{
  "schema": "ferrofinder.endpoint_parent_recovery.v4_variable_cell",
  "status": "complete",
  "input_atom_count": 24,
  "input_formula": "Li8O12Si4",
  "input_spacegroup": "Cmc2_1",
  "input_pointgroup": "mm2",
  "input_is_polar_point_group": true,
  "input_energy_eV": -151.0262723424384,
  "input_cartesian_polarization_e_A2": [
    4.69728645548546e-18,
    3.212329895362258e-17,
    0.0019292257678429337
  ],
  "input_reduced_polarization": [
    1.2048673424538447e-16,
    1.4340355206739457e-15,
    0.09922873755116855
  ],
  "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": "Cmcm",
      "spacegroup_number": 63,
      "pointgroup": "mmm",
      "has_inversion": true,
      "is_polar_point_group": false,
      "nonpolar_parent_hypothesis": true,
      "symmetry_tolerance_A": null,
      "target_reduced_polarization": [
        0.0,
        0.0,
        0.0
      ],
      "formal_class": [
        0.0,
        0.0,
        0.0
      ],
      "target_residual": 1.3489558720131349e-16,
      "parent_symmetrization_rmsd_A": 0.3754048267283,
      "parent_cell_rmsd_A": 0.0,
      "energy_eV": -146.02873833181374,
      "reduced_polarization": [
        1.190860102655265e-16,
        3.829200322226824e-18,
        6.325091960057455e-17
      ],
      "cartesian_polarization_e_A2": [
        4.642677939289308e-18,
        8.577649920860501e-20,
        1.2297375432219543e-18
      ],
      "ranking_score": 0.3754048267283003
    },
    {
      "candidate_id": "inversion_parent_endpoint_01",
      "source": "same_species_inversion_center_projection_from_endpoint",
      "spacegroup": "Cmcm",
      "spacegroup_number": 63,
      "pointgroup": "mmm",
      "has_inversion": true,
      "is_polar_point_group": false,
      "nonpolar_parent_hypothesis": true,
      "symmetry_tolerance_A": null,
      "target_reduced_polarization": [
        0.0,
        0.0,
        0.0
      ],
      "formal_class": [
        0.0,
        0.0,
        0.0
      ],
      "target_residual": 8.317334079996584e-16,
      "parent_symmetrization_rmsd_A": 0.39595346828555184,
      "parent_cell_rmsd_A": 0.0,
      "energy_eV": -144.2189481546959,
      "reduced_polarization": [
        -1.9801867263124748e-16,
        -7.260236546322944e-16,
        -3.5420152482231336e-16
      ],
      "cartesian_polarization_e_A2": [
        -7.719940578600253e-18,
        -1.626338718178625e-17,
        -6.88645976518743e-18
      ],
      "ranking_score": 0.3959534682855535
    },
    {
      "candidate_id": "bec_projection_00",
      "source": "MACEField_BEC_backprojection",
      "spacegroup": "Cmc2_1",
      "spacegroup_number": 36,
      "pointgroup": "mm2",
      "has_inversion": false,
      "is_polar_point_group": true,
      "nonpolar_parent_hypothesis": false,
      "symmetry_tolerance_A": null,
      "target_reduced_polarization": [
        0.0,
        0.0,
        0.0
      ],
      "formal_class": [
        0.0,
        0.0,
        0.0
      ],
      "target_residual": 0.0009572931657744456,
      "parent_symmetrization_rmsd_A": 0.007922521425625887,
      "parent_cell_rmsd_A": 0.010955344513093813,
      "energy_eV": -151.02318133341242,
      "reduced_polarization": [
        -4.196249397675977e-15,
        -2.917132006362721e-15,
        -0.0009572931657744456
      ],
      "cartesian_polarization_e_A2": [
        -1.6399081374835922e-16,
        -6.553062214587487e-17,
        -1.8575870893548315e-05
      ],
      "ranking_score": 0.5125759438854482
    },
    {
      "candidate_id": "inversion_parent_bec_00_00",
      "source": "same_species_inversion_center_projection_after_BEC",
      "spacegroup": "Cmcm",
      "spacegroup_number": 63,
      "pointgroup": "mmm",
      "has_inversion": true,
      "is_polar_point_group": false,
      "nonpolar_parent_hypothesis": true,
      "symmetry_tolerance_A": null,
      "target_reduced_polarization": [
        0.0,
        0.0,
        0.0
      ],
      "formal_class": [
        0.0,
        0.0,
        0.0
      ],
      "target_residual": 1.805484052131e-15,
      "parent_symmetrization_rmsd_A": 0.37540569307979227,
      "parent_cell_rmsd_A": 0.010955344513093813,
      "energy_eV": -146.19309811783955,
      "reduced_polarization": [
        -1.7826657749047215e-16,
        -3.365840970204131e-16,
        1.7648526384608324e-15
      ],
      "cartesian_polarization_e_A2": [
        -6.967278062422486e-18,
        -7.561225632216331e-18,
        3.424622250558395e-17
      ],
      "ranking_score": 0.37814452920806935
    },
    {
      "candidate_id": "bec_projection_01",
      "source": "MACEField_BEC_backprojection",
      "spacegroup": "Cmc2_1",
      "spacegroup_number": 36,
      "pointgroup": "mm2",
      "has_inversion": false,
      "is_polar_point_group": true,
      "nonpolar_parent_hypothesis": false,
      "symmetry_tolerance_A": null,
      "target_reduced_polarization": [
        0.0,
        0.0,
        0.5
      ],
      "formal_class": [
        0.0,
        0.0,
        0.5
      ],
      "target_residual": 0.00020563780115651076,
      "parent_symmetrization_rmsd_A": 0.032676340164447634,
      "parent_cell_rmsd_A": 0.04650590230757003,
      "energy_eV": -150.47565858082936,
      "reduced_polarization": [
        2.505057713948513e-15,
        4.9902923825711435e-15,
        0.4997943621988435
      ],
      "cartesian_polarization_e_A2": [
        1.283242264085282e-16,
        1.1633136079312217e-16,
        0.009796727556905459
      ],
      "ranking_score": 0.5447140913436531
    },
    {
      "candidate_id": "bec_projection_02",
      "source": "MACEField_BEC_backprojection",
      "spacegroup": "Cm",
      "spacegroup_number": 8,
      "pointgroup": "m",
      "has_inversion": false,
      "is_polar_point_group": true,
      "nonpolar_parent_hypothesis": false,
      "symmetry_tolerance_A": null,
      "target_reduced_polarization": [
        0.0,
        0.5,
        0.0
      ],
      "formal_class": [
        0.0,
        0.5,
        0.0
      ],
      "target_residual": 6.138478522860682e-05,
      "parent_symmetrization_rmsd_A": 0.05990466914287518,
      "parent_cell_rmsd_A": 0.03429077452574292,
      "energy_eV": -149.88845277971956,
      "reduced_polarization": [
        -6.77286886062602e-16,
        0.49993862484352164,
        -1.0872096481156676e-06
      ],
      "cartesian_polarization_e_A2": [
        -3.1967952069342427e-17,
        0.011234587996293245,
        -0.00010243348133275053
      ],
      "ranking_score": 0.5686001323447681
    },
    {
      "candidate_id": "bec_projection_03",
      "source": "MACEField_BEC_backprojection",
      "spacegroup": "Cc",
      "spacegroup_number": 9,
      "pointgroup": "m",
      "has_inversion": false,
      "is_polar_point_group": true,
      "nonpolar_parent_hypothesis": false,
      "symmetry_tolerance_A": null,
      "target_reduced_polarization": [
        0.5,
        0.0,
        0.0
      ],
      "formal_class": [
        0.5,
        0.0,
        0.0
      ],
      "target_residual": 1.2715443771618991e-05,
      "parent_symmetrization_rmsd_A": 0.10219740146945029,
      "parent_cell_rmsd_A": 0.08777586427448365,
      "energy_eV": -145.79441637737756,
      "reduced_polarization": [
        0.4999931309900898,
        -3.12351468360691e-15,
        1.070043051296163e-05
      ],
      "cartesian_polarization_e_A2": [
        0.019554599245368755,
        -2.1550741900449155e-16,
        -0.0002759947336663564
      ],
      "ranking_score": 0.6241667984256144
    },
    {
      "candidate_id": "bec_projection_04",
      "source": "MACEField_BEC_backprojection",
      "spacegroup": "Cm",
      "spacegroup_number": 8,
      "pointgroup": "m",
      "has_inversion": false,
      "is_polar_point_group": true,
      "nonpolar_parent_hypothesis": false,
      "symmetry_tolerance_A": null,
      "target_reduced_polarization": [
        0.0,
        0.5,
        0.5
      ],
      "formal_class": [
        0.0,
        0.5,
        0.5
      ],
      "target_residual": 0.0001505331938445442,
      "parent_symmetrization_rmsd_A": 0.06706293454400206,
      "parent_cell_rmsd_A": 0.05561724387153474,
      "energy_eV": -149.08743731964893,
      "reduced_polarization": [
        -2.3110298896156323e-15,
        0.5000233430408196,
        0.4998512877110178
      ],
      "cartesian_polarization_e_A2": [
        -7.975468124419027e-17,
        0.010983630340973693,
        0.009696882215959095
      ],
      "ranking_score": 0.5812683118995748
    },
    {
      "candidate_id": "bec_projection_05",
      "source": "MACEField_BEC_backprojection",
      "spacegroup": "Cc",
      "spacegroup_number": 9,
      "pointgroup": "m",
      "has_inversion": false,
      "is_polar_point_group": true,
      "nonpolar_parent_hypothesis": false,
      "symmetry_tolerance_A": null,
      "target_reduced_polarization": [
        0.5,
        0.0,
        0.5
      ],
      "formal_class": [
        0.5,
        0.0,
        0.5
      ],
      "target_residual": 3.2385246683564495e-05,
      "parent_symmetrization_rmsd_A": 0.10676168956522736,
      "parent_cell_rmsd_A": 0.09806561189553006,
      "energy_eV": -144.38038016203382,
      "reduced_polarization": [
        0.5000058030215389,
        -5.972480855756774e-16,
        0.49996813890862235
      ],
      "cartesian_polarization_e_A2": [
        0.01915471027377634,
        -1.9287259447842422e-16,
        0.009529587470896824
      ],
      "ranking_score": 0.631342863032477
    },
    {
      "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": 6.005526739409596e-05,
      "parent_symmetrization_rmsd_A": 0.11839381160675651,
      "parent_cell_rmsd_A": 0.0940295097167647,
      "energy_eV": -144.27828145325742,
      "reduced_polarization": [
        0.499974832780268,
        0.4999690351921091,
        4.488236697209579e-05
      ],
      "cartesian_polarization_e_A2": [
        0.019561181000758106,
        0.011244968774710398,
        -0.0003796132873601365
      ],
      "ranking_score": 0.6420212995707358
    },
    {
      "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": 2.7470699402738076e-05,
      "parent_symmetrization_rmsd_A": 0.12206361874425167,
      "parent_cell_rmsd_A": 0.10284510138792614,
      "energy_eV": -142.6065637522354,
      "reduced_polarization": [
        0.5000044754747204,
        0.5000034909205169,
        0.49997312207363565
      ],
      "cartesian_polarization_e_A2": [
        0.019159957123832737,
        0.010983683183262921,
        0.009426928687350263
      ],
      "ranking_score": 0.6478298354900387
    }
  ],
  "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": [
              1.2048673424538447e-16,
              1.4340355206739457e-15,
              0.09922873755116855
            ],
            "branch_aligned_reduced_polarization": [
              1.2048673424538447e-16,
              1.4340355206739457e-15,
              0.09922873755116855
            ],
            "target_residual": 0.09922873755116855,
            "energy_eV": -151.0262723424384,
            "max_atomic_step_A": 0.012626848712844675,
            "max_log_strain_component": 0.003644003827270839,
            "step_scale": 1.0,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 6.261809254955732,
            "cell_principal_stretches": [
              1.0011454235032502,
              1.0007928547238218,
              0.9963626274973727
            ],
            "cell_volume_ratio": 0.9982947603356587,
            "cell_rmsd_from_input_A": 0.010955344513093813
          },
          {
            "iteration": 1,
            "reduced_polarization": [
              -4.196249397675977e-15,
              -2.917132006362721e-15,
              -0.0009572931657744456
            ],
            "branch_aligned_reduced_polarization": [
              -4.196249397675977e-15,
              -2.917132006362721e-15,
              -0.0009572931657744456
            ],
            "target_residual": 0.0009572931657744456,
            "energy_eV": -151.02318133341242
          }
        ],
        "iterations": 1
      },
      "parent": {
        "candidate_id": "inversion_parent_endpoint_00",
        "source": "same_species_inversion_center_projection_from_endpoint",
        "spacegroup": "Cmcm",
        "spacegroup_number": 63,
        "pointgroup": "mmm",
        "has_inversion": true,
        "is_polar_point_group": false,
        "nonpolar_parent_hypothesis": true,
        "symmetry_tolerance_A": null,
        "target_reduced_polarization": [
          0.0,
          0.0,
          0.0
        ],
        "formal_class": [
          0.0,
          0.0,
          0.0
        ],
        "target_residual": 1.3489558720131349e-16,
        "parent_symmetrization_rmsd_A": 0.3754048267283,
        "parent_cell_rmsd_A": 0.0,
        "energy_eV": -146.02873833181374,
        "reduced_polarization": [
          1.190860102655265e-16,
          3.829200322226824e-18,
          6.325091960057455e-17
        ],
        "cartesian_polarization_e_A2": [
          4.642677939289308e-18,
          8.577649920860501e-20,
          1.2297375432219543e-18
        ],
        "ranking_score": 0.3754048267283003
      },
      "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": [
          -151.0262723424384,
          -150.66949262630817,
          -149.9798255313267,
          -149.12207737919925,
          -148.217453654015,
          -147.35083364243727,
          -146.6233258384509,
          -146.17025137562422,
          -146.0287383318137
        ],
        "cartesian_polarizations_e_A2": [
          [
            -2.433691232215407e-17,
            2.2158928962222963e-18,
            0.0019292257678429037
          ],
          [
            -5.431820504189329e-17,
            2.746277582995504e-17,
            0.007656912646739785
          ],
          [
            -2.883352457431613e-17,
            -2.836342907164539e-17,
            0.012752427553095974
          ],
          [
            -5.0646124722604325e-17,
            4.766314139358152e-17,
            0.01701098995656935
          ],
          [
            -3.47470700592075e-17,
            -2.2244705461431567e-17,
            0.019973115240331952
          ],
          [
            -1.177529727304214e-17,
            2.859216640286834e-18,
            0.020687075886054635
          ],
          [
            1.586699937442024e-17,
            5.901423145552025e-17,
            0.01773976450524921
          ],
          [
            -6.759669904749053e-18,
            2.701959725071058e-17,
            0.010394225266708594
          ],
          [
            6.229705312523601e-18,
            3.225196370243549e-17,
            2.5920300445425843e-18
          ]
        ],
        "raw_reduced_polarization": [
          [
            -6.242487263871907e-16,
            9.892100832419297e-17,
            0.09922873755116701
          ],
          [
            -1.3932774161401485e-15,
            1.2259823031662881e-15,
            0.39382937349270514
          ],
          [
            -7.395881102133782e-16,
            -1.2661889065496699e-15,
            0.6559145683717993
          ],
          [
            -1.299087511021375e-15,
            2.127758979050705e-15,
            0.8749515406759846
          ],
          [
            -8.91272234662302e-16,
            -9.930392835641564e-16,
            1.0273069348840977
          ],
          [
            -3.0203972583801056e-16,
            1.2764001074089413e-16,
            1.064029134388768
          ],
          [
            4.069930490751546e-16,
            2.6344898216920553e-15,
            0.9124356856787651
          ],
          [
            -1.7338745659186111e-16,
            1.2061981015014497e-15,
            0.534621643682049
          ],
          [
            1.5979371399428895e-16,
            1.439779321157286e-15,
            1.3331973546167142e-16
          ]
        ],
        "unwrapped_reduced_polarization": [
          [
            -6.242487263871907e-16,
            9.892100832419297e-17,
            0.09922873755116701
          ],
          [
            -1.3932774161401485e-15,
            1.2259823031662881e-15,
            0.39382937349270514
          ],
          [
            -7.395881102133782e-16,
            -1.26618890654967e-15,
            0.6559145683717993
          ],
          [
            -1.299087511021375e-15,
            2.127758979050705e-15,
            0.8749515406759846
          ],
          [
            -8.91272234662302e-16,
            -9.930392835641566e-16,
            1.0273069348840977
          ],
          [
            -3.020397258380106e-16,
            1.2764001074089406e-16,
            1.064029134388768
          ],
          [
            4.0699304907515464e-16,
            2.6344898216920553e-15,
            0.9124356856787651
          ],
          [
            -1.7338745659186107e-16,
            1.2061981015014497e-15,
            0.534621643682049
          ],
          [
            1.5979371399428892e-16,
            1.439779321157286e-15,
            1.0
          ]
        ],
        "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,
            1
          ]
        ],
        "folded_reduced_polarization": [
          [
            -6.106226635438361e-16,
            1.1102230246251565e-16,
            0.09922873755116701
          ],
          [
            -1.3877787807814457e-15,
            1.2212453270876722e-15,
            0.3938293734927052
          ],
          [
            -7.216449660063518e-16,
            -1.27675647831893e-15,
            -0.3440854316282007
          ],
          [
            -1.27675647831893e-15,
            2.1094237467877974e-15,
            -0.12504845932401532
          ],
          [
            -8.881784197001252e-16,
            -9.992007221626409e-16,
            0.027306934884097744
          ],
          [
            -2.7755575615628914e-16,
            1.1102230246251565e-16,
            0.064029134388768
          ],
          [
            4.440892098500626e-16,
            2.6645352591003757e-15,
            -0.08756431432123479
          ],
          [
            -1.6653345369377348e-16,
            1.2212453270876722e-15,
            -0.465378356317951
          ],
          [
            1.1102230246251565e-16,
            1.4432899320127035e-15,
            0.0
          ]
        ]
      },
      "reflected": {
        "reached": true,
        "construction": "reflect_displacements_about_reconstructed_parent",
        "energies_eV": [
          -146.0287383318137,
          -146.17025137562422,
          -146.6233258384509,
          -147.35083364243724,
          -148.217453654015,
          -149.12207737919928,
          -149.97982553132672,
          -150.66949262630823,
          -151.0262723424384
        ],
        "cartesian_polarizations_e_A2": [
          [
            6.229705312523601e-18,
            3.225196370243549e-17,
            2.5920300445425843e-18
          ],
          [
            -5.380781812743844e-18,
            2.2330481960640173e-17,
            -0.010394225266708594
          ],
          [
            1.2156562732699977e-17,
            4.337431643315127e-17,
            -0.017739764505249143
          ],
          [
            -1.059482815336363e-17,
            -4.072954104088595e-17,
            -0.0206870758860546
          ],
          [
            -7.490438795844376e-18,
            -6.4618296070482446e-18,
            -0.019973115240331903
          ],
          [
            1.3123790849750028e-17,
            9.206677581723605e-18,
            -0.017010989956569255
          ],
          [
            4.0171596578589154e-17,
            1.5925836686397663e-17,
            -0.012752427553095977
          ],
          [
            -1.0790552933113972e-17,
            4.5604505412575e-18,
            -0.007656912646739839
          ],
          [
            2.118613665262817e-17,
            3.1379902627148e-17,
            -0.0019292257678429263
          ]
        ],
        "raw_reduced_polarization": [
          [
            1.5979371399428895e-16,
            1.439779321157286e-15,
            1.3331973546167142e-16
          ],
          [
            -1.3801858465484262e-16,
            9.968684838863832e-16,
            -0.534621643682049
          ],
          [
            3.1181929337132387e-16,
            1.936298962939364e-15,
            -0.9124356856787618
          ],
          [
            -2.7176035700337384e-16,
            -1.818231953004037e-15,
            -1.0640291343887665
          ],
          [
            -1.921318865964172e-16,
            -2.8846642427442076e-16,
            -1.0273069348840953
          ],
          [
            3.3662896980857427e-16,
            4.1100083458567913e-16,
            -0.8749515406759798
          ],
          [
            1.0304128834904198e-15,
            7.109548598267803e-16,
            -0.6559145683717995
          ],
          [
            -2.767807532995113e-16,
            2.0358581713172616e-16,
            -0.3938293734927079
          ],
          [
            5.434304338775515e-16,
            1.4008491178813131e-15,
            -0.09922873755116819
          ]
        ],
        "unwrapped_reduced_polarization": [
          [
            1.5979371399428895e-16,
            1.439779321157286e-15,
            1.0000000000000002
          ],
          [
            -1.3801858465484264e-16,
            9.968684838863832e-16,
            1.465378356317951
          ],
          [
            3.1181929337132382e-16,
            1.936298962939364e-15,
            1.0875643143212383
          ],
          [
            -2.7176035700337384e-16,
            -1.8182319530040368e-15,
            0.9359708656112335
          ],
          [
            -1.921318865964172e-16,
            -2.884664242744207e-16,
            0.9726930651159047
          ],
          [
            3.366289698085742e-16,
            4.1100083458567913e-16,
            1.1250484593240202
          ],
          [
            1.0304128834904198e-15,
            7.109548598267803e-16,
            1.3440854316282005
          ],
          [
            -2.767807532995113e-16,
            2.0358581713172619e-16,
            1.6061706265072921
          ],
          [
            5.434304338775515e-16,
            1.4008491178813131e-15,
            1.9007712624488318
          ]
        ],
        "gauge_integer_shift": [
          0,
          0,
          1
        ],
        "expected_opposite_endpoint_reduced_polarization": [
          9.438361543757685e-16,
          2.7806376339903793e-15,
          -0.09922873755116675
        ],
        "actual_opposite_endpoint_branch_residual": 2.1166075716659203e-15
      },
      "pnp_branch": {
        "construction": "incoming_path_concatenated_with_parent_reflection",
        "reduced_polarization": [
          [
            -6.242487263871907e-16,
            9.892100832419297e-17,
            0.09922873755116701
          ],
          [
            -1.3932774161401485e-15,
            1.2259823031662881e-15,
            0.39382937349270514
          ],
          [
            -7.395881102133782e-16,
            -1.2661889065496699e-15,
            0.6559145683717993
          ],
          [
            -1.299087511021375e-15,
            2.127758979050705e-15,
            0.8749515406759846
          ],
          [
            -8.91272234662302e-16,
            -9.930392835641564e-16,
            1.0273069348840977
          ],
          [
            -3.0203972583801056e-16,
            1.2764001074089413e-16,
            1.064029134388768
          ],
          [
            4.069930490751546e-16,
            2.6344898216920553e-15,
            0.9124356856787651
          ],
          [
            -1.7338745659186111e-16,
            1.2061981015014497e-15,
            0.534621643682049
          ],
          [
            1.5979371399428895e-16,
            1.439779321157286e-15,
            1.3331973546167142e-16
          ],
          [
            -1.3801858465484262e-16,
            9.968684838863832e-16,
            -0.534621643682049
          ],
          [
            3.1181929337132387e-16,
            1.936298962939364e-15,
            -0.9124356856787618
          ],
          [
            -2.7176035700337384e-16,
            -1.818231953004037e-15,
            -1.0640291343887665
          ],
          [
            -1.921318865964172e-16,
            -2.8846642427442076e-16,
            -1.0273069348840953
          ],
          [
            3.3662896980857427e-16,
            4.1100083458567913e-16,
            -0.8749515406759798
          ],
          [
            1.0304128834904198e-15,
            7.109548598267803e-16,
            -0.6559145683717995
          ],
          [
            -2.767807532995113e-16,
            2.0358581713172616e-16,
            -0.3938293734927079
          ],
          [
            5.434304338775515e-16,
            1.4008491178813131e-15,
            -0.09922873755116819
          ]
        ],
        "unwrapped_reduced_polarization": [
          [
            -6.242487263871907e-16,
            9.892100832419297e-17,
            0.09922873755116701
          ],
          [
            -1.3932774161401485e-15,
            1.2259823031662881e-15,
            0.39382937349270514
          ],
          [
            -7.395881102133782e-16,
            -1.26618890654967e-15,
            0.6559145683717993
          ],
          [
            -1.299087511021375e-15,
            2.127758979050705e-15,
            0.8749515406759846
          ],
          [
            -8.91272234662302e-16,
            -9.930392835641566e-16,
            1.0273069348840977
          ],
          [
            -3.020397258380106e-16,
            1.2764001074089406e-16,
            1.064029134388768
          ],
          [
            4.0699304907515464e-16,
            2.6344898216920553e-15,
            0.9124356856787651
          ],
          [
            -1.7338745659186107e-16,
            1.2061981015014497e-15,
            0.534621643682049
          ],
          [
            1.5979371399428892e-16,
            1.439779321157286e-15,
            1.0
          ],
          [
            -1.3801858465484262e-16,
            9.968684838863832e-16,
            1.465378356317951
          ],
          [
            3.1181929337132387e-16,
            1.936298962939364e-15,
            1.0875643143212383
          ],
          [
            -2.717603570033738e-16,
            -1.8182319530040368e-15,
            0.9359708656112335
          ],
          [
            -1.921318865964172e-16,
            -2.884664242744207e-16,
            0.9726930651159047
          ],
          [
            3.366289698085742e-16,
            4.1100083458567913e-16,
            1.1250484593240202
          ],
          [
            1.0304128834904198e-15,
            7.109548598267803e-16,
            1.3440854316282005
          ],
          [
            -2.767807532995113e-16,
            2.0358581713172619e-16,
            1.6061706265072921
          ],
          [
            5.434304338775515e-16,
            1.4008491178813131e-15,
            1.9007712624488318
          ]
        ],
        "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,
            1
          ],
          [
            0,
            0,
            2
          ],
          [
            0,
            0,
            2
          ],
          [
            0,
            0,
            2
          ],
          [
            0,
            0,
            2
          ],
          [
            0,
            0,
            2
          ],
          [
            0,
            0,
            2
          ],
          [
            0,
            0,
            2
          ],
          [
            0,
            0,
            2
          ]
        ],
        "folded_reduced_polarization": [
          [
            -6.106226635438361e-16,
            1.1102230246251565e-16,
            0.09922873755116701
          ],
          [
            -1.3877787807814457e-15,
            1.2212453270876722e-15,
            0.3938293734927052
          ],
          [
            -7.216449660063518e-16,
            -1.27675647831893e-15,
            -0.3440854316282007
          ],
          [
            -1.27675647831893e-15,
            2.1094237467877974e-15,
            -0.12504845932401532
          ],
          [
            -8.881784197001252e-16,
            -9.992007221626409e-16,
            0.027306934884097744
          ],
          [
            -2.7755575615628914e-16,
            1.1102230246251565e-16,
            0.064029134388768
          ],
          [
            4.440892098500626e-16,
            2.6645352591003757e-15,
            -0.08756431432123479
          ],
          [
            -1.6653345369377348e-16,
            1.2212453270876722e-15,
            -0.465378356317951
          ],
          [
            1.1102230246251565e-16,
            1.4432899320127035e-15,
            0.0
          ],
          [
            -1.1102230246251565e-16,
            9.992007221626409e-16,
            0.465378356317951
          ],
          [
            3.3306690738754696e-16,
            1.887379141862766e-15,
            0.08756431432123835
          ],
          [
            -2.7755575615628914e-16,
            -1.8318679906315083e-15,
            -0.06402913438876645
          ],
          [
            -1.6653345369377348e-16,
            -2.7755575615628914e-16,
            -0.027306934884095302
          ],
          [
            3.3306690738754696e-16,
            4.440892098500626e-16,
            0.1250484593240202
          ],
          [
            9.992007221626409e-16,
            6.661338147750939e-16,
            0.3440854316282005
          ],
          [
            -2.7755575615628914e-16,
            2.220446049250313e-16,
            -0.3938293734927081
          ],
          [
            5.551115123125783e-16,
            1.4432899320127035e-15,
            -0.09922873755116823
          ]
        ]
      },
      "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": [
              1.2048673424538447e-16,
              1.4340355206739457e-15,
              0.09922873755116855
            ],
            "branch_aligned_reduced_polarization": [
              1.2048673424538447e-16,
              1.4340355206739457e-15,
              0.09922873755116857
            ],
            "target_residual": 0.40077126244883143,
            "energy_eV": -151.0262723424384,
            "max_atomic_step_A": 0.05099811026808299,
            "max_log_strain_component": 0.014717631708965638,
            "step_scale": 1.0,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 6.261809254955732,
            "cell_principal_stretches": [
              1.0148264693390703,
              0.9968041549057506,
              0.9953871112234768
            ],
            "cell_volume_ratio": 1.0069169201659194,
            "cell_rmsd_from_input_A": 0.044579105523427094
          },
          {
            "iteration": 1,
            "reduced_polarization": [
              9.449320232666185e-15,
              6.462610651842149e-15,
              0.48465646214532077
            ],
            "branch_aligned_reduced_polarization": [
              9.449320232666185e-15,
              6.462610651842149e-15,
              0.48465646214532077
            ],
            "target_residual": 0.015343537854679234,
            "energy_eV": -150.51054384737398,
            "max_atomic_step_A": 0.0020191168682493848,
            "max_log_strain_component": 0.0006320874048226233,
            "step_scale": 1.0,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 6.261809254955732,
            "cell_principal_stretches": [
              1.0154681311402272,
              0.9966671299064187,
              0.9951894758448975
            ],
            "cell_volume_ratio": 1.0072150546517282,
            "cell_rmsd_from_input_A": 0.04650590230757003
          },
          {
            "iteration": 2,
            "reduced_polarization": [
              2.505057713948513e-15,
              4.9902923825711435e-15,
              0.4997943621988435
            ],
            "branch_aligned_reduced_polarization": [
              2.505057713948513e-15,
              4.9902923825711435e-15,
              0.4997943621988435
            ],
            "target_residual": 0.00020563780115651076,
            "energy_eV": -150.47565858082936
          }
        ],
        "iterations": 2
      },
      "parent": {
        "candidate_id": "bec_projection_01",
        "source": "MACEField_BEC_backprojection",
        "spacegroup": "Cmc2_1",
        "spacegroup_number": 36,
        "pointgroup": "mm2",
        "has_inversion": false,
        "is_polar_point_group": true,
        "nonpolar_parent_hypothesis": false,
        "symmetry_tolerance_A": null,
        "target_reduced_polarization": [
          0.0,
          0.0,
          0.5
        ],
        "formal_class": [
          0.0,
          0.0,
          0.5
        ],
        "target_residual": 0.00020563780115651076,
        "parent_symmetrization_rmsd_A": 0.032676340164447634,
        "parent_cell_rmsd_A": 0.04650590230757003,
        "energy_eV": -150.47565858082936,
        "reduced_polarization": [
          2.505057713948513e-15,
          4.9902923825711435e-15,
          0.4997943621988435
        ],
        "cartesian_polarization_e_A2": [
          1.283242264085282e-16,
          1.1633136079312217e-16,
          0.009796727556905459
        ],
        "ranking_score": 0.5447140913436531
      },
      "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": [
              1.2048673424538447e-16,
              1.4340355206739457e-15,
              0.09922873755116855
            ],
            "branch_aligned_reduced_polarization": [
              1.2048673424538447e-16,
              1.4432899320127035e-15,
              0.09922873755116855
            ],
            "target_residual": 0.5097512553746163,
            "energy_eV": -151.0262723424384,
            "max_atomic_step_A": 0.07964132961555383,
            "max_log_strain_component": 0.009085939208464297,
            "step_scale": 1.0,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 6.261809254955732,
            "cell_principal_stretches": [
              1.008179791447222,
              1.0007928547238276,
              0.9894107113938242
            ],
            "cell_volume_ratio": 0.9982947603356691,
            "cell_rmsd_from_input_A": 0.033744813104599945
          },
          {
            "iteration": 1,
            "reduced_polarization": [
              -4.4872110907683975e-15,
              0.4972637546736059,
              0.009974789397955888
            ],
            "branch_aligned_reduced_polarization": [
              -4.4872110907683975e-15,
              0.4972637546736059,
              0.009974789397955888
            ],
            "target_residual": 0.010343281008451177,
            "energy_eV": -149.9002383071388,
            "max_atomic_step_A": 0.0014085653111758974,
            "max_log_strain_component": 0.00036407427743223033,
            "step_scale": 1.0,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 6.261809254955732,
            "cell_principal_stretches": [
              1.0081726603248076,
              1.000872103774962,
              0.9891706831235122
            ],
            "cell_volume_ratio": 0.9981245488297344,
            "cell_rmsd_from_input_A": 0.03429077452574292
          },
          {
            "iteration": 2,
            "reduced_polarization": [
              -6.77286886062602e-16,
              0.49993862484352164,
              -1.0872096481156676e-06
            ],
            "branch_aligned_reduced_polarization": [
              -6.77286886062602e-16,
              0.49993862484352164,
              -1.0872096481156676e-06
            ],
            "target_residual": 6.138478522860682e-05,
            "energy_eV": -149.88845277971956
          }
        ],
        "iterations": 2
      },
      "parent": {
        "candidate_id": "bec_projection_02",
        "source": "MACEField_BEC_backprojection",
        "spacegroup": "Cm",
        "spacegroup_number": 8,
        "pointgroup": "m",
        "has_inversion": false,
        "is_polar_point_group": true,
        "nonpolar_parent_hypothesis": false,
        "symmetry_tolerance_A": null,
        "target_reduced_polarization": [
          0.0,
          0.5,
          0.0
        ],
        "formal_class": [
          0.0,
          0.5,
          0.0
        ],
        "target_residual": 6.138478522860682e-05,
        "parent_symmetrization_rmsd_A": 0.05990466914287518,
        "parent_cell_rmsd_A": 0.03429077452574292,
        "energy_eV": -149.88845277971956,
        "reduced_polarization": [
          -6.77286886062602e-16,
          0.49993862484352164,
          -1.0872096481156676e-06
        ],
        "cartesian_polarization_e_A2": [
          -3.1967952069342427e-17,
          0.011234587996293245,
          -0.00010243348133275053
        ],
        "ranking_score": 0.5686001323447681
      },
      "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": [
              1.2048673424538447e-16,
              1.4340355206739457e-15,
              0.09922873755116855
            ],
            "branch_aligned_reduced_polarization": [
              1.1102230246251565e-16,
              1.4340355206739457e-15,
              0.09922873755116855
            ],
            "target_residual": 0.5097512553746175,
            "energy_eV": -151.0262723424384,
            "max_atomic_step_A": 0.12,
            "max_log_strain_component": 0.01229692184431307,
            "step_scale": 0.8892583110150531,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 6.261809254955732,
            "cell_principal_stretches": [
              1.0112490928686122,
              1.0010185127959808,
              0.9863717374712101
            ],
            "cell_volume_ratio": 0.9984834581865308,
            "cell_rmsd_from_input_A": 0.07593838631567568
          },
          {
            "iteration": 1,
            "reduced_polarization": [
              0.4374574323517197,
              1.4595554927217422e-16,
              0.025780441611292487
            ],
            "branch_aligned_reduced_polarization": [
              0.4374574323517197,
              1.4595554927217422e-16,
              0.025780441611292487
            ],
            "target_residual": 0.06764764547057776,
            "energy_eV": -147.11536244018404,
            "max_atomic_step_A": 0.01767459713225788,
            "max_log_strain_component": 0.0018582738886216226,
            "step_scale": 1.0,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 6.261809254955732,
            "cell_principal_stretches": [
              1.0127564106454687,
              1.0013935666705627,
              0.983985120113983
            ],
            "cell_volume_ratio": 0.9979259794565619,
            "cell_rmsd_from_input_A": 0.08766915499783132
          },
          {
            "iteration": 2,
            "reduced_polarization": [
              0.49953898605679664,
              1.5005019295608311e-15,
              0.0011218584973564122
            ],
            "branch_aligned_reduced_polarization": [
              0.49953898605679664,
              1.5005019295608311e-15,
              0.0011218584973564122
            ],
            "target_residual": 0.0012128892545977548,
            "energy_eV": -145.80370613810035,
            "max_atomic_step_A": 0.00019651221059474342,
            "max_log_strain_component": 4.440439914359327e-05,
            "step_scale": 1.0,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 6.261809254955732,
            "cell_principal_stretches": [
              1.0127584451629486,
              1.0014075359010415,
              0.9839489537165835
            ],
            "cell_volume_ratio": 0.9979052256882723,
            "cell_rmsd_from_input_A": 0.08777586427448365
          },
          {
            "iteration": 3,
            "reduced_polarization": [
              0.4999931309900898,
              -3.12351468360691e-15,
              1.070043051296163e-05
            ],
            "branch_aligned_reduced_polarization": [
              0.4999931309900898,
              -3.12351468360691e-15,
              1.070043051296163e-05
            ],
            "target_residual": 1.2715443771618991e-05,
            "energy_eV": -145.79441637737756
          }
        ],
        "iterations": 3
      },
      "parent": {
        "candidate_id": "bec_projection_03",
        "source": "MACEField_BEC_backprojection",
        "spacegroup": "Cc",
        "spacegroup_number": 9,
        "pointgroup": "m",
        "has_inversion": false,
        "is_polar_point_group": true,
        "nonpolar_parent_hypothesis": false,
        "symmetry_tolerance_A": null,
        "target_reduced_polarization": [
          0.5,
          0.0,
          0.0
        ],
        "formal_class": [
          0.5,
          0.0,
          0.0
        ],
        "target_residual": 1.2715443771618991e-05,
        "parent_symmetrization_rmsd_A": 0.10219740146945029,
        "parent_cell_rmsd_A": 0.08777586427448365,
        "energy_eV": -145.79441637737756,
        "reduced_polarization": [
          0.4999931309900898,
          -3.12351468360691e-15,
          1.070043051296163e-05
        ],
        "cartesian_polarization_e_A2": [
          0.019554599245368755,
          -2.1550741900449155e-16,
          -0.0002759947336663564
        ],
        "ranking_score": 0.6241667984256144
      },
      "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": [
              1.2048673424538447e-16,
              1.4340355206739457e-15,
              0.09922873755116855
            ],
            "branch_aligned_reduced_polarization": [
              1.2048673424538447e-16,
              1.4432899320127035e-15,
              0.09922873755116857
            ],
            "target_residual": 0.6407945105919906,
            "energy_eV": -151.0262723424384,
            "max_atomic_step_A": 0.09400666709450053,
            "max_log_strain_component": 0.01471763170896611,
            "step_scale": 1.0,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 6.261809254955732,
            "cell_principal_stretches": [
              1.0184851237398496,
              0.9968041549057564,
              0.9918114306857192
            ],
            "cell_volume_ratio": 1.00691692016593,
            "cell_rmsd_from_input_A": 0.05512530972207064
          },
          {
            "iteration": 1,
            "reduced_polarization": [
              9.423844251816147e-15,
              0.5090297009026283,
              0.492325175028642
            ],
            "branch_aligned_reduced_polarization": [
              9.423844251816147e-15,
              0.5090297009026283,
              0.492325175028642
            ],
            "target_residual": 0.011850672416867642,
            "energy_eV": -149.05819347866935,
            "max_atomic_step_A": 0.0018421475041431447,
            "max_log_strain_component": 0.0003327840105121537,
            "step_scale": 1.0,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 6.261809254955732,
            "cell_principal_stretches": [
              1.0186522109304699,
              0.9967320110651287,
              0.991875105401369
            ],
            "cell_volume_ratio": 1.007073872250569,
            "cell_rmsd_from_input_A": 0.05561724387153474
          },
          {
            "iteration": 2,
            "reduced_polarization": [
              -2.3110298896156323e-15,
              0.5000233430408196,
              0.4998512877110178
            ],
            "branch_aligned_reduced_polarization": [
              -2.3110298896156323e-15,
              0.5000233430408196,
              0.4998512877110178
            ],
            "target_residual": 0.0001505331938445442,
            "energy_eV": -149.08743731964893
          }
        ],
        "iterations": 2
      },
      "parent": {
        "candidate_id": "bec_projection_04",
        "source": "MACEField_BEC_backprojection",
        "spacegroup": "Cm",
        "spacegroup_number": 8,
        "pointgroup": "m",
        "has_inversion": false,
        "is_polar_point_group": true,
        "nonpolar_parent_hypothesis": false,
        "symmetry_tolerance_A": null,
        "target_reduced_polarization": [
          0.0,
          0.5,
          0.5
        ],
        "formal_class": [
          0.0,
          0.5,
          0.5
        ],
        "target_residual": 0.0001505331938445442,
        "parent_symmetrization_rmsd_A": 0.06706293454400206,
        "parent_cell_rmsd_A": 0.05561724387153474,
        "energy_eV": -149.08743731964893,
        "reduced_polarization": [
          -2.3110298896156323e-15,
          0.5000233430408196,
          0.4998512877110178
        ],
        "cartesian_polarization_e_A2": [
          -7.975468124419027e-17,
          0.010983630340973693,
          0.009696882215959095
        ],
        "ranking_score": 0.5812683118995748
      },
      "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": [
              1.2048673424538447e-16,
              1.4340355206739457e-15,
              0.09922873755116855
            ],
            "branch_aligned_reduced_polarization": [
              1.1102230246251565e-16,
              1.4340355206739457e-15,
              0.09922873755116857
            ],
            "target_residual": 0.6407945105919916,
            "energy_eV": -151.0262723424384,
            "max_atomic_step_A": 0.12,
            "max_log_strain_component": 0.012289839386916294,
            "step_scale": 0.835041916386208,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 6.261809254955732,
            "cell_principal_stretches": [
              1.0187408593260951,
              0.9961465763436367,
              0.9910894248467542
            ],
            "cell_volume_ratio": 1.0057726319217337,
            "cell_rmsd_from_input_A": 0.08036488633959861
          },
          {
            "iteration": 1,
            "reduced_polarization": [
              0.4169930673345797,
              9.981124404344334e-15,
              0.42602771516836013
            ],
            "branch_aligned_reduced_polarization": [
              0.4169930673345797,
              9.981124404344334e-15,
              0.42602771516836013
            ],
            "target_residual": 0.11118475522181483,
            "energy_eV": -146.64820316463042,
            "max_atomic_step_A": 0.0244349543635683,
            "max_log_strain_component": 0.0030505780752729406,
            "step_scale": 1.0,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 6.261809254955732,
            "cell_principal_stretches": [
              1.023053410441587,
              0.9951923839167792,
              0.9892702872596009
            ],
            "cell_volume_ratio": 1.007210666733921,
            "cell_rmsd_from_input_A": 0.09795383857554764
          },
          {
            "iteration": 2,
            "reduced_polarization": [
              0.49992462904766094,
              5.698334259416589e-16,
              0.4984397987372165
            ],
            "branch_aligned_reduced_polarization": [
              0.49992462904766094,
              5.698334259416589e-16,
              0.4984397987372165
            ],
            "target_residual": 0.001562020729967348,
            "energy_eV": -144.38878078974705,
            "max_atomic_step_A": 0.0002083654138928503,
            "max_log_strain_component": 6.748445890628246e-05,
            "step_scale": 1.0,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 6.261809254955732,
            "cell_principal_stretches": [
              1.0231056202433644,
              0.9951712857428076,
              0.9892720433559565
            ],
            "cell_volume_ratio": 1.0072425019720515,
            "cell_rmsd_from_input_A": 0.09806561189553006
          },
          {
            "iteration": 3,
            "reduced_polarization": [
              0.5000058030215389,
              -5.972480855756774e-16,
              0.49996813890862235
            ],
            "branch_aligned_reduced_polarization": [
              0.5000058030215389,
              -5.972480855756774e-16,
              0.49996813890862235
            ],
            "target_residual": 3.2385246683564495e-05,
            "energy_eV": -144.38038016203382
          }
        ],
        "iterations": 3
      },
      "parent": {
        "candidate_id": "bec_projection_05",
        "source": "MACEField_BEC_backprojection",
        "spacegroup": "Cc",
        "spacegroup_number": 9,
        "pointgroup": "m",
        "has_inversion": false,
        "is_polar_point_group": true,
        "nonpolar_parent_hypothesis": false,
        "symmetry_tolerance_A": null,
        "target_reduced_polarization": [
          0.5,
          0.0,
          0.5
        ],
        "formal_class": [
          0.5,
          0.0,
          0.5
        ],
        "target_residual": 3.2385246683564495e-05,
        "parent_symmetrization_rmsd_A": 0.10676168956522736,
        "parent_cell_rmsd_A": 0.09806561189553006,
        "energy_eV": -144.38038016203382,
        "reduced_polarization": [
          0.5000058030215389,
          -5.972480855756774e-16,
          0.49996813890862235
        ],
        "cartesian_polarization_e_A2": [
          0.01915471027377634,
          -1.9287259447842422e-16,
          0.009529587470896824
        ],
        "ranking_score": 0.631342863032477
      },
      "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": [
              1.2048673424538447e-16,
              1.4340355206739457e-15,
              0.09922873755116855
            ],
            "branch_aligned_reduced_polarization": [
              1.1102230246251565e-16,
              1.4432899320127035e-15,
              0.09922873755116855
            ],
            "target_residual": 0.7140352528804143,
            "energy_eV": -151.0262723424384,
            "max_atomic_step_A": 0.12,
            "max_log_strain_component": 0.010624674902736149,
            "step_scale": 0.7683289020382487,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 6.261809254955732,
            "cell_principal_stretches": [
              1.0118479357300132,
              1.000797927731921,
              0.9862087712194328
            ],
            "cell_volume_ratio": 0.9986895561022505,
            "cell_rmsd_from_input_A": 0.07006387399739054
          },
          {
            "iteration": 1,
            "reduced_polarization": [
              0.3790461994378959,
              0.38044434553997664,
              0.03980475554351496
            ],
            "branch_aligned_reduced_polarization": [
              0.3790461994378959,
              0.38044434553997664,
              0.03980475554351496
            ],
            "target_residual": 0.17466480741025292,
            "energy_eV": -147.35712805521703,
            "max_atomic_step_A": 0.03980914354582896,
            "max_log_strain_component": 0.0035571941848503456,
            "step_scale": 1.0,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 6.261809254955732,
            "cell_principal_stretches": [
              1.0154943670554102,
              1.0013684789241475,
              0.9811902950604027
            ],
            "cell_volume_ratio": 0.9977567607617834,
            "cell_rmsd_from_input_A": 0.09376767339727769
          },
          {
            "iteration": 2,
            "reduced_polarization": [
              0.4990863181004117,
              0.4993433689461541,
              0.004376867628510206
            ],
            "branch_aligned_reduced_polarization": [
              0.4990863181004117,
              0.4993433689461541,
              0.004376867628510206
            ],
            "target_residual": 0.004519175720417452,
            "energy_eV": -144.2971804816246,
            "max_atomic_step_A": 0.0006675316252367105,
            "max_log_strain_component": 0.0001708520911475914,
            "step_scale": 1.0,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 6.261809254955732,
            "cell_principal_stretches": [
              1.015481643425632,
              1.0014173122431476,
              0.9810762328042665
            ],
            "cell_volume_ratio": 0.9976769236614824,
            "cell_rmsd_from_input_A": 0.0940295097167647
          },
          {
            "iteration": 3,
            "reduced_polarization": [
              0.499974832780268,
              0.4999690351921091,
              4.488236697209579e-05
            ],
            "branch_aligned_reduced_polarization": [
              0.499974832780268,
              0.4999690351921091,
              4.488236697209579e-05
            ],
            "target_residual": 6.005526739409596e-05,
            "energy_eV": -144.27828145325742
          }
        ],
        "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": 6.005526739409596e-05,
        "parent_symmetrization_rmsd_A": 0.11839381160675651,
        "parent_cell_rmsd_A": 0.0940295097167647,
        "energy_eV": -144.27828145325742,
        "reduced_polarization": [
          0.499974832780268,
          0.4999690351921091,
          4.488236697209579e-05
        ],
        "cartesian_polarization_e_A2": [
          0.019561181000758106,
          0.011244968774710398,
          -0.0003796132873601365
        ],
        "ranking_score": 0.6420212995707358
      },
      "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": [
              1.2048673424538447e-16,
              1.4340355206739457e-15,
              0.09922873755116855
            ],
            "branch_aligned_reduced_polarization": [
              1.1102230246251565e-16,
              1.4432899320127035e-15,
              0.09922873755116857
            ],
            "target_residual": 0.8127838610632157,
            "energy_eV": -151.0262723424384,
            "max_atomic_step_A": 0.12,
            "max_log_strain_component": 0.010770665443733802,
            "step_scale": 0.7318205575953105,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 6.261809254955732,
            "cell_principal_stretches": [
              1.0180665900748325,
              0.9969572862367231,
              0.9902345365978311
            ],
            "cell_volume_ratio": 1.0050572631546342,
            "cell_rmsd_from_input_A": 0.07424792793884807
          },
          {
            "iteration": 1,
            "reduced_polarization": [
              0.3658299998167489,
              0.36830038074156335,
              0.39177529424766805
            ],
            "branch_aligned_reduced_polarization": [
              0.3658299998167489,
              0.36830038074156335,
              0.39177529424766805
            ],
            "target_residual": 0.2169307852684114,
            "energy_eV": -146.89359215065474,
            "max_atomic_step_A": 0.04522601484994416,
            "max_log_strain_component": 0.004222902309548628,
            "step_scale": 1.0,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 6.261809254955732,
            "cell_principal_stretches": [
              1.0250514934407267,
              0.99575648905521,
              0.9866223232367253
            ],
            "cell_volume_ratio": 1.007047059113277,
            "cell_rmsd_from_input_A": 0.10280462753963732
          },
          {
            "iteration": 2,
            "reduced_polarization": [
              0.4999643121875466,
              0.5011927959104728,
              0.4990351856101264
            ],
            "branch_aligned_reduced_polarization": [
              0.4999643121875466,
              0.5011927959104728,
              0.4990351856101264
            ],
            "target_residual": 0.0015345691613301812,
            "energy_eV": -142.60379308404723,
            "max_atomic_step_A": 0.00024542307508924915,
            "max_log_strain_component": 4.371449584599744e-05,
            "step_scale": 1.0,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 6.261809254955732,
            "cell_principal_stretches": [
              1.0250725015923785,
              0.9957428443441522,
              0.9866358227216233
            ],
            "cell_volume_ratio": 1.00706767760242,
            "cell_rmsd_from_input_A": 0.10284510138792614
          },
          {
            "iteration": 3,
            "reduced_polarization": [
              0.5000044754747204,
              0.5000034909205169,
              0.49997312207363565
            ],
            "branch_aligned_reduced_polarization": [
              0.5000044754747204,
              0.5000034909205169,
              0.49997312207363565
            ],
            "target_residual": 2.7470699402738076e-05,
            "energy_eV": -142.6065637522354
          }
        ],
        "iterations": 3
      },
      "parent": {
        "candidate_id": "bec_projection_07",
        "source": "MACEField_BEC_backprojection",
        "spacegroup": "P1",
        "spacegroup_number": 1,
        "pointgroup": "1",
        "has_inversion": false,
        "is_polar_point_group": true,
        "nonpolar_parent_hypothesis": false,
        "symmetry_tolerance_A": null,
        "target_reduced_polarization": [
          0.5,
          0.5,
          0.5
        ],
        "formal_class": [
          0.5,
          0.5,
          0.5
        ],
        "target_residual": 2.7470699402738076e-05,
        "parent_symmetrization_rmsd_A": 0.12206361874425167,
        "parent_cell_rmsd_A": 0.10284510138792614,
        "energy_eV": -142.6065637522354,
        "reduced_polarization": [
          0.5000044754747204,
          0.5000034909205169,
          0.49997312207363565
        ],
        "cartesian_polarization_e_A2": [
          0.019159957123832737,
          0.010983683183262921,
          0.009426928687350263
        ],
        "ranking_score": 0.6478298354900387
      },
      "branch_status": "awaiting_branch_sampling"
    }
  ],
  "sampled_polarization_branches": [
    {
      "orbit_id": 0,
      "candidate_id": "inversion_parent_endpoint_00",
      "formal_class": [
        0.0,
        0.0,
        0.0
      ],
      "construction": "MACEField-BEC-parent plus variable-cell P-N-P path and symmetric log-strain continuation beyond both polar endpoints",
      "geometry_diagnostics": {
        "collision_aware": false,
        "permutations_tested": 1,
        "selected_order": [
          0,
          1,
          2,
          3,
          4,
          5,
          6,
          7,
          8,
          9,
          10,
          11,
          12,
          13,
          14,
          15,
          16,
          17,
          18,
          19,
          20,
          21,
          22,
          23
        ],
        "endpoint_rmsd_A": 0.3754048267283,
        "minimum_distance_A_by_image": [
          1.610892153573931,
          1.600119571953465,
          1.5907243245674878,
          1.5827309395827556,
          1.5761607454742688,
          1.571031598076615,
          1.5646877136115356,
          1.5575654247240491,
          1.5551840799999996
        ],
        "minimum_distance_A": 1.5551840799999996,
        "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": [
          242.68513991339688,
          242.68513991339688,
          242.68513991339688,
          242.68513991339688,
          242.68513991339688,
          242.68513991339688,
          242.68513991339688,
          242.68513991339688,
          242.68513991339688
        ],
        "cell_deformation_log_strain_norm": 0.0
      },
      "parent_reduced_polarization": [
        1.5979371399428895e-16,
        1.439779321157286e-15,
        1.3331973546167142e-16
      ],
      "incoming": {
        "reached": true,
        "construction": "variable_cell_linear_interpolation",
        "continuation_fractions": [
          0.0,
          0.125,
          0.25,
          0.375,
          0.5,
          0.625,
          0.75,
          0.875,
          1.0
        ],
        "energies_eV": [
          -151.0262723424384,
          -150.66949262630817,
          -149.9798255313267,
          -149.12207737919925,
          -148.217453654015,
          -147.35083364243727,
          -146.6233258384509,
          -146.17025137562422,
          -146.0287383318137
        ],
        "cartesian_polarizations_e_A2": [
          [
            -2.433691232215407e-17,
            2.2158928962222963e-18,
            0.0019292257678429037
          ],
          [
            -5.431820504189329e-17,
            2.746277582995504e-17,
            0.007656912646739785
          ],
          [
            -2.883352457431613e-17,
            -2.836342907164539e-17,
            0.012752427553095974
          ],
          [
            -5.0646124722604325e-17,
            4.766314139358152e-17,
            0.01701098995656935
          ],
          [
            -3.47470700592075e-17,
            -2.2244705461431567e-17,
            0.019973115240331952
          ],
          [
            -1.177529727304214e-17,
            2.859216640286834e-18,
            0.020687075886054635
          ],
          [
            1.586699937442024e-17,
            5.901423145552025e-17,
            0.01773976450524921
          ],
          [
            -6.759669904749053e-18,
            2.701959725071058e-17,
            0.010394225266708594
          ],
          [
            6.229705312523601e-18,
            3.225196370243549e-17,
            2.5920300445425843e-18
          ]
        ],
        "raw_reduced_polarization": [
          [
            -6.242487263871907e-16,
            9.892100832419297e-17,
            0.09922873755116701
          ],
          [
            -1.3932774161401485e-15,
            1.2259823031662881e-15,
            0.39382937349270514
          ],
          [
            -7.395881102133782e-16,
            -1.2661889065496699e-15,
            0.6559145683717993
          ],
          [
            -1.299087511021375e-15,
            2.127758979050705e-15,
            0.8749515406759846
          ],
          [
            -8.91272234662302e-16,
            -9.930392835641564e-16,
            1.0273069348840977
          ],
          [
            -3.0203972583801056e-16,
            1.2764001074089413e-16,
            1.064029134388768
          ],
          [
            4.069930490751546e-16,
            2.6344898216920553e-15,
            0.9124356856787651
          ],
          [
            -1.7338745659186111e-16,
            1.2061981015014497e-15,
            0.534621643682049
          ],
          [
            1.5979371399428895e-16,
            1.439779321157286e-15,
            1.3331973546167142e-16
          ]
        ],
        "unwrapped_reduced_polarization": [
          [
            -6.242487263871907e-16,
            9.892100832419297e-17,
            0.09922873755116701
          ],
          [
            -1.3932774161401485e-15,
            1.2259823031662881e-15,
            0.39382937349270514
          ],
          [
            -7.395881102133782e-16,
            -1.26618890654967e-15,
            0.6559145683717993
          ],
          [
            -1.299087511021375e-15,
            2.127758979050705e-15,
            0.8749515406759846
          ],
          [
            -8.91272234662302e-16,
            -9.930392835641566e-16,
            1.0273069348840977
          ],
          [
            -3.020397258380106e-16,
            1.2764001074089406e-16,
            1.064029134388768
          ],
          [
            4.0699304907515464e-16,
            2.6344898216920553e-15,
            0.9124356856787651
          ],
          [
            -1.7338745659186107e-16,
            1.2061981015014497e-15,
            0.534621643682049
          ],
          [
            1.5979371399428892e-16,
            1.439779321157286e-15,
            1.0
          ]
        ],
        "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,
            1
          ]
        ],
        "folded_reduced_polarization": [
          [
            -6.106226635438361e-16,
            1.1102230246251565e-16,
            0.09922873755116701
          ],
          [
            -1.3877787807814457e-15,
            1.2212453270876722e-15,
            0.3938293734927052
          ],
          [
            -7.216449660063518e-16,
            -1.27675647831893e-15,
            -0.3440854316282007
          ],
          [
            -1.27675647831893e-15,
            2.1094237467877974e-15,
            -0.12504845932401532
          ],
          [
            -8.881784197001252e-16,
            -9.992007221626409e-16,
            0.027306934884097744
          ],
          [
            -2.7755575615628914e-16,
            1.1102230246251565e-16,
            0.064029134388768
          ],
          [
            4.440892098500626e-16,
            2.6645352591003757e-15,
            -0.08756431432123479
          ],
          [
            -1.6653345369377348e-16,
            1.2212453270876722e-15,
            -0.465378356317951
          ],
          [
            1.1102230246251565e-16,
            1.4432899320127035e-15,
            0.0
          ]
        ]
      },
      "reflected": {
        "reached": true,
        "construction": "reflect_displacements_about_reconstructed_parent",
        "energies_eV": [
          -146.0287383318137,
          -146.17025137562422,
          -146.6233258384509,
          -147.35083364243724,
          -148.217453654015,
          -149.12207737919928,
          -149.97982553132672,
          -150.66949262630823,
          -151.0262723424384
        ],
        "cartesian_polarizations_e_A2": [
          [
            6.229705312523601e-18,
            3.225196370243549e-17,
            2.5920300445425843e-18
          ],
          [
            -5.380781812743844e-18,
            2.2330481960640173e-17,
            -0.010394225266708594
          ],
          [
            1.2156562732699977e-17,
            4.337431643315127e-17,
            -0.017739764505249143
          ],
          [
            -1.059482815336363e-17,
            -4.072954104088595e-17,
            -0.0206870758860546
          ],
          [
            -7.490438795844376e-18,
            -6.4618296070482446e-18,
            -0.019973115240331903
          ],
          [
            1.3123790849750028e-17,
            9.206677581723605e-18,
            -0.017010989956569255
          ],
          [
            4.0171596578589154e-17,
            1.5925836686397663e-17,
            -0.012752427553095977
          ],
          [
            -1.0790552933113972e-17,
            4.5604505412575e-18,
            -0.007656912646739839
          ],
          [
            2.118613665262817e-17,
            3.1379902627148e-17,
            -0.0019292257678429263
          ]
        ],
        "raw_reduced_polarization": [
          [
            1.5979371399428895e-16,
            1.439779321157286e-15,
            1.3331973546167142e-16
          ],
          [
            -1.3801858465484262e-16,
            9.968684838863832e-16,
            -0.534621643682049
          ],
          [
            3.1181929337132387e-16,
            1.936298962939364e-15,
            -0.9124356856787618
          ],
          [
            -2.7176035700337384e-16,
            -1.818231953004037e-15,
            -1.0640291343887665
          ],
          [
            -1.921318865964172e-16,
            -2.8846642427442076e-16,
            -1.0273069348840953
          ],
          [
            3.3662896980857427e-16,
            4.1100083458567913e-16,
            -0.8749515406759798
          ],
          [
            1.0304128834904198e-15,
            7.109548598267803e-16,
            -0.6559145683717995
          ],
          [
            -2.767807532995113e-16,
            2.0358581713172616e-16,
            -0.3938293734927079
          ],
          [
            5.434304338775515e-16,
            1.4008491178813131e-15,
            -0.09922873755116819
          ]
        ],
        "unwrapped_reduced_polarization": [
          [
            1.5979371399428895e-16,
            1.439779321157286e-15,
            1.0000000000000002
          ],
          [
            -1.3801858465484264e-16,
            9.968684838863832e-16,
            1.465378356317951
          ],
          [
            3.1181929337132382e-16,
            1.936298962939364e-15,
            1.0875643143212383
          ],
          [
            -2.7176035700337384e-16,
            -1.8182319530040368e-15,
            0.9359708656112335
          ],
          [
            -1.921318865964172e-16,
            -2.884664242744207e-16,
            0.9726930651159047
          ],
          [
            3.366289698085742e-16,
            4.1100083458567913e-16,
            1.1250484593240202
          ],
          [
            1.0304128834904198e-15,
            7.109548598267803e-16,
            1.3440854316282005
          ],
          [
            -2.767807532995113e-16,
            2.0358581713172619e-16,
            1.6061706265072921
          ],
          [
            5.434304338775515e-16,
            1.4008491178813131e-15,
            1.9007712624488318
          ]
        ],
        "gauge_integer_shift": [
          0,
          0,
          1
        ],
        "expected_opposite_endpoint_reduced_polarization": [
          9.438361543757685e-16,
          2.7806376339903793e-15,
          -0.09922873755116675
        ],
        "actual_opposite_endpoint_branch_residual": 2.1166075716659203e-15
      },
      "pnp_branch": {
        "construction": "incoming_path_concatenated_with_parent_reflection",
        "reduced_polarization": [
          [
            -6.242487263871907e-16,
            9.892100832419297e-17,
            0.09922873755116701
          ],
          [
            -1.3932774161401485e-15,
            1.2259823031662881e-15,
            0.39382937349270514
          ],
          [
            -7.395881102133782e-16,
            -1.2661889065496699e-15,
            0.6559145683717993
          ],
          [
            -1.299087511021375e-15,
            2.127758979050705e-15,
            0.8749515406759846
          ],
          [
            -8.91272234662302e-16,
            -9.930392835641564e-16,
            1.0273069348840977
          ],
          [
            -3.0203972583801056e-16,
            1.2764001074089413e-16,
            1.064029134388768
          ],
          [
            4.069930490751546e-16,
            2.6344898216920553e-15,
            0.9124356856787651
          ],
          [
            -1.7338745659186111e-16,
            1.2061981015014497e-15,
            0.534621643682049
          ],
          [
            1.5979371399428895e-16,
            1.439779321157286e-15,
            1.3331973546167142e-16
          ],
          [
            -1.3801858465484262e-16,
            9.968684838863832e-16,
            -0.534621643682049
          ],
          [
            3.1181929337132387e-16,
            1.936298962939364e-15,
            -0.9124356856787618
          ],
          [
            -2.7176035700337384e-16,
            -1.818231953004037e-15,
            -1.0640291343887665
          ],
          [
            -1.921318865964172e-16,
            -2.8846642427442076e-16,
            -1.0273069348840953
          ],
          [
            3.3662896980857427e-16,
            4.1100083458567913e-16,
            -0.8749515406759798
          ],
          [
            1.0304128834904198e-15,
            7.109548598267803e-16,
            -0.6559145683717995
          ],
          [
            -2.767807532995113e-16,
            2.0358581713172616e-16,
            -0.3938293734927079
          ],
          [
            5.434304338775515e-16,
            1.4008491178813131e-15,
            -0.09922873755116819
          ]
        ],
        "unwrapped_reduced_polarization": [
          [
            -6.242487263871907e-16,
            9.892100832419297e-17,
            0.09922873755116701
          ],
          [
            -1.3932774161401485e-15,
            1.2259823031662881e-15,
            0.39382937349270514
          ],
          [
            -7.395881102133782e-16,
            -1.26618890654967e-15,
            0.6559145683717993
          ],
          [
            -1.299087511021375e-15,
            2.127758979050705e-15,
            0.8749515406759846
          ],
          [
            -8.91272234662302e-16,
            -9.930392835641566e-16,
            1.0273069348840977
          ],
          [
            -3.020397258380106e-16,
            1.2764001074089406e-16,
            1.064029134388768
          ],
          [
            4.0699304907515464e-16,
            2.6344898216920553e-15,
            0.9124356856787651
          ],
          [
            -1.7338745659186107e-16,
            1.2061981015014497e-15,
            0.534621643682049
          ],
          [
            1.5979371399428892e-16,
            1.439779321157286e-15,
            1.0
          ],
          [
            -1.3801858465484262e-16,
            9.968684838863832e-16,
            1.465378356317951
          ],
          [
            3.1181929337132387e-16,
            1.936298962939364e-15,
            1.0875643143212383
          ],
          [
            -2.717603570033738e-16,
            -1.8182319530040368e-15,
            0.9359708656112335
          ],
          [
            -1.921318865964172e-16,
            -2.884664242744207e-16,
            0.9726930651159047
          ],
          [
            3.366289698085742e-16,
            4.1100083458567913e-16,
            1.1250484593240202
          ],
          [
            1.0304128834904198e-15,
            7.109548598267803e-16,
            1.3440854316282005
          ],
          [
            -2.767807532995113e-16,
            2.0358581713172619e-16,
            1.6061706265072921
          ],
          [
            5.434304338775515e-16,
            1.4008491178813131e-15,
            1.9007712624488318
          ]
        ],
        "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,
            1
          ],
          [
            0,
            0,
            2
          ],
          [
            0,
            0,
            2
          ],
          [
            0,
            0,
            2
          ],
          [
            0,
            0,
            2
          ],
          [
            0,
            0,
            2
          ],
          [
            0,
            0,
            2
          ],
          [
            0,
            0,
            2
          ],
          [
            0,
            0,
            2
          ]
        ],
        "folded_reduced_polarization": [
          [
            -6.106226635438361e-16,
            1.1102230246251565e-16,
            0.09922873755116701
          ],
          [
            -1.3877787807814457e-15,
            1.2212453270876722e-15,
            0.3938293734927052
          ],
          [
            -7.216449660063518e-16,
            -1.27675647831893e-15,
            -0.3440854316282007
          ],
          [
            -1.27675647831893e-15,
            2.1094237467877974e-15,
            -0.12504845932401532
          ],
          [
            -8.881784197001252e-16,
            -9.992007221626409e-16,
            0.027306934884097744
          ],
          [
            -2.7755575615628914e-16,
            1.1102230246251565e-16,
            0.064029134388768
          ],
          [
            4.440892098500626e-16,
            2.6645352591003757e-15,
            -0.08756431432123479
          ],
          [
            -1.6653345369377348e-16,
            1.2212453270876722e-15,
            -0.465378356317951
          ],
          [
            1.1102230246251565e-16,
            1.4432899320127035e-15,
            0.0
          ],
          [
            -1.1102230246251565e-16,
            9.992007221626409e-16,
            0.465378356317951
          ],
          [
            3.3306690738754696e-16,
            1.887379141862766e-15,
            0.08756431432123835
          ],
          [
            -2.7755575615628914e-16,
            -1.8318679906315083e-15,
            -0.06402913438876645
          ],
          [
            -1.6653345369377348e-16,
            -2.7755575615628914e-16,
            -0.027306934884095302
          ],
          [
            3.3306690738754696e-16,
            4.440892098500626e-16,
            0.1250484593240202
          ],
          [
            9.992007221626409e-16,
            6.661338147750939e-16,
            0.3440854316282005
          ],
          [
            -2.7755575615628914e-16,
            2.220446049250313e-16,
            -0.3938293734927081
          ],
          [
            5.551115123125783e-16,
            1.4432899320127035e-15,
            -0.09922873755116823
          ]
        ]
      },
      "incoming_structure_ids": [
        "incoming_00_000",
        "incoming_00_001",
        "incoming_00_002",
        "incoming_00_003",
        "incoming_00_004",
        "incoming_00_005",
        "incoming_00_006",
        "incoming_00_007",
        "incoming_00_008"
      ],
      "reflected_structure_ids": [
        "reflected_00_001",
        "reflected_00_002",
        "reflected_00_003",
        "reflected_00_004",
        "reflected_00_005",
        "reflected_00_006",
        "reflected_00_007",
        "reflected_00_008"
      ],
      "positive_extension_structure_ids": [
        "extension_plus_00_000",
        "extension_plus_00_001",
        "extension_plus_00_002",
        "extension_plus_00_003"
      ],
      "negative_extension_structure_ids": [
        "extension_minus_00_000",
        "extension_minus_00_001",
        "extension_minus_00_002",
        "extension_minus_00_003"
      ],
      "extension": {
        "enabled": true,
        "fraction_beyond_polar_endpoint": 0.35,
        "images_per_side": 4,
        "construction": "continue fractional atomic displacements and symmetric log strain beyond +P; reflect these structures about N for the -P side",
        "positive_path_coordinates": [
          1.35,
          1.2625,
          1.175,
          1.0875
        ],
        "negative_path_coordinates": [
          -1.0875,
          -1.175,
          -1.2625,
          -1.35
        ]
      },
      "branch_coordinates": [
        1.35,
        1.2625,
        1.175,
        1.0875,
        1.0,
        0.875,
        0.75,
        0.625,
        0.5,
        0.375,
        0.25,
        0.125,
        0.0,
        -0.125,
        -0.25,
        -0.375,
        -0.5,
        -0.625,
        -0.75,
        -0.875,
        -1.0,
        -1.0875,
        -1.175,
        -1.2625,
        -1.35
      ],
      "parent": {
        "candidate_id": "inversion_parent_endpoint_00",
        "source": "same_species_inversion_center_projection_from_endpoint",
        "spacegroup": "Cmcm",
        "spacegroup_number": 63,
        "pointgroup": "mmm",
        "has_inversion": true,
        "is_polar_point_group": false,
        "nonpolar_parent_hypothesis": true,
        "symmetry_tolerance_A": null,
        "target_reduced_polarization": [
          0.0,
          0.0,
          0.0
        ],
        "formal_class": [
          0.0,
          0.0,
          0.0
        ],
        "target_residual": 1.3489558720131349e-16,
        "parent_symmetrization_rmsd_A": 0.3754048267283,
        "parent_cell_rmsd_A": 0.0,
        "energy_eV": -146.02873833181374,
        "reduced_polarization": [
          1.190860102655265e-16,
          3.829200322226824e-18,
          6.325091960057455e-17
        ],
        "cartesian_polarization_e_A2": [
          4.642677939289308e-18,
          8.577649920860501e-20,
          1.2297375432219543e-18
        ],
        "ranking_score": 0.3754048267283003
      }
    }
  ],
  "path_sampling": {
    "num_images": 17,
    "images_per_leg_including_parent": 9,
    "extension_fraction_beyond_polar_endpoint": 0.35,
    "extension_images_per_side": 4,
    "total_images_per_sampled_branch": 25,
    "construction": "linear polar-to-parent interpolation plus parent-reflected second leg and symmetric log-strain continuation beyond both polar endpoints"
  },
  "branch_folding": "componentwise integer unwrap with per-image shifts, then reduced-coordinate fold [-0.5, 0.5)",
  "bec_backprojection_settings": {
    "variable_cell": true,
    "max_strain_step_log_component": 0.02,
    "strain_response_refresh_iterations": 4,
    "cell_principal_stretch_bounds": [
      0.85,
      1.15
    ],
    "cell_volume_ratio_bounds": [
      0.7,
      1.3
    ],
    "strain_jacobian": "branch-matched finite differences of reduced polarization in six symmetric log-strain coordinates at fixed fractional positions"
  },
  "model_input_contract": "one polar endpoint structure; no reference parent or path frame",
  "run": {
    "model_file": "MACEField-MH-0-omat-dielectric.model",
    "model_sha256": "f92e043aaf2cd8879919db8452503553fe7b608cb749d8d169dd96d4aa094aa2",
    "model_head": "mp-ferroelectric",
    "device": "cpu",
    "dtype": "float64",
    "num_images": 17,
    "compute_becs_for_every_image": true,
    "compute_polarizability_for_every_image": true,
    "initial_structure_relaxation": {
      "enabled": false
    },
    "model_evaluations_for_recovery": {
      "total": 53,
      "full_response": 20,
      "energy_polarization": 33
    },
    "model_evaluations_for_recovery_and_path_properties": {
      "total": 78,
      "full_response": 45,
      "energy_polarization": 33
    },
    "elapsed_seconds": 531.1512192450464
  }
}