{
  "schema": "ferrofinder.endpoint_parent_recovery.v4_variable_cell",
  "status": "complete",
  "input_atom_count": 40,
  "input_formula": "Ba8F28Y4",
  "input_spacegroup": "P2_1",
  "input_pointgroup": "2",
  "input_is_polar_point_group": true,
  "input_energy_eV": -239.77225651538697,
  "input_cartesian_polarization_e_A2": [
    -1.959245642102275e-17,
    -0.00041759989809559106,
    1.2374058644102285e-17
  ],
  "input_reduced_polarization": [
    -2.401092611821093e-15,
    -0.02514642953969206,
    8.945869932735861e-16
  ],
  "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,
        0.5,
        0.0
      ],
      "target_reduced_polarization": [
        0.0,
        -0.5,
        0.0
      ]
    },
    {
      "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,
        0.0,
        0.5
      ],
      "target_reduced_polarization": [
        0.0,
        0.0,
        0.5
      ]
    },
    {
      "orbit_id": 4,
      "representative_formal_class": [
        0.5,
        0.5,
        0.0
      ],
      "target_reduced_polarization": [
        -0.5,
        -0.5,
        0.0
      ]
    },
    {
      "orbit_id": 5,
      "representative_formal_class": [
        0.0,
        0.5,
        0.5
      ],
      "target_reduced_polarization": [
        0.0,
        -0.5,
        0.5
      ]
    },
    {
      "orbit_id": 6,
      "representative_formal_class": [
        0.5,
        0.0,
        0.5
      ],
      "target_reduced_polarization": [
        -0.5,
        0.0,
        0.5
      ]
    },
    {
      "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": "P2_1/c",
      "spacegroup_number": 14,
      "pointgroup": "2/m",
      "has_inversion": true,
      "is_polar_point_group": false,
      "nonpolar_parent_hypothesis": true,
      "symmetry_tolerance_A": null,
      "target_reduced_polarization": [
        0.0,
        0.0,
        0.0
      ],
      "formal_class": [
        0.0,
        0.0,
        0.0
      ],
      "target_residual": 2.6061298080005922e-15,
      "parent_symmetrization_rmsd_A": 0.11370543309429537,
      "parent_cell_rmsd_A": 0.0,
      "energy_eV": -239.73458801840368,
      "reduced_polarization": [
        -1.046818867463807e-15,
        1.3806904775006631e-15,
        -1.9467348664391843e-15
      ],
      "cartesian_polarization_e_A2": [
        -8.529759729847097e-18,
        2.2928750254414468e-17,
        -2.6605289351268232e-17
      ],
      "ranking_score": 0.11370543309430059
    },
    {
      "candidate_id": "bec_projection_00",
      "source": "MACEField_BEC_backprojection",
      "spacegroup": "P2_1",
      "spacegroup_number": 4,
      "pointgroup": "2",
      "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": 3.281281238305844e-06,
      "parent_symmetrization_rmsd_A": 0.006422081907370456,
      "parent_cell_rmsd_A": 0.0018955397896058223,
      "energy_eV": -239.7679475795764,
      "reduced_polarization": [
        -4.410884620775074e-15,
        -3.281281238305844e-06,
        3.6897066507277545e-15
      ],
      "cartesian_polarization_e_A2": [
        -3.5990020463024863e-17,
        -5.449398927633887e-08,
        5.0738556947413074e-17
      ],
      "ranking_score": 0.5069025294172486
    },
    {
      "candidate_id": "inversion_parent_bec_00_00",
      "source": "same_species_inversion_center_projection_after_BEC",
      "spacegroup": "P2_1/c",
      "spacegroup_number": 14,
      "pointgroup": "2/m",
      "has_inversion": true,
      "is_polar_point_group": false,
      "nonpolar_parent_hypothesis": true,
      "symmetry_tolerance_A": null,
      "target_reduced_polarization": [
        0.0,
        0.0,
        0.0
      ],
      "formal_class": [
        0.0,
        0.0,
        0.0
      ],
      "target_residual": 3.175636265919766e-15,
      "parent_symmetrization_rmsd_A": 0.11370560446728795,
      "parent_cell_rmsd_A": 0.0018955397896058223,
      "energy_eV": -239.7340497417533,
      "reduced_polarization": [
        9.786741033958013e-16,
        -2.183024479576628e-15,
        2.0883646267681444e-15
      ],
      "cartesian_polarization_e_A2": [
        7.98150532589929e-18,
        -3.625465296642946e-17,
        2.854723130477064e-17
      ],
      "ranking_score": 0.11417948941469576
    },
    {
      "candidate_id": "bec_projection_01",
      "source": "MACEField_BEC_backprojection",
      "spacegroup": "P2_1",
      "spacegroup_number": 4,
      "pointgroup": "2",
      "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": 5.238509352767373e-05,
      "parent_symmetrization_rmsd_A": 0.12168787535034152,
      "parent_cell_rmsd_A": 0.03598595500238595,
      "energy_eV": -238.722602239346,
      "reduced_polarization": [
        -1.447918069234203e-15,
        -0.5000523850935277,
        -9.537046880769593e-16
      ],
      "cartesian_polarization_e_A2": [
        6.532080768492104e-17,
        -0.008296603765363444,
        -5.311924002655464e-16
      ],
      "ranking_score": 0.6307891342879933
    },
    {
      "candidate_id": "bec_projection_02",
      "source": "MACEField_BEC_backprojection",
      "spacegroup": "P1",
      "spacegroup_number": 1,
      "pointgroup": "1",
      "has_inversion": false,
      "is_polar_point_group": true,
      "nonpolar_parent_hypothesis": false,
      "symmetry_tolerance_A": null,
      "target_reduced_polarization": [
        -0.5,
        0.0,
        0.0
      ],
      "formal_class": [
        0.5,
        0.0,
        0.0
      ],
      "target_residual": 5.412030535519595e-06,
      "parent_symmetrization_rmsd_A": 0.06918683197709505,
      "parent_cell_rmsd_A": 0.02114973304738115,
      "energy_eV": -239.5178708137899,
      "reduced_polarization": [
        -0.49999921649428336,
        -2.6998996811662613e-06,
        4.624579442611854e-06
      ],
      "cartesian_polarization_e_A2": [
        -0.004079140106612364,
        1.027916407900839e-05,
        2.4552632624757797e-05
      ],
      "ranking_score": 0.5744850893000114
    },
    {
      "candidate_id": "bec_projection_03",
      "source": "MACEField_BEC_backprojection",
      "spacegroup": "P1",
      "spacegroup_number": 1,
      "pointgroup": "1",
      "has_inversion": false,
      "is_polar_point_group": true,
      "nonpolar_parent_hypothesis": false,
      "symmetry_tolerance_A": null,
      "target_reduced_polarization": [
        0.0,
        0.0,
        0.5
      ],
      "formal_class": [
        0.0,
        0.0,
        0.5
      ],
      "target_residual": 5.423104153262068e-05,
      "parent_symmetrization_rmsd_A": 0.1219986856513098,
      "parent_cell_rmsd_A": 0.08627982351486588,
      "energy_eV": -238.91412015002035,
      "reduced_polarization": [
        4.928225946141118e-05,
        -6.015928459600632e-07,
        0.4999773747297444
      ],
      "cartesian_polarization_e_A2": [
        -8.046896606557472e-07,
        -4.624970588873063e-05,
        0.006846355236821941
      ],
      "ranking_score": 0.6436771036130915
    },
    {
      "candidate_id": "bec_projection_04",
      "source": "MACEField_BEC_backprojection",
      "spacegroup": "P1",
      "spacegroup_number": 1,
      "pointgroup": "1",
      "has_inversion": false,
      "is_polar_point_group": true,
      "nonpolar_parent_hypothesis": false,
      "symmetry_tolerance_A": null,
      "target_reduced_polarization": [
        -0.5,
        -0.5,
        0.0
      ],
      "formal_class": [
        0.5,
        0.5,
        0.0
      ],
      "target_residual": 2.7915101341764414e-05,
      "parent_symmetrization_rmsd_A": 0.1393451291752568,
      "parent_cell_rmsd_A": 0.04149861576719653,
      "energy_eV": -238.39591886348356,
      "reduced_polarization": [
        -0.4999730886521362,
        -0.4999933563210493,
        -3.300571022398721e-06
      ],
      "cartesian_polarization_e_A2": [
        -0.004055104308929611,
        -0.008285779818563302,
        5.583230059080033e-05
      ],
      "ranking_score": 0.6497756133197394
    },
    {
      "candidate_id": "bec_projection_05",
      "source": "MACEField_BEC_backprojection",
      "spacegroup": "P1",
      "spacegroup_number": 1,
      "pointgroup": "1",
      "has_inversion": false,
      "is_polar_point_group": true,
      "nonpolar_parent_hypothesis": false,
      "symmetry_tolerance_A": null,
      "target_reduced_polarization": [
        0.0,
        -0.5,
        0.5
      ],
      "formal_class": [
        0.0,
        0.5,
        0.5
      ],
      "target_residual": 4.801152703188685e-05,
      "parent_symmetrization_rmsd_A": 0.17457555517577047,
      "parent_cell_rmsd_A": 0.09714979232239412,
      "energy_eV": -237.7806582075247,
      "reduced_polarization": [
        -7.316666341900358e-06,
        -0.4999856758330039,
        0.4999547629426085
      ],
      "cartesian_polarization_e_A2": [
        -7.762058652438164e-05,
        -0.008343992273549969,
        0.006920808662308622
      ],
      "ranking_score": 0.6989590263104328
    },
    {
      "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,
        0.0,
        0.5
      ],
      "formal_class": [
        0.5,
        0.0,
        0.5
      ],
      "target_residual": 0.0006391282728839627,
      "parent_symmetrization_rmsd_A": 0.12963005767524555,
      "parent_cell_rmsd_A": 0.0925478280769627,
      "energy_eV": -238.48688796268394,
      "reduced_polarization": [
        -0.49970565610906226,
        0.0005608726583981842,
        0.4999147445947249
      ],
      "cartesian_polarization_e_A2": [
        -0.00407800606678588,
        -5.182700970663011e-05,
        0.00687049763237622
      ],
      "ranking_score": 0.6540452712402541
    },
    {
      "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": 0.00014292715443336396,
      "parent_symmetrization_rmsd_A": 0.18167233331436036,
      "parent_cell_rmsd_A": 0.1044121261120098,
      "energy_eV": -237.2224352811045,
      "reduced_polarization": [
        -0.49992322369601655,
        -0.4999584586335459,
        0.4998868280710857
      ],
      "cartesian_polarization_e_A2": [
        -0.004132521409152029,
        -0.008359529321007681,
        0.006977084995880591
      ],
      "ranking_score": 0.7080612191512295
    }
  ],
  "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": [
              -2.401092611821093e-15,
              -0.02514642953969206,
              8.945869932735861e-16
            ],
            "branch_aligned_reduced_polarization": [
              -2.401092611821093e-15,
              -0.02514642953969206,
              8.945869932735861e-16
            ],
            "target_residual": 0.02514642953969206,
            "energy_eV": -239.77225651538697,
            "max_atomic_step_A": 0.007054836236987622,
            "max_log_strain_component": 0.0002809085337243089,
            "step_scale": 1.0,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 0.7621755475549568,
            "cell_principal_stretches": [
              1.0002682638900124,
              1.0000587770426086,
              0.9996832554286444
            ],
            "cell_volume_ratio": 1.0000102085355898,
            "cell_rmsd_from_input_A": 0.0018955397896058223
          },
          {
            "iteration": 1,
            "reduced_polarization": [
              -4.410884620775074e-15,
              -3.281281238305844e-06,
              3.6897066507277545e-15
            ],
            "branch_aligned_reduced_polarization": [
              -4.410884620775074e-15,
              -3.281281238305844e-06,
              3.6897066507277545e-15
            ],
            "target_residual": 3.281281238305844e-06,
            "energy_eV": -239.7679475795764
          }
        ],
        "iterations": 1
      },
      "parent": {
        "candidate_id": "inversion_parent_endpoint_00",
        "source": "same_species_inversion_center_projection_from_endpoint",
        "spacegroup": "P2_1/c",
        "spacegroup_number": 14,
        "pointgroup": "2/m",
        "has_inversion": true,
        "is_polar_point_group": false,
        "nonpolar_parent_hypothesis": true,
        "symmetry_tolerance_A": null,
        "target_reduced_polarization": [
          0.0,
          0.0,
          0.0
        ],
        "formal_class": [
          0.0,
          0.0,
          0.0
        ],
        "target_residual": 2.6061298080005922e-15,
        "parent_symmetrization_rmsd_A": 0.11370543309429537,
        "parent_cell_rmsd_A": 0.0,
        "energy_eV": -239.73458801840368,
        "reduced_polarization": [
          -1.046818867463807e-15,
          1.3806904775006631e-15,
          -1.9467348664391843e-15
        ],
        "cartesian_polarization_e_A2": [
          -8.529759729847097e-18,
          2.2928750254414468e-17,
          -2.6605289351268232e-17
        ],
        "ranking_score": 0.11370543309430059
      },
      "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": [
          -239.772256515387,
          -239.76475625829417,
          -239.75761452645136,
          -239.7510953163331,
          -239.7454290194655,
          -239.74080995936745,
          -239.73739359451005,
          -239.7352955120554,
          -239.73458801840377
        ],
        "cartesian_polarizations_e_A2": [
          [
            -1.814641405130906e-18,
            -0.00041759989809561746,
            -2.594370133898092e-18
          ],
          [
            1.8963947809349806e-17,
            -0.0003687750445129151,
            -1.1024891661902094e-17
          ],
          [
            7.735854115102326e-18,
            -0.0003187495383771502,
            -1.0620850411540915e-17
          ],
          [
            1.7447021009748192e-17,
            -0.00026760295638627956,
            2.566725206241801e-17
          ],
          [
            -2.242783361653979e-17,
            -0.00021544610801323063,
            6.1504056999423805e-18
          ],
          [
            1.5726892177801187e-17,
            -0.00016241293709609873,
            3.005972390113983e-17
          ],
          [
            1.6454638991317227e-17,
            -0.00010867903551782335,
            -5.635312176090118e-17
          ],
          [
            3.757819909791918e-17,
            -5.446318341242978e-05,
            -5.618772475782935e-17
          ],
          [
            7.277468135160405e-19,
            1.2967125040831266e-17,
            -1.900175283862337e-17
          ]
        ],
        "raw_reduced_polarization": [
          [
            -2.225608532197849e-16,
            -0.02514642953969365,
            -1.9028460035866145e-16
          ],
          [
            2.324111762488985e-15,
            -0.0222063647887148,
            -7.96355106746239e-16
          ],
          [
            9.477781303749167e-16,
            -0.01919400087060271,
            -7.720143060909088e-16
          ],
          [
            2.139863353297547e-15,
            -0.01611412962040642,
            1.8823370564175865e-15
          ],
          [
            -2.7489443743073257e-15,
            -0.012973423603459417,
            4.388099290002736e-16
          ],
          [
            1.929211321543572e-15,
            -0.009779948456995575,
            2.2022997724712093e-15
          ],
          [
            2.0144199947845054e-15,
            -0.006544277720261946,
            -4.107536401416703e-15
          ],
          [
            4.603777364983507e-15,
            -0.003279585580441142,
            -4.085743960266684e-15
          ],
          [
            8.832858481737841e-17,
            7.808356698808365e-16,
            -1.3872403460897309e-15
          ]
        ],
        "unwrapped_reduced_polarization": [
          [
            -2.225608532197849e-16,
            -0.02514642953969365,
            -1.9028460035866145e-16
          ],
          [
            2.324111762488985e-15,
            -0.0222063647887148,
            -7.963551067462391e-16
          ],
          [
            9.477781303749167e-16,
            -0.01919400087060271,
            -7.720143060909088e-16
          ],
          [
            2.139863353297547e-15,
            -0.01611412962040642,
            1.8823370564175865e-15
          ],
          [
            -2.7489443743073257e-15,
            -0.012973423603459417,
            4.3880992900027356e-16
          ],
          [
            1.9292113215435714e-15,
            -0.009779948456995575,
            2.2022997724712093e-15
          ],
          [
            2.0144199947845054e-15,
            -0.006544277720261946,
            -4.107536401416702e-15
          ],
          [
            4.603777364983507e-15,
            -0.003279585580441142,
            -4.085743960266684e-15
          ],
          [
            8.832858481737856e-17,
            7.806255641895632e-16,
            -1.3872403460897309e-15
          ]
        ],
        "berry_integer_shifts": [
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ]
        ],
        "folded_reduced_polarization": [
          [
            -2.220446049250313e-16,
            -0.02514642953969365,
            -1.6653345369377348e-16
          ],
          [
            2.3314683517128287e-15,
            -0.022206364788714794,
            -7.771561172376096e-16
          ],
          [
            9.992007221626409e-16,
            -0.01919400087060269,
            -7.771561172376096e-16
          ],
          [
            2.1094237467877974e-15,
            -0.016114129620406425,
            1.887379141862766e-15
          ],
          [
            -2.7755575615628914e-15,
            -0.012973423603459433,
            4.440892098500626e-16
          ],
          [
            1.887379141862766e-15,
            -0.00977994845699559,
            2.220446049250313e-15
          ],
          [
            1.9984014443252818e-15,
            -0.006544277720261948,
            -4.107825191113079e-15
          ],
          [
            4.551914400963142e-15,
            -0.003279585580441169,
            -4.107825191113079e-15
          ],
          [
            1.1102230246251565e-16,
            7.771561172376096e-16,
            -1.3877787807814457e-15
          ]
        ]
      },
      "reflected": {
        "reached": true,
        "construction": "reflect_displacements_about_reconstructed_parent",
        "energies_eV": [
          -239.73458801840374,
          -239.73529551205542,
          -239.73739359451008,
          -239.74080995936743,
          -239.74542901946546,
          -239.7510953163331,
          -239.75761452645133,
          -239.7647562582942,
          -239.77225651538697
        ],
        "cartesian_polarizations_e_A2": [
          [
            1.6898848085281564e-17,
            -3.1567199443423054e-18,
            5.132977849617683e-17
          ],
          [
            1.7966840162259648e-17,
            5.446318341243847e-05,
            1.14974545278216e-17
          ],
          [
            -1.5065304165513878e-17,
            0.00010867903551783022,
            5.838514208435507e-17
          ],
          [
            -6.313439888684611e-18,
            0.00016241293709612237,
            -6.972192523776403e-17
          ],
          [
            4.775247760116616e-17,
            0.0002154461080132318,
            -3.72757588637307e-17
          ],
          [
            1.0783884600283145e-17,
            0.00026760295638626123,
            1.646881587729481e-17
          ],
          [
            7.365837391087352e-17,
            0.0003187495383771097,
            -6.696215810079411e-17
          ],
          [
            1.1587241472346307e-17,
            0.000368775044512893,
            2.3595063895360973e-17
          ],
          [
            5.1320327238858436e-18,
            0.00041759989809557767,
            -1.4526582498365638e-17
          ]
        ],
        "raw_reduced_polarization": [
          [
            2.0738554104963337e-15,
            -1.9008681759489756e-16,
            3.756053174677147e-15
          ],
          [
            2.2029275639060307e-15,
            0.003279585580441666,
            8.478475096293681e-16
          ],
          [
            -1.844019726193223e-15,
            0.0065442777202623596,
            4.256560639279375e-15
          ],
          [
            -7.77135411486711e-16,
            0.009779948456997,
            -5.0942444675596624e-15
          ],
          [
            5.851827128737473e-15,
            0.012973423603459489,
            -2.7000464131404513e-15
          ],
          [
            1.3226628900353376e-15,
            0.016114129620405315,
            1.207570466657098e-15
          ],
          [
            9.026027043285432e-15,
            0.01919400087060027,
            -4.855938091218413e-15
          ],
          [
            1.421469093518076e-15,
            0.02220636478871347,
            1.7283236965697111e-15
          ],
          [
            6.284180160864428e-16,
            0.025146429539691255,
            -1.058422120821426e-15
          ]
        ],
        "unwrapped_reduced_polarization": [
          [
            2.0738554104963337e-15,
            -1.9008681759489756e-16,
            3.756053174677147e-15
          ],
          [
            2.2029275639060307e-15,
            0.003279585580441666,
            8.478475096293681e-16
          ],
          [
            -1.8440197261932235e-15,
            0.0065442777202623596,
            4.256560639279375e-15
          ],
          [
            -7.77135411486711e-16,
            0.009779948456997,
            -5.094244467559663e-15
          ],
          [
            5.851827128737473e-15,
            0.012973423603459489,
            -2.7000464131404513e-15
          ],
          [
            1.3226628900353374e-15,
            0.016114129620405315,
            1.2075704666570977e-15
          ],
          [
            9.026027043285432e-15,
            0.01919400087060027,
            -4.855938091218413e-15
          ],
          [
            1.4214690935180758e-15,
            0.02220636478871347,
            1.7283236965697107e-15
          ],
          [
            6.284180160864428e-16,
            0.025146429539691255,
            -1.0584221208214258e-15
          ]
        ],
        "gauge_integer_shift": [
          0,
          0,
          0
        ],
        "expected_opposite_endpoint_reduced_polarization": [
          3.9921802285454167e-16,
          0.02514642953969521,
          -2.5841960918208e-15
        ],
        "actual_opposite_endpoint_branch_residual": 4.24545460707826e-15
      },
      "pnp_branch": {
        "construction": "incoming_path_concatenated_with_parent_reflection",
        "reduced_polarization": [
          [
            -2.225608532197849e-16,
            -0.02514642953969365,
            -1.9028460035866145e-16
          ],
          [
            2.324111762488985e-15,
            -0.0222063647887148,
            -7.96355106746239e-16
          ],
          [
            9.477781303749167e-16,
            -0.01919400087060271,
            -7.720143060909088e-16
          ],
          [
            2.139863353297547e-15,
            -0.01611412962040642,
            1.8823370564175865e-15
          ],
          [
            -2.7489443743073257e-15,
            -0.012973423603459417,
            4.388099290002736e-16
          ],
          [
            1.929211321543572e-15,
            -0.009779948456995575,
            2.2022997724712093e-15
          ],
          [
            2.0144199947845054e-15,
            -0.006544277720261946,
            -4.107536401416703e-15
          ],
          [
            4.603777364983507e-15,
            -0.003279585580441142,
            -4.085743960266684e-15
          ],
          [
            8.832858481737841e-17,
            7.808356698808365e-16,
            -1.3872403460897309e-15
          ],
          [
            2.2029275639060307e-15,
            0.003279585580441666,
            8.478475096293681e-16
          ],
          [
            -1.844019726193223e-15,
            0.0065442777202623596,
            4.256560639279375e-15
          ],
          [
            -7.77135411486711e-16,
            0.009779948456997,
            -5.0942444675596624e-15
          ],
          [
            5.851827128737473e-15,
            0.012973423603459489,
            -2.7000464131404513e-15
          ],
          [
            1.3226628900353376e-15,
            0.016114129620405315,
            1.207570466657098e-15
          ],
          [
            9.026027043285432e-15,
            0.01919400087060027,
            -4.855938091218413e-15
          ],
          [
            1.421469093518076e-15,
            0.02220636478871347,
            1.7283236965697111e-15
          ],
          [
            6.284180160864428e-16,
            0.025146429539691255,
            -1.058422120821426e-15
          ]
        ],
        "unwrapped_reduced_polarization": [
          [
            -2.225608532197849e-16,
            -0.02514642953969365,
            -1.9028460035866145e-16
          ],
          [
            2.324111762488985e-15,
            -0.0222063647887148,
            -7.963551067462391e-16
          ],
          [
            9.477781303749167e-16,
            -0.01919400087060271,
            -7.720143060909088e-16
          ],
          [
            2.139863353297547e-15,
            -0.01611412962040642,
            1.8823370564175865e-15
          ],
          [
            -2.7489443743073257e-15,
            -0.012973423603459417,
            4.3880992900027356e-16
          ],
          [
            1.9292113215435714e-15,
            -0.009779948456995575,
            2.2022997724712093e-15
          ],
          [
            2.0144199947845054e-15,
            -0.006544277720261946,
            -4.107536401416702e-15
          ],
          [
            4.603777364983507e-15,
            -0.003279585580441142,
            -4.085743960266684e-15
          ],
          [
            8.832858481737856e-17,
            7.806255641895632e-16,
            -1.3872403460897309e-15
          ],
          [
            2.2029275639060307e-15,
            0.003279585580441666,
            8.478475096293681e-16
          ],
          [
            -1.8440197261932235e-15,
            0.0065442777202623596,
            4.256560639279375e-15
          ],
          [
            -7.77135411486711e-16,
            0.009779948456997,
            -5.094244467559663e-15
          ],
          [
            5.851827128737473e-15,
            0.012973423603459489,
            -2.7000464131404513e-15
          ],
          [
            1.3226628900353374e-15,
            0.016114129620405315,
            1.2075704666570977e-15
          ],
          [
            9.026027043285432e-15,
            0.01919400087060027,
            -4.855938091218413e-15
          ],
          [
            1.4214690935180758e-15,
            0.02220636478871347,
            1.7283236965697107e-15
          ],
          [
            6.284180160864428e-16,
            0.025146429539691255,
            -1.0584221208214258e-15
          ]
        ],
        "berry_integer_shifts": [
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            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": [
          [
            -2.220446049250313e-16,
            -0.02514642953969365,
            -1.6653345369377348e-16
          ],
          [
            2.3314683517128287e-15,
            -0.022206364788714794,
            -7.771561172376096e-16
          ],
          [
            9.992007221626409e-16,
            -0.01919400087060269,
            -7.771561172376096e-16
          ],
          [
            2.1094237467877974e-15,
            -0.016114129620406425,
            1.887379141862766e-15
          ],
          [
            -2.7755575615628914e-15,
            -0.012973423603459433,
            4.440892098500626e-16
          ],
          [
            1.887379141862766e-15,
            -0.00977994845699559,
            2.220446049250313e-15
          ],
          [
            1.9984014443252818e-15,
            -0.006544277720261948,
            -4.107825191113079e-15
          ],
          [
            4.551914400963142e-15,
            -0.003279585580441169,
            -4.107825191113079e-15
          ],
          [
            1.1102230246251565e-16,
            7.771561172376096e-16,
            -1.3877787807814457e-15
          ],
          [
            2.220446049250313e-15,
            0.003279585580441613,
            8.881784197001252e-16
          ],
          [
            -1.8318679906315083e-15,
            0.006544277720262337,
            4.218847493575595e-15
          ],
          [
            -7.771561172376096e-16,
            0.009779948456997034,
            -5.10702591327572e-15
          ],
          [
            5.88418203051333e-15,
            0.012973423603459544,
            -2.7200464103316335e-15
          ],
          [
            1.3322676295501878e-15,
            0.01611412962040526,
            1.2212453270876722e-15
          ],
          [
            8.992806499463768e-15,
            0.019194000870600303,
            -4.829470157119431e-15
          ],
          [
            1.4432899320127035e-15,
            0.022206364788713517,
            1.7763568394002505e-15
          ],
          [
            6.661338147750939e-16,
            0.025146429539691262,
            -1.0547118733938987e-15
          ]
        ]
      },
      "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,
        0.5,
        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": [
              -2.401092611821093e-15,
              -0.02514642953969206,
              8.945869932735861e-16
            ],
            "branch_aligned_reduced_polarization": [
              -2.401092611821093e-15,
              -0.02514642953969204,
              8.945869932735861e-16
            ],
            "target_residual": 0.47485357046030796,
            "energy_eV": -239.77225651538697,
            "max_atomic_step_A": 0.12,
            "max_log_strain_component": 0.0047781440864899365,
            "step_scale": 0.9007638135532642,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 0.7621755475549568,
            "cell_principal_stretches": [
              1.005403098859604,
              0.9990007544959854,
              0.9954479404636791
            ],
            "cell_volume_ratio": 0.9998263727710319,
            "cell_rmsd_from_input_A": 0.032331302205651474
          },
          {
            "iteration": 1,
            "reduced_polarization": [
              -8.628517383220074e-15,
              -0.4524084592256864,
              1.970511017882724e-14
            ],
            "branch_aligned_reduced_polarization": [
              -8.628517383220074e-15,
              -0.4524084592256864,
              1.970511017882724e-14
            ],
            "target_residual": 0.0475915407743136,
            "energy_eV": -238.93002537155624,
            "max_atomic_step_A": 0.012968131319866768,
            "max_log_strain_component": 0.0005385321158586437,
            "step_scale": 1.0,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 0.7621755475549568,
            "cell_principal_stretches": [
              1.0060138956564708,
              0.9988881947792916,
              0.9949361908281467
            ],
            "cell_volume_ratio": 0.9998068055908607,
            "cell_rmsd_from_input_A": 0.03598595500238595
          },
          {
            "iteration": 2,
            "reduced_polarization": [
              -1.447918069234203e-15,
              -0.5000523850935277,
              -9.537046880769593e-16
            ],
            "branch_aligned_reduced_polarization": [
              -1.447918069234203e-15,
              -0.5000523850935277,
              -9.537046880769593e-16
            ],
            "target_residual": 5.238509352767373e-05,
            "energy_eV": -238.722602239346
          }
        ],
        "iterations": 2
      },
      "parent": {
        "candidate_id": "bec_projection_01",
        "source": "MACEField_BEC_backprojection",
        "spacegroup": "P2_1",
        "spacegroup_number": 4,
        "pointgroup": "2",
        "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": 5.238509352767373e-05,
        "parent_symmetrization_rmsd_A": 0.12168787535034152,
        "parent_cell_rmsd_A": 0.03598595500238595,
        "energy_eV": -238.722602239346,
        "reduced_polarization": [
          -1.447918069234203e-15,
          -0.5000523850935277,
          -9.537046880769593e-16
        ],
        "cartesian_polarization_e_A2": [
          6.532080768492104e-17,
          -0.008296603765363444,
          -5.311924002655464e-16
        ],
        "ranking_score": 0.6307891342879933
      },
      "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": [
              -2.401092611821093e-15,
              -0.02514642953969206,
              8.945869932735861e-16
            ],
            "branch_aligned_reduced_polarization": [
              -2.3869795029440866e-15,
              -0.02514642953969206,
              8.945869932735861e-16
            ],
            "target_residual": 0.5006319435659218,
            "energy_eV": -239.77225651538697,
            "max_atomic_step_A": 0.06598750153564613,
            "max_log_strain_component": 0.0025306401459019166,
            "step_scale": 1.0,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 0.7621755475549568,
            "cell_principal_stretches": [
              1.0028490122551605,
              0.9997317145480037,
              0.9974368588887715
            ],
            "cell_volume_ratio": 1.0000102085355616,
            "cell_rmsd_from_input_A": 0.021099732819446167
          },
          {
            "iteration": 1,
            "reduced_polarization": [
              -0.49895157943351426,
              -0.000996876247525175,
              7.240377170610706e-05
            ],
            "branch_aligned_reduced_polarization": [
              -0.49895157943351426,
              -0.000996876247525175,
              7.240377170610706e-05
            ],
            "target_residual": 0.001448513114634254,
            "energy_eV": -239.51916317112415,
            "max_atomic_step_A": 0.00032690912132809407,
            "max_log_strain_component": 1.1181728374105298e-05,
            "step_scale": 1.0,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 0.7621755475549568,
            "cell_principal_stretches": [
              1.0028610316679614,
              0.9997212774012723,
              0.9974357229703794
            ],
            "cell_volume_ratio": 1.000010614894444,
            "cell_rmsd_from_input_A": 0.02114973304738115
          },
          {
            "iteration": 2,
            "reduced_polarization": [
              -0.49999921649428336,
              -2.6998996811662613e-06,
              4.624579442611854e-06
            ],
            "branch_aligned_reduced_polarization": [
              -0.49999921649428336,
              -2.6998996811662613e-06,
              4.624579442611854e-06
            ],
            "target_residual": 5.412030535519595e-06,
            "energy_eV": -239.5178708137899
          }
        ],
        "iterations": 2
      },
      "parent": {
        "candidate_id": "bec_projection_02",
        "source": "MACEField_BEC_backprojection",
        "spacegroup": "P1",
        "spacegroup_number": 1,
        "pointgroup": "1",
        "has_inversion": false,
        "is_polar_point_group": true,
        "nonpolar_parent_hypothesis": false,
        "symmetry_tolerance_A": null,
        "target_reduced_polarization": [
          -0.5,
          0.0,
          0.0
        ],
        "formal_class": [
          0.5,
          0.0,
          0.0
        ],
        "target_residual": 5.412030535519595e-06,
        "parent_symmetrization_rmsd_A": 0.06918683197709505,
        "parent_cell_rmsd_A": 0.02114973304738115,
        "energy_eV": -239.5178708137899,
        "reduced_polarization": [
          -0.49999921649428336,
          -2.6998996811662613e-06,
          4.624579442611854e-06
        ],
        "cartesian_polarization_e_A2": [
          -0.004079140106612364,
          1.027916407900839e-05,
          2.4552632624757797e-05
        ],
        "ranking_score": 0.5744850893000114
      },
      "branch_status": "awaiting_branch_sampling"
    },
    {
      "orbit_id": 3,
      "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": [
              -2.401092611821093e-15,
              -0.02514642953969206,
              8.945869932735861e-16
            ],
            "branch_aligned_reduced_polarization": [
              -2.401092611821093e-15,
              -0.02514642953969206,
              8.881784197001252e-16
            ],
            "target_residual": 0.5006319435659233,
            "energy_eV": -239.77225651538697,
            "max_atomic_step_A": 0.10994002830541126,
            "max_log_strain_component": 0.006758385288147455,
            "step_scale": 1.0,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 0.7621755475549568,
            "cell_principal_stretches": [
              1.0080491803570641,
              1.0002666587378617,
              0.9917607569604198
            ],
            "cell_volume_ratio": 1.0000102085356577,
            "cell_rmsd_from_input_A": 0.08636495834936132
          },
          {
            "iteration": 1,
            "reduced_polarization": [
              0.0004237268452191499,
              0.005738784570865465,
              0.5007347605450597
            ],
            "branch_aligned_reduced_polarization": [
              0.0004237268452191499,
              0.005738784570865465,
              0.5007347605450597
            ],
            "target_residual": 0.005801126256921095,
            "energy_eV": -238.90963141367632,
            "max_atomic_step_A": 0.0016133057244769513,
            "max_log_strain_component": 6.427397101054878e-05,
            "step_scale": 1.0,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 0.7621755475549568,
            "cell_principal_stretches": [
              1.0080687223276796,
              1.000205618695806,
              0.9917997380027506
            ],
            "cell_volume_ratio": 1.0000078727372583,
            "cell_rmsd_from_input_A": 0.08627982351486588
          },
          {
            "iteration": 2,
            "reduced_polarization": [
              4.928225946141118e-05,
              -6.015928459600632e-07,
              0.4999773747297444
            ],
            "branch_aligned_reduced_polarization": [
              4.928225946141118e-05,
              -6.015928459600632e-07,
              0.4999773747297444
            ],
            "target_residual": 5.423104153262068e-05,
            "energy_eV": -238.91412015002035
          }
        ],
        "iterations": 2
      },
      "parent": {
        "candidate_id": "bec_projection_03",
        "source": "MACEField_BEC_backprojection",
        "spacegroup": "P1",
        "spacegroup_number": 1,
        "pointgroup": "1",
        "has_inversion": false,
        "is_polar_point_group": true,
        "nonpolar_parent_hypothesis": false,
        "symmetry_tolerance_A": null,
        "target_reduced_polarization": [
          0.0,
          0.0,
          0.5
        ],
        "formal_class": [
          0.0,
          0.0,
          0.5
        ],
        "target_residual": 5.423104153262068e-05,
        "parent_symmetrization_rmsd_A": 0.1219986856513098,
        "parent_cell_rmsd_A": 0.08627982351486588,
        "energy_eV": -238.91412015002035,
        "reduced_polarization": [
          4.928225946141118e-05,
          -6.015928459600632e-07,
          0.4999773747297444
        ],
        "cartesian_polarization_e_A2": [
          -8.046896606557472e-07,
          -4.624970588873063e-05,
          0.006846355236821941
        ],
        "ranking_score": 0.6436771036130915
      },
      "branch_status": "awaiting_branch_sampling"
    },
    {
      "orbit_id": 4,
      "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": [
              -2.401092611821093e-15,
              -0.02514642953969206,
              8.945869932735861e-16
            ],
            "branch_aligned_reduced_polarization": [
              -2.3869795029440866e-15,
              -0.02514642953969204,
              8.945869932735861e-16
            ],
            "target_residual": 0.6895548661121175,
            "energy_eV": -239.77225651538697,
            "max_atomic_step_A": 0.12,
            "max_log_strain_component": 0.004100593587457379,
            "step_scale": 0.7730336822855254,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 0.7621755475549568,
            "cell_principal_stretches": [
              1.0047047154220874,
              1.0000693176698148,
              0.9951000266500218
            ],
            "cell_volume_ratio": 0.9998509916289328,
            "cell_rmsd_from_input_A": 0.03207936116295678
          },
          {
            "iteration": 1,
            "reduced_polarization": [
              -0.3897973406591223,
              -0.39264849756131615,
              -0.003711719573084418
            ],
            "branch_aligned_reduced_polarization": [
              -0.3897973406591223,
              -0.39264849756131615,
              -0.003711719573084418
            ],
            "target_residual": 0.15389200129907174,
            "energy_eV": -238.980092596482,
            "max_atomic_step_A": 0.03635703369509603,
            "max_log_strain_component": 0.0012042330281493302,
            "step_scale": 1.0,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 0.7621755475549568,
            "cell_principal_stretches": [
              1.0060668873203278,
              1.0000976155204342,
              0.9936810977032218
            ],
            "cell_volume_ratio": 0.999807236132993,
            "cell_rmsd_from_input_A": 0.04151763389229938
          },
          {
            "iteration": 2,
            "reduced_polarization": [
              -0.5010723139921996,
              -0.5002907685668687,
              -0.001024338686859465
            ],
            "branch_aligned_reduced_polarization": [
              -0.5010723139921996,
              -0.5002907685668687,
              -0.001024338686859465
            ],
            "target_residual": 0.0015111827827046617,
            "energy_eV": -238.3932900525275,
            "max_atomic_step_A": 0.0002813373097473705,
            "max_log_strain_component": 1.4385244800828418e-05,
            "step_scale": 1.0,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 0.7621755475549568,
            "cell_principal_stretches": [
              1.0060598158699021,
              1.0000984449853738,
              0.993687369694223
            ],
            "cell_volume_ratio": 0.9998073485180246,
            "cell_rmsd_from_input_A": 0.04149861576719653
          },
          {
            "iteration": 3,
            "reduced_polarization": [
              -0.4999730886521362,
              -0.4999933563210493,
              -3.300571022398721e-06
            ],
            "branch_aligned_reduced_polarization": [
              -0.4999730886521362,
              -0.4999933563210493,
              -3.300571022398721e-06
            ],
            "target_residual": 2.7915101341764414e-05,
            "energy_eV": -238.39591886348356
          }
        ],
        "iterations": 3
      },
      "parent": {
        "candidate_id": "bec_projection_04",
        "source": "MACEField_BEC_backprojection",
        "spacegroup": "P1",
        "spacegroup_number": 1,
        "pointgroup": "1",
        "has_inversion": false,
        "is_polar_point_group": true,
        "nonpolar_parent_hypothesis": false,
        "symmetry_tolerance_A": null,
        "target_reduced_polarization": [
          -0.5,
          -0.5,
          0.0
        ],
        "formal_class": [
          0.5,
          0.5,
          0.0
        ],
        "target_residual": 2.7915101341764414e-05,
        "parent_symmetrization_rmsd_A": 0.1393451291752568,
        "parent_cell_rmsd_A": 0.04149861576719653,
        "energy_eV": -238.39591886348356,
        "reduced_polarization": [
          -0.4999730886521362,
          -0.4999933563210493,
          -3.300571022398721e-06
        ],
        "cartesian_polarization_e_A2": [
          -0.004055104308929611,
          -0.008285779818563302,
          5.583230059080033e-05
        ],
        "ranking_score": 0.6497756133197394
      },
      "branch_status": "awaiting_branch_sampling"
    },
    {
      "orbit_id": 5,
      "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": [
              -2.401092611821093e-15,
              -0.02514642953969206,
              8.945869932735861e-16
            ],
            "branch_aligned_reduced_polarization": [
              -2.401092611821093e-15,
              -0.02514642953969204,
              8.881784197001252e-16
            ],
            "target_residual": 0.6895548661121186,
            "energy_eV": -239.77225651538697,
            "max_atomic_step_A": 0.12,
            "max_log_strain_component": 0.004418141490586235,
            "step_scale": 0.6537273775108794,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 0.7621755475549568,
            "cell_principal_stretches": [
              1.0074216047617088,
              0.996749041504626,
              0.9957451114547385
            ],
            "cell_volume_ratio": 0.9998739874160947,
            "cell_rmsd_from_input_A": 0.06130175868095282
          },
          {
            "iteration": 1,
            "reduced_polarization": [
              0.010320744544789082,
              -0.33251669711792864,
              0.3211502262034733
            ],
            "branch_aligned_reduced_polarization": [
              0.010320744544789082,
              -0.33251669711792864,
              0.3211502262034733
            ],
            "target_residual": 0.2452435852358125,
            "energy_eV": -238.99217757844414,
            "max_atomic_step_A": 0.06464711977699224,
            "max_log_strain_component": 0.002570370355043807,
            "step_scale": 1.0,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 0.7621755475549568,
            "cell_principal_stretches": [
              1.011616853628486,
              0.9949922647831475,
              0.9932965646154072
            ],
            "cell_volume_ratio": 0.9998035950682965,
            "cell_rmsd_from_input_A": 0.09652441270257173
          },
          {
            "iteration": 2,
            "reduced_polarization": [
              0.007245508653197652,
              -0.49814226531094685,
              0.49717652394327644
            ],
            "branch_aligned_reduced_polarization": [
              0.007245508653197652,
              -0.49814226531094685,
              0.49717652394327644
            ],
            "target_residual": 0.007995035388374755,
            "energy_eV": -237.80357476312295,
            "max_atomic_step_A": 0.001488190508118681,
            "max_log_strain_component": 5.7078506064945366e-05,
            "step_scale": 1.0,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 0.7621755475549568,
            "cell_principal_stretches": [
              1.0116722584113589,
              0.994987873881409,
              0.9932456754307158
            ],
            "cell_volume_ratio": 0.9998027153441674,
            "cell_rmsd_from_input_A": 0.09714979232239412
          },
          {
            "iteration": 3,
            "reduced_polarization": [
              -7.316666341900358e-06,
              -0.4999856758330039,
              0.4999547629426085
            ],
            "branch_aligned_reduced_polarization": [
              -7.316666341900358e-06,
              -0.4999856758330039,
              0.4999547629426085
            ],
            "target_residual": 4.801152703188685e-05,
            "energy_eV": -237.7806582075247
          }
        ],
        "iterations": 3
      },
      "parent": {
        "candidate_id": "bec_projection_05",
        "source": "MACEField_BEC_backprojection",
        "spacegroup": "P1",
        "spacegroup_number": 1,
        "pointgroup": "1",
        "has_inversion": false,
        "is_polar_point_group": true,
        "nonpolar_parent_hypothesis": false,
        "symmetry_tolerance_A": null,
        "target_reduced_polarization": [
          0.0,
          -0.5,
          0.5
        ],
        "formal_class": [
          0.0,
          0.5,
          0.5
        ],
        "target_residual": 4.801152703188685e-05,
        "parent_symmetrization_rmsd_A": 0.17457555517577047,
        "parent_cell_rmsd_A": 0.09714979232239412,
        "energy_eV": -237.7806582075247,
        "reduced_polarization": [
          -7.316666341900358e-06,
          -0.4999856758330039,
          0.4999547629426085
        ],
        "cartesian_polarization_e_A2": [
          -7.762058652438164e-05,
          -0.008343992273549969,
          0.006920808662308622
        ],
        "ranking_score": 0.6989590263104328
      },
      "branch_status": "awaiting_branch_sampling"
    },
    {
      "orbit_id": 6,
      "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": [
              -2.401092611821093e-15,
              -0.02514642953969206,
              8.945869932735861e-16
            ],
            "branch_aligned_reduced_polarization": [
              -2.3869795029440866e-15,
              -0.02514642953969206,
              8.881784197001252e-16
            ],
            "target_residual": 0.7075537738706448,
            "energy_eV": -239.77225651538697,
            "max_atomic_step_A": 0.12,
            "max_log_strain_component": 0.006483911801660001,
            "step_scale": 0.8422100784709211,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 0.7621755475549568,
            "cell_principal_stretches": [
              1.0066537236327648,
              1.000155140009189,
              0.9932447046818643
            ],
            "cell_volume_ratio": 1.0000085977246689,
            "cell_rmsd_from_input_A": 0.07778780223215757
          },
          {
            "iteration": 1,
            "reduced_polarization": [
              -0.41853448126873716,
              0.0017318262972756597,
              0.42084018376626
            ],
            "branch_aligned_reduced_polarization": [
              -0.41853448126873716,
              0.0017318262972756597,
              0.42084018376626
            ],
            "target_residual": 0.11360416572748186,
            "energy_eV": -238.8760045540046,
            "max_atomic_step_A": 0.022524262105224766,
            "max_log_strain_component": 0.0012332084477621168,
            "step_scale": 1.0,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 0.7621755475549568,
            "cell_principal_stretches": [
              1.0079452521532208,
              1.000122148546596,
              0.9920029672032622
            ],
            "cell_volume_ratio": 1.0000068153749733,
            "cell_rmsd_from_input_A": 0.0925478280769627
          },
          {
            "iteration": 2,
            "reduced_polarization": [
              -0.49970565610906226,
              0.0005608726583981842,
              0.4999147445947249
            ],
            "branch_aligned_reduced_polarization": [
              -0.49970565610906226,
              0.0005608726583981842,
              0.4999147445947249
            ],
            "target_residual": 0.0006391282728839627,
            "energy_eV": -238.48688796268394
          }
        ],
        "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,
          0.0,
          0.5
        ],
        "formal_class": [
          0.5,
          0.0,
          0.5
        ],
        "target_residual": 0.0006391282728839627,
        "parent_symmetrization_rmsd_A": 0.12963005767524555,
        "parent_cell_rmsd_A": 0.0925478280769627,
        "energy_eV": -238.48688796268394,
        "reduced_polarization": [
          -0.49970565610906226,
          0.0005608726583981842,
          0.4999147445947249
        ],
        "cartesian_polarization_e_A2": [
          -0.00407800606678588,
          -5.182700970663011e-05,
          0.00687049763237622
        ],
        "ranking_score": 0.6540452712402541
      },
      "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": [
              -2.401092611821093e-15,
              -0.02514642953969206,
              8.945869932735861e-16
            ],
            "branch_aligned_reduced_polarization": [
              -2.3869795029440866e-15,
              -0.02514642953969204,
              8.881784197001252e-16
            ],
            "target_residual": 0.8517546086631403,
            "energy_eV": -239.77225651538697,
            "max_atomic_step_A": 0.12000000000000001,
            "max_log_strain_component": 0.004402688689316147,
            "step_scale": 0.5718752660383188,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 0.7621755475549568,
            "cell_principal_stretches": [
              1.0061816034203217,
              0.9983243796033936,
              0.9954147529197376
            ],
            "cell_volume_ratio": 0.9998897643712591,
            "cell_rmsd_from_input_A": 0.05673442455312732
          },
          {
            "iteration": 1,
            "reduced_polarization": [
              -0.2795702487266349,
              -0.2933834130517376,
              0.2794498639834887
            ],
            "branch_aligned_reduced_polarization": [
              -0.2795702487266349,
              -0.2933834130517376,
              0.2794498639834887
            ],
            "target_residual": 0.37406156143807145,
            "energy_eV": -239.05394456012127,
            "max_atomic_step_A": 0.09268843118715706,
            "max_log_strain_component": 0.003594955529575932,
            "step_scale": 1.0,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 0.7621755475549568,
            "cell_principal_stretches": [
              1.0111974914486492,
              0.9970015781519309,
              0.9917045798345934
            ],
            "cell_volume_ratio": 0.9998023384219662,
            "cell_rmsd_from_input_A": 0.1030050186130504
          },
          {
            "iteration": 2,
            "reduced_polarization": [
              -0.49173562234478035,
              -0.49627484992675186,
              0.4933766955896871
            ],
            "branch_aligned_reduced_polarization": [
              -0.49173562234478035,
              -0.49627484992675186,
              0.4933766955896871
            ],
            "target_residual": 0.011226969422243235,
            "energy_eV": -237.28770204588227,
            "max_atomic_step_A": 0.0024634253717282302,
            "max_log_strain_component": 0.00011572417787922729,
            "step_scale": 1.0,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 0.7621755475549568,
            "cell_principal_stretches": [
              1.011333489448123,
              0.9969790383616831,
              0.9915919113917603
            ],
            "cell_volume_ratio": 0.9998005965707794,
            "cell_rmsd_from_input_A": 0.1044121261120098
          },
          {
            "iteration": 3,
            "reduced_polarization": [
              -0.49992322369601655,
              -0.4999584586335459,
              0.4998868280710857
            ],
            "branch_aligned_reduced_polarization": [
              -0.49992322369601655,
              -0.4999584586335459,
              0.4998868280710857
            ],
            "target_residual": 0.00014292715443336396,
            "energy_eV": -237.2224352811045
          }
        ],
        "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": 0.00014292715443336396,
        "parent_symmetrization_rmsd_A": 0.18167233331436036,
        "parent_cell_rmsd_A": 0.1044121261120098,
        "energy_eV": -237.2224352811045,
        "reduced_polarization": [
          -0.49992322369601655,
          -0.4999584586335459,
          0.4998868280710857
        ],
        "cartesian_polarization_e_A2": [
          -0.004132521409152029,
          -0.008359529321007681,
          0.006977084995880591
        ],
        "ranking_score": 0.7080612191512295
      },
      "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,
          24,
          25,
          26,
          27,
          28,
          29,
          30,
          31,
          32,
          33,
          34,
          35,
          36,
          37,
          38,
          39
        ],
        "endpoint_rmsd_A": 0.11370543309429537,
        "minimum_distance_A_by_image": [
          2.1612965859700832,
          2.161303850914816,
          2.1613209510730913,
          2.1613478862114683,
          2.1613846559622534,
          2.161431259823539,
          2.161487697159225,
          2.161553967199064,
          2.1616300690387185
        ],
        "minimum_distance_A": 2.1612965859700832,
        "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": [
          734.1768052813047,
          734.1768052813047,
          734.1768052813047,
          734.1768052813047,
          734.1768052813047,
          734.1768052813047,
          734.1768052813047,
          734.1768052813047,
          734.1768052813047
        ],
        "cell_deformation_log_strain_norm": 0.0
      },
      "parent_reduced_polarization": [
        8.832858481737841e-17,
        7.808356698808365e-16,
        -1.3872403460897309e-15
      ],
      "incoming": {
        "reached": true,
        "construction": "variable_cell_linear_interpolation",
        "continuation_fractions": [
          0.0,
          0.125,
          0.25,
          0.375,
          0.5,
          0.625,
          0.75,
          0.875,
          1.0
        ],
        "energies_eV": [
          -239.772256515387,
          -239.76475625829417,
          -239.75761452645136,
          -239.7510953163331,
          -239.7454290194655,
          -239.74080995936745,
          -239.73739359451005,
          -239.7352955120554,
          -239.73458801840377
        ],
        "cartesian_polarizations_e_A2": [
          [
            -1.814641405130906e-18,
            -0.00041759989809561746,
            -2.594370133898092e-18
          ],
          [
            1.8963947809349806e-17,
            -0.0003687750445129151,
            -1.1024891661902094e-17
          ],
          [
            7.735854115102326e-18,
            -0.0003187495383771502,
            -1.0620850411540915e-17
          ],
          [
            1.7447021009748192e-17,
            -0.00026760295638627956,
            2.566725206241801e-17
          ],
          [
            -2.242783361653979e-17,
            -0.00021544610801323063,
            6.1504056999423805e-18
          ],
          [
            1.5726892177801187e-17,
            -0.00016241293709609873,
            3.005972390113983e-17
          ],
          [
            1.6454638991317227e-17,
            -0.00010867903551782335,
            -5.635312176090118e-17
          ],
          [
            3.757819909791918e-17,
            -5.446318341242978e-05,
            -5.618772475782935e-17
          ],
          [
            7.277468135160405e-19,
            1.2967125040831266e-17,
            -1.900175283862337e-17
          ]
        ],
        "raw_reduced_polarization": [
          [
            -2.225608532197849e-16,
            -0.02514642953969365,
            -1.9028460035866145e-16
          ],
          [
            2.324111762488985e-15,
            -0.0222063647887148,
            -7.96355106746239e-16
          ],
          [
            9.477781303749167e-16,
            -0.01919400087060271,
            -7.720143060909088e-16
          ],
          [
            2.139863353297547e-15,
            -0.01611412962040642,
            1.8823370564175865e-15
          ],
          [
            -2.7489443743073257e-15,
            -0.012973423603459417,
            4.388099290002736e-16
          ],
          [
            1.929211321543572e-15,
            -0.009779948456995575,
            2.2022997724712093e-15
          ],
          [
            2.0144199947845054e-15,
            -0.006544277720261946,
            -4.107536401416703e-15
          ],
          [
            4.603777364983507e-15,
            -0.003279585580441142,
            -4.085743960266684e-15
          ],
          [
            8.832858481737841e-17,
            7.808356698808365e-16,
            -1.3872403460897309e-15
          ]
        ],
        "unwrapped_reduced_polarization": [
          [
            -2.225608532197849e-16,
            -0.02514642953969365,
            -1.9028460035866145e-16
          ],
          [
            2.324111762488985e-15,
            -0.0222063647887148,
            -7.963551067462391e-16
          ],
          [
            9.477781303749167e-16,
            -0.01919400087060271,
            -7.720143060909088e-16
          ],
          [
            2.139863353297547e-15,
            -0.01611412962040642,
            1.8823370564175865e-15
          ],
          [
            -2.7489443743073257e-15,
            -0.012973423603459417,
            4.3880992900027356e-16
          ],
          [
            1.9292113215435714e-15,
            -0.009779948456995575,
            2.2022997724712093e-15
          ],
          [
            2.0144199947845054e-15,
            -0.006544277720261946,
            -4.107536401416702e-15
          ],
          [
            4.603777364983507e-15,
            -0.003279585580441142,
            -4.085743960266684e-15
          ],
          [
            8.832858481737856e-17,
            7.806255641895632e-16,
            -1.3872403460897309e-15
          ]
        ],
        "berry_integer_shifts": [
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ]
        ],
        "folded_reduced_polarization": [
          [
            -2.220446049250313e-16,
            -0.02514642953969365,
            -1.6653345369377348e-16
          ],
          [
            2.3314683517128287e-15,
            -0.022206364788714794,
            -7.771561172376096e-16
          ],
          [
            9.992007221626409e-16,
            -0.01919400087060269,
            -7.771561172376096e-16
          ],
          [
            2.1094237467877974e-15,
            -0.016114129620406425,
            1.887379141862766e-15
          ],
          [
            -2.7755575615628914e-15,
            -0.012973423603459433,
            4.440892098500626e-16
          ],
          [
            1.887379141862766e-15,
            -0.00977994845699559,
            2.220446049250313e-15
          ],
          [
            1.9984014443252818e-15,
            -0.006544277720261948,
            -4.107825191113079e-15
          ],
          [
            4.551914400963142e-15,
            -0.003279585580441169,
            -4.107825191113079e-15
          ],
          [
            1.1102230246251565e-16,
            7.771561172376096e-16,
            -1.3877787807814457e-15
          ]
        ]
      },
      "reflected": {
        "reached": true,
        "construction": "reflect_displacements_about_reconstructed_parent",
        "energies_eV": [
          -239.73458801840374,
          -239.73529551205542,
          -239.73739359451008,
          -239.74080995936743,
          -239.74542901946546,
          -239.7510953163331,
          -239.75761452645133,
          -239.7647562582942,
          -239.77225651538697
        ],
        "cartesian_polarizations_e_A2": [
          [
            1.6898848085281564e-17,
            -3.1567199443423054e-18,
            5.132977849617683e-17
          ],
          [
            1.7966840162259648e-17,
            5.446318341243847e-05,
            1.14974545278216e-17
          ],
          [
            -1.5065304165513878e-17,
            0.00010867903551783022,
            5.838514208435507e-17
          ],
          [
            -6.313439888684611e-18,
            0.00016241293709612237,
            -6.972192523776403e-17
          ],
          [
            4.775247760116616e-17,
            0.0002154461080132318,
            -3.72757588637307e-17
          ],
          [
            1.0783884600283145e-17,
            0.00026760295638626123,
            1.646881587729481e-17
          ],
          [
            7.365837391087352e-17,
            0.0003187495383771097,
            -6.696215810079411e-17
          ],
          [
            1.1587241472346307e-17,
            0.000368775044512893,
            2.3595063895360973e-17
          ],
          [
            5.1320327238858436e-18,
            0.00041759989809557767,
            -1.4526582498365638e-17
          ]
        ],
        "raw_reduced_polarization": [
          [
            2.0738554104963337e-15,
            -1.9008681759489756e-16,
            3.756053174677147e-15
          ],
          [
            2.2029275639060307e-15,
            0.003279585580441666,
            8.478475096293681e-16
          ],
          [
            -1.844019726193223e-15,
            0.0065442777202623596,
            4.256560639279375e-15
          ],
          [
            -7.77135411486711e-16,
            0.009779948456997,
            -5.0942444675596624e-15
          ],
          [
            5.851827128737473e-15,
            0.012973423603459489,
            -2.7000464131404513e-15
          ],
          [
            1.3226628900353376e-15,
            0.016114129620405315,
            1.207570466657098e-15
          ],
          [
            9.026027043285432e-15,
            0.01919400087060027,
            -4.855938091218413e-15
          ],
          [
            1.421469093518076e-15,
            0.02220636478871347,
            1.7283236965697111e-15
          ],
          [
            6.284180160864428e-16,
            0.025146429539691255,
            -1.058422120821426e-15
          ]
        ],
        "unwrapped_reduced_polarization": [
          [
            2.0738554104963337e-15,
            -1.9008681759489756e-16,
            3.756053174677147e-15
          ],
          [
            2.2029275639060307e-15,
            0.003279585580441666,
            8.478475096293681e-16
          ],
          [
            -1.8440197261932235e-15,
            0.0065442777202623596,
            4.256560639279375e-15
          ],
          [
            -7.77135411486711e-16,
            0.009779948456997,
            -5.094244467559663e-15
          ],
          [
            5.851827128737473e-15,
            0.012973423603459489,
            -2.7000464131404513e-15
          ],
          [
            1.3226628900353374e-15,
            0.016114129620405315,
            1.2075704666570977e-15
          ],
          [
            9.026027043285432e-15,
            0.01919400087060027,
            -4.855938091218413e-15
          ],
          [
            1.4214690935180758e-15,
            0.02220636478871347,
            1.7283236965697107e-15
          ],
          [
            6.284180160864428e-16,
            0.025146429539691255,
            -1.0584221208214258e-15
          ]
        ],
        "gauge_integer_shift": [
          0,
          0,
          0
        ],
        "expected_opposite_endpoint_reduced_polarization": [
          3.9921802285454167e-16,
          0.02514642953969521,
          -2.5841960918208e-15
        ],
        "actual_opposite_endpoint_branch_residual": 4.24545460707826e-15
      },
      "pnp_branch": {
        "construction": "incoming_path_concatenated_with_parent_reflection",
        "reduced_polarization": [
          [
            -2.225608532197849e-16,
            -0.02514642953969365,
            -1.9028460035866145e-16
          ],
          [
            2.324111762488985e-15,
            -0.0222063647887148,
            -7.96355106746239e-16
          ],
          [
            9.477781303749167e-16,
            -0.01919400087060271,
            -7.720143060909088e-16
          ],
          [
            2.139863353297547e-15,
            -0.01611412962040642,
            1.8823370564175865e-15
          ],
          [
            -2.7489443743073257e-15,
            -0.012973423603459417,
            4.388099290002736e-16
          ],
          [
            1.929211321543572e-15,
            -0.009779948456995575,
            2.2022997724712093e-15
          ],
          [
            2.0144199947845054e-15,
            -0.006544277720261946,
            -4.107536401416703e-15
          ],
          [
            4.603777364983507e-15,
            -0.003279585580441142,
            -4.085743960266684e-15
          ],
          [
            8.832858481737841e-17,
            7.808356698808365e-16,
            -1.3872403460897309e-15
          ],
          [
            2.2029275639060307e-15,
            0.003279585580441666,
            8.478475096293681e-16
          ],
          [
            -1.844019726193223e-15,
            0.0065442777202623596,
            4.256560639279375e-15
          ],
          [
            -7.77135411486711e-16,
            0.009779948456997,
            -5.0942444675596624e-15
          ],
          [
            5.851827128737473e-15,
            0.012973423603459489,
            -2.7000464131404513e-15
          ],
          [
            1.3226628900353376e-15,
            0.016114129620405315,
            1.207570466657098e-15
          ],
          [
            9.026027043285432e-15,
            0.01919400087060027,
            -4.855938091218413e-15
          ],
          [
            1.421469093518076e-15,
            0.02220636478871347,
            1.7283236965697111e-15
          ],
          [
            6.284180160864428e-16,
            0.025146429539691255,
            -1.058422120821426e-15
          ]
        ],
        "unwrapped_reduced_polarization": [
          [
            -2.225608532197849e-16,
            -0.02514642953969365,
            -1.9028460035866145e-16
          ],
          [
            2.324111762488985e-15,
            -0.0222063647887148,
            -7.963551067462391e-16
          ],
          [
            9.477781303749167e-16,
            -0.01919400087060271,
            -7.720143060909088e-16
          ],
          [
            2.139863353297547e-15,
            -0.01611412962040642,
            1.8823370564175865e-15
          ],
          [
            -2.7489443743073257e-15,
            -0.012973423603459417,
            4.3880992900027356e-16
          ],
          [
            1.9292113215435714e-15,
            -0.009779948456995575,
            2.2022997724712093e-15
          ],
          [
            2.0144199947845054e-15,
            -0.006544277720261946,
            -4.107536401416702e-15
          ],
          [
            4.603777364983507e-15,
            -0.003279585580441142,
            -4.085743960266684e-15
          ],
          [
            8.832858481737856e-17,
            7.806255641895632e-16,
            -1.3872403460897309e-15
          ],
          [
            2.2029275639060307e-15,
            0.003279585580441666,
            8.478475096293681e-16
          ],
          [
            -1.8440197261932235e-15,
            0.0065442777202623596,
            4.256560639279375e-15
          ],
          [
            -7.77135411486711e-16,
            0.009779948456997,
            -5.094244467559663e-15
          ],
          [
            5.851827128737473e-15,
            0.012973423603459489,
            -2.7000464131404513e-15
          ],
          [
            1.3226628900353374e-15,
            0.016114129620405315,
            1.2075704666570977e-15
          ],
          [
            9.026027043285432e-15,
            0.01919400087060027,
            -4.855938091218413e-15
          ],
          [
            1.4214690935180758e-15,
            0.02220636478871347,
            1.7283236965697107e-15
          ],
          [
            6.284180160864428e-16,
            0.025146429539691255,
            -1.0584221208214258e-15
          ]
        ],
        "berry_integer_shifts": [
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            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": [
          [
            -2.220446049250313e-16,
            -0.02514642953969365,
            -1.6653345369377348e-16
          ],
          [
            2.3314683517128287e-15,
            -0.022206364788714794,
            -7.771561172376096e-16
          ],
          [
            9.992007221626409e-16,
            -0.01919400087060269,
            -7.771561172376096e-16
          ],
          [
            2.1094237467877974e-15,
            -0.016114129620406425,
            1.887379141862766e-15
          ],
          [
            -2.7755575615628914e-15,
            -0.012973423603459433,
            4.440892098500626e-16
          ],
          [
            1.887379141862766e-15,
            -0.00977994845699559,
            2.220446049250313e-15
          ],
          [
            1.9984014443252818e-15,
            -0.006544277720261948,
            -4.107825191113079e-15
          ],
          [
            4.551914400963142e-15,
            -0.003279585580441169,
            -4.107825191113079e-15
          ],
          [
            1.1102230246251565e-16,
            7.771561172376096e-16,
            -1.3877787807814457e-15
          ],
          [
            2.220446049250313e-15,
            0.003279585580441613,
            8.881784197001252e-16
          ],
          [
            -1.8318679906315083e-15,
            0.006544277720262337,
            4.218847493575595e-15
          ],
          [
            -7.771561172376096e-16,
            0.009779948456997034,
            -5.10702591327572e-15
          ],
          [
            5.88418203051333e-15,
            0.012973423603459544,
            -2.7200464103316335e-15
          ],
          [
            1.3322676295501878e-15,
            0.01611412962040526,
            1.2212453270876722e-15
          ],
          [
            8.992806499463768e-15,
            0.019194000870600303,
            -4.829470157119431e-15
          ],
          [
            1.4432899320127035e-15,
            0.022206364788713517,
            1.7763568394002505e-15
          ],
          [
            6.661338147750939e-16,
            0.025146429539691262,
            -1.0547118733938987e-15
          ]
        ]
      },
      "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": "P2_1/c",
        "spacegroup_number": 14,
        "pointgroup": "2/m",
        "has_inversion": true,
        "is_polar_point_group": false,
        "nonpolar_parent_hypothesis": true,
        "symmetry_tolerance_A": null,
        "target_reduced_polarization": [
          0.0,
          0.0,
          0.0
        ],
        "formal_class": [
          0.0,
          0.0,
          0.0
        ],
        "target_residual": 2.6061298080005922e-15,
        "parent_symmetrization_rmsd_A": 0.11370543309429537,
        "parent_cell_rmsd_A": 0.0,
        "energy_eV": -239.73458801840368,
        "reduced_polarization": [
          -1.046818867463807e-15,
          1.3806904775006631e-15,
          -1.9467348664391843e-15
        ],
        "cartesian_polarization_e_A2": [
          -8.529759729847097e-18,
          2.2928750254414468e-17,
          -2.6605289351268232e-17
        ],
        "ranking_score": 0.11370543309430059
      }
    }
  ],
  "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": 51,
      "full_response": 19,
      "energy_polarization": 32
    },
    "model_evaluations_for_recovery_and_path_properties": {
      "total": 76,
      "full_response": 44,
      "energy_polarization": 32
    },
    "elapsed_seconds": 512.9404482629616
  }
}