{
  "schema": "ferrofinder.endpoint_parent_recovery.v4_variable_cell",
  "status": "complete",
  "input_atom_count": 24,
  "input_formula": "Mg8N12V4",
  "input_spacegroup": "Cmc2_1",
  "input_pointgroup": "mm2",
  "input_is_polar_point_group": true,
  "input_energy_eV": -164.6017678326242,
  "input_cartesian_polarization_e_A2": [
    5.526219372688897e-17,
    -2.937720801202555e-17,
    0.0016610467521657104
  ],
  "input_reduced_polarization": [
    1.64871515500274e-15,
    -1.4936743355313194e-15,
    0.09606683379186727
  ],
  "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": [
        0.5,
        0.0,
        0.0
      ],
      "target_reduced_polarization": [
        0.5,
        0.0,
        0.0
      ]
    },
    {
      "orbit_id": 3,
      "representative_formal_class": [
        0.0,
        0.5,
        0.0
      ],
      "target_reduced_polarization": [
        0.0,
        -0.5,
        0.0
      ]
    },
    {
      "orbit_id": 4,
      "representative_formal_class": [
        0.0,
        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": 1.2723271128109783e-15,
      "parent_symmetrization_rmsd_A": 0.3755075220757377,
      "parent_cell_rmsd_A": 0.0,
      "energy_eV": -158.3953096253852,
      "reduced_polarization": [
        4.2022563890998353e-16,
        -6.1938648682319465e-16,
        1.0288766079260605e-15
      ],
      "cartesian_polarization_e_A2": [
        1.4085265484449682e-17,
        -1.2181936336725107e-17,
        1.7789824859612843e-17
      ],
      "ranking_score": 0.37550752207574023
    },
    {
      "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": 0.0007255058529566145,
      "parent_symmetrization_rmsd_A": 0.00400173409620547,
      "parent_cell_rmsd_A": 0.010431914580433733,
      "energy_eV": -164.60390349154846,
      "reduced_polarization": [
        -7.250714501512997e-15,
        4.409736446685845e-15,
        -0.0007255058529566145
      ],
      "cartesian_polarization_e_A2": [
        -2.4350555255960347e-16,
        8.693973407066428e-17,
        -1.2521068044257982e-05
      ],
      "ranking_score": 0.5080607244472272
    },
    {
      "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": 1.0117275798262867e-15,
      "parent_symmetrization_rmsd_A": 0.375508969999098,
      "parent_cell_rmsd_A": 0.010431914580433733,
      "energy_eV": -158.5614340078925,
      "reduced_polarization": [
        -2.3255169896428267e-16,
        -6.329778623524335e-16,
        7.542224001325635e-16
      ],
      "cartesian_polarization_e_A2": [
        -7.809283290220295e-18,
        -1.2476918944050013e-17,
        1.3016669616210711e-17
      ],
      "ranking_score": 0.3781169486442084
    },
    {
      "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": 0.0006541830227468903,
      "parent_symmetrization_rmsd_A": 0.01727884230728399,
      "parent_cell_rmsd_A": 0.04607834290422553,
      "energy_eV": -164.3931424814421,
      "reduced_polarization": [
        -3.612930897235544e-15,
        1.1214688757242065e-14,
        0.4993458169772531
      ],
      "cartesian_polarization_e_A2": [
        -1.7914187419131726e-16,
        2.6464529208522535e-16,
        0.008704821501805342
      ],
      "ranking_score": 0.5301067940788342
    },
    {
      "candidate_id": "bec_projection_02",
      "source": "MACEField_BEC_backprojection",
      "spacegroup": "Cc",
      "spacegroup_number": 9,
      "pointgroup": "m",
      "has_inversion": false,
      "is_polar_point_group": true,
      "nonpolar_parent_hypothesis": false,
      "symmetry_tolerance_A": null,
      "target_reduced_polarization": [
        0.5,
        0.0,
        0.0
      ],
      "formal_class": [
        0.5,
        0.0,
        0.0
      ],
      "target_residual": 0.0005354841031514692,
      "parent_symmetrization_rmsd_A": 0.0791588258032528,
      "parent_cell_rmsd_A": 0.12527410107444648,
      "energy_eV": -162.21507174048617,
      "reduced_polarization": [
        0.4999157209930965,
        -1.6596012242429797e-14,
        -0.0005288102435877102
      ],
      "cartesian_polarization_e_A2": [
        0.016783462115210507,
        2.2161869419750593e-16,
        -0.00032727630239988523
      ],
      "ranking_score": 0.6115483192781673
    },
    {
      "candidate_id": "bec_projection_03",
      "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": 0.0002430686152459071,
      "parent_symmetrization_rmsd_A": 0.04211156598922031,
      "parent_cell_rmsd_A": 0.052011605259642164,
      "energy_eV": -163.93698222751073,
      "reduced_polarization": [
        2.177000811361379e-15,
        -0.49980478302751596,
        0.0001448194923749218
      ],
      "cartesian_polarization_e_A2": [
        9.26158593300909e-17,
        -0.00985551532768351,
        -0.00012659124519905763
      ],
      "ranking_score": 0.5556006045346227
    },
    {
      "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": 0.0008076712631868212,
      "parent_symmetrization_rmsd_A": 0.045195917878587406,
      "parent_cell_rmsd_A": 0.06823434618123954,
      "energy_eV": -163.66859576756767,
      "reduced_polarization": [
        -6.1034715030450255e-15,
        -0.5001028260288661,
        0.4991989009567067
      ],
      "cartesian_polarization_e_A2": [
        -2.564079368045667e-16,
        -0.009630182317768105,
        0.00857642614312434
      ],
      "ranking_score": 0.563869846950271
    },
    {
      "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": 0.00024292728826839504,
      "parent_symmetrization_rmsd_A": 0.08311062682829533,
      "parent_cell_rmsd_A": 0.13755310721825875,
      "energy_eV": -161.66330144198383,
      "reduced_polarization": [
        0.49999450865880707,
        4.238333842911143e-15,
        0.49975713478520517
      ],
      "cartesian_polarization_e_A2": [
        0.016444180546026175,
        7.461594318397174e-16,
        0.00839873583286757
      ],
      "ranking_score": 0.6179847582093968
    },
    {
      "candidate_id": "bec_projection_06",
      "source": "MACEField_BEC_backprojection",
      "spacegroup": "P1",
      "spacegroup_number": 1,
      "pointgroup": "1",
      "has_inversion": false,
      "is_polar_point_group": true,
      "nonpolar_parent_hypothesis": false,
      "symmetry_tolerance_A": null,
      "target_reduced_polarization": [
        0.5,
        -0.5,
        0.0
      ],
      "formal_class": [
        0.5,
        0.5,
        0.0
      ],
      "target_residual": 0.0007317534251305609,
      "parent_symmetrization_rmsd_A": 0.09178694230222308,
      "parent_cell_rmsd_A": 0.13854528665896926,
      "energy_eV": -161.2653588001477,
      "reduced_polarization": [
        0.49972008713087773,
        -0.4993384531027874,
        0.0001395262114386979
      ],
      "cartesian_polarization_e_A2": [
        0.016783041017864115,
        -0.00984434549277133,
        -0.0004589275623945838
      ],
      "ranking_score": 0.6278867708172265
    },
    {
      "candidate_id": "bec_projection_07",
      "source": "MACEField_BEC_backprojection",
      "spacegroup": "P1",
      "spacegroup_number": 1,
      "pointgroup": "1",
      "has_inversion": false,
      "is_polar_point_group": true,
      "nonpolar_parent_hypothesis": false,
      "symmetry_tolerance_A": null,
      "target_reduced_polarization": [
        0.5,
        -0.5,
        0.5
      ],
      "formal_class": [
        0.5,
        0.5,
        0.5
      ],
      "target_residual": 0.0002796837695730668,
      "parent_symmetrization_rmsd_A": 0.09497820213282315,
      "parent_cell_rmsd_A": 0.1491901570066066,
      "energy_eV": -160.6468281399527,
      "reduced_polarization": [
        0.49999671950218527,
        -0.500025879580192,
        0.4997215354661258
      ],
      "cartesian_polarization_e_A2": [
        0.01644362752897334,
        -0.00961344153645124,
        0.008259463445875385
      ],
      "ranking_score": 0.6328351089236209
    }
  ],
  "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": [
              1.64871515500274e-15,
              -1.4936743355313194e-15,
              0.09606683379186727
            ],
            "branch_aligned_reduced_polarization": [
              1.64871515500274e-15,
              -1.4936743355313194e-15,
              0.09606683379186727
            ],
            "target_residual": 0.09606683379186727,
            "energy_eV": -164.6017678326242,
            "max_atomic_step_A": 0.006176304186973832,
            "max_log_strain_component": 0.0029718621709963577,
            "step_scale": 1.0,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 14.222175725216156,
            "cell_principal_stretches": [
              1.001109294374776,
              1.0007519163327807,
              0.9970325494400697
            ],
            "cell_volume_ratio": 0.9988890687182883,
            "cell_rmsd_from_input_A": 0.010431914580433733
          },
          {
            "iteration": 1,
            "reduced_polarization": [
              -7.250714501512997e-15,
              4.409736446685845e-15,
              -0.0007255058529566145
            ],
            "branch_aligned_reduced_polarization": [
              -7.250714501512997e-15,
              4.409736446685845e-15,
              -0.0007255058529566145
            ],
            "target_residual": 0.0007255058529566145,
            "energy_eV": -164.60390349154846
          }
        ],
        "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": 1.2723271128109783e-15,
        "parent_symmetrization_rmsd_A": 0.3755075220757377,
        "parent_cell_rmsd_A": 0.0,
        "energy_eV": -158.3953096253852,
        "reduced_polarization": [
          4.2022563890998353e-16,
          -6.1938648682319465e-16,
          1.0288766079260605e-15
        ],
        "cartesian_polarization_e_A2": [
          1.4085265484449682e-17,
          -1.2181936336725107e-17,
          1.7789824859612843e-17
        ],
        "ranking_score": 0.37550752207574023
      },
      "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": [
          -164.6017678326242,
          -164.25231714044043,
          -163.48013669894362,
          -162.42738144099042,
          -161.2601838605476,
          -160.1486501548303,
          -159.23026429442749,
          -158.6145423199477,
          -158.39530962538512
        ],
        "cartesian_polarizations_e_A2": [
          [
            3.2702309098299294e-17,
            1.6726735662349472e-17,
            0.0016610467521657826
          ],
          [
            -1.728222133901687e-17,
            -5.945722004347754e-17,
            0.00844949254653018
          ],
          [
            -1.6095646817479807e-17,
            -2.904923280295987e-18,
            0.01347230849890867
          ],
          [
            -3.263671001134084e-18,
            -9.183305853838927e-18,
            0.01633182831508806
          ],
          [
            -1.7417796121627035e-17,
            -1.22756435393153e-17,
            0.016797630003476376
          ],
          [
            -1.3499066465118162e-17,
            -2.576948071230311e-17,
            0.014915901574499634
          ],
          [
            1.3269565952693107e-17,
            -2.04281701646621e-17,
            0.01105906984042288
          ],
          [
            1.577940104651843e-17,
            3.748288103607725e-18,
            0.005856555724970473
          ],
          [
            1.6979573291035952e-17,
            -2.5863187914893303e-17,
            5.3334589082353355e-18
          ]
        ],
        "raw_reduced_polarization": [
          [
            9.756542217707094e-16,
            8.504652915226172e-16,
            0.09606683379187146
          ],
          [
            -5.15604942767315e-16,
            -3.0230825068408998e-15,
            0.488677392755383
          ],
          [
            -4.802041874902693e-16,
            -1.4769985455014641e-16,
            0.7791725426571877
          ],
          [
            -9.736971114656561e-17,
            -4.669221208359467e-16,
            0.9445532067157337
          ],
          [
            -5.1964973693220565e-16,
            -6.241509982602962e-16,
            0.9714929020133092
          ],
          [
            -4.0273673479958876e-16,
            -1.3102406452029116e-15,
            0.8626629175518569
          ],
          [
            3.958897215451733e-16,
            -1.0386634932881262e-15,
            0.6396026017132648
          ],
          [
            4.707691802977146e-16,
            1.9058045748405988e-16,
            0.33871458746720373
          ],
          [
            5.065756156688624e-16,
            -1.3150051566400132e-15,
            3.084612216996061e-16
          ]
        ],
        "unwrapped_reduced_polarization": [
          [
            9.756542217707094e-16,
            8.504652915226172e-16,
            0.09606683379187146
          ],
          [
            -5.15604942767315e-16,
            -3.0230825068408998e-15,
            0.488677392755383
          ],
          [
            -4.802041874902693e-16,
            -1.4769985455014659e-16,
            0.7791725426571877
          ],
          [
            -9.736971114656564e-17,
            -4.669221208359467e-16,
            0.9445532067157337
          ],
          [
            -5.1964973693220565e-16,
            -6.241509982602962e-16,
            0.9714929020133092
          ],
          [
            -4.0273673479958876e-16,
            -1.3102406452029116e-15,
            0.8626629175518569
          ],
          [
            3.958897215451733e-16,
            -1.0386634932881262e-15,
            0.6396026017132648
          ],
          [
            4.707691802977146e-16,
            1.9058045748405983e-16,
            0.33871458746720373
          ],
          [
            5.065756156688624e-16,
            -1.3150051566400132e-15,
            3.3306690738754696e-16
          ]
        ],
        "berry_integer_shifts": [
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ]
        ],
        "folded_reduced_polarization": [
          [
            9.992007221626409e-16,
            8.881784197001252e-16,
            0.09606683379187142
          ],
          [
            -4.996003610813204e-16,
            -2.9976021664879227e-15,
            0.488677392755383
          ],
          [
            -4.996003610813204e-16,
            -1.6653345369377348e-16,
            -0.2208274573428124
          ],
          [
            -1.1102230246251565e-16,
            -4.440892098500626e-16,
            -0.05544679328426616
          ],
          [
            -4.996003610813204e-16,
            -6.106226635438361e-16,
            -0.02850709798669082
          ],
          [
            -3.885780586188048e-16,
            -1.3322676295501878e-15,
            -0.13733708244814302
          ],
          [
            4.440892098500626e-16,
            -1.0547118733938987e-15,
            -0.3603973982867352
          ],
          [
            4.440892098500626e-16,
            2.220446049250313e-16,
            0.33871458746720373
          ],
          [
            5.551115123125783e-16,
            -1.3322676295501878e-15,
            3.3306690738754696e-16
          ]
        ]
      },
      "reflected": {
        "reached": true,
        "construction": "reflect_displacements_about_reconstructed_parent",
        "energies_eV": [
          -158.3953096253851,
          -158.61454231994767,
          -159.23026429442746,
          -160.1486501548303,
          -161.2601838605476,
          -162.42738144099044,
          -163.4801366989436,
          -164.25231714044043,
          -164.60176783262415
        ],
        "cartesian_polarizations_e_A2": [
          [
            -6.894683179457075e-18,
            -1.349383717298781e-17,
            1.5019697210854003e-17
          ],
          [
            -3.566667490963991e-18,
            1.021408508233105e-17,
            -0.005856555724970495
          ],
          [
            4.1054463215667855e-18,
            2.3145679039777702e-17,
            -0.011059069840422908
          ],
          [
            -2.2622596884779603e-17,
            -6.746918586493905e-18,
            -0.014915901574499613
          ],
          [
            -4.1135561073246634e-18,
            -5.1538961424606216e-18,
            -0.0167976300034764
          ],
          [
            -2.7435517026668683e-18,
            -1.6398760453283797e-17,
            -0.01633182831508801
          ],
          [
            -2.461083614672139e-17,
            5.903553763182167e-18,
            -0.013472308498908497
          ],
          [
            -2.995702550027515e-17,
            6.2315289722478426e-18,
            -0.00844949254653031
          ],
          [
            -4.5061091138297664e-18,
            9.291069136817648e-17,
            -0.0016610467521659634
          ]
        ],
        "raw_reduced_polarization": [
          [
            -2.0569883097822673e-16,
            -6.860896469426156e-16,
            8.686659503581132e-16
          ],
          [
            -1.0640943380332531e-16,
            5.193317466440631e-16,
            -0.338714587467205
          ],
          [
            1.224835843808342e-16,
            1.1768343249640698e-15,
            -0.6396026017132665
          ],
          [
            -6.7493191663337255e-16,
            -3.430448234713078e-16,
            -0.8626629175518556
          ],
          [
            -1.2272553508494337e-16,
            -2.620481290405823e-16,
            -0.9714929020133106
          ],
          [
            -8.185225677205634e-17,
            -8.33789501492762e-16,
            -0.944553206715731
          ],
          [
            -7.342498695024763e-16,
            3.001642205373943e-16,
            -0.7791725426571777
          ],
          [
            -8.937502949159103e-16,
            3.168400105672495e-16,
            -0.4886773927553905
          ],
          [
            -1.3443712391844892e-16,
            4.7240130898861345e-15,
            -0.09606683379188191
          ]
        ],
        "unwrapped_reduced_polarization": [
          [
            -2.0569883097822673e-16,
            -6.860896469426156e-16,
            8.686659503581132e-16
          ],
          [
            -1.0640943380332531e-16,
            5.193317466440631e-16,
            -0.338714587467205
          ],
          [
            1.2248358438083423e-16,
            1.1768343249640698e-15,
            -0.6396026017132665
          ],
          [
            -6.7493191663337255e-16,
            -3.4304482347130774e-16,
            -0.8626629175518556
          ],
          [
            -1.227255350849434e-16,
            -2.620481290405823e-16,
            -0.9714929020133106
          ],
          [
            -8.185225677205634e-17,
            -8.337895014927621e-16,
            -0.944553206715731
          ],
          [
            -7.342498695024763e-16,
            3.001642205373943e-16,
            -0.7791725426571777
          ],
          [
            -8.937502949159103e-16,
            3.168400105672495e-16,
            -0.4886773927553905
          ],
          [
            -1.3443712391844892e-16,
            4.7240130898861345e-15,
            -0.09606683379188191
          ]
        ],
        "gauge_integer_shift": [
          0,
          0,
          0
        ],
        "expected_opposite_endpoint_reduced_polarization": [
          3.749700956701539e-17,
          -3.4804756048026437e-15,
          -0.09606683379187084
        ],
        "actual_opposite_endpoint_branch_residual": 1.3783583906883227e-14
      },
      "pnp_branch": {
        "construction": "incoming_path_concatenated_with_parent_reflection",
        "reduced_polarization": [
          [
            9.756542217707094e-16,
            8.504652915226172e-16,
            0.09606683379187146
          ],
          [
            -5.15604942767315e-16,
            -3.0230825068408998e-15,
            0.488677392755383
          ],
          [
            -4.802041874902693e-16,
            -1.4769985455014641e-16,
            0.7791725426571877
          ],
          [
            -9.736971114656561e-17,
            -4.669221208359467e-16,
            0.9445532067157337
          ],
          [
            -5.1964973693220565e-16,
            -6.241509982602962e-16,
            0.9714929020133092
          ],
          [
            -4.0273673479958876e-16,
            -1.3102406452029116e-15,
            0.8626629175518569
          ],
          [
            3.958897215451733e-16,
            -1.0386634932881262e-15,
            0.6396026017132648
          ],
          [
            4.707691802977146e-16,
            1.9058045748405988e-16,
            0.33871458746720373
          ],
          [
            5.065756156688624e-16,
            -1.3150051566400132e-15,
            3.084612216996061e-16
          ],
          [
            -1.0640943380332531e-16,
            5.193317466440631e-16,
            -0.338714587467205
          ],
          [
            1.224835843808342e-16,
            1.1768343249640698e-15,
            -0.6396026017132665
          ],
          [
            -6.7493191663337255e-16,
            -3.430448234713078e-16,
            -0.8626629175518556
          ],
          [
            -1.2272553508494337e-16,
            -2.620481290405823e-16,
            -0.9714929020133106
          ],
          [
            -8.185225677205634e-17,
            -8.33789501492762e-16,
            -0.944553206715731
          ],
          [
            -7.342498695024763e-16,
            3.001642205373943e-16,
            -0.7791725426571777
          ],
          [
            -8.937502949159103e-16,
            3.168400105672495e-16,
            -0.4886773927553905
          ],
          [
            -1.3443712391844892e-16,
            4.7240130898861345e-15,
            -0.09606683379188191
          ]
        ],
        "unwrapped_reduced_polarization": [
          [
            9.756542217707094e-16,
            8.504652915226172e-16,
            0.09606683379187146
          ],
          [
            -5.15604942767315e-16,
            -3.0230825068408998e-15,
            0.488677392755383
          ],
          [
            -4.802041874902693e-16,
            -1.4769985455014659e-16,
            0.7791725426571877
          ],
          [
            -9.736971114656564e-17,
            -4.669221208359467e-16,
            0.9445532067157337
          ],
          [
            -5.1964973693220565e-16,
            -6.241509982602962e-16,
            0.9714929020133092
          ],
          [
            -4.0273673479958876e-16,
            -1.3102406452029116e-15,
            0.8626629175518569
          ],
          [
            3.958897215451733e-16,
            -1.0386634932881262e-15,
            0.6396026017132648
          ],
          [
            4.707691802977146e-16,
            1.9058045748405983e-16,
            0.33871458746720373
          ],
          [
            5.065756156688624e-16,
            -1.3150051566400132e-15,
            3.3306690738754696e-16
          ],
          [
            -1.0640943380332531e-16,
            5.193317466440632e-16,
            -0.338714587467205
          ],
          [
            1.2248358438083423e-16,
            1.1768343249640698e-15,
            -0.6396026017132665
          ],
          [
            -6.7493191663337255e-16,
            -3.4304482347130774e-16,
            -0.8626629175518556
          ],
          [
            -1.227255350849434e-16,
            -2.620481290405823e-16,
            -0.9714929020133106
          ],
          [
            -8.185225677205634e-17,
            -8.337895014927621e-16,
            -0.944553206715731
          ],
          [
            -7.342498695024763e-16,
            3.001642205373943e-16,
            -0.7791725426571777
          ],
          [
            -8.937502949159103e-16,
            3.168400105672495e-16,
            -0.4886773927553905
          ],
          [
            -1.3443712391844892e-16,
            4.7240130898861345e-15,
            -0.09606683379188191
          ]
        ],
        "berry_integer_shifts": [
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ]
        ],
        "folded_reduced_polarization": [
          [
            9.992007221626409e-16,
            8.881784197001252e-16,
            0.09606683379187142
          ],
          [
            -4.996003610813204e-16,
            -2.9976021664879227e-15,
            0.488677392755383
          ],
          [
            -4.996003610813204e-16,
            -1.6653345369377348e-16,
            -0.2208274573428124
          ],
          [
            -1.1102230246251565e-16,
            -4.440892098500626e-16,
            -0.05544679328426616
          ],
          [
            -4.996003610813204e-16,
            -6.106226635438361e-16,
            -0.02850709798669082
          ],
          [
            -3.885780586188048e-16,
            -1.3322676295501878e-15,
            -0.13733708244814302
          ],
          [
            4.440892098500626e-16,
            -1.0547118733938987e-15,
            -0.3603973982867352
          ],
          [
            4.440892098500626e-16,
            2.220446049250313e-16,
            0.33871458746720373
          ],
          [
            5.551115123125783e-16,
            -1.3322676295501878e-15,
            3.3306690738754696e-16
          ],
          [
            -1.1102230246251565e-16,
            5.551115123125783e-16,
            -0.338714587467205
          ],
          [
            1.1102230246251565e-16,
            1.2212453270876722e-15,
            0.36039739828673345
          ],
          [
            -6.661338147750939e-16,
            -3.3306690738754696e-16,
            0.13733708244814435
          ],
          [
            -1.1102230246251565e-16,
            -2.7755575615628914e-16,
            0.028507097986689378
          ],
          [
            -5.551115123125783e-17,
            -8.326672684688674e-16,
            0.05544679328426905
          ],
          [
            -7.216449660063518e-16,
            3.3306690738754696e-16,
            0.22082745734282228
          ],
          [
            -8.881784197001252e-16,
            3.3306690738754696e-16,
            -0.4886773927553905
          ],
          [
            -1.1102230246251565e-16,
            4.773959005888173e-15,
            -0.09606683379188191
          ]
        ]
      },
      "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": [
              1.64871515500274e-15,
              -1.4936743355313194e-15,
              0.09606683379186727
            ],
            "branch_aligned_reduced_polarization": [
              1.64871515500274e-15,
              -1.4936743355313194e-15,
              0.09606683379186726
            ],
            "target_residual": 0.40393316620813274,
            "energy_eV": -164.6017678326242,
            "max_atomic_step_A": 0.02596956730263477,
            "max_log_strain_component": 0.012495818264038167,
            "step_scale": 1.0,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 14.222175725216156,
            "cell_principal_stretches": [
              1.0125742172137626,
              0.9968445868022149,
              0.9953491728252811
            ],
            "cell_volume_ratio": 1.0046846792908166,
            "cell_rmsd_from_input_A": 0.04408434401051929
          },
          {
            "iteration": 1,
            "reduced_polarization": [
              -4.120343685305375e-16,
              -2.039521331353915e-14,
              0.48348942737221867
            ],
            "branch_aligned_reduced_polarization": [
              -4.120343685305375e-16,
              -2.039521331353915e-14,
              0.48348942737221867
            ],
            "target_residual": 0.016510572627781328,
            "energy_eV": -164.40750436433498,
            "max_atomic_step_A": 0.001078997632051973,
            "max_log_strain_component": 0.0005627558378830911,
            "step_scale": 1.0,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 14.222175725216156,
            "cell_principal_stretches": [
              1.0131442096340284,
              0.9967027156203332,
              0.9951402300978847
            ],
            "cell_volume_ratio": 1.0048961719875427,
            "cell_rmsd_from_input_A": 0.04607834290422553
          },
          {
            "iteration": 2,
            "reduced_polarization": [
              -3.612930897235544e-15,
              1.1214688757242065e-14,
              0.4993458169772531
            ],
            "branch_aligned_reduced_polarization": [
              -3.612930897235544e-15,
              1.1214688757242065e-14,
              0.4993458169772531
            ],
            "target_residual": 0.0006541830227468903,
            "energy_eV": -164.3931424814421
          }
        ],
        "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": 0.0006541830227468903,
        "parent_symmetrization_rmsd_A": 0.01727884230728399,
        "parent_cell_rmsd_A": 0.04607834290422553,
        "energy_eV": -164.3931424814421,
        "reduced_polarization": [
          -3.612930897235544e-15,
          1.1214688757242065e-14,
          0.4993458169772531
        ],
        "cartesian_polarization_e_A2": [
          -1.7914187419131726e-16,
          2.6464529208522535e-16,
          0.008704821501805342
        ],
        "ranking_score": 0.5301067940788342
      },
      "branch_status": "awaiting_branch_sampling"
    },
    {
      "orbit_id": 2,
      "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": [
              1.64871515500274e-15,
              -1.4936743355313194e-15,
              0.09606683379186727
            ],
            "branch_aligned_reduced_polarization": [
              1.6653345369377348e-15,
              -1.4936743355313194e-15,
              0.09606683379186727
            ],
            "target_residual": 0.5091452018381324,
            "energy_eV": -164.6017678326242,
            "max_atomic_step_A": 0.0883212921426212,
            "max_log_strain_component": 0.018429659297783528,
            "step_scale": 1.0,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 14.222175725216156,
            "cell_principal_stretches": [
              1.0175658386049595,
              1.0011092943747704,
              0.9805579124651337
            ],
            "cell_volume_ratio": 0.9988890687182873,
            "cell_rmsd_from_input_A": 0.12182727480920855
          },
          {
            "iteration": 1,
            "reduced_polarization": [
              0.4869805448249232,
              1.4057494993727769e-14,
              -0.020374436668201035
            ],
            "branch_aligned_reduced_polarization": [
              0.4869805448249232,
              1.4057494993727769e-14,
              -0.020374436668201035
            ],
            "target_residual": 0.024178996724479058,
            "energy_eV": -162.34347105109617,
            "max_atomic_step_A": 0.0027051959898923153,
            "max_log_strain_component": 0.0006959186746183803,
            "step_scale": 1.0,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 14.222175725216156,
            "cell_principal_stretches": [
              1.0183458554943625,
              1.0008494214778216,
              0.9803163828105811
            ],
            "cell_volume_ratio": 0.9991491039257208,
            "cell_rmsd_from_input_A": 0.12527410107444648
          },
          {
            "iteration": 2,
            "reduced_polarization": [
              0.4999157209930965,
              -1.6596012242429797e-14,
              -0.0005288102435877102
            ],
            "branch_aligned_reduced_polarization": [
              0.4999157209930965,
              -1.6596012242429797e-14,
              -0.0005288102435877102
            ],
            "target_residual": 0.0005354841031514692,
            "energy_eV": -162.21507174048617
          }
        ],
        "iterations": 2
      },
      "parent": {
        "candidate_id": "bec_projection_02",
        "source": "MACEField_BEC_backprojection",
        "spacegroup": "Cc",
        "spacegroup_number": 9,
        "pointgroup": "m",
        "has_inversion": false,
        "is_polar_point_group": true,
        "nonpolar_parent_hypothesis": false,
        "symmetry_tolerance_A": null,
        "target_reduced_polarization": [
          0.5,
          0.0,
          0.0
        ],
        "formal_class": [
          0.5,
          0.0,
          0.0
        ],
        "target_residual": 0.0005354841031514692,
        "parent_symmetrization_rmsd_A": 0.0791588258032528,
        "parent_cell_rmsd_A": 0.12527410107444648,
        "energy_eV": -162.21507174048617,
        "reduced_polarization": [
          0.4999157209930965,
          -1.6596012242429797e-14,
          -0.0005288102435877102
        ],
        "cartesian_polarization_e_A2": [
          0.016783462115210507,
          2.2161869419750593e-16,
          -0.00032727630239988523
        ],
        "ranking_score": 0.6115483192781673
      },
      "branch_status": "awaiting_branch_sampling"
    },
    {
      "orbit_id": 3,
      "formal_class": [
        0.0,
        0.5,
        0.0
      ],
      "formal_classes_in_orbit": [
        [
          0.0,
          0.5,
          0.0
        ]
      ],
      "target_reduced_polarization": [
        0.0,
        -0.5,
        0.0
      ],
      "bec_backprojection": {
        "converged_to_target": true,
        "history": [
          {
            "iteration": 0,
            "reduced_polarization": [
              1.64871515500274e-15,
              -1.4936743355313194e-15,
              0.09606683379186727
            ],
            "branch_aligned_reduced_polarization": [
              1.64871515500274e-15,
              -1.4988010832439613e-15,
              0.09606683379186727
            ],
            "target_residual": 0.5091452018381325,
            "energy_eV": -164.6017678326242,
            "max_atomic_step_A": 0.050142254651512855,
            "max_log_strain_component": 0.012922331519717195,
            "step_scale": 1.0,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 14.222175725216156,
            "cell_principal_stretches": [
              1.0122249361517923,
              1.0007519163327872,
              0.9860837412613973
            ],
            "cell_volume_ratio": 0.9988890687183009,
            "cell_rmsd_from_input_A": 0.05094587279140416
          },
          {
            "iteration": 1,
            "reduced_polarization": [
              -9.296956010076565e-15,
              -0.49253017190760606,
              0.01177874606317338
            ],
            "branch_aligned_reduced_polarization": [
              -9.296956010076565e-15,
              -0.49253017190760606,
              0.01177874606317338
            ],
            "target_residual": 0.013947658963089112,
            "energy_eV": -163.95692685289401,
            "max_atomic_step_A": 0.0011630440922588124,
            "max_log_strain_component": 0.00038265030710454763,
            "step_scale": 1.0,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 14.222175725216156,
            "cell_principal_stretches": [
              1.0123567237894353,
              1.0008487724692328,
              0.9857188722663928
            ],
            "cell_volume_ratio": 0.9987461174120297,
            "cell_rmsd_from_input_A": 0.052011605259642164
          },
          {
            "iteration": 2,
            "reduced_polarization": [
              2.177000811361379e-15,
              -0.49980478302751596,
              0.0001448194923749218
            ],
            "branch_aligned_reduced_polarization": [
              2.177000811361379e-15,
              -0.49980478302751596,
              0.0001448194923749218
            ],
            "target_residual": 0.0002430686152459071,
            "energy_eV": -163.93698222751073
          }
        ],
        "iterations": 2
      },
      "parent": {
        "candidate_id": "bec_projection_03",
        "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": 0.0002430686152459071,
        "parent_symmetrization_rmsd_A": 0.04211156598922031,
        "parent_cell_rmsd_A": 0.052011605259642164,
        "energy_eV": -163.93698222751073,
        "reduced_polarization": [
          2.177000811361379e-15,
          -0.49980478302751596,
          0.0001448194923749218
        ],
        "cartesian_polarization_e_A2": [
          9.26158593300909e-17,
          -0.00985551532768351,
          -0.00012659124519905763
        ],
        "ranking_score": 0.5556006045346227
      },
      "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": [
              1.64871515500274e-15,
              -1.4936743355313194e-15,
              0.09606683379186727
            ],
            "branch_aligned_reduced_polarization": [
              1.64871515500274e-15,
              -1.4988010832439613e-15,
              0.09606683379186726
            ],
            "target_residual": 0.6427767907780472,
            "energy_eV": -164.6017678326242,
            "max_atomic_step_A": 0.05914614056693465,
            "max_log_strain_component": 0.012922331519724205,
            "step_scale": 1.0,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 14.222175725216156,
            "cell_principal_stretches": [
              1.0196177098319426,
              0.9968445868022214,
              0.9884733266294989
            ],
            "cell_volume_ratio": 1.0046846792908288,
            "cell_rmsd_from_input_A": 0.06701422579903313
          },
          {
            "iteration": 1,
            "reduced_polarization": [
              1.3321460202254796e-15,
              -0.5020007189297306,
              0.48373816055102287
            ],
            "branch_aligned_reduced_polarization": [
              1.3321460202254796e-15,
              -0.5020007189297306,
              0.48373816055102287
            ],
            "target_residual": 0.01638445295089499,
            "energy_eV": -163.6799704878837,
            "max_atomic_step_A": 0.0012190780000451264,
            "max_log_strain_component": 0.0005689121906967632,
            "step_scale": 1.0,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 14.222175725216156,
            "cell_principal_stretches": [
              1.0199827545801041,
              0.9967011637106904,
              0.9884720587452762
            ],
            "cell_volume_ratio": 1.0048984858901444,
            "cell_rmsd_from_input_A": 0.06823434618123954
          },
          {
            "iteration": 2,
            "reduced_polarization": [
              -6.1034715030450255e-15,
              -0.5001028260288661,
              0.4991989009567067
            ],
            "branch_aligned_reduced_polarization": [
              -6.1034715030450255e-15,
              -0.5001028260288661,
              0.4991989009567067
            ],
            "target_residual": 0.0008076712631868212,
            "energy_eV": -163.66859576756767
          }
        ],
        "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": 0.0008076712631868212,
        "parent_symmetrization_rmsd_A": 0.045195917878587406,
        "parent_cell_rmsd_A": 0.06823434618123954,
        "energy_eV": -163.66859576756767,
        "reduced_polarization": [
          -6.1034715030450255e-15,
          -0.5001028260288661,
          0.4991989009567067
        ],
        "cartesian_polarization_e_A2": [
          -2.564079368045667e-16,
          -0.009630182317768105,
          0.00857642614312434
        ],
        "ranking_score": 0.563869846950271
      },
      "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": [
              1.64871515500274e-15,
              -1.4936743355313194e-15,
              0.09606683379186727
            ],
            "branch_aligned_reduced_polarization": [
              1.6653345369377348e-15,
              -1.4936743355313194e-15,
              0.09606683379186726
            ],
            "target_residual": 0.6427767907780472,
            "energy_eV": -164.6017678326242,
            "max_atomic_step_A": 0.09142386727676788,
            "max_log_strain_component": 0.018429659297791678,
            "step_scale": 1.0,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 14.222175725216156,
            "cell_principal_stretches": [
              1.0249983325761622,
              0.9953491728252749,
              0.9847617260294739
            ],
            "cell_volume_ratio": 1.004684679290815,
            "cell_rmsd_from_input_A": 0.12987009369800218
          },
          {
            "iteration": 1,
            "reduced_polarization": [
              0.4820043344491093,
              -4.299362108529599e-15,
              0.44986048956572755
            ],
            "branch_aligned_reduced_polarization": [
              0.4820043344491093,
              -4.299362108529599e-15,
              0.44986048956572755
            ],
            "target_residual": 0.05327114120429588,
            "energy_eV": -161.92010375099974,
            "max_atomic_step_A": 0.004274755262131662,
            "max_log_strain_component": 0.0018790693792245733,
            "step_scale": 1.0,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 14.222175725216156,
            "cell_principal_stretches": [
              1.026958198007202,
              0.9946516740632207,
              0.9842631491984517
            ],
            "cell_volume_ratio": 1.0053910376651498,
            "cell_rmsd_from_input_A": 0.13727839075919115
          },
          {
            "iteration": 2,
            "reduced_polarization": [
              0.4997613054180903,
              -1.7838580948917438e-14,
              0.49625516054606583
            ],
            "branch_aligned_reduced_polarization": [
              0.4997613054180903,
              -1.7838580948917438e-14,
              0.49625516054606583
            ],
            "target_residual": 0.003752438892130692,
            "energy_eV": -161.67107423787115,
            "max_atomic_step_A": 0.00024955692390082613,
            "max_log_strain_component": 0.00013492296544532988,
            "step_scale": 1.0,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 14.222175725216156,
            "cell_principal_stretches": [
              1.0270605023284634,
              0.9946016103170582,
              0.9842643154208094
            ],
            "cell_volume_ratio": 1.0054417754759963,
            "cell_rmsd_from_input_A": 0.13755310721825875
          },
          {
            "iteration": 3,
            "reduced_polarization": [
              0.49999450865880707,
              4.238333842911143e-15,
              0.49975713478520517
            ],
            "branch_aligned_reduced_polarization": [
              0.49999450865880707,
              4.238333842911143e-15,
              0.49975713478520517
            ],
            "target_residual": 0.00024292728826839504,
            "energy_eV": -161.66330144198383
          }
        ],
        "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": 0.00024292728826839504,
        "parent_symmetrization_rmsd_A": 0.08311062682829533,
        "parent_cell_rmsd_A": 0.13755310721825875,
        "energy_eV": -161.66330144198383,
        "reduced_polarization": [
          0.49999450865880707,
          4.238333842911143e-15,
          0.49975713478520517
        ],
        "cartesian_polarization_e_A2": [
          0.016444180546026175,
          7.461594318397174e-16,
          0.00839873583286757
        ],
        "ranking_score": 0.6179847582093968
      },
      "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": [
              1.64871515500274e-15,
              -1.4936743355313194e-15,
              0.09606683379186727
            ],
            "branch_aligned_reduced_polarization": [
              1.6653345369377348e-15,
              -1.4988010832439613e-15,
              0.09606683379186727
            ],
            "target_residual": 0.7136027161907325,
            "energy_eV": -164.6017678326242,
            "max_atomic_step_A": 0.11281512933020839,
            "max_log_strain_component": 0.018429659297783122,
            "step_scale": 1.0,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 14.222175725216156,
            "cell_principal_stretches": [
              1.0217735612445025,
              1.000991268827491,
              0.9766350584147196
            ],
            "cell_volume_ratio": 0.9988890687182996,
            "cell_rmsd_from_input_A": 0.1316692005688855
          },
          {
            "iteration": 1,
            "reduced_polarization": [
              0.4806743602422955,
              -0.4641023732130958,
              -0.007100416040117793
            ],
            "branch_aligned_reduced_polarization": [
              0.4806743602422955,
              -0.4641023732130958,
              -0.007100416040117793
            ],
            "target_residual": 0.041382796774978796,
            "energy_eV": -161.57101726377442,
            "max_atomic_step_A": 0.00686598900116134,
            "max_log_strain_component": 0.0011316942485043186,
            "step_scale": 1.0,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 14.222175725216156,
            "cell_principal_stretches": [
              1.0232310219087961,
              1.000911439317127,
              0.9754028860861045
            ],
            "cell_volume_ratio": 0.9989721652987436,
            "cell_rmsd_from_input_A": 0.13854528665896926
          },
          {
            "iteration": 2,
            "reduced_polarization": [
              0.49972008713087773,
              -0.4993384531027874,
              0.0001395262114386979
            ],
            "branch_aligned_reduced_polarization": [
              0.49972008713087773,
              -0.4993384531027874,
              0.0001395262114386979
            ],
            "target_residual": 0.0007317534251305609,
            "energy_eV": -161.2653588001477
          }
        ],
        "iterations": 2
      },
      "parent": {
        "candidate_id": "bec_projection_06",
        "source": "MACEField_BEC_backprojection",
        "spacegroup": "P1",
        "spacegroup_number": 1,
        "pointgroup": "1",
        "has_inversion": false,
        "is_polar_point_group": true,
        "nonpolar_parent_hypothesis": false,
        "symmetry_tolerance_A": null,
        "target_reduced_polarization": [
          0.5,
          -0.5,
          0.0
        ],
        "formal_class": [
          0.5,
          0.5,
          0.0
        ],
        "target_residual": 0.0007317534251305609,
        "parent_symmetrization_rmsd_A": 0.09178694230222308,
        "parent_cell_rmsd_A": 0.13854528665896926,
        "energy_eV": -161.2653588001477,
        "reduced_polarization": [
          0.49972008713087773,
          -0.4993384531027874,
          0.0001395262114386979
        ],
        "cartesian_polarization_e_A2": [
          0.016783041017864115,
          -0.00984434549277133,
          -0.0004589275623945838
        ],
        "ranking_score": 0.6278867708172265
      },
      "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": [
              1.64871515500274e-15,
              -1.4936743355313194e-15,
              0.09606683379186727
            ],
            "branch_aligned_reduced_polarization": [
              1.6653345369377348e-15,
              -1.4988010832439613e-15,
              0.09606683379186726
            ],
            "target_residual": 0.8143475933303443,
            "energy_eV": -164.6017678326242,
            "max_atomic_step_A": 0.11567919772780451,
            "max_log_strain_component": 0.018429659297791272,
            "step_scale": 1.0,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 14.222175725216156,
            "cell_principal_stretches": [
              1.0287441873283352,
              0.9958583727173127,
              0.9806743273015363
            ],
            "cell_volume_ratio": 1.0046846792908275,
            "cell_rmsd_from_input_A": 0.13936316638318194
          },
          {
            "iteration": 1,
            "reduced_polarization": [
              0.47636988395275454,
              -0.4755458959735518,
              0.45287358965606594
            ],
            "branch_aligned_reduced_polarization": [
              0.47636988395275454,
              -0.4755458959735518,
              0.45287358965606594
            ],
            "target_residual": 0.05811440561553988,
            "energy_eV": -161.06167900626824,
            "max_atomic_step_A": 0.006689588215001955,
            "max_log_strain_component": 0.0018408192795537578,
            "step_scale": 1.0,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 14.222175725216156,
            "cell_principal_stretches": [
              1.0311189806394498,
              0.9952552159313331,
              0.979682956280885
            ],
            "cell_volume_ratio": 1.00537665417259,
            "cell_rmsd_from_input_A": 0.14889919838547916
          },
          {
            "iteration": 2,
            "reduced_polarization": [
              0.49968731630489666,
              -0.49985160329307976,
              0.4961634504475372
            ],
            "branch_aligned_reduced_polarization": [
              0.49968731630489666,
              -0.49985160329307976,
              0.4961634504475372
            ],
            "target_residual": 0.0038521299490425964,
            "energy_eV": -160.65680785764584,
            "max_atomic_step_A": 0.00026513790647833405,
            "max_log_strain_component": 0.0001422364980752098,
            "step_scale": 1.0,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 14.222175725216156,
            "cell_principal_stretches": [
              1.0312224953702294,
              0.9952082939381506,
              0.979682918149909
            ],
            "cell_volume_ratio": 1.005430141546928,
            "cell_rmsd_from_input_A": 0.1491901570066066
          },
          {
            "iteration": 3,
            "reduced_polarization": [
              0.49999671950218527,
              -0.500025879580192,
              0.4997215354661258
            ],
            "branch_aligned_reduced_polarization": [
              0.49999671950218527,
              -0.500025879580192,
              0.4997215354661258
            ],
            "target_residual": 0.0002796837695730668,
            "energy_eV": -160.6468281399527
          }
        ],
        "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": 0.0002796837695730668,
        "parent_symmetrization_rmsd_A": 0.09497820213282315,
        "parent_cell_rmsd_A": 0.1491901570066066,
        "energy_eV": -160.6468281399527,
        "reduced_polarization": [
          0.49999671950218527,
          -0.500025879580192,
          0.4997215354661258
        ],
        "cartesian_polarization_e_A2": [
          0.01644362752897334,
          -0.00961344153645124,
          0.008259463445875385
        ],
        "ranking_score": 0.6328351089236209
      },
      "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": 0.3755075220757377,
        "minimum_distance_A_by_image": [
          1.7832532868664173,
          1.7695045680286363,
          1.757502014206896,
          1.7472816104226407,
          1.7388747812346164,
          1.732307930484384,
          1.7276020403256065,
          1.7247723432291187,
          1.723828078641164
        ],
        "minimum_distance_A": 1.723828078641164,
        "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": [
          296.19468779802895,
          296.19468779802895,
          296.19468779802895,
          296.19468779802895,
          296.19468779802895,
          296.19468779802895,
          296.19468779802895,
          296.19468779802895,
          296.19468779802895
        ],
        "cell_deformation_log_strain_norm": 0.0
      },
      "parent_reduced_polarization": [
        5.065756156688624e-16,
        -1.3150051566400132e-15,
        3.084612216996061e-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": [
          -164.6017678326242,
          -164.25231714044043,
          -163.48013669894362,
          -162.42738144099042,
          -161.2601838605476,
          -160.1486501548303,
          -159.23026429442749,
          -158.6145423199477,
          -158.39530962538512
        ],
        "cartesian_polarizations_e_A2": [
          [
            3.2702309098299294e-17,
            1.6726735662349472e-17,
            0.0016610467521657826
          ],
          [
            -1.728222133901687e-17,
            -5.945722004347754e-17,
            0.00844949254653018
          ],
          [
            -1.6095646817479807e-17,
            -2.904923280295987e-18,
            0.01347230849890867
          ],
          [
            -3.263671001134084e-18,
            -9.183305853838927e-18,
            0.01633182831508806
          ],
          [
            -1.7417796121627035e-17,
            -1.22756435393153e-17,
            0.016797630003476376
          ],
          [
            -1.3499066465118162e-17,
            -2.576948071230311e-17,
            0.014915901574499634
          ],
          [
            1.3269565952693107e-17,
            -2.04281701646621e-17,
            0.01105906984042288
          ],
          [
            1.577940104651843e-17,
            3.748288103607725e-18,
            0.005856555724970473
          ],
          [
            1.6979573291035952e-17,
            -2.5863187914893303e-17,
            5.3334589082353355e-18
          ]
        ],
        "raw_reduced_polarization": [
          [
            9.756542217707094e-16,
            8.504652915226172e-16,
            0.09606683379187146
          ],
          [
            -5.15604942767315e-16,
            -3.0230825068408998e-15,
            0.488677392755383
          ],
          [
            -4.802041874902693e-16,
            -1.4769985455014641e-16,
            0.7791725426571877
          ],
          [
            -9.736971114656561e-17,
            -4.669221208359467e-16,
            0.9445532067157337
          ],
          [
            -5.1964973693220565e-16,
            -6.241509982602962e-16,
            0.9714929020133092
          ],
          [
            -4.0273673479958876e-16,
            -1.3102406452029116e-15,
            0.8626629175518569
          ],
          [
            3.958897215451733e-16,
            -1.0386634932881262e-15,
            0.6396026017132648
          ],
          [
            4.707691802977146e-16,
            1.9058045748405988e-16,
            0.33871458746720373
          ],
          [
            5.065756156688624e-16,
            -1.3150051566400132e-15,
            3.084612216996061e-16
          ]
        ],
        "unwrapped_reduced_polarization": [
          [
            9.756542217707094e-16,
            8.504652915226172e-16,
            0.09606683379187146
          ],
          [
            -5.15604942767315e-16,
            -3.0230825068408998e-15,
            0.488677392755383
          ],
          [
            -4.802041874902693e-16,
            -1.4769985455014659e-16,
            0.7791725426571877
          ],
          [
            -9.736971114656564e-17,
            -4.669221208359467e-16,
            0.9445532067157337
          ],
          [
            -5.1964973693220565e-16,
            -6.241509982602962e-16,
            0.9714929020133092
          ],
          [
            -4.0273673479958876e-16,
            -1.3102406452029116e-15,
            0.8626629175518569
          ],
          [
            3.958897215451733e-16,
            -1.0386634932881262e-15,
            0.6396026017132648
          ],
          [
            4.707691802977146e-16,
            1.9058045748405983e-16,
            0.33871458746720373
          ],
          [
            5.065756156688624e-16,
            -1.3150051566400132e-15,
            3.3306690738754696e-16
          ]
        ],
        "berry_integer_shifts": [
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ]
        ],
        "folded_reduced_polarization": [
          [
            9.992007221626409e-16,
            8.881784197001252e-16,
            0.09606683379187142
          ],
          [
            -4.996003610813204e-16,
            -2.9976021664879227e-15,
            0.488677392755383
          ],
          [
            -4.996003610813204e-16,
            -1.6653345369377348e-16,
            -0.2208274573428124
          ],
          [
            -1.1102230246251565e-16,
            -4.440892098500626e-16,
            -0.05544679328426616
          ],
          [
            -4.996003610813204e-16,
            -6.106226635438361e-16,
            -0.02850709798669082
          ],
          [
            -3.885780586188048e-16,
            -1.3322676295501878e-15,
            -0.13733708244814302
          ],
          [
            4.440892098500626e-16,
            -1.0547118733938987e-15,
            -0.3603973982867352
          ],
          [
            4.440892098500626e-16,
            2.220446049250313e-16,
            0.33871458746720373
          ],
          [
            5.551115123125783e-16,
            -1.3322676295501878e-15,
            3.3306690738754696e-16
          ]
        ]
      },
      "reflected": {
        "reached": true,
        "construction": "reflect_displacements_about_reconstructed_parent",
        "energies_eV": [
          -158.3953096253851,
          -158.61454231994767,
          -159.23026429442746,
          -160.1486501548303,
          -161.2601838605476,
          -162.42738144099044,
          -163.4801366989436,
          -164.25231714044043,
          -164.60176783262415
        ],
        "cartesian_polarizations_e_A2": [
          [
            -6.894683179457075e-18,
            -1.349383717298781e-17,
            1.5019697210854003e-17
          ],
          [
            -3.566667490963991e-18,
            1.021408508233105e-17,
            -0.005856555724970495
          ],
          [
            4.1054463215667855e-18,
            2.3145679039777702e-17,
            -0.011059069840422908
          ],
          [
            -2.2622596884779603e-17,
            -6.746918586493905e-18,
            -0.014915901574499613
          ],
          [
            -4.1135561073246634e-18,
            -5.1538961424606216e-18,
            -0.0167976300034764
          ],
          [
            -2.7435517026668683e-18,
            -1.6398760453283797e-17,
            -0.01633182831508801
          ],
          [
            -2.461083614672139e-17,
            5.903553763182167e-18,
            -0.013472308498908497
          ],
          [
            -2.995702550027515e-17,
            6.2315289722478426e-18,
            -0.00844949254653031
          ],
          [
            -4.5061091138297664e-18,
            9.291069136817648e-17,
            -0.0016610467521659634
          ]
        ],
        "raw_reduced_polarization": [
          [
            -2.0569883097822673e-16,
            -6.860896469426156e-16,
            8.686659503581132e-16
          ],
          [
            -1.0640943380332531e-16,
            5.193317466440631e-16,
            -0.338714587467205
          ],
          [
            1.224835843808342e-16,
            1.1768343249640698e-15,
            -0.6396026017132665
          ],
          [
            -6.7493191663337255e-16,
            -3.430448234713078e-16,
            -0.8626629175518556
          ],
          [
            -1.2272553508494337e-16,
            -2.620481290405823e-16,
            -0.9714929020133106
          ],
          [
            -8.185225677205634e-17,
            -8.33789501492762e-16,
            -0.944553206715731
          ],
          [
            -7.342498695024763e-16,
            3.001642205373943e-16,
            -0.7791725426571777
          ],
          [
            -8.937502949159103e-16,
            3.168400105672495e-16,
            -0.4886773927553905
          ],
          [
            -1.3443712391844892e-16,
            4.7240130898861345e-15,
            -0.09606683379188191
          ]
        ],
        "unwrapped_reduced_polarization": [
          [
            -2.0569883097822673e-16,
            -6.860896469426156e-16,
            8.686659503581132e-16
          ],
          [
            -1.0640943380332531e-16,
            5.193317466440631e-16,
            -0.338714587467205
          ],
          [
            1.2248358438083423e-16,
            1.1768343249640698e-15,
            -0.6396026017132665
          ],
          [
            -6.7493191663337255e-16,
            -3.4304482347130774e-16,
            -0.8626629175518556
          ],
          [
            -1.227255350849434e-16,
            -2.620481290405823e-16,
            -0.9714929020133106
          ],
          [
            -8.185225677205634e-17,
            -8.337895014927621e-16,
            -0.944553206715731
          ],
          [
            -7.342498695024763e-16,
            3.001642205373943e-16,
            -0.7791725426571777
          ],
          [
            -8.937502949159103e-16,
            3.168400105672495e-16,
            -0.4886773927553905
          ],
          [
            -1.3443712391844892e-16,
            4.7240130898861345e-15,
            -0.09606683379188191
          ]
        ],
        "gauge_integer_shift": [
          0,
          0,
          0
        ],
        "expected_opposite_endpoint_reduced_polarization": [
          3.749700956701539e-17,
          -3.4804756048026437e-15,
          -0.09606683379187084
        ],
        "actual_opposite_endpoint_branch_residual": 1.3783583906883227e-14
      },
      "pnp_branch": {
        "construction": "incoming_path_concatenated_with_parent_reflection",
        "reduced_polarization": [
          [
            9.756542217707094e-16,
            8.504652915226172e-16,
            0.09606683379187146
          ],
          [
            -5.15604942767315e-16,
            -3.0230825068408998e-15,
            0.488677392755383
          ],
          [
            -4.802041874902693e-16,
            -1.4769985455014641e-16,
            0.7791725426571877
          ],
          [
            -9.736971114656561e-17,
            -4.669221208359467e-16,
            0.9445532067157337
          ],
          [
            -5.1964973693220565e-16,
            -6.241509982602962e-16,
            0.9714929020133092
          ],
          [
            -4.0273673479958876e-16,
            -1.3102406452029116e-15,
            0.8626629175518569
          ],
          [
            3.958897215451733e-16,
            -1.0386634932881262e-15,
            0.6396026017132648
          ],
          [
            4.707691802977146e-16,
            1.9058045748405988e-16,
            0.33871458746720373
          ],
          [
            5.065756156688624e-16,
            -1.3150051566400132e-15,
            3.084612216996061e-16
          ],
          [
            -1.0640943380332531e-16,
            5.193317466440631e-16,
            -0.338714587467205
          ],
          [
            1.224835843808342e-16,
            1.1768343249640698e-15,
            -0.6396026017132665
          ],
          [
            -6.7493191663337255e-16,
            -3.430448234713078e-16,
            -0.8626629175518556
          ],
          [
            -1.2272553508494337e-16,
            -2.620481290405823e-16,
            -0.9714929020133106
          ],
          [
            -8.185225677205634e-17,
            -8.33789501492762e-16,
            -0.944553206715731
          ],
          [
            -7.342498695024763e-16,
            3.001642205373943e-16,
            -0.7791725426571777
          ],
          [
            -8.937502949159103e-16,
            3.168400105672495e-16,
            -0.4886773927553905
          ],
          [
            -1.3443712391844892e-16,
            4.7240130898861345e-15,
            -0.09606683379188191
          ]
        ],
        "unwrapped_reduced_polarization": [
          [
            9.756542217707094e-16,
            8.504652915226172e-16,
            0.09606683379187146
          ],
          [
            -5.15604942767315e-16,
            -3.0230825068408998e-15,
            0.488677392755383
          ],
          [
            -4.802041874902693e-16,
            -1.4769985455014659e-16,
            0.7791725426571877
          ],
          [
            -9.736971114656564e-17,
            -4.669221208359467e-16,
            0.9445532067157337
          ],
          [
            -5.1964973693220565e-16,
            -6.241509982602962e-16,
            0.9714929020133092
          ],
          [
            -4.0273673479958876e-16,
            -1.3102406452029116e-15,
            0.8626629175518569
          ],
          [
            3.958897215451733e-16,
            -1.0386634932881262e-15,
            0.6396026017132648
          ],
          [
            4.707691802977146e-16,
            1.9058045748405983e-16,
            0.33871458746720373
          ],
          [
            5.065756156688624e-16,
            -1.3150051566400132e-15,
            3.3306690738754696e-16
          ],
          [
            -1.0640943380332531e-16,
            5.193317466440632e-16,
            -0.338714587467205
          ],
          [
            1.2248358438083423e-16,
            1.1768343249640698e-15,
            -0.6396026017132665
          ],
          [
            -6.7493191663337255e-16,
            -3.4304482347130774e-16,
            -0.8626629175518556
          ],
          [
            -1.227255350849434e-16,
            -2.620481290405823e-16,
            -0.9714929020133106
          ],
          [
            -8.185225677205634e-17,
            -8.337895014927621e-16,
            -0.944553206715731
          ],
          [
            -7.342498695024763e-16,
            3.001642205373943e-16,
            -0.7791725426571777
          ],
          [
            -8.937502949159103e-16,
            3.168400105672495e-16,
            -0.4886773927553905
          ],
          [
            -1.3443712391844892e-16,
            4.7240130898861345e-15,
            -0.09606683379188191
          ]
        ],
        "berry_integer_shifts": [
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ]
        ],
        "folded_reduced_polarization": [
          [
            9.992007221626409e-16,
            8.881784197001252e-16,
            0.09606683379187142
          ],
          [
            -4.996003610813204e-16,
            -2.9976021664879227e-15,
            0.488677392755383
          ],
          [
            -4.996003610813204e-16,
            -1.6653345369377348e-16,
            -0.2208274573428124
          ],
          [
            -1.1102230246251565e-16,
            -4.440892098500626e-16,
            -0.05544679328426616
          ],
          [
            -4.996003610813204e-16,
            -6.106226635438361e-16,
            -0.02850709798669082
          ],
          [
            -3.885780586188048e-16,
            -1.3322676295501878e-15,
            -0.13733708244814302
          ],
          [
            4.440892098500626e-16,
            -1.0547118733938987e-15,
            -0.3603973982867352
          ],
          [
            4.440892098500626e-16,
            2.220446049250313e-16,
            0.33871458746720373
          ],
          [
            5.551115123125783e-16,
            -1.3322676295501878e-15,
            3.3306690738754696e-16
          ],
          [
            -1.1102230246251565e-16,
            5.551115123125783e-16,
            -0.338714587467205
          ],
          [
            1.1102230246251565e-16,
            1.2212453270876722e-15,
            0.36039739828673345
          ],
          [
            -6.661338147750939e-16,
            -3.3306690738754696e-16,
            0.13733708244814435
          ],
          [
            -1.1102230246251565e-16,
            -2.7755575615628914e-16,
            0.028507097986689378
          ],
          [
            -5.551115123125783e-17,
            -8.326672684688674e-16,
            0.05544679328426905
          ],
          [
            -7.216449660063518e-16,
            3.3306690738754696e-16,
            0.22082745734282228
          ],
          [
            -8.881784197001252e-16,
            3.3306690738754696e-16,
            -0.4886773927553905
          ],
          [
            -1.1102230246251565e-16,
            4.773959005888173e-15,
            -0.09606683379188191
          ]
        ]
      },
      "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": 1.2723271128109783e-15,
        "parent_symmetrization_rmsd_A": 0.3755075220757377,
        "parent_cell_rmsd_A": 0.0,
        "energy_eV": -158.3953096253852,
        "reduced_polarization": [
          4.2022563890998353e-16,
          -6.1938648682319465e-16,
          1.0288766079260605e-15
        ],
        "cartesian_polarization_e_A2": [
          1.4085265484449682e-17,
          -1.2181936336725107e-17,
          1.7789824859612843e-17
        ],
        "ranking_score": 0.37550752207574023
      }
    }
  ],
  "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": 50,
      "full_response": 18,
      "energy_polarization": 32
    },
    "model_evaluations_for_recovery_and_path_properties": {
      "total": 75,
      "full_response": 43,
      "energy_polarization": 32
    },
    "elapsed_seconds": 548.7784111729707
  }
}