polarization": [
              -0.007011015791388988,
              0.4911387467237642,
              0.007753905332656907
            ],
            "branch_aligned_reduced_polarization": [
              -0.007011015791388988,
              0.4911387467237642,
              0.007753905332656907
            ],
            "target_residual": 0.01370398482050061,
            "energy_eV": -245.2973247418246,
            "max_atomic_step_A": 0.0013914025339042833,
            "max_log_strain_component": 0.0005160356031977235,
            "step_scale": 1.0,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 8.51374711949435,
            "cell_principal_stretches": [
              1.022907328461464,
              1.0009593049022212,
              0.9763542745536439
            ],
            "cell_volume_ratio": 0.999678019552496,
            "cell_rmsd_from_input_A": 0.211675732287877
          },
          {
            "iteration": 2,
            "reduced_polarization": [
              -7.65711930143842e-05,
              0.4998850290265055,
              7.376216683739838e-05
            ],
            "branch_aligned_reduced_polarization": [
              -7.65711930143842e-05,
              0.4998850290265055,
              7.376216683739838e-05
            ],
            "target_residual": 0.0001565960714783967,
            "energy_eV": -245.26749289483698
          }
        ],
        "iterations": 2
      },
      "parent": {
        "candidate_id": "bec_projection_02",
        "source": "MACEField_BEC_backprojection",
        "spacegroup": "P1",
        "spacegroup_number": 1,
        "pointgroup": "1",
        "has_inversion": false,
        "is_polar_point_group": true,
        "nonpolar_parent_hypothesis": false,
        "symmetry_tolerance_A": null,
        "target_reduced_polarization": [
          0.0,
          0.5,
          0.0
        ],
        "formal_class": [
          0.0,
          0.5,
          0.0
        ],
        "target_residual": 0.0001565960714783967,
        "parent_symmetrization_rmsd_A": 0.04103351885062665,
        "parent_cell_rmsd_A": 0.211675732287877,
        "energy_eV": -245.26749289483698,
        "reduced_polarization": [
          -7.65711930143842e-05,
          0.4998850290265055,
          7.376216683739838e-05
        ],
        "cartesian_polarization_e_A2": [
          -0.0030635473231651993,
          0.005504890061130843,
          -0.00010307542381953337
        ],
        "ranking_score": 0.5942656440655527
      },
      "branch_status": "awaiting_branch_sampling"
    },
    {
      "orbit_id": 3,
      "formal_class": [
        0.5,
        0.0,
        0.0
      ],
      "formal_classes_in_orbit": [
        [
          0.5,
          0.0,
          0.0
        ]
      ],
      "target_reduced_polarization": [
        -0.5,
        0.0,
        0.0
      ],
      "bec_backprojection": {
        "converged_to_target": true,
        "history": [
          {
            "iteration": 0,
            "reduced_polarization": [
              -1.1433529682789355e-05,
              1.1500157957619056e-05,
              0.004330921366717734
            ],
            "branch_aligned_reduced_polarization": [
              -1.1433529682802757e-05,
              1.1500157957619056e-05,
              0.004330921366717734
            ],
            "target_residual": 0.5000073235595466,
            "energy_eV": -247.56934685966073,
            "max_atomic_step_A": 0.0450648459402613,
            "max_log_strain_component": 0.02,
            "step_scale": 0.8506056073673622,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 8.51374711949435,
            "cell_principal_stretches": [
              1.0240458831913923,
              0.9998543013763496,
              0.976568301930766
            ],
            "cell_volume_ratio": 0.9999050432296639,
            "cell_rmsd_from_input_A": 0.20364129290337282
          },
          {
            "iteration": 1,
            "reduced_polarization": [
              -0.4169418652044949,
              0.007649149024925207,
              0.0056298505196763216
            ],
            "branch_aligned_reduced_polarization": [
              -0.4169418652044949,
              0.007649149024925207,
              0.0056298505196763216
            ],
            "target_residual": 0.08359939266159601,
            "energy_eV": -245.88173495930664,
            "max_atomic_step_A": 0.008398897102280608,
            "max_log_strain_component": 0.003897825692393447,
            "step_scale": 1.0,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 8.51374711949435,
            "cell_principal_stretches": [
              1.029013092984836,
              0.9992459744715182,
              0.9722668468540498
            ],
            "cell_volume_ratio": 0.9997209313595568,
            "cell_rmsd_from_input_A": 0.24140760472801698
          },
          {
            "iteration": 2,
            "reduced_polarization": [
              -0.4978210686816795,
              0.0013069131130993546,
              0.00072282242952937
            ],
            "branch_aligned_reduced_polarization": [
              -0.4978210686816795,
              0.0013069131130993546,
              0.00072282242952937
            ],
            "target_residual": 0.0026416350693802496,
            "energy_eV": -245.1827087718576,
            "max_atomic_step_A": 0.0002296988589031185,
            "max_log_strain_component": 7.891843523746687e-05,
            "step_scale": 1.0,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 8.51374711949435,
            "cell_principal_stretches": [
              1.0291389830642483,
              0.9991685750162529,
              0.9722034550820082
            ],
            "cell_volume_ratio": 0.9997006073978024,
            "cell_rmsd_from_input_A": 0.24203002181598376
          },
          {
            "iteration": 3,
            "reduced_polarization": [
              -0.49995164291869404,
              2.8381511524597028e-05,
              1.8260950373094252e-05
            ],
            "branch_aligned_reduced_polarization": [
              -0.49995164291869404,
              2.8381511524597028e-05,
              1.8260950373094252e-05
            ],
            "target_residual": 5.8969312505579984e-05,
            "energy_eV": -245.17040814530466
          }
        ],
        "iterations": 3
      },
      "parent": {
        "candidate_id": "bec_projection_03",
        "source": "MACEField_BEC_backprojection",
        "spacegroup": "P1",
        "spacegroup_number": 1,
        "pointgroup": "1",
        "has_inversion": false,
        "is_polar_point_group": true,
        "nonpolar_parent_hypothesis": false,
        "symmetry_tolerance_A": null,
        "target_reduced_polarization": [
          -0.5,
          0.0,
          0.0
        ],
        "formal_class": [
          0.5,
          0.0,
          0.0
        ],
        "target_residual": 5.8969312505579984e-05,
        "parent_symmetrization_rmsd_A": 0.03776809087441365,
        "parent_cell_rmsd_A": 0.24203002181598376,
        "energy_eV": -245.17040814530466,
        "reduced_polarization": [
          -0.49995164291869404,
          2.8381511524597028e-05,
          1.8260950373094252e-05
        ],
        "cartesian_polarization_e_A2": [
          -0.006329075666472781,
          -0.00015135610589655396,
          -9.662508982790814e-05
        ],
        "ranking_score": 0.5983935349534207
      },
      "branch_status": "awaiting_branch_sampling"
    },
    {
      "orbit_id": 4,
      "formal_class": [
        0.0,
        0.5,
        0.5
      ],
      "formal_classes_in_orbit": [
        [
          0.0,
          0.5,
          0.5
        ]
      ],
      "target_reduced_polarization": [
        0.0,
        0.5,
        0.5
      ],
      "bec_backprojection": {
        "converged_to_target": true,
        "history": [
          {
            "iteration": 0,
            "reduced_polarization": [
              -1.1433529682789355e-05,
              1.1500157957619056e-05,
              0.004330921366717734
            ],
            "branch_aligned_reduced_polarization": [
              -1.1433529682789355e-05,
              1.1500157957644586e-05,
              0.004330921366717755
            ],
            "target_residual": 0.7040428506974477,
            "energy_eV": -247.56934685966073,
            "max_atomic_step_A": 0.055037622477009523,
            "max_log_strain_component": 0.02,
            "step_scale": 0.6381466890348797,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 8.51374711949435,
            "cell_principal_stretches": [
              1.0241653601564087,
              1.0024076602872467,
              0.9820344214599417
            ],
            "cell_volume_ratio": 1.0081871789228507,
            "cell_rmsd_from_input_A": 0.23362330567451806
          },
          {
            "iteration": 1,
            "reduced_polarization": [
              -0.0005321116717966911,
              0.32013079063336686,
              0.31173253768009335
            ],
            "branch_aligned_reduced_polarization": [
              -0.0005321116717966911,
              0.32013079063336686,
              0.31173253768009335
            ],
            "target_residual": 0.2603802085208982,
            "energy_eV": -245.6446606023101,
            "max_atomic_step_A": 0.032028511127605894,
            "max_log_strain_component": 0.012862563362474941,
            "step_scale": 1.0,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 8.51374711949435,
            "cell_principal_stretches": [
              1.0394305493925924,
              1.0036041111344078,
              0.9715400043629482
            ],
            "cell_volume_ratio": 1.0134879662119725,
            "cell_rmsd_from_input_A": 0.3796538199149362
          },
          {
            "iteration": 2,
            "reduced_polarization": [
              0.0010672717265881716,
              0.49877034049914964,
              0.4846134242408871
            ],
            "branch_aligned_reduced_polarization": [
              0.0010672717265881716,
              0.49877034049914964,
              0.4846134242408871
            ],
            "target_residual": 0.015472486710846665,
            "energy_eV": -242.5722575053809,
            "max_atomic_step_A": 0.0020025499946453268,
            "max_log_strain_component": 0.0011794655359285808,
            "step_scale": 1.0,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 8.51374711949435,
            "cell_principal_stretches": [
              1.0404887572356496,
              1.0034680554278779,
              0.9711503860968398
            ],
            "cell_volume_ratio": 1.0139754279573379,
            "cell_rmsd_from_input_A": 0.3891283180935737
          },
          {
            "iteration": 3,
            "reduced_polarization": [
              2.5676405117045744e-05,
              0.4999776065326153,
              0.4986849799203615
            ],
            "branch_aligned_reduced_polarization": [
              2.5676405117045744e-05,
              0.4999776065326153,
              0.4986849799203615
            ],
            "target_residual": 0.0013154613468337785,
            "energy_eV": -242.40699738544745,
            "max_atomic_step_A": 0.0001701110464279644,
            "max_log_strain_component": 0.00010184128592123401,
            "step_scale": 1.0,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 8.51374711949435,
            "cell_principal_stretches": [
              1.0405786203389757,
              1.0034508887761098,
              0.971123451457201
            ],
            "cell_volume_ratio": 1.0140175289708195,
            "cell_rmsd_from_input_A": 0.3899076042223225
          },
          {
            "iteration": 4,
            "reduced_polarization": [
              1.4382343905923721e-06,
              0.49999864001742095,
              0.49988782208213844
            ],
            "branch_aligned_reduced_polarization": [
              1.4382343905923721e-06,
              0.49999864001742095,
              0.49988782208213844
            ],
            "target_residual": 0.00011219538014789882,
            "energy_eV": -242.39428154229904
          }
        ],
        "iterations": 4
      },
      "parent": {
        "candidate_id": "bec_projection_04",
        "source": "MACEField_BEC_backprojection",
        "spacegroup": "P1",
        "spacegroup_number": 1,
        "pointgroup": "1",
        "has_inversion": false,
        "is_polar_point_group": true,
        "nonpolar_parent_hypothesis": false,
        "symmetry_tolerance_A": null,
        "target_reduced_polarization": [
          0.0,
          0.5,
          0.5
        ],
        "formal_class": [
          0.0,
          0.5,
          0.5
        ],
        "target_residual": 0.00011219538014789882,
        "parent_symmetrization_rmsd_A": 0.06367659203550156,
        "parent_cell_rmsd_A": 0.3899076042223225,
        "energy_eV": -242.39428154229904,
        "reduced_polarization": [
          1.4382343905923721e-06,
          0.49999864001742095,
          0.49988782208213844
        ],
        "cartesian_polarization_e_A2": [
          -0.002929396934393759,
          0.005257499773150536,
          0.007832879889209741
        ],
        "ranking_score": 0.661377883851378
      },
      "branch_status": "awaiting_branch_sampling"
    },
    {
      "orbit_id": 5,
      "formal_class": [
        0.5,
        0.0,
        0.5
      ],
      "formal_classes_in_orbit": [
        [
          0.5,
          0.0,
          0.5
        ]
      ],
      "target_reduced_polarization": [
        -0.5,
        0.0,
        0.5
      ],
      "bec_backprojection": {
        "converged_to_target": true,
        "history": [
          {
            "iteration": 0,
            "reduced_polarization": [
              -1.1433529682789355e-05,
              1.1500157957619056e-05,
              0.004330921366717734
            ],
            "branch_aligned_reduced_polarization": [
              -1.1433529682802757e-05,
              1.1500157957619056e-05,
              0.004330921366717755
            ],
            "target_residual": 0.7040428980157838,
            "energy_eV": -247.56934685966073,
            "max_atomic_step_A": 0.053129648552650975,
            "max_log_strain_component": 0.02,
            "step_scale": 0.638146520477483,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 8.51374711949435,
            "cell_principal_stretches": [
              1.0243781764978082,
              1.0061473450271612,
              0.9781811029941093
            ],
            "cell_volume_ratio": 1.0081871825678612,
            "cell_rmsd_from_input_A": 0.24772812002459904
          },
          {
            "iteration": 1,
            "reduced_polarization": [
              -0.3172858227792906,
              0.002769011779484789,
              0.31122041459664695
            ],
            "branch_aligned_reduced_polarization": [
              -0.3172858227792906,
              0.002769011779484789,
              0.31122041459664695
            ],
            "target_residual": 0.2627353608647637,
            "energy_eV": -245.60412183144507,
            "max_atomic_step_A": 0.03118960882784772,
            "max_log_strain_component": 0.012963058277557197,
            "step_scale": 1.0,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 8.51374711949435,
            "cell_principal_stretches": [
              1.0398920291538238,
              1.0095594237910572,
              0.9654199207738586
            ],
            "cell_volume_ratio": 1.013529496436794,
            "cell_rmsd_from_input_A": 0.4017787448114185
          },
          {
            "iteration": 2,
            "reduced_polarization": [
              -0.49541574798459015,
              0.0014446652996554278,
              0.4840547153019002
            ],
            "branch_aligned_reduced_polarization": [
              -0.49541574798459015,
              0.0014446652996554278,
              0.4840547153019002
            ],
            "target_residual": 0.01665396434703382,
            "energy_eV": -242.41667392046813,
            "max_atomic_step_A": 0.002112451965467102,
            "max_log_strain_component": 0.001225584624296279,
            "step_scale": 1.0,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 8.51374711949435,
            "cell_principal_stretches": [
              1.0410220556041614,
              1.0095080851600855,
              0.9649030076031863
            ],
            "cell_volume_ratio": 1.0140360443263812,
            "cell_rmsd_from_input_A": 0.41192081145551573
          },
          {
            "iteration": 3,
            "reduced_polarization": [
              -0.4998810593872887,
              3.710397809308144e-05,
              0.4986057503576822
            ],
            "branch_aligned_reduced_polarization": [
              -0.4998810593872887,
              3.710397809308144e-05,
              0.4986057503576822
            ],
            "target_residual": 0.0013998055720870124,
            "energy_eV": -242.22036467538902,
            "max_atomic_step_A": 0.00018073762432016077,
            "max_log_strain_component": 0.00010840580713051156,
            "step_scale": 1.0,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 8.51374711949435,
            "cell_principal_stretches": [
              1.0411147337744842,
              1.0094978636683467,
              0.9648695253593059
            ],
            "cell_volume_ratio": 1.0140808618419308,
            "cell_rmsd_from_input_A": 0.4127426905041598
          },
          {
            "iteration": 4,
            "reduced_polarization": [
              -0.4999955948136586,
              7.364925848248722e-07,
              0.4998788853146596
            ],
            "branch_aligned_reduced_polarization": [
              -0.4999955948136586,
              7.364925848248722e-07,
              0.4998788853146596
            ],
            "target_residual": 0.00012119700942320248,
            "energy_eV": -242.20589436929384
          }
        ],
        "iterations": 4
      },
      "parent": {
        "candidate_id": "bec_projection_05",
        "source": "MACEField_BEC_backprojection",
        "spacegroup": "P1",
        "spacegroup_number": 1,
        "pointgroup": "1",
        "has_inversion": false,
        "is_polar_point_group": true,
        "nonpolar_parent_hypothesis": false,
        "symmetry_tolerance_A": null,
        "target_reduced_polarization": [
          -0.5,
          0.0,
          0.5
        ],
        "formal_class": [
          0.5,
          0.0,
          0.5
        ],
        "target_residual": 0.00012119700942320248,
        "parent_symmetrization_rmsd_A": 0.06177613527628021,
        "parent_cell_rmsd_A": 0.4127426905041598,
        "energy_eV": -242.20589436929384,
        "reduced_polarization": [
          -0.4999955948136586,
          7.364925848248722e-07,
          0.4998788853146596
        ],
        "cartesian_polarization_e_A2": [
          -0.00605561019330837,
          -0.00014556344075629518,
          0.007840156513639207
        ],
        "ranking_score": 0.6652042019211666
      },
      "branch_status": "awaiting_branch_sampling"
    },
    {
      "orbit_id": 6,
      "formal_class": [
        0.5,
        0.5,
        0.0
      ],
      "formal_classes_in_orbit": [
        [
          0.5,
          0.5,
          0.0
        ]
      ],
      "target_reduced_polarization": [
        -0.5,
        0.5,
        0.0
      ],
      "bec_backprojection": {
        "converged_to_target": true,
        "history": [
          {
            "iteration": 0,
            "reduced_polarization": [
              -1.1433529682789355e-05,
              1.1500157957619056e-05,
              0.004330921366717734
            ],
            "branch_aligned_reduced_polarization": [
              -1.1433529682802757e-05,
              1.1500157957644586e-05,
              0.004330921366717734
            ],
            "target_residual": 0.7071038279172469,
            "energy_eV": -247.56934685966073,
            "max_atomic_step_A": 0.05357765080369033,
            "max_log_strain_component": 0.02,
            "step_scale": 0.56706544823348,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 8.51374711949435,
            "cell_principal_stretches": [
              1.0213285318601781,
              1.007820748868456,
              0.9714573642480755
            ],
            "cell_volume_ratio": 0.9999366917088875,
            "cell_rmsd_from_input_A": 0.2391007964771445
          },
          {
            "iteration": 1,
            "reduced_polarization": [
              -0.2816214890753223,
              0.2854453047189577,
              0.007020437692619502
            ],
            "branch_aligned_reduced_polarization": [
              -0.2816214890753223,
              0.2854453047189577,
              0.007020437692619502
            ],
            "target_residual": 0.306222431977503,
            "energy_eV": -244.96695831925766,
            "max_atomic_step_A": 0.04018869913489655,
            "max_log_strain_component": 0.015902887595086887,
            "step_scale": 1.0,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 8.51374711949435,
            "cell_principal_stretches": [
              1.0387485406254218,
              1.0136526848041816,
              0.949429457599078
            ],
            "cell_volume_ratio": 0.9996829933381645,
            "cell_rmsd_from_input_A": 0.4201330629129296
          },
          {
            "iteration": 2,
            "reduced_polarization": [
              -0.4878968814581165,
              0.49821492638281994,
              0.003756796312718698
            ],
            "branch_aligned_reduced_polarization": [
              -0.4878968814581165,
              0.49821492638281994,
              0.003756796312718698
            ],
            "target_residual": 0.012797870322553414,
            "energy_eV": -238.30717544702833,
            "max_atomic_step_A": 0.0014170978605231419,
            "max_log_strain_component": 0.0006900315467128313,
            "step_scale": 1.0,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 8.51374711949435,
            "cell_principal_stretches": [
              1.0395527612820163,
              1.0136231077540592,
              0.9486291552774571
            ],
            "cell_volume_ratio": 0.999584486300406,
            "cell_rmsd_from_input_A": 0.4263833574074132
          },
          {
            "iteration": 3,
            "reduced_polarization": [
              -0.49936869808965695,
              0.5002073729843567,
              0.0002012722551478557
            ],
            "branch_aligned_reduced_polarization": [
              -0.49936869808965695,
              0.5002073729843567,
              0.0002012722551478557
            ],
            "target_residual": 0.0006943026554292374,
            "energy_eV": -238.0290615367193
          }
        ],
        "iterations": 3
      },
      "parent": {
        "candidate_id": "bec_projection_06",
        "source": "MACEField_BEC_backprojection",
        "spacegroup": "P1",
        "spacegroup_number": 1,
        "pointgroup": "1",
        "has_inversion": false,
        "is_polar_point_group": true,
        "nonpolar_parent_hypothesis": false,
        "symmetry_tolerance_A": null,
        "target_reduced_polarization": [
          -0.5,
          0.5,
          0.0
        ],
        "formal_class": [
          0.5,
          0.5,
          0.0
        ],
        "target_residual": 0.0006943026554292374,
        "parent_symmetrization_rmsd_A": 0.0697036327773138,
        "parent_cell_rmsd_A": 0.4263833574074132,
        "energy_eV": -238.0290615367193,
        "reduced_polarization": [
          -0.49936869808965695,
          0.5002073729843567,
          0.0002012722551478557
        ],
        "cartesian_polarization_e_A2": [
          -0.009183897779343513,
          0.005203371953236484,
          -0.000293309745173332
        ],
        "ranking_score": 0.6776880774400256
      },
      "branch_status": "awaiting_branch_sampling"
    },
    {
      "orbit_id": 7,
      "formal_class": [
        0.5,
        0.5,
        0.5
      ],
      "formal_classes_in_orbit": [
        [
          0.5,
          0.5,
          0.5
        ]
      ],
      "target_reduced_polarization": [
        -0.5,
        0.5,
        0.5
      ],
      "bec_backprojection": {
        "converged_to_target": true,
        "history": [
          {
            "iteration": 0,
            "reduced_polarization": [
              -1.1433529682789355e-05,
              1.1500157957619056e-05,
              0.004330921366717734
            ],
            "branch_aligned_reduced_polarization": [
              -1.1433529682802757e-05,
              1.1500157957644586e-05,
              0.004330921366717755
            ],
            "target_residual": 0.8635189066190189,
            "energy_eV": -247.56934685966073,
            "max_atomic_step_A": 0.0647835833277339,
            "max_log_strain_component": 0.02,
            "step_scale": 0.5670650252045588,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 8.51374711949435,
            "cell_principal_stretches": [
              1.0228538357745018,
              1.0157652519109222,
              0.9694821072595208
            ],
            "cell_volume_ratio": 1.0072719227580678,
            "cell_rmsd_from_input_A": 0.30415611613658994
          },
          {
            "iteration": 1,
            "reduced_polarization": [
              -0.28012148374042,
              0.28595994334507796,
              0.2783597850861432
            ],
            "branch_aligned_reduced_polarization": [
              -0.28012148374042,
              0.28595994334507796,
              0.2783597850861432
            ],
            "target_residual": 0.3785288531042479,
            "energy_eV": -243.81580627299536,
            "max_atomic_step_A": 0.04938325194478092,
            "max_log_strain_component": 0.016479933434100313,
            "step_scale": 1.0,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 8.51374711949435,
            "cell_principal_stretches": [
              1.0427106212126096,
              1.0286127672412826,
              0.9450412587252801
            ],
            "cell_volume_ratio": 1.0135997092123055,
            "cell_rmsd_from_input_A": 0.5534635776834106
          },
          {
            "iteration": 2,
            "reduced_polarization": [
              -0.48025337752929903,
              0.49586679909000253,
              0.47315964397532584
            ],
            "branch_aligned_reduced_polarization": [
              -0.48025337752929903,
              0.49586679909000253,
              0.47315964397532584
            ],
            "target_residual": 0.03357703322650855,
            "energy_eV": -233.38897428450568,
            "max_atomic_step_A": 0.004057025043330253,
            "max_log_strain_component": 0.0021429651044519373,
            "step_scale": 1.0,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 8.51374711949435,
            "cell_principal_stretches": [
              1.045135738823236,
              1.0292224056738608,
              0.9431135330038359
            ],
            "cell_volume_ratio": 1.0144856484179585,
            "cell_rmsd_from_input_A": 0.577157659012764
          },
          {
            "iteration": 3,
            "reduced_polarization": [
              -0.4984702052204582,
              0.5002248495288754,
              0.4964744864909483
            ],
            "branch_aligned_reduced_polarization": [
              -0.4984702052204582,
              0.5002248495288754,
              0.4964744864909483
            ],
            "target_residual": 0.0038496850365523417,
            "energy_eV": -232.39330722804647,
            "max_atomic_step_A": 0.0004858666570358158,
            "max_log_strain_component": 0.00028159808355755913,
            "step_scale": 1.0,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 8.51374711949435,
            "cell_principal_stretches": [
              1.0454246751537455,
              1.0292194800021377,
              0.9429638048457915
            ],
            "cell_volume_ratio": 1.0146021234799683,
            "cell_rmsd_from_input_A": 0.5795193507445275
          },
          {
            "iteration": 4,
            "reduced_polarization": [
              -0.49988559157487056,
              0.5000261292440213,
              0.49955614648439833
            ],
            "branch_aligned_reduced_polarization": [
              -0.49988559157487056,
              0.5000261292440213,
              0.49955614648439833
            ],
            "target_residual": 0.00045910561796354103,
            "energy_eV": -232.31134247875863
          }
        ],
        "iterations": 4
      },
      "parent": {
        "candidate_id": "bec_projection_07",
        "source": "MACEField_BEC_backprojection",
        "spacegroup": "P1",
        "spacegroup_number": 1,
        "pointgroup": "1",
        "has_inversion": false,
        "is_polar_point_group": true,
        "nonpolar_parent_hypothesis": false,
        "symmetry_tolerance_A": null,
        "target_reduced_polarization": [
          -0.5,
          0.5,
          0.5
        ],
        "formal_class": [
          0.5,
          0.5,
          0.5
        ],
        "target_residual": 0.00045910561796354103,
        "parent_symmetrization_rmsd_A": 0.08864738379978339,
        "parent_cell_rmsd_A": 0.5795193507445275,
        "energy_eV": -232.31134247875863,
        "reduced_polarization": [
          -0.49988559157487056,
          0.5000261292440213,
          0.49955614648439833
        ],
        "cartesian_polarization_e_A2": [
          -0.008763308527015306,
          0.004945536863986719,
          0.007634316489225644
        ],
        "ranking_score": 0.7344454327218424
      },
      "branch_status": "awaiting_branch_sampling"
    }
  ],
  "sampled_polarization_branches": [
    {
      "orbit_id": 0,
      "candidate_id": "bec_projection_00",
      "formal_class": [
        0.0,
        0.0,
        0.0
      ],
      "construction": "MACEField-BEC-parent plus variable-cell P-N-P path and symmetric log-strain continuation beyond both polar endpoints",
      "geometry_diagnostics": {
        "collision_aware": false,
        "permutations_tested": 1,
        "selected_order": [
          0,
          1,
          2,
          3,
          4,
          5,
          6,
          7,
          8,
          9,
          10,
          11,
          12,
          13,
          14,
          15,
          16,
          17,
          18,
          19,
          20,
          21,
          22,
          23,
          24,
          25,
          26,
          27,
          28,
          29,
          30,
          31,
          32,
          33,
          34,
          35,
          36,
          37,
          38,
          39,
          40,
          41,
          42,
          43,
          44,
          45,
          46,
          47
        ],
        "endpoint_rmsd_A": 0.00040085439201025956,
        "minimum_distance_A_by_image": [
          1.5656343574313778,
          1.5656842135333,
          1.5657340695749666,
          1.5657839271566822,
          1.5658333571704812,
          1.5658821898412199,
          1.5659310240215285,
          1.5659798597103858,
          1.566028696906766
        ],
        "minimum_distance_A": 1.5656343574313778,
        "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": [
          681.3887811289554,
          681.3792721780459,
          681.3697633598362,
          681.3602546743249,
          681.3507461215092,
          681.3412377013889,
          681.3317294139604,
          681.3222212592212,
          681.3127132371726
        ],
        "cell_deformation_log_strain_norm": 0.0002968925849763811
      },
      "parent_reduced_polarization": [
        -8.012705546481341e-10,
        1.904670861894687e-09,
        -1.2230565559324713e-06
      ],
      "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": [
          -247.56934685966078,
          -247.5693055004472,
          -247.56925823279954,
          -247.56920505154912,
          -247.5691459515222,
          -247.5690809275397,
          -247.56900997441707,
          -247.56893308696485,
          -247.5688502599878
        ],
        "cartesian_polarizations_e_A2": [
          [
            -2.1727160428140587e-07,
            1.2592823086919723e-07,
            6.737246186233976e-05
          ],
          [
            -1.901248721491128e-07,
            1.10195059564023e-07,
            5.8948125998341e-05
          ],
          [
            -1.629754378285502e-07,
            9.446038595392808e-08,
            5.052390131789988e-05
          ],
          [
            -1.3582330275594567e-07,
            7.872421111747367e-08,
            4.209978941039949e-05
          ],
          [
            -1.086684683687581e-07,
            6.298653609742487e-08,
            3.3675791864388756e-05
          ],
          [
            -8.151093616334316e-08,
            4.724736181983496e-08,
            2.52519102674458e-05
          ],
          [
            -5.4350707665967516e-08,
            3.150668938043008e-08,
            1.68281462062039e-05
          ],
          [
            -2.7187784141854036e-08,
            1.576451984802055e-08,
            8.404501266870771e-06
          ],
          [
            -2.216726829905467e-11,
            2.085407294708057e-11,
            -1.9022965326100564e-08
          ]
        ],
        "raw_reduced_polarization": [
          [
            -1.143352968242519e-05,
            1.1500157956532835e-05,
            0.0043309213667178485
          ],
          [
            -1.0004515555917484e-05,
            1.006288717207093e-05,
            0.0037894544370219636
          ],
          [
            -8.575479302892984e-06,
            8.625613078890528e-06,
            0.0032479726969246625
          ],
          [
            -7.146420994300568e-06,
            7.188335781257812e-06,
            0.0027064762483698427
          ],
          [
            -5.717340702793873e-06,
            5.751055380136176e-06,
            0.0021649651932560596
          ],
          [
            -4.288238510985561e-06,
            4.313771965798082e-06,
            0.0016234396334277438
          ],
          [
            -2.8591144960790743e-06,
            2.8764856439760712e-06,
            0.00108189967067685
          ],
          [
            -1.429968715837185e-06,
            1.4391965179108995e-06,
            0.0005403454067762502
          ],
          [
            -8.012705546481341e-10,
            1.904670861894687e-09,
            -1.2230565559324713e-06
          ]
        ],
        "unwrapped_reduced_polarization": [
          [
            -1.143352968242519e-05,
            1.1500157956532835e-05,
            0.0043309213667178485
          ],
          [
            -1.0004515555917484e-05,
            1.006288717207093e-05,
            0.0037894544370219636
          ],
          [
            -8.575479302892984e-06,
            8.625613078890528e-06,
            0.0032479726969246625
          ],
          [
            -7.146420994300568e-06,
            7.188335781257812e-06,
            0.0027064762483698427
          ],
          [
            -5.717340702793873e-06,
            5.751055380136176e-06,
            0.0021649651932560596
          ],
          [
            -4.288238510985561e-06,
            4.313771965798082e-06,
            0.0016234396334277438
          ],
          [
            -2.8591144960790743e-06,
            2.8764856439760712e-06,
            0.00108189967067685
          ],
          [
            -1.429968715837185e-06,
            1.4391965179108995e-06,
            0.0005403454067762502
          ],
          [
            -8.012705546481936e-10,
            1.9046708618947063e-09,
            -1.223056555932421e-06
          ]
        ],
        "berry_integer_shifts": [
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ]
        ],
        "folded_reduced_polarization": [
          [
            -1.1433529682414179e-05,
            1.1500157956478851e-05,
            0.004330921366717866
          ],
          [
            -1.0004515555939175e-05,
            1.0062887172090917e-05,
            0.003789454437021944
          ],
          [
            -8.575479302885824e-06,
            8.625613078905303e-06,
            0.0032479726969246725
          ],
          [
            -7.1464209943084e-06,
            7.188335781282973e-06,
            0.002706476248369838
          ],
          [
            -5.717340702815488e-06,
            5.7510553801432e-06,
            0.002164965193256041
          ],
          [
            -4.28823851100768e-06,
            4.313771965747115e-06,
            0.0016234396334277035
          ],
          [
            -2.8591144961009896e-06,
            2.876485644009996e-06,
            0.0010818996706768447
          ],
          [
            -1.4299687158270125e-06,
            1.4391965179605393e-06,
            0.000540345406776277
          ],
          [
            -8.012705499105266e-10,
            1.904670865471303e-09,
            -1.2230565559212536e-06
          ]
        ]
      },
      "reflected": {
        "reached": true,
        "construction": "reflect_displacements_about_reconstructed_parent",
        "energies_eV": [
          -247.56885025998778,
          -247.56857989425302,
          -247.56830728521714,
          -247.56803243196478,
          -247.56775533358064,
          -247.56747598914816,
          -247.5671943977509,
          -247.56691055847142,
          -247.56662447039187
        ],
        "cartesian_polarizations_e_A2": [
          [
            -2.21672937172571e-11,
            2.085404133409837e-11,
            -1.9022965350543592e-08
          ],
          [
            1.1495122463830964e-08,
            -9.204605716584576e-09,
            -3.649146745620589e-06
          ],
          [
            2.301000995120482e-08,
            -1.8428600365721716e-08,
            -7.279863593982786e-06
          ],
          [
            3.452249591512468e-08,
            -2.765113035996144e-08,
            -1.0911173446938333e-05
          ],
          [
            4.603258132574767e-08,
            -3.687219631447914e-08,
            -1.4543076239958687e-05
          ],
          [
            5.7540266917865525e-08,
            -4.609179852244378e-08,
            -1.8175571907792118e-05
          ],
          [
            6.904555347223155e-08,
            -5.530993756282647e-08,
            -2.1808660384320956e-05
          ],
          [
            8.054844195759581e-08,
            -6.452661397929163e-08,
            -2.5442341602415203e-05
          ],
          [
            9.204893311002357e-08,
            -7.374182821926165e-08,
            -2.9076615494108314e-05
          ]
        ],
        "raw_reduced_polarization": [
          [
            -8.012740077620152e-10,
            1.9046679754532743e-09,
            -1.2230565575040041e-06
          ],
          [
            4.886666684573585e-07,
            -8.403535515166546e-07,
            -0.00023461233685860105
          ],
          [
            9.780584903623264e-07,
            -1.6825464048999195e-06,
            -0.0004680302825577404
          ],
          [
            1.4673742278072837e-06,
            -2.524673932322749e-06,
            -0.000701476887541224
          ],
          [
            1.9566139272003367e-06,
            -3.3667361886644697e-06,
            -0.0009349521456295711
          ],
          [
            2.4457776310421363e-06,
            -4.208733199404042e-06,
            -0.0011684560505972347
          ],
          [
            2.9348653724217638e-06,
            -5.050665016120771e-06,
            -0.0014019885961634227
          ],
          [
            3.423877200910632e-06,
            -5.892531687173504e-06,
            -0.0016355497759826998
          ],
          [
            3.912813152075901e-06,
            -6.734333252135407e-06,
            -0.0018691395836562892
          ]
        ],
        "unwrapped_reduced_polarization": [
          [
            -8.012740077620152e-10,
            1.9046679754532743e-09,
            -1.2230565575040041e-06
          ],
          [
            4.886666684573585e-07,
            -8.403535515166546e-07,
            -0.00023461233685860105
          ],
          [
            9.780584903623264e-07,
            -1.6825464048999195e-06,
            -0.0004680302825577404
          ],
          [
            1.4673742278072837e-06,
            -2.524673932322749e-06,
            -0.000701476887541224
          ],
          [
            1.9566139272003367e-06,
            -3.3667361886644697e-06,
            -0.0009349521456295711
          ],
          [
            2.4457776310421363e-06,
            -4.208733199404042e-06,
            -0.0011684560505972347
          ],
          [
            2.9348653724217638e-06,
            -5.050665016120771e-06,
            -0.0014019885961634227
          ],
          [
            3.423877200910632e-06,
            -5.892531687173504e-06,
            -0.0016355497759826998
          ],
          [
            3.912813152075901e-06,
            -6.734333252135407e-06,
            -0.0018691395836562892
          ]
        ],
        "gauge_integer_shift": [
          0,
          0,
          0
        ],
        "expected_opposite_endpoint_reduced_polarization": [
          1.143192780475487e-05,
          -1.1496349038845779e-05,
          -0.004333367083104389
        ],
        "actual_opposite_endpoint_branch_residual": 0.0024642435721567275
      },
      "pnp_branch": {
        "construction": "incoming_path_concatenated_with_parent_reflection",
        "reduced_polarization": [
          [
            -1.143352968242519e-05,
            1.1500157956532835e-05,
            0.0043309213667178485
          ],
          [
            -1.0004515555917484e-05,
            1.006288717207093e-05,
            0.0037894544370219636
          ],
          [
            -8.575479302892984e-06,
            8.625613078890528e-06,
            0.0032479726969246625
          ],
          [
            -7.146420994300568e-06,
            7.188335781257812e-06,
            0.0027064762483698427
          ],
          [
            -5.717340702793873e-06,
            5.751055380136176e-06,
            0.0021649651932560596
          ],
          [
            -4.288238510985561e-06,
            4.313771965798082e-06,
            0.0016234396334277438
          ],
          [
            -2.8591144960790743e-06,
            2.8764856439760712e-06,
            0.00108189967067685
          ],
          [
            -1.429968715837185e-06,
            1.4391965179108995e-06,
            0.0005403454067762502
          ],
          [
            -8.012705546481341e-10,
            1.904670861894687e-09,
            -1.2230565559324713e-06
          ],
          [
            4.886666684573585e-07,
            -8.403535515166546e-07,
            -0.00023461233685860105
          ],
          [
            9.780584903623264e-07,
            -1.6825464048999195e-06,
            -0.0004680302825577404
          ],
          [
            1.4673742278072837e-06,
            -2.524673932322749e-06,
            -0.000701476887541224
          ],
          [
            1.9566139272003367e-06,
            -3.3667361886644697e-06,
            -0.0009349521456295711
          ],
          [
            2.4457776310421363e-06,
            -4.208733199404042e-06,
            -0.0011684560505972347
          ],
          [
            2.9348653724217638e-06,
            -5.050665016120771e-06,
            -0.0014019885961634227
          ],
          [
            3.423877200910632e-06,
            -5.892531687173504e-06,
            -0.0016355497759826998
          ],
          [
            3.912813152075901e-06,
            -6.734333252135407e-06,
            -0.0018691395836562892
          ]
        ],
        "unwrapped_reduced_polarization": [
          [
            -1.143352968242519e-05,
            1.1500157956532835e-05,
            0.0043309213667178485
          ],
          [
            -1.0004515555917484e-05,
            1.006288717207093e-05,
            0.0037894544370219636
          ],
          [
            -8.575479302892984e-06,
            8.625613078890528e-06,
            0.0032479726969246625
          ],
          [
            -7.146420994300568e-06,
            7.188335781257812e-06,
            0.0027064762483698427
          ],
          [
            -5.717340702793873e-06,
            5.751055380136176e-06,
            0.0021649651932560596
          ],
          [
            -4.288238510985561e-06,
            4.313771965798082e-06,
            0.0016234396334277438
          ],
          [
            -2.8591144960790743e-06,
            2.8764856439760712e-06,
            0.00108189967067685
          ],
          [
            -1.429968715837185e-06,
            1.4391965179108995e-06,
            0.0005403454067762502
          ],
          [
            -8.012705546481936e-10,
            1.9046708618947063e-09,
            -1.223056555932421e-06
          ],
          [
            4.886666684573585e-07,
            -8.403535515166546e-07,
            -0.00023461233685860105
          ],
          [
            9.780584903623264e-07,
            -1.6825464048999195e-06,
            -0.0004680302825577404
          ],
          [
            1.4673742278072837e-06,
            -2.524673932322749e-06,
            -0.000701476887541224
          ],
          [
            1.9566139272003367e-06,
            -3.3667361886644697e-06,
            -0.0009349521456295711
          ],
          [
            2.4457776310421363e-06,
            -4.208733199404042e-06,
            -0.0011684560505972347
          ],
          [
            2.9348653724217638e-06,
            -5.050665016120771e-06,
            -0.0014019885961634227
          ],
          [
            3.423877200910632e-06,
            -5.892531687173504e-06,
            -0.0016355497759826998
          ],
          [
            3.912813152075901e-06,
            -6.734333252135407e-06,
            -0.0018691395836562892
          ]
        ],
        "berry_integer_shifts": [
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ]
        ],
        "folded_reduced_polarization": [
          [
            -1.1433529682414179e-05,
            1.1500157956478851e-05,
            0.004330921366717866
          ],
          [
            -1.0004515555939175e-05,
            1.0062887172090917e-05,
            0.003789454437021944
          ],
          [
            -8.575479302885824e-06,
            8.625613078905303e-06,
            0.0032479726969246725
          ],
          [
            -7.1464209943084e-06,
            7.188335781282973e-06,
            0.002706476248369838
          ],
          [
            -5.717340702815488e-06,
            5.7510553801432e-06,
            0.002164965193256041
          ],
          [
            -4.28823851100768e-06,
            4.313771965747115e-06,
            0.0016234396334277035
          ],
          [
            -2.8591144961009896e-06,
            2.876485644009996e-06,
            0.0010818996706768447
          ],
          [
            -1.4299687158270125e-06,
            1.4391965179605393e-06,
            0.000540345406776277
          ],
          [
            -8.012705499105266e-10,
            1.904670865471303e-09,
            -1.2230565559212536e-06
          ],
          [
            4.886666684633667e-07,
            -8.403535515233429e-07,
            -0.00023461233685861949
          ],
          [
            9.780584903085199e-07,
            -1.6825464049241567e-06,
            -0.00046803028255776313
          ],
          [
            1.4673742277926394e-06,
            -2.5246739323026013e-06,
            -0.0007014768875412414
          ],
          [
            1.9566139272120253e-06,
            -3.3667361886702274e-06,
            -0.0009349521456295529
          ],
          [
            2.4457776310882196e-06,
            -4.208733199395631e-06,
            -0.001168456050597233
          ],
          [
            2.934865372394846e-06,
            -5.050665016104183e-06,
            -0.001401988596163417
          ],
          [
            3.423877200869896e-06,
            -5.8925316871460964e-06,
            -0.001635549775982681
          ],
          [
            3.912813152040506e-06,
            -6.734333252156333e-06,
            -0.0018691395836563096
          ]
        ]
      },
      "incoming_structure_ids": [
        "incoming_00_000",
        "incoming_00_001",
        "incoming_00_002",
        "incoming_00_003",
        "incoming_00_004",
        "incoming_00_005",
        "incoming_00_006",
        "incoming_00_007",
        "incoming_00_008"
      ],
      "reflected_structure_ids": [
        "reflected_00_001",
        "reflected_00_002",
        "reflected_00_003",
        "reflected_00_004",
        "reflected_00_005",
        "reflected_00_006",
        "reflected_00_007",
        "reflected_00_008"
      ],
      "positive_extension_structure_ids": [
        "extension_plus_00_000",
        "extension_plus_00_001",
        "extension_plus_00_002",
        "extension_plus_00_003"
      ],
      "negative_extension_structure_ids": [
        "extension_minus_00_000",
        "extension_minus_00_001",
        "extension_minus_00_002",
        "extension_minus_00_003"
      ],
      "extension": {
        "enabled": true,
        "fraction_beyond_polar_endpoint": 0.35,
        "images_per_side": 4,
        "construction": "continue fractional atomic displacements and symmetric log strain beyond +P; reflect these structures about N for the -P side",
        "positive_path_coordinates": [
          1.35,
          1.2625,
          1.175,
          1.0875
        ],
        "negative_path_coordinates": [
          -1.0875,
          -1.175,
          -1.2625,
          -1.35
        ]
      },
      "branch_coordinates": [
        1.35,
        1.2625,
        1.175,
        1.0875,
        1.0,
        0.875,
        0.75,
        0.625,
        0.5,
        0.375,
        0.25,
        0.125,
        0.0,
        -0.125,
        -0.25,
        -0.375,
        -0.5,
        -0.625,
        -0.75,
        -0.875,
        -1.0,
        -1.0875,
        -1.175,
        -1.2625,
        -1.35
      ],
      "parent": {
        "candidate_id": "bec_projection_00",
        "source": "MACEField_BEC_backprojection",
        "spacegroup": "R3c",
        "spacegroup_number": 161,
        "pointgroup": "3m",
        "has_inversion": false,
        "is_polar_point_group": true,
        "nonpolar_parent_hypothesis": false,
        "symmetry_tolerance_A": null,
        "target_reduced_polarization": [
          0.0,
          0.0,
          0.0
        ],
        "formal_class": [
          0.0,
          0.0,
          0.0
        ],
        "target_residual": 1.2230583002344048e-06,
        "parent_symmetrization_rmsd_A": 0.00040085439201025956,
        "parent_cell_rmsd_A": 0.0023038509277992386,
        "energy_eV": -247.56885025998784,
        "reduced_polarization": [
          -8.012771198741645e-10,
          1.904667405414541e-09,
          -1.2230565546896527e-06
        ],
        "cartesian_polarization_e_A2": [
          -2.216732947027708e-11,
          2.085403509094177e-11,
          -1.9022965306770204e-08
        ],
        "ranking_score": 0.5009792632405605
      }
    }
  ],
  "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": 60,
      "full_response": 25,
      "energy_polarization": 35
    },
    "model_evaluations_for_recovery_and_path_properties": {
      "total": 85,
      "full_response": 50,
      "energy_polarization": 35
    },
    "elapsed_seconds": 1087.1391210699803
  }
}