{
  "schema": "ferrofinder.endpoint_parent_recovery.v4_variable_cell",
  "status": "complete",
  "input_atom_count": 14,
  "input_formula": "BiLi7O6",
  "input_spacegroup": "P1",
  "input_pointgroup": "1",
  "input_is_polar_point_group": true,
  "input_energy_eV": -68.82981663392609,
  "input_cartesian_polarization_e_A2": [
    -0.00030234746947760307,
    -0.0005922490951037998,
    0.0012388433513821416
  ],
  "input_reduced_polarization": [
    -0.00945592835261243,
    -0.028162692279892144,
    0.03324196566336734
  ],
  "input_formal_targets": [
    {
      "orbit_id": 0,
      "representative_formal_class": [
        0.0,
        0.0,
        0.0
      ],
      "target_reduced_polarization": [
        0.0,
        0.0,
        0.0
      ]
    },
    {
      "orbit_id": 1,
      "representative_formal_class": [
        0.0,
        0.0,
        0.5
      ],
      "target_reduced_polarization": [
        0.0,
        0.0,
        0.5
      ]
    },
    {
      "orbit_id": 2,
      "representative_formal_class": [
        0.0,
        0.5,
        0.0
      ],
      "target_reduced_polarization": [
        0.0,
        -0.5,
        0.0
      ]
    },
    {
      "orbit_id": 3,
      "representative_formal_class": [
        0.5,
        0.0,
        0.0
      ],
      "target_reduced_polarization": [
        -0.5,
        0.0,
        0.0
      ]
    },
    {
      "orbit_id": 4,
      "representative_formal_class": [
        0.0,
        0.5,
        0.5
      ],
      "target_reduced_polarization": [
        0.0,
        -0.5,
        0.5
      ]
    },
    {
      "orbit_id": 5,
      "representative_formal_class": [
        0.5,
        0.0,
        0.5
      ],
      "target_reduced_polarization": [
        -0.5,
        0.0,
        0.5
      ]
    },
    {
      "orbit_id": 6,
      "representative_formal_class": [
        0.5,
        0.5,
        0.0
      ],
      "target_reduced_polarization": [
        -0.5,
        -0.5,
        0.0
      ]
    },
    {
      "orbit_id": 7,
      "representative_formal_class": [
        0.5,
        0.5,
        0.5
      ],
      "target_reduced_polarization": [
        -0.5,
        -0.5,
        0.5
      ]
    }
  ],
  "parent_candidates": [
    {
      "candidate_id": "inversion_parent_endpoint_00",
      "source": "same_species_inversion_center_projection_from_endpoint",
      "spacegroup": "P-1",
      "spacegroup_number": 2,
      "pointgroup": "-1",
      "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": 2.8320640545438903e-15,
      "parent_symmetrization_rmsd_A": 0.2912369756967939,
      "parent_cell_rmsd_A": 0.0,
      "energy_eV": -68.2883712202584,
      "reduced_polarization": [
        -1.002079441029645e-15,
        -1.123366079228811e-15,
        2.3988481100193447e-15
      ],
      "cartesian_polarization_e_A2": [
        -1.684941351390253e-17,
        -1.1000651068160885e-17,
        8.93989561919319e-17
      ],
      "ranking_score": 0.29123697569679957
    },
    {
      "candidate_id": "inversion_parent_endpoint_01",
      "source": "same_species_inversion_center_projection_from_endpoint",
      "spacegroup": "P-1",
      "spacegroup_number": 2,
      "pointgroup": "-1",
      "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": 1.5630175326855203e-15,
      "parent_symmetrization_rmsd_A": 0.6034233026788528,
      "parent_cell_rmsd_A": 0.0,
      "energy_eV": -52.75557273073649,
      "reduced_polarization": [
        2.0474339602145154e-16,
        -1.5082691506193034e-15,
        -3.5528596729685174e-16
      ],
      "cartesian_polarization_e_A2": [
        -2.7725622827898702e-17,
        -5.684499330244222e-17,
        -1.3240602643125772e-17
      ],
      "ranking_score": 0.6034233026788559
    },
    {
      "candidate_id": "bec_projection_00",
      "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,
        0.0
      ],
      "formal_class": [
        0.0,
        0.0,
        0.0
      ],
      "target_residual": 2.6791105640470724e-05,
      "parent_symmetrization_rmsd_A": 0.008515237291264268,
      "parent_cell_rmsd_A": 0.002845017077719775,
      "energy_eV": -68.82334725897134,
      "reduced_polarization": [
        -7.866805304276179e-06,
        1.2525390150343625e-05,
        2.233811355788911e-05
      ],
      "cartesian_polarization_e_A2": [
        3.462088136140325e-07,
        6.998584117852337e-07,
        8.318752799351667e-07
      ],
      "ranking_score": 0.5092800737719752
    },
    {
      "candidate_id": "inversion_parent_bec_00_00",
      "source": "same_species_inversion_center_projection_after_BEC",
      "spacegroup": "P-1",
      "spacegroup_number": 2,
      "pointgroup": "-1",
      "has_inversion": true,
      "is_polar_point_group": false,
      "nonpolar_parent_hypothesis": true,
      "symmetry_tolerance_A": null,
      "target_reduced_polarization": [
        0.0,
        0.0,
        0.0
      ],
      "formal_class": [
        0.0,
        0.0,
        0.0
      ],
      "target_residual": 8.478977215174753e-16,
      "parent_symmetrization_rmsd_A": 0.291237302139645,
      "parent_cell_rmsd_A": 0.002845017077719775,
      "energy_eV": -68.28676001461724,
      "reduced_polarization": [
        -2.2311928957825647e-16,
        6.148846153309183e-16,
        -5.395046233369729e-16
      ],
      "cartesian_polarization_e_A2": [
        -6.917157970098469e-18,
        1.5128172826690176e-17,
        -2.0104545467048788e-17
      ],
      "ranking_score": 0.29194855640907663
    },
    {
      "candidate_id": "bec_projection_01",
      "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": 2.0336006173121235e-05,
      "parent_symmetrization_rmsd_A": 0.13319387509601413,
      "parent_cell_rmsd_A": 0.015342176927994467,
      "energy_eV": -67.41378915818589,
      "reduced_polarization": [
        1.4784363505284592e-05,
        -3.734328325361838e-06,
        0.4999865452411848
      ],
      "cartesian_polarization_e_A2": [
        0.00928601829602417,
        0.00588865922542354,
        0.018718577358394647
      ],
      "ranking_score": 0.637070091340359
    },
    {
      "candidate_id": "bec_projection_02",
      "source": "MACEField_BEC_backprojection",
      "spacegroup": "P1",
      "spacegroup_number": 1,
      "pointgroup": "1",
      "has_inversion": false,
      "is_polar_point_group": true,
      "nonpolar_parent_hypothesis": false,
      "symmetry_tolerance_A": null,
      "target_reduced_polarization": [
        0.0,
        -0.5,
        0.0
      ],
      "formal_class": [
        0.0,
        0.5,
        0.0
      ],
      "target_residual": 6.179835835253788e-05,
      "parent_symmetrization_rmsd_A": 0.12003026410753287,
      "parent_cell_rmsd_A": 0.03715002254069573,
      "energy_eV": -67.51149352861952,
      "reduced_polarization": [
        -2.4179523086273034e-05,
        -0.5000449855282143,
        3.479497103992508e-05
      ],
      "cartesian_polarization_e_A2": [
        -0.009647316063466782,
        -0.017434128064310345,
        -0.00014416271520175923
      ],
      "ranking_score": 0.6294413664594118
    },
    {
      "candidate_id": "bec_projection_03",
      "source": "MACEField_BEC_backprojection",
      "spacegroup": "P1",
      "spacegroup_number": 1,
      "pointgroup": "1",
      "has_inversion": false,
      "is_polar_point_group": true,
      "nonpolar_parent_hypothesis": false,
      "symmetry_tolerance_A": null,
      "target_reduced_polarization": [
        -0.5,
        0.0,
        0.0
      ],
      "formal_class": [
        0.5,
        0.0,
        0.0
      ],
      "target_residual": 5.603670220911914e-05,
      "parent_symmetrization_rmsd_A": 0.1220950568979636,
      "parent_cell_rmsd_A": 0.03866575974362848,
      "energy_eV": -67.58179437289257,
      "reduced_polarization": [
        -0.4999566088806113,
        4.530960957956683e-07,
        3.54558522192726e-05
      ],
      "cartesian_polarization_e_A2": [
        -0.019820814318949925,
        1.3461708407110947e-05,
        -0.00010266208981103701
      ],
      "ranking_score": 0.6318735702382889
    },
    {
      "candidate_id": "bec_projection_04",
      "source": "MACEField_BEC_backprojection",
      "spacegroup": "P1",
      "spacegroup_number": 1,
      "pointgroup": "1",
      "has_inversion": false,
      "is_polar_point_group": true,
      "nonpolar_parent_hypothesis": false,
      "symmetry_tolerance_A": null,
      "target_reduced_polarization": [
        0.0,
        -0.5,
        0.5
      ],
      "formal_class": [
        0.0,
        0.5,
        0.5
      ],
      "target_residual": 4.2997619603162636e-05,
      "parent_symmetrization_rmsd_A": 0.12928765293164232,
      "parent_cell_rmsd_A": 0.03907950103869442,
      "energy_eV": -67.26966653299084,
      "reduced_polarization": [
        -2.0961881818748323e-05,
        -0.500033896150888,
        0.5000161383319192
      ],
      "cartesian_polarization_e_A2": [
        -0.0003045291041518807,
        -0.011472251503920441,
        0.0186286415874533
      ],
      "ranking_score": 0.6391435234305223
    },
    {
      "candidate_id": "bec_projection_05",
      "source": "MACEField_BEC_backprojection",
      "spacegroup": "P1",
      "spacegroup_number": 1,
      "pointgroup": "1",
      "has_inversion": false,
      "is_polar_point_group": true,
      "nonpolar_parent_hypothesis": false,
      "symmetry_tolerance_A": null,
      "target_reduced_polarization": [
        -0.5,
        0.0,
        0.5
      ],
      "formal_class": [
        0.5,
        0.0,
        0.5
      ],
      "target_residual": 0.0005108480699298262,
      "parent_symmetrization_rmsd_A": 0.1494831124248176,
      "parent_cell_rmsd_A": 0.03892965978621257,
      "energy_eV": -66.77879444138358,
      "reduced_polarization": [
        -0.5003012063756012,
        0.00040171496915589276,
        0.5000941570677343
      ],
      "cartesian_polarization_e_A2": [
        -0.010410736956961977,
        0.005911050409526852,
        0.018669373382544912
      ],
      "ranking_score": 0.6602372235112304
    },
    {
      "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": 3.215524105983172e-07,
      "parent_symmetrization_rmsd_A": 0.23055220063277504,
      "parent_cell_rmsd_A": 0.08653188135215052,
      "energy_eV": -64.22872159999807,
      "reduced_polarization": [
        -0.5000002640305764,
        -0.5000000668289317,
        -1.709318617787667e-07
      ],
      "cartesian_polarization_e_A2": [
        -0.029539881691499854,
        -0.017291883066249382,
        -0.0004660966892975427
      ],
      "ranking_score": 0.7521858140756339
    },
    {
      "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": 1.4901227957855717e-05,
      "parent_symmetrization_rmsd_A": 0.1897677421457719,
      "parent_cell_rmsd_A": 0.07916755439699945,
      "energy_eV": -64.40209901794958,
      "reduced_polarization": [
        -0.49999983565428113,
        -0.4999920678305951,
        0.5000126134956958
      ],
      "cartesian_polarization_e_A2": [
        -0.020052712422951733,
        -0.011328696819600447,
        0.018403848618400866
      ],
      "ranking_score": 0.7095894332009375
    }
  ],
  "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": [
              -0.00945592835261243,
              -0.028162692279892144,
              0.03324196566336734
            ],
            "branch_aligned_reduced_polarization": [
              -0.00945592835261243,
              -0.028162692279892144,
              0.03324196566336734
            ],
            "target_residual": 0.04458228458284893,
            "energy_eV": -68.82981663392609,
            "max_atomic_step_A": 0.014182574496025148,
            "max_log_strain_component": 0.00040109966102791955,
            "step_scale": 1.0,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 1.113561068778823,
            "cell_principal_stretches": [
              1.0006948569406278,
              0.9999411423805108,
              0.9996250174028755
            ],
            "cell_volume_ratio": 1.0002607373530477,
            "cell_rmsd_from_input_A": 0.002845017077719775
          },
          {
            "iteration": 1,
            "reduced_polarization": [
              -7.866805304276179e-06,
              1.2525390150343625e-05,
              2.233811355788911e-05
            ],
            "branch_aligned_reduced_polarization": [
              -7.866805304276179e-06,
              1.2525390150343625e-05,
              2.233811355788911e-05
            ],
            "target_residual": 2.6791105640470724e-05,
            "energy_eV": -68.82334725897134
          }
        ],
        "iterations": 1
      },
      "parent": {
        "candidate_id": "inversion_parent_endpoint_00",
        "source": "same_species_inversion_center_projection_from_endpoint",
        "spacegroup": "P-1",
        "spacegroup_number": 2,
        "pointgroup": "-1",
        "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": 2.8320640545438903e-15,
        "parent_symmetrization_rmsd_A": 0.2912369756967939,
        "parent_cell_rmsd_A": 0.0,
        "energy_eV": -68.2883712202584,
        "reduced_polarization": [
          -1.002079441029645e-15,
          -1.123366079228811e-15,
          2.3988481100193447e-15
        ],
        "cartesian_polarization_e_A2": [
          -1.684941351390253e-17,
          -1.1000651068160885e-17,
          8.93989561919319e-17
        ],
        "ranking_score": 0.29123697569679957
      },
      "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": [
          -68.82981663392609,
          -68.80341538139626,
          -68.74007010616377,
          -68.65543413700053,
          -68.56061089735297,
          -68.46043905939382,
          -68.36838800170501,
          -68.30900905646921,
          -68.28837122025837
        ],
        "cartesian_polarizations_e_A2": [
          [
            -0.0003023474694776208,
            -0.000592249095103824,
            0.0012388433513821492
          ],
          [
            0.0006538540778202915,
            -0.0006477936714786557,
            0.0004205312331839123
          ],
          [
            0.0016116073682361433,
            -0.0006721485340824353,
            -0.0003433540676029421
          ],
          [
            0.0024979715231221375,
            -0.000659151981822529,
            -0.001017168060860195
          ],
          [
            0.003177171429123984,
            -0.0005789371541540105,
            -0.0015386394870854473
          ],
          [
            0.003440540040504551,
            -0.00038270187804293143,
            -0.0018031194830549382
          ],
          [
            0.0030274035801117014,
            -0.00010555765320946084,
            -0.0016675791925681697
          ],
          [
            0.0018252449835254813,
            3.276048593691271e-05,
            -0.0010317136677560456
          ],
          [
            -3.402237558863333e-17,
            -2.762606942456693e-17,
            7.426683888550245e-17
          ]
        ],
        "raw_reduced_polarization": [
          [
            -0.009455928352612605,
            -0.028162692279892904,
            0.03324196566336755
          ],
          [
            0.022188525630470593,
            -0.022354509544492116,
            0.011284142420651372
          ],
          [
            0.052989895996117725,
            -0.016145193587814723,
            -0.009213242427220929
          ],
          [
            0.08072604620480688,
            -0.009680565666943171,
            -0.027293737917118203
          ],
          [
            0.10103576733972988,
            -0.0026683048545483117,
            -0.04128641522023903
          ],
          [
            0.10710269908380034,
            0.00534303387248941,
            -0.04838322446158221
          ],
          [
            0.09165933358042198,
            0.012054667561894711,
            -0.04474626287371302
          ],
          [
            0.05412437568678491,
            0.010266667052668274,
            -0.02768404114992423
          ],
          [
            -1.0794133276883535e-15,
            -1.4626823147200249e-15,
            1.992807004537229e-15
          ]
        ],
        "unwrapped_reduced_polarization": [
          [
            -0.009455928352612605,
            -0.028162692279892904,
            0.03324196566336755
          ],
          [
            0.022188525630470596,
            -0.022354509544492116,
            0.011284142420651372
          ],
          [
            0.052989895996117725,
            -0.016145193587814723,
            -0.009213242427220929
          ],
          [
            0.08072604620480688,
            -0.009680565666943171,
            -0.027293737917118203
          ],
          [
            0.10103576733972988,
            -0.002668304854548312,
            -0.04128641522023903
          ],
          [
            0.10710269908380034,
            0.005343033872489409,
            -0.04838322446158221
          ],
          [
            0.09165933358042198,
            0.012054667561894711,
            -0.04474626287371302
          ],
          [
            0.05412437568678491,
            0.010266667052668274,
            -0.02768404114992423
          ],
          [
            -1.0824674490095276e-15,
            -1.4623718902484484e-15,
            1.9914625504213745e-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": [
          [
            -0.009455928352612608,
            -0.028162692279892876,
            0.03324196566336757
          ],
          [
            0.02218852563047058,
            -0.02235450954449214,
            0.011284142420651344
          ],
          [
            0.0529898959961177,
            -0.016145193587814743,
            -0.009213242427220936
          ],
          [
            0.08072604620480683,
            -0.009680565666943197,
            -0.0272937379171182
          ],
          [
            0.10103576733972985,
            -0.0026683048545483312,
            -0.041286415220239014
          ],
          [
            0.10710269908380032,
            0.005343033872489356,
            -0.04838322446158222
          ],
          [
            0.091659333580422,
            0.01205466756189466,
            -0.04474626287371303
          ],
          [
            0.054124375686784854,
            0.010266667052668321,
            -0.027684041149924232
          ],
          [
            -1.1102230246251565e-15,
            -1.4432899320127035e-15,
            1.9984014443252818e-15
          ]
        ]
      },
      "reflected": {
        "reached": true,
        "construction": "reflect_displacements_about_reconstructed_parent",
        "energies_eV": [
          -68.28837122025837,
          -68.3090090564692,
          -68.36838800170503,
          -68.46043905939382,
          -68.56061089735297,
          -68.65543413700053,
          -68.74007010616376,
          -68.80341538139626,
          -68.82981663392607
        ],
        "cartesian_polarizations_e_A2": [
          [
            -3.402237558863333e-17,
            -2.762606942456693e-17,
            7.426683888550245e-17
          ],
          [
            -0.0018252449835254375,
            -3.2760485936988597e-05,
            0.00103171366775598
          ],
          [
            -0.003027403580111808,
            0.00010555765320944922,
            0.0016675791925682343
          ],
          [
            -0.003440540040504537,
            0.00038270187804283255,
            0.0018031194830549673
          ],
          [
            -0.003177171429123939,
            0.0005789371541539335,
            0.0015386394870853897
          ],
          [
            -0.0024979715231222533,
            0.0006591519818225116,
            0.0010171680608602309
          ],
          [
            -0.0016116073682361847,
            0.0006721485340824658,
            0.0003433540676029688
          ],
          [
            -0.0006538540778202597,
            0.0006477936714786091,
            -0.00042053123318382075
          ],
          [
            0.000302347469477685,
            0.0005922490951038158,
            -0.0012388433513821572
          ]
        ],
        "raw_reduced_polarization": [
          [
            -1.0794133276883535e-15,
            -1.4626823147200249e-15,
            1.992807004537229e-15
          ],
          [
            -0.054124375686782196,
            -0.010266667052669855,
            0.02768404114992247
          ],
          [
            -0.09165933358042505,
            -0.012054667561895629,
            0.04474626287371475
          ],
          [
            -0.10710269908379885,
            -0.005343033872492509,
            0.048383224461582997
          ],
          [
            -0.1010357673397272,
            0.002668304854546628,
            0.04128641522023748
          ],
          [
            -0.08072604620480987,
            0.009680565666942352,
            0.02729373791711916
          ],
          [
            -0.05298989599611941,
            0.016145193587815354,
            0.009213242427221642
          ],
          [
            -0.022188525630469885,
            0.022354509544489955,
            -0.011284142420648915
          ],
          [
            0.009455928352614405,
            0.02816269227989274,
            -0.03324196566336776
          ]
        ],
        "unwrapped_reduced_polarization": [
          [
            -1.0794133276883535e-15,
            -1.4626823147200249e-15,
            1.992807004537229e-15
          ],
          [
            -0.054124375686782196,
            -0.010266667052669855,
            0.02768404114992247
          ],
          [
            -0.09165933358042505,
            -0.012054667561895629,
            0.04474626287371475
          ],
          [
            -0.10710269908379885,
            -0.005343033872492509,
            0.048383224461582997
          ],
          [
            -0.1010357673397272,
            0.0026683048545466277,
            0.04128641522023748
          ],
          [
            -0.08072604620480987,
            0.009680565666942352,
            0.02729373791711916
          ],
          [
            -0.05298989599611941,
            0.016145193587815354,
            0.00921324242722164
          ],
          [
            -0.022188525630469885,
            0.022354509544489955,
            -0.011284142420648915
          ],
          [
            0.009455928352614405,
            0.02816269227989274,
            -0.03324196566336776
          ]
        ],
        "gauge_integer_shift": [
          0,
          0,
          0
        ],
        "expected_opposite_endpoint_reduced_polarization": [
          0.009455928352610441,
          0.02816269227988998,
          -0.03324196566336356
        ],
        "actual_opposite_endpoint_branch_residual": 6.404740264709041e-15
      },
      "pnp_branch": {
        "construction": "incoming_path_concatenated_with_parent_reflection",
        "reduced_polarization": [
          [
            -0.009455928352612605,
            -0.028162692279892904,
            0.03324196566336755
          ],
          [
            0.022188525630470593,
            -0.022354509544492116,
            0.011284142420651372
          ],
          [
            0.052989895996117725,
            -0.016145193587814723,
            -0.009213242427220929
          ],
          [
            0.08072604620480688,
            -0.009680565666943171,
            -0.027293737917118203
          ],
          [
            0.10103576733972988,
            -0.0026683048545483117,
            -0.04128641522023903
          ],
          [
            0.10710269908380034,
            0.00534303387248941,
            -0.04838322446158221
          ],
          [
            0.09165933358042198,
            0.012054667561894711,
            -0.04474626287371302
          ],
          [
            0.05412437568678491,
            0.010266667052668274,
            -0.02768404114992423
          ],
          [
            -1.0794133276883535e-15,
            -1.4626823147200249e-15,
            1.992807004537229e-15
          ],
          [
            -0.054124375686782196,
            -0.010266667052669855,
            0.02768404114992247
          ],
          [
            -0.09165933358042505,
            -0.012054667561895629,
            0.04474626287371475
          ],
          [
            -0.10710269908379885,
            -0.005343033872492509,
            0.048383224461582997
          ],
          [
            -0.1010357673397272,
            0.002668304854546628,
            0.04128641522023748
          ],
          [
            -0.08072604620480987,
            0.009680565666942352,
            0.02729373791711916
          ],
          [
            -0.05298989599611941,
            0.016145193587815354,
            0.009213242427221642
          ],
          [
            -0.022188525630469885,
            0.022354509544489955,
            -0.011284142420648915
          ],
          [
            0.009455928352614405,
            0.02816269227989274,
            -0.03324196566336776
          ]
        ],
        "unwrapped_reduced_polarization": [
          [
            -0.009455928352612605,
            -0.028162692279892904,
            0.03324196566336755
          ],
          [
            0.022188525630470596,
            -0.022354509544492116,
            0.011284142420651372
          ],
          [
            0.052989895996117725,
            -0.016145193587814723,
            -0.009213242427220929
          ],
          [
            0.08072604620480688,
            -0.009680565666943171,
            -0.027293737917118203
          ],
          [
            0.10103576733972988,
            -0.002668304854548312,
            -0.04128641522023903
          ],
          [
            0.10710269908380034,
            0.005343033872489409,
            -0.04838322446158221
          ],
          [
            0.09165933358042198,
            0.012054667561894711,
            -0.04474626287371302
          ],
          [
            0.05412437568678491,
            0.010266667052668274,
            -0.02768404114992423
          ],
          [
            -1.0824674490095276e-15,
            -1.4623718902484484e-15,
            1.9914625504213745e-15
          ],
          [
            -0.054124375686782196,
            -0.010266667052669855,
            0.02768404114992247
          ],
          [
            -0.09165933358042505,
            -0.012054667561895629,
            0.04474626287371475
          ],
          [
            -0.10710269908379885,
            -0.005343033872492509,
            0.048383224461582997
          ],
          [
            -0.1010357673397272,
            0.0026683048545466277,
            0.04128641522023748
          ],
          [
            -0.08072604620480987,
            0.009680565666942352,
            0.02729373791711916
          ],
          [
            -0.05298989599611941,
            0.016145193587815354,
            0.00921324242722164
          ],
          [
            -0.022188525630469885,
            0.022354509544489955,
            -0.011284142420648915
          ],
          [
            0.009455928352614405,
            0.02816269227989274,
            -0.03324196566336776
          ]
        ],
        "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": [
          [
            -0.009455928352612608,
            -0.028162692279892876,
            0.03324196566336757
          ],
          [
            0.02218852563047058,
            -0.02235450954449214,
            0.011284142420651344
          ],
          [
            0.0529898959961177,
            -0.016145193587814743,
            -0.009213242427220936
          ],
          [
            0.08072604620480683,
            -0.009680565666943197,
            -0.0272937379171182
          ],
          [
            0.10103576733972985,
            -0.0026683048545483312,
            -0.041286415220239014
          ],
          [
            0.10710269908380032,
            0.005343033872489356,
            -0.04838322446158222
          ],
          [
            0.091659333580422,
            0.01205466756189466,
            -0.04474626287371303
          ],
          [
            0.054124375686784854,
            0.010266667052668321,
            -0.027684041149924232
          ],
          [
            -1.1102230246251565e-15,
            -1.4432899320127035e-15,
            1.9984014443252818e-15
          ],
          [
            -0.05412437568678219,
            -0.010266667052669876,
            0.02768404114992251
          ],
          [
            -0.09165933358042505,
            -0.012054667561895605,
            0.04474626287371475
          ],
          [
            -0.10710269908379888,
            -0.00534303387249252,
            0.04838322446158294
          ],
          [
            -0.10103576733972719,
            0.0026683048545466104,
            0.04128641522023746
          ],
          [
            -0.08072604620480989,
            0.009680565666942309,
            0.0272937379171192
          ],
          [
            -0.05298989599611942,
            0.01614519358781541,
            0.009213242427221657
          ],
          [
            -0.022188525630469913,
            0.02235450954448992,
            -0.011284142420648902
          ],
          [
            0.00945592835261444,
            0.028162692279892765,
            -0.03324196566336779
          ]
        ]
      },
      "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": [
              -0.00945592835261243,
              -0.028162692279892144,
              0.03324196566336734
            ],
            "branch_aligned_reduced_polarization": [
              -0.00945592835261243,
              -0.028162692279892144,
              0.033241965663367345
            ],
            "target_residual": 0.4677024849573271,
            "energy_eV": -68.82981663392609,
            "max_atomic_step_A": 0.12,
            "max_log_strain_component": 0.0015571015823797932,
            "step_scale": 0.5794581715806744,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 1.113561068778823,
            "cell_principal_stretches": [
              1.0010244769906473,
              0.9991460091949589,
              0.9982274342034884
            ],
            "cell_volume_ratio": 0.9983967448479899,
            "cell_rmsd_from_input_A": 0.008157691172568165
          },
          {
            "iteration": 1,
            "reduced_polarization": [
              -0.005822047099287902,
              -0.010816653271969017,
              0.3001581062205628
            ],
            "branch_aligned_reduced_polarization": [
              -0.005822047099287902,
              -0.010816653271969017,
              0.3001581062205628
            ],
            "target_residual": 0.20021907683780826,
            "energy_eV": -68.4024049767245,
            "max_atomic_step_A": 0.0870916802520144,
            "max_log_strain_component": 0.0012688849742350954,
            "step_scale": 1.0,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 1.113561068778823,
            "cell_principal_stretches": [
              1.0018435838168123,
              0.9984709224571303,
              0.9968142706674016
            ],
            "cell_volume_ratio": 0.9971249650073845,
            "cell_rmsd_from_input_A": 0.01491538462147366
          },
          {
            "iteration": 2,
            "reduced_polarization": [
              -0.001805644817314532,
              0.0013022475264641378,
              0.4907742095781106
            ],
            "branch_aligned_reduced_polarization": [
              -0.001805644817314532,
              0.0013022475264641378,
              0.4907742095781106
            ],
            "target_residual": 0.009490595910431728,
            "energy_eV": -67.47179301397638,
            "max_atomic_step_A": 0.003534598241392967,
            "max_log_strain_component": 7.567827304509084e-05,
            "step_scale": 1.0,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 1.113561068778823,
            "cell_principal_stretches": [
              1.0018811771753349,
              0.9984313075928549,
              0.9967430305526961
            ],
            "cell_volume_ratio": 0.9970515561904703,
            "cell_rmsd_from_input_A": 0.015342176927994467
          },
          {
            "iteration": 3,
            "reduced_polarization": [
              1.4784363505284592e-05,
              -3.734328325361838e-06,
              0.4999865452411848
            ],
            "branch_aligned_reduced_polarization": [
              1.4784363505284592e-05,
              -3.734328325361838e-06,
              0.4999865452411848
            ],
            "target_residual": 2.0336006173121235e-05,
            "energy_eV": -67.41378915818589
          }
        ],
        "iterations": 3
      },
      "parent": {
        "candidate_id": "bec_projection_01",
        "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": 2.0336006173121235e-05,
        "parent_symmetrization_rmsd_A": 0.13319387509601413,
        "parent_cell_rmsd_A": 0.015342176927994467,
        "energy_eV": -67.41378915818589,
        "reduced_polarization": [
          1.4784363505284592e-05,
          -3.734328325361838e-06,
          0.4999865452411848
        ],
        "cartesian_polarization_e_A2": [
          0.00928601829602417,
          0.00588865922542354,
          0.018718577358394647
        ],
        "ranking_score": 0.637070091340359
      },
      "branch_status": "awaiting_branch_sampling"
    },
    {
      "orbit_id": 2,
      "formal_class": [
        0.0,
        0.5,
        0.0
      ],
      "formal_classes_in_orbit": [
        [
          0.0,
          0.5,
          0.0
        ]
      ],
      "target_reduced_polarization": [
        0.0,
        -0.5,
        0.0
      ],
      "bec_backprojection": {
        "converged_to_target": true,
        "history": [
          {
            "iteration": 0,
            "reduced_polarization": [
              -0.00945592835261243,
              -0.028162692279892144,
              0.03324196566336734
            ],
            "branch_aligned_reduced_polarization": [
              -0.00945592835261243,
              -0.028162692279892154,
              0.03324196566336734
            ],
            "target_residual": 0.47310135047232105,
            "energy_eV": -68.82981663392609,
            "max_atomic_step_A": 0.12,
            "max_log_strain_component": 0.003505792533879178,
            "step_scale": 0.5647684075367634,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 1.113561068778823,
            "cell_principal_stretches": [
              1.0030327480301378,
              1.001849195766744,
              0.9947823644289084
            ],
            "cell_volume_ratio": 0.9996444149057426,
            "cell_rmsd_from_input_A": 0.02014028031526261
          },
          {
            "iteration": 1,
            "reduced_polarization": [
              -0.0052433598901271165,
              -0.2918887680647801,
              0.015007179532842488
            ],
            "branch_aligned_reduced_polarization": [
              -0.0052433598901271165,
              -0.2918887680647801,
              0.015007179532842488
            ],
            "target_residual": 0.20871749595580927,
            "energy_eV": -68.43493895708224,
            "max_atomic_step_A": 0.09293084533643058,
            "max_log_strain_component": 0.0029041548746063734,
            "step_scale": 1.0,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 1.113561068778823,
            "cell_principal_stretches": [
              1.0055555011718933,
              1.0033623727666583,
              0.9904889501320339
            ],
            "cell_volume_ratio": 0.9993405077294516,
            "cell_rmsd_from_input_A": 0.03672158736839671
          },
          {
            "iteration": 2,
            "reduced_polarization": [
              -0.0008527907222849109,
              -0.4947031283879827,
              0.00012831514557380038
            ],
            "branch_aligned_reduced_polarization": [
              -0.0008527907222849109,
              -0.4947031283879827,
              0.00012831514557380038
            ],
            "target_residual": 0.005366615848632512,
            "energy_eV": -67.539455943808,
            "max_atomic_step_A": 0.0020949908046170936,
            "max_log_strain_component": 8.15869149087772e-05,
            "step_scale": 1.0,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 1.113561068778823,
            "cell_principal_stretches": [
              1.0056291953604923,
              1.003395852440386,
              0.9903731784065433
            ],
            "cell_volume_ratio": 0.999330275573652,
            "cell_rmsd_from_input_A": 0.03715002254069573
          },
          {
            "iteration": 3,
            "reduced_polarization": [
              -2.4179523086273034e-05,
              -0.5000449855282143,
              3.479497103992508e-05
            ],
            "branch_aligned_reduced_polarization": [
              -2.4179523086273034e-05,
              -0.5000449855282143,
              3.479497103992508e-05
            ],
            "target_residual": 6.179835835253788e-05,
            "energy_eV": -67.51149352861952
          }
        ],
        "iterations": 3
      },
      "parent": {
        "candidate_id": "bec_projection_02",
        "source": "MACEField_BEC_backprojection",
        "spacegroup": "P1",
        "spacegroup_number": 1,
        "pointgroup": "1",
        "has_inversion": false,
        "is_polar_point_group": true,
        "nonpolar_parent_hypothesis": false,
        "symmetry_tolerance_A": null,
        "target_reduced_polarization": [
          0.0,
          -0.5,
          0.0
        ],
        "formal_class": [
          0.0,
          0.5,
          0.0
        ],
        "target_residual": 6.179835835253788e-05,
        "parent_symmetrization_rmsd_A": 0.12003026410753287,
        "parent_cell_rmsd_A": 0.03715002254069573,
        "energy_eV": -67.51149352861952,
        "reduced_polarization": [
          -2.4179523086273034e-05,
          -0.5000449855282143,
          3.479497103992508e-05
        ],
        "cartesian_polarization_e_A2": [
          -0.009647316063466782,
          -0.017434128064310345,
          -0.00014416271520175923
        ],
        "ranking_score": 0.6294413664594118
      },
      "branch_status": "awaiting_branch_sampling"
    },
    {
      "orbit_id": 3,
      "formal_class": [
        0.5,
        0.0,
        0.0
      ],
      "formal_classes_in_orbit": [
        [
          0.5,
          0.0,
          0.0
        ]
      ],
      "target_reduced_polarization": [
        -0.5,
        0.0,
        0.0
      ],
      "bec_backprojection": {
        "converged_to_target": true,
        "history": [
          {
            "iteration": 0,
            "reduced_polarization": [
              -0.00945592835261243,
              -0.028162692279892144,
              0.03324196566336734
            ],
            "branch_aligned_reduced_polarization": [
              -0.009455928352612442,
              -0.028162692279892144,
              0.03324196566336734
            ],
            "target_residual": 0.4924750265201411,
            "energy_eV": -68.82981663392609,
            "max_atomic_step_A": 0.12000000000000001,
            "max_log_strain_component": 0.0027776831946526,
            "step_scale": 0.5523608581193775,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 1.113561068778823,
            "cell_principal_stretches": [
              1.0032994323355304,
              0.9993341858286049,
              0.9972534302684601
            ],
            "cell_volume_ratio": 0.9998776242415438,
            "cell_rmsd_from_input_A": 0.02036200007215197
          },
          {
            "iteration": 1,
            "reduced_polarization": [
              -0.27822157150296595,
              -0.01184966805336944,
              0.014619509194798397
            ],
            "branch_aligned_reduced_polarization": [
              -0.27822157150296595,
              -0.01184966805336944,
              0.014619509194798397
            ],
            "target_residual": 0.22257541649671442,
            "energy_eV": -68.46441544194019,
            "max_atomic_step_A": 0.09652290968101135,
            "max_log_strain_component": 0.002394995268235285,
            "step_scale": 1.0,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 1.113561068778823,
            "cell_principal_stretches": [
              1.0061506228685058,
              0.9987750791516743,
              0.9948755310311524
            ],
            "cell_volume_ratio": 0.999768496025882,
            "cell_rmsd_from_input_A": 0.03801829760713799
          },
          {
            "iteration": 2,
            "reduced_polarization": [
              -0.4929551397018924,
              -0.0009421298212672452,
              0.0030738233388455938
            ],
            "branch_aligned_reduced_polarization": [
              -0.4929551397018924,
              -0.0009421298212672452,
              0.0030738233388455938
            ],
            "target_residual": 0.007743775251026166,
            "energy_eV": -67.62167897867752,
            "max_atomic_step_A": 0.003213582070610012,
            "max_log_strain_component": 8.216189797005332e-05,
            "step_scale": 1.0,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 1.113561068778823,
            "cell_principal_stretches": [
              1.0062575920763506,
              0.9987620671656539,
              0.9948007137714969
            ],
            "cell_volume_ratio": 0.9997865681657975,
            "cell_rmsd_from_input_A": 0.03866575974362848
          },
          {
            "iteration": 3,
            "reduced_polarization": [
              -0.4999566088806113,
              4.530960957956683e-07,
              3.54558522192726e-05
            ],
            "branch_aligned_reduced_polarization": [
              -0.4999566088806113,
              4.530960957956683e-07,
              3.54558522192726e-05
            ],
            "target_residual": 5.603670220911914e-05,
            "energy_eV": -67.58179437289257
          }
        ],
        "iterations": 3
      },
      "parent": {
        "candidate_id": "bec_projection_03",
        "source": "MACEField_BEC_backprojection",
        "spacegroup": "P1",
        "spacegroup_number": 1,
        "pointgroup": "1",
        "has_inversion": false,
        "is_polar_point_group": true,
        "nonpolar_parent_hypothesis": false,
        "symmetry_tolerance_A": null,
        "target_reduced_polarization": [
          -0.5,
          0.0,
          0.0
        ],
        "formal_class": [
          0.5,
          0.0,
          0.0
        ],
        "target_residual": 5.603670220911914e-05,
        "parent_symmetrization_rmsd_A": 0.1220950568979636,
        "parent_cell_rmsd_A": 0.03866575974362848,
        "energy_eV": -67.58179437289257,
        "reduced_polarization": [
          -0.4999566088806113,
          4.530960957956683e-07,
          3.54558522192726e-05
        ],
        "cartesian_polarization_e_A2": [
          -0.019820814318949925,
          1.3461708407110947e-05,
          -0.00010266208981103701
        ],
        "ranking_score": 0.6318735702382889
      },
      "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": [
              -0.00945592835261243,
              -0.028162692279892144,
              0.03324196566336734
            ],
            "branch_aligned_reduced_polarization": [
              -0.00945592835261243,
              -0.028162692279892154,
              0.033241965663367345
            ],
            "target_residual": 0.6637642067446592,
            "energy_eV": -68.82981663392609,
            "max_atomic_step_A": 0.11999999999999998,
            "max_log_strain_component": 0.0036310647756897245,
            "step_scale": 0.5835151047667815,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 1.113561068778823,
            "cell_principal_stretches": [
              1.0031187180208676,
              1.0004486914699127,
              0.9943183925091097
            ],
            "cell_volume_ratio": 0.9978669247710642,
            "cell_rmsd_from_input_A": 0.021931266875013
          },
          {
            "iteration": 1,
            "reduced_polarization": [
              -0.004703714179973174,
              -0.3002386486376193,
              0.30442276932159185
            ],
            "branch_aligned_reduced_polarization": [
              -0.004703714179973174,
              -0.3002386486376193,
              0.30442276932159185
            ],
            "target_residual": 0.2796018161333125,
            "energy_eV": -68.34694647805094,
            "max_atomic_step_A": 0.08438150653386146,
            "max_log_strain_component": 0.002794436436086525,
            "step_scale": 1.0,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 1.113561068778823,
            "cell_principal_stretches": [
              1.005521350003793,
              1.0008167644154817,
              0.9899765798860752
            ],
            "cell_volume_ratio": 0.9962556291619653,
            "cell_rmsd_from_input_A": 0.038691097122943996
          },
          {
            "iteration": 2,
            "reduced_polarization": [
              -0.0015629432343284835,
              -0.4949722094154288,
              0.4953339529826085
            ],
            "branch_aligned_reduced_polarization": [
              -0.0015629432343284835,
              -0.4949722094154288,
              0.4953339529826085
            ],
            "target_residual": 0.007035159165544442,
            "energy_eV": -67.30219556746002,
            "max_atomic_step_A": 0.0020117864464803997,
            "max_log_strain_component": 7.421335336516612e-05,
            "step_scale": 1.0,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 1.113561068778823,
            "cell_principal_stretches": [
              1.0055847498656758,
              1.0008171298568969,
              0.9898713012823973
            ],
            "cell_volume_ratio": 0.9962128555379212,
            "cell_rmsd_from_input_A": 0.03907950103869442
          },
          {
            "iteration": 3,
            "reduced_polarization": [
              -2.0961881818748323e-05,
              -0.500033896150888,
              0.5000161383319192
            ],
            "branch_aligned_reduced_polarization": [
              -2.0961881818748323e-05,
              -0.500033896150888,
              0.5000161383319192
            ],
            "target_residual": 4.2997619603162636e-05,
            "energy_eV": -67.26966653299084
          }
        ],
        "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": [
          0.0,
          -0.5,
          0.5
        ],
        "formal_class": [
          0.0,
          0.5,
          0.5
        ],
        "target_residual": 4.2997619603162636e-05,
        "parent_symmetrization_rmsd_A": 0.12928765293164232,
        "parent_cell_rmsd_A": 0.03907950103869442,
        "energy_eV": -67.26966653299084,
        "reduced_polarization": [
          -2.0961881818748323e-05,
          -0.500033896150888,
          0.5000161383319192
        ],
        "cartesian_polarization_e_A2": [
          -0.0003045291041518807,
          -0.011472251503920441,
          0.0186286415874533
        ],
        "ranking_score": 0.6391435234305223
      },
      "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": [
              -0.00945592835261243,
              -0.028162692279892144,
              0.03324196566336734
            ],
            "branch_aligned_reduced_polarization": [
              -0.009455928352612442,
              -0.028162692279892144,
              0.033241965663367345
            ],
            "target_residual": 0.6777091456389285,
            "energy_eV": -68.82981663392609,
            "max_atomic_step_A": 0.12,
            "max_log_strain_component": 0.002584682627794042,
            "step_scale": 0.4933774490833917,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 1.113561068778823,
            "cell_principal_stretches": [
              1.0027439812097838,
              0.9983514334258435,
              0.9973092095178246
            ],
            "cell_volume_ratio": 0.9983971651586305,
            "cell_rmsd_from_input_A": 0.017012125313730805
          },
          {
            "iteration": 1,
            "reduced_polarization": [
              -0.24663841108926576,
              -0.014986581191096124,
              0.26012415377991444
            ],
            "branch_aligned_reduced_polarization": [
              -0.24663841108926576,
              -0.014986581191096124,
              0.26012415377991444
            ],
            "target_residual": 0.34922358733477804,
            "energy_eV": -68.43394102829889,
            "max_atomic_step_A": 0.12,
            "max_log_strain_component": 0.0029224739925354393,
            "step_scale": 0.9729454372137984,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 1.113561068778823,
            "cell_principal_stretches": [
              1.0058672113718872,
              0.9963989148255564,
              0.9943978988152541
            ],
            "cell_volume_ratio": 0.9966303199795863,
            "cell_rmsd_from_input_A": 0.03615030380420857
          },
          {
            "iteration": 2,
            "reduced_polarization": [
              -0.4686020053561434,
              -0.01015315873738913,
              0.4761989664485331
            ],
            "branch_aligned_reduced_polarization": [
              -0.4686020053561434,
              -0.01015315873738913,
              0.4761989664485331
            ],
            "target_residual": 0.04068672877143508,
            "energy_eV": -67.03318843335941,
            "max_atomic_step_A": 0.013290042494701795,
            "max_log_strain_component": 0.000456374251979897,
            "step_scale": 1.0,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 1.113561068778823,
            "cell_principal_stretches": [
              1.0063707519393426,
              0.9959593785844527,
              0.9940858864564649
            ],
            "cell_volume_ratio": 0.9963766467669609,
            "cell_rmsd_from_input_A": 0.03892965978621257
          },
          {
            "iteration": 3,
            "reduced_polarization": [
              -0.5003012063756012,
              0.00040171496915589276,
              0.5000941570677343
            ],
            "branch_aligned_reduced_polarization": [
              -0.5003012063756012,
              0.00040171496915589276,
              0.5000941570677343
            ],
            "target_residual": 0.0005108480699298262,
            "energy_eV": -66.77879444138358
          }
        ],
        "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": [
          -0.5,
          0.0,
          0.5
        ],
        "formal_class": [
          0.5,
          0.0,
          0.5
        ],
        "target_residual": 0.0005108480699298262,
        "parent_symmetrization_rmsd_A": 0.1494831124248176,
        "parent_cell_rmsd_A": 0.03892965978621257,
        "energy_eV": -66.77879444138358,
        "reduced_polarization": [
          -0.5003012063756012,
          0.00040171496915589276,
          0.5000941570677343
        ],
        "cartesian_polarization_e_A2": [
          -0.010410736956961977,
          0.005911050409526852,
          0.018669373382544912
        ],
        "ranking_score": 0.6602372235112304
      },
      "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": [
              -0.00945592835261243,
              -0.028162692279892144,
              0.03324196566336734
            ],
            "branch_aligned_reduced_polarization": [
              -0.009455928352612442,
              -0.028162692279892154,
              0.03324196566336734
            ],
            "target_residual": 0.6814462263936323,
            "energy_eV": -68.82981663392609,
            "max_atomic_step_A": 0.11999999999999998,
            "max_log_strain_component": 0.002861704187618855,
            "step_scale": 0.3345143503057702,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 1.113561068778823,
            "cell_principal_stretches": [
              1.0032376130526393,
              1.0012827133811888,
              0.9951256665192383
            ],
            "cell_volume_ratio": 0.9996280920614077,
            "cell_rmsd_from_input_A": 0.02374711725988842
          },
          {
            "iteration": 1,
            "reduced_polarization": [
              -0.17251815856551292,
              -0.18345707142684334,
              0.021833036151352868
            ],
            "branch_aligned_reduced_polarization": [
              -0.1725181585655129,
              -0.1834570714268433,
              0.021833036151352868
            ],
            "target_residual": 0.4559829641188138,
            "energy_eV": -68.42689500764821,
            "max_atomic_step_A": 0.12000000000000001,
            "max_log_strain_component": 0.0030946187828663273,
            "step_scale": 0.5065255523556443,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 1.113561068778823,
            "cell_principal_stretches": [
              1.0067429084622592,
              1.0026818703075717,
              0.9898547738500746
            ],
            "cell_volume_ratio": 0.9992018362515916,
            "cell_rmsd_from_input_A": 0.049497440246950734
          },
          {
            "iteration": 2,
            "reduced_polarization": [
              -0.3289631001798611,
              -0.3387743835531241,
              0.013912349883980156
            ],
            "branch_aligned_reduced_polarization": [
              -0.3289631001798611,
              -0.3387743835531241,
              0.013912349883980156
            ],
            "target_residual": 0.2354588583554538,
            "energy_eV": -67.09804752983038,
            "max_atomic_step_A": 0.1093830427567742,
            "max_log_strain_component": 0.003985637504291401,
            "step_scale": 1.0,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 1.113561068778823,
            "cell_principal_stretches": [
              1.0112975129457904,
              1.004404205371569,
              0.9832332702683574
            ],
            "cell_volume_ratio": 0.9987206444306534,
            "cell_rmsd_from_input_A": 0.0826067053255131
          },
          {
            "iteration": 3,
            "reduced_polarization": [
              -0.4753822746754524,
              -0.49747187176880153,
              0.014416730278486077
            ],
            "branch_aligned_reduced_polarization": [
              -0.4753822746754524,
              -0.49747187176880153,
              0.014416730278486077
            ],
            "target_residual": 0.0286402853412963,
            "energy_eV": -64.4472819100973,
            "max_atomic_step_A": 0.01456709059224123,
            "max_log_strain_component": 0.0005740173638874353,
            "step_scale": 1.0,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 1.113561068778823,
            "cell_principal_stretches": [
              1.0120065695418548,
              1.0045075052553905,
              0.9825232090061258
            ],
            "cell_volume_ratio": 0.998801844606737,
            "cell_rmsd_from_input_A": 0.08716084738535651
          },
          {
            "iteration": 4,
            "reduced_polarization": [
              -0.4991412916565061,
              -0.5011744989785243,
              0.0012071214171490222
            ],
            "branch_aligned_reduced_polarization": [
              -0.4991412916565061,
              -0.5011744989785243,
              0.0012071214171490222
            ],
            "target_residual": 0.0018904946404262738,
            "energy_eV": -64.22668902170635,
            "max_atomic_step_A": 0.0005045757392045888,
            "max_log_strain_component": 7.527372354237597e-05,
            "step_scale": 1.0,
            "strain_jacobian_refreshed": true,
            "strain_jacobian_frobenius_norm": 3.636702070139241,
            "cell_principal_stretches": [
              1.011901703747829,
              1.0045058554854118,
              0.982589725086922
            ],
            "cell_volume_ratio": 0.9987643178933473,
            "cell_rmsd_from_input_A": 0.08653188135215052
          },
          {
            "iteration": 5,
            "reduced_polarization": [
              -0.5000002640305764,
              -0.5000000668289317,
              -1.709318617787667e-07
            ],
            "branch_aligned_reduced_polarization": [
              -0.5000002640305764,
              -0.5000000668289317,
              -1.709318617787667e-07
            ],
            "target_residual": 3.215524105983172e-07,
            "energy_eV": -64.22872159999807
          }
        ],
        "iterations": 5
      },
      "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": 3.215524105983172e-07,
        "parent_symmetrization_rmsd_A": 0.23055220063277504,
        "parent_cell_rmsd_A": 0.08653188135215052,
        "energy_eV": -64.22872159999807,
        "reduced_polarization": [
          -0.5000002640305764,
          -0.5000000668289317,
          -1.709318617787667e-07
        ],
        "cartesian_polarization_e_A2": [
          -0.029539881691499854,
          -0.017291883066249382,
          -0.0004660966892975427
        ],
        "ranking_score": 0.7521858140756339
      },
      "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": [
              -0.00945592835261243,
              -0.028162692279892144,
              0.03324196566336734
            ],
            "branch_aligned_reduced_polarization": [
              -0.009455928352612442,
              -0.028162692279892154,
              0.033241965663367345
            ],
            "target_residual": 0.8253041825913365,
            "energy_eV": -68.82981663392609,
            "max_atomic_step_A": 0.12,
            "max_log_strain_component": 0.003410502755195017,
            "step_scale": 0.38911322166052037,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 1.113561068778823,
            "cell_principal_stretches": [
              1.0036595306521074,
              1.0005877358819066,
              0.9941650725572502
            ],
            "cell_volume_ratio": 0.9983896948867026,
            "cell_rmsd_from_input_A": 0.027015924034628998
          },
          {
            "iteration": 1,
            "reduced_polarization": [
              -0.19901508317217173,
              -0.20779818164174327,
              0.21303129392788805
            ],
            "branch_aligned_reduced_polarization": [
              -0.19901508317217176,
              -0.20779818164174324,
              0.21303129392788805
            ],
            "target_residual": 0.5082566881748124,
            "energy_eV": -68.36046131995965,
            "max_atomic_step_A": 0.12,
            "max_log_strain_component": 0.0037348205987467378,
            "step_scale": 0.6409912844410797,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 1.113561068778823,
            "cell_principal_stretches": [
              1.0076866214926583,
              1.0012847064287662,
              0.9877592741847869
            ],
            "cell_volume_ratio": 0.9966305407151695,
            "cell_rmsd_from_input_A": 0.05674818625883174
          },
          {
            "iteration": 2,
            "reduced_polarization": [
              -0.384125587420887,
              -0.3870705865833348,
              0.3894778133894648
            ],
            "branch_aligned_reduced_polarization": [
              -0.384125587420887,
              -0.3870705865833348,
              0.3894778133894648
            ],
            "target_residual": 0.19594663977307838,
            "energy_eV": -66.549447214205,
            "max_atomic_step_A": 0.0650595529646201,
            "max_log_strain_component": 0.0027702130131980417,
            "step_scale": 1.0,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 1.113561068778823,
            "cell_principal_stretches": [
              1.010687481025401,
              1.0018410512969185,
              0.9829850759787622
            ],
            "cell_volume_ratio": 0.9953197776872607,
            "cell_rmsd_from_input_A": 0.07892270369308475
          },
          {
            "iteration": 3,
            "reduced_polarization": [
              -0.4943467693764303,
              -0.5035259377835997,
              0.49848072982358255
            ],
            "branch_aligned_reduced_polarization": [
              -0.4943467693764303,
              -0.5035259377835997,
              0.49848072982358255
            ],
            "target_residual": 0.006833698530520171,
            "energy_eV": -64.41539018382525,
            "max_atomic_step_A": 0.002254732799797081,
            "max_log_strain_component": 5.3271719238488346e-05,
            "step_scale": 1.0,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 1.113561068778823,
            "cell_principal_stretches": [
              1.0107390847983475,
              1.0017784301893653,
              0.9829798565251311
            ],
            "cell_volume_ratio": 0.9953030952615869,
            "cell_rmsd_from_input_A": 0.07916755439699945
          },
          {
            "iteration": 4,
            "reduced_polarization": [
              -0.49999983565428113,
              -0.4999920678305951,
              0.5000126134956958
            ],
            "branch_aligned_reduced_polarization": [
              -0.49999983565428113,
              -0.4999920678305951,
              0.5000126134956958
            ],
            "target_residual": 1.4901227957855717e-05,
            "energy_eV": -64.40209901794958
          }
        ],
        "iterations": 4
      },
      "parent": {
        "candidate_id": "bec_projection_07",
        "source": "MACEField_BEC_backprojection",
        "spacegroup": "P1",
        "spacegroup_number": 1,
        "pointgroup": "1",
        "has_inversion": false,
        "is_polar_point_group": true,
        "nonpolar_parent_hypothesis": false,
        "symmetry_tolerance_A": null,
        "target_reduced_polarization": [
          -0.5,
          -0.5,
          0.5
        ],
        "formal_class": [
          0.5,
          0.5,
          0.5
        ],
        "target_residual": 1.4901227957855717e-05,
        "parent_symmetrization_rmsd_A": 0.1897677421457719,
        "parent_cell_rmsd_A": 0.07916755439699945,
        "energy_eV": -64.40209901794958,
        "reduced_polarization": [
          -0.49999983565428113,
          -0.4999920678305951,
          0.5000126134956958
        ],
        "cartesian_polarization_e_A2": [
          -0.020052712422951733,
          -0.011328696819600447,
          0.018403848618400866
        ],
        "ranking_score": 0.7095894332009375
      },
      "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
        ],
        "endpoint_rmsd_A": 0.2912369756967939,
        "minimum_distance_A_by_image": [
          1.8413333920711068,
          1.8485521537544898,
          1.8239972672567693,
          1.7861318701366766,
          1.7552438390658365,
          1.731706575070399,
          1.7158226132699061,
          1.7078055125738236,
          1.7077660694162868
        ],
        "minimum_distance_A": 1.7077660694162868,
        "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": [
          139.40043577983153,
          139.40043577983153,
          139.40043577983153,
          139.40043577983153,
          139.40043577983153,
          139.40043577983153,
          139.40043577983153,
          139.40043577983153,
          139.40043577983153
        ],
        "cell_deformation_log_strain_norm": 0.0
      },
      "parent_reduced_polarization": [
        -1.0794133276883535e-15,
        -1.4626823147200249e-15,
        1.992807004537229e-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": [
          -68.82981663392609,
          -68.80341538139626,
          -68.74007010616377,
          -68.65543413700053,
          -68.56061089735297,
          -68.46043905939382,
          -68.36838800170501,
          -68.30900905646921,
          -68.28837122025837
        ],
        "cartesian_polarizations_e_A2": [
          [
            -0.0003023474694776208,
            -0.000592249095103824,
            0.0012388433513821492
          ],
          [
            0.0006538540778202915,
            -0.0006477936714786557,
            0.0004205312331839123
          ],
          [
            0.0016116073682361433,
            -0.0006721485340824353,
            -0.0003433540676029421
          ],
          [
            0.0024979715231221375,
            -0.000659151981822529,
            -0.001017168060860195
          ],
          [
            0.003177171429123984,
            -0.0005789371541540105,
            -0.0015386394870854473
          ],
          [
            0.003440540040504551,
            -0.00038270187804293143,
            -0.0018031194830549382
          ],
          [
            0.0030274035801117014,
            -0.00010555765320946084,
            -0.0016675791925681697
          ],
          [
            0.0018252449835254813,
            3.276048593691271e-05,
            -0.0010317136677560456
          ],
          [
            -3.402237558863333e-17,
            -2.762606942456693e-17,
            7.426683888550245e-17
          ]
        ],
        "raw_reduced_polarization": [
          [
            -0.009455928352612605,
            -0.028162692279892904,
            0.03324196566336755
          ],
          [
            0.022188525630470593,
            -0.022354509544492116,
            0.011284142420651372
          ],
          [
            0.052989895996117725,
            -0.016145193587814723,
            -0.009213242427220929
          ],
          [
            0.08072604620480688,
            -0.009680565666943171,
            -0.027293737917118203
          ],
          [
            0.10103576733972988,
            -0.0026683048545483117,
            -0.04128641522023903
          ],
          [
            0.10710269908380034,
            0.00534303387248941,
            -0.04838322446158221
          ],
          [
            0.09165933358042198,
            0.012054667561894711,
            -0.04474626287371302
          ],
          [
            0.05412437568678491,
            0.010266667052668274,
            -0.02768404114992423
          ],
          [
            -1.0794133276883535e-15,
            -1.4626823147200249e-15,
            1.992807004537229e-15
          ]
        ],
        "unwrapped_reduced_polarization": [
          [
            -0.009455928352612605,
            -0.028162692279892904,
            0.03324196566336755
          ],
          [
            0.022188525630470596,
            -0.022354509544492116,
            0.011284142420651372
          ],
          [
            0.052989895996117725,
            -0.016145193587814723,
            -0.009213242427220929
          ],
          [
            0.08072604620480688,
            -0.009680565666943171,
            -0.027293737917118203
          ],
          [
            0.10103576733972988,
            -0.002668304854548312,
            -0.04128641522023903
          ],
          [
            0.10710269908380034,
            0.005343033872489409,
            -0.04838322446158221
          ],
          [
            0.09165933358042198,
            0.012054667561894711,
            -0.04474626287371302
          ],
          [
            0.05412437568678491,
            0.010266667052668274,
            -0.02768404114992423
          ],
          [
            -1.0824674490095276e-15,
            -1.4623718902484484e-15,
            1.9914625504213745e-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": [
          [
            -0.009455928352612608,
            -0.028162692279892876,
            0.03324196566336757
          ],
          [
            0.02218852563047058,
            -0.02235450954449214,
            0.011284142420651344
          ],
          [
            0.0529898959961177,
            -0.016145193587814743,
            -0.009213242427220936
          ],
          [
            0.08072604620480683,
            -0.009680565666943197,
            -0.0272937379171182
          ],
          [
            0.10103576733972985,
            -0.0026683048545483312,
            -0.041286415220239014
          ],
          [
            0.10710269908380032,
            0.005343033872489356,
            -0.04838322446158222
          ],
          [
            0.091659333580422,
            0.01205466756189466,
            -0.04474626287371303
          ],
          [
            0.054124375686784854,
            0.010266667052668321,
            -0.027684041149924232
          ],
          [
            -1.1102230246251565e-15,
            -1.4432899320127035e-15,
            1.9984014443252818e-15
          ]
        ]
      },
      "reflected": {
        "reached": true,
        "construction": "reflect_displacements_about_reconstructed_parent",
        "energies_eV": [
          -68.28837122025837,
          -68.3090090564692,
          -68.36838800170503,
          -68.46043905939382,
          -68.56061089735297,
          -68.65543413700053,
          -68.74007010616376,
          -68.80341538139626,
          -68.82981663392607
        ],
        "cartesian_polarizations_e_A2": [
          [
            -3.402237558863333e-17,
            -2.762606942456693e-17,
            7.426683888550245e-17
          ],
          [
            -0.0018252449835254375,
            -3.2760485936988597e-05,
            0.00103171366775598
          ],
          [
            -0.003027403580111808,
            0.00010555765320944922,
            0.0016675791925682343
          ],
          [
            -0.003440540040504537,
            0.00038270187804283255,
            0.0018031194830549673
          ],
          [
            -0.003177171429123939,
            0.0005789371541539335,
            0.0015386394870853897
          ],
          [
            -0.0024979715231222533,
            0.0006591519818225116,
            0.0010171680608602309
          ],
          [
            -0.0016116073682361847,
            0.0006721485340824658,
            0.0003433540676029688
          ],
          [
            -0.0006538540778202597,
            0.0006477936714786091,
            -0.00042053123318382075
          ],
          [
            0.000302347469477685,
            0.0005922490951038158,
            -0.0012388433513821572
          ]
        ],
        "raw_reduced_polarization": [
          [
            -1.0794133276883535e-15,
            -1.4626823147200249e-15,
            1.992807004537229e-15
          ],
          [
            -0.054124375686782196,
            -0.010266667052669855,
            0.02768404114992247
          ],
          [
            -0.09165933358042505,
            -0.012054667561895629,
            0.04474626287371475
          ],
          [
            -0.10710269908379885,
            -0.005343033872492509,
            0.048383224461582997
          ],
          [
            -0.1010357673397272,
            0.002668304854546628,
            0.04128641522023748
          ],
          [
            -0.08072604620480987,
            0.009680565666942352,
            0.02729373791711916
          ],
          [
            -0.05298989599611941,
            0.016145193587815354,
            0.009213242427221642
          ],
          [
            -0.022188525630469885,
            0.022354509544489955,
            -0.011284142420648915
          ],
          [
            0.009455928352614405,
            0.02816269227989274,
            -0.03324196566336776
          ]
        ],
        "unwrapped_reduced_polarization": [
          [
            -1.0794133276883535e-15,
            -1.4626823147200249e-15,
            1.992807004537229e-15
          ],
          [
            -0.054124375686782196,
            -0.010266667052669855,
            0.02768404114992247
          ],
          [
            -0.09165933358042505,
            -0.012054667561895629,
            0.04474626287371475
          ],
          [
            -0.10710269908379885,
            -0.005343033872492509,
            0.048383224461582997
          ],
          [
            -0.1010357673397272,
            0.0026683048545466277,
            0.04128641522023748
          ],
          [
            -0.08072604620480987,
            0.009680565666942352,
            0.02729373791711916
          ],
          [
            -0.05298989599611941,
            0.016145193587815354,
            0.00921324242722164
          ],
          [
            -0.022188525630469885,
            0.022354509544489955,
            -0.011284142420648915
          ],
          [
            0.009455928352614405,
            0.02816269227989274,
            -0.03324196566336776
          ]
        ],
        "gauge_integer_shift": [
          0,
          0,
          0
        ],
        "expected_opposite_endpoint_reduced_polarization": [
          0.009455928352610441,
          0.02816269227988998,
          -0.03324196566336356
        ],
        "actual_opposite_endpoint_branch_residual": 6.404740264709041e-15
      },
      "pnp_branch": {
        "construction": "incoming_path_concatenated_with_parent_reflection",
        "reduced_polarization": [
          [
            -0.009455928352612605,
            -0.028162692279892904,
            0.03324196566336755
          ],
          [
            0.022188525630470593,
            -0.022354509544492116,
            0.011284142420651372
          ],
          [
            0.052989895996117725,
            -0.016145193587814723,
            -0.009213242427220929
          ],
          [
            0.08072604620480688,
            -0.009680565666943171,
            -0.027293737917118203
          ],
          [
            0.10103576733972988,
            -0.0026683048545483117,
            -0.04128641522023903
          ],
          [
            0.10710269908380034,
            0.00534303387248941,
            -0.04838322446158221
          ],
          [
            0.09165933358042198,
            0.012054667561894711,
            -0.04474626287371302
          ],
          [
            0.05412437568678491,
            0.010266667052668274,
            -0.02768404114992423
          ],
          [
            -1.0794133276883535e-15,
            -1.4626823147200249e-15,
            1.992807004537229e-15
          ],
          [
            -0.054124375686782196,
            -0.010266667052669855,
            0.02768404114992247
          ],
          [
            -0.09165933358042505,
            -0.012054667561895629,
            0.04474626287371475
          ],
          [
            -0.10710269908379885,
            -0.005343033872492509,
            0.048383224461582997
          ],
          [
            -0.1010357673397272,
            0.002668304854546628,
            0.04128641522023748
          ],
          [
            -0.08072604620480987,
            0.009680565666942352,
            0.02729373791711916
          ],
          [
            -0.05298989599611941,
            0.016145193587815354,
            0.009213242427221642
          ],
          [
            -0.022188525630469885,
            0.022354509544489955,
            -0.011284142420648915
          ],
          [
            0.009455928352614405,
            0.02816269227989274,
            -0.03324196566336776
          ]
        ],
        "unwrapped_reduced_polarization": [
          [
            -0.009455928352612605,
            -0.028162692279892904,
            0.03324196566336755
          ],
          [
            0.022188525630470596,
            -0.022354509544492116,
            0.011284142420651372
          ],
          [
            0.052989895996117725,
            -0.016145193587814723,
            -0.009213242427220929
          ],
          [
            0.08072604620480688,
            -0.009680565666943171,
            -0.027293737917118203
          ],
          [
            0.10103576733972988,
            -0.002668304854548312,
            -0.04128641522023903
          ],
          [
            0.10710269908380034,
            0.005343033872489409,
            -0.04838322446158221
          ],
          [
            0.09165933358042198,
            0.012054667561894711,
            -0.04474626287371302
          ],
          [
            0.05412437568678491,
            0.010266667052668274,
            -0.02768404114992423
          ],
          [
            -1.0824674490095276e-15,
            -1.4623718902484484e-15,
            1.9914625504213745e-15
          ],
          [
            -0.054124375686782196,
            -0.010266667052669855,
            0.02768404114992247
          ],
          [
            -0.09165933358042505,
            -0.012054667561895629,
            0.04474626287371475
          ],
          [
            -0.10710269908379885,
            -0.005343033872492509,
            0.048383224461582997
          ],
          [
            -0.1010357673397272,
            0.0026683048545466277,
            0.04128641522023748
          ],
          [
            -0.08072604620480987,
            0.009680565666942352,
            0.02729373791711916
          ],
          [
            -0.05298989599611941,
            0.016145193587815354,
            0.00921324242722164
          ],
          [
            -0.022188525630469885,
            0.022354509544489955,
            -0.011284142420648915
          ],
          [
            0.009455928352614405,
            0.02816269227989274,
            -0.03324196566336776
          ]
        ],
        "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": [
          [
            -0.009455928352612608,
            -0.028162692279892876,
            0.03324196566336757
          ],
          [
            0.02218852563047058,
            -0.02235450954449214,
            0.011284142420651344
          ],
          [
            0.0529898959961177,
            -0.016145193587814743,
            -0.009213242427220936
          ],
          [
            0.08072604620480683,
            -0.009680565666943197,
            -0.0272937379171182
          ],
          [
            0.10103576733972985,
            -0.0026683048545483312,
            -0.041286415220239014
          ],
          [
            0.10710269908380032,
            0.005343033872489356,
            -0.04838322446158222
          ],
          [
            0.091659333580422,
            0.01205466756189466,
            -0.04474626287371303
          ],
          [
            0.054124375686784854,
            0.010266667052668321,
            -0.027684041149924232
          ],
          [
            -1.1102230246251565e-15,
            -1.4432899320127035e-15,
            1.9984014443252818e-15
          ],
          [
            -0.05412437568678219,
            -0.010266667052669876,
            0.02768404114992251
          ],
          [
            -0.09165933358042505,
            -0.012054667561895605,
            0.04474626287371475
          ],
          [
            -0.10710269908379888,
            -0.00534303387249252,
            0.04838322446158294
          ],
          [
            -0.10103576733972719,
            0.0026683048545466104,
            0.04128641522023746
          ],
          [
            -0.08072604620480989,
            0.009680565666942309,
            0.0272937379171192
          ],
          [
            -0.05298989599611942,
            0.01614519358781541,
            0.009213242427221657
          ],
          [
            -0.022188525630469913,
            0.02235450954448992,
            -0.011284142420648902
          ],
          [
            0.00945592835261444,
            0.028162692279892765,
            -0.03324196566336779
          ]
        ]
      },
      "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": "P-1",
        "spacegroup_number": 2,
        "pointgroup": "-1",
        "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": 2.8320640545438903e-15,
        "parent_symmetrization_rmsd_A": 0.2912369756967939,
        "parent_cell_rmsd_A": 0.0,
        "energy_eV": -68.2883712202584,
        "reduced_polarization": [
          -1.002079441029645e-15,
          -1.123366079228811e-15,
          2.3988481100193447e-15
        ],
        "cartesian_polarization_e_A2": [
          -1.684941351390253e-17,
          -1.1000651068160885e-17,
          8.93989561919319e-17
        ],
        "ranking_score": 0.29123697569679957
      }
    }
  ],
  "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": 71,
      "full_response": 26,
      "energy_polarization": 45
    },
    "model_evaluations_for_recovery_and_path_properties": {
      "total": 96,
      "full_response": 51,
      "energy_polarization": 45
    },
    "elapsed_seconds": 315.7593821780174
  }
}
