{
  "schema": "ferrofinder.endpoint_parent_recovery.v4_variable_cell",
  "status": "complete",
  "input_atom_count": 42,
  "input_formula": "Be6F26Na6Pb4",
  "input_spacegroup": "P2_1",
  "input_pointgroup": "2",
  "input_is_polar_point_group": true,
  "input_energy_eV": -207.05334624718208,
  "input_cartesian_polarization_e_A2": [
    -3.544888011953928e-11,
    0.0013113558162246247,
    4.305005171809547e-12
  ],
  "input_reduced_polarization": [
    -1.9811285888463236e-09,
    0.10540820570608662,
    2.945421047622473e-10
  ],
  "input_formal_targets": [
    {
      "orbit_id": 0,
      "representative_formal_class": [
        0.0,
        0.0,
        0.0
      ],
      "target_reduced_polarization": [
        0.0,
        0.0,
        0.0
      ]
    },
    {
      "orbit_id": 1,
      "representative_formal_class": [
        0.0,
        0.5,
        0.0
      ],
      "target_reduced_polarization": [
        0.0,
        0.5,
        0.0
      ]
    },
    {
      "orbit_id": 2,
      "representative_formal_class": [
        0.5,
        0.0,
        0.0
      ],
      "target_reduced_polarization": [
        -0.5,
        0.0,
        0.0
      ]
    },
    {
      "orbit_id": 3,
      "representative_formal_class": [
        0.0,
        0.0,
        0.5
      ],
      "target_reduced_polarization": [
        0.0,
        0.0,
        0.5
      ]
    },
    {
      "orbit_id": 4,
      "representative_formal_class": [
        0.5,
        0.5,
        0.0
      ],
      "target_reduced_polarization": [
        -0.5,
        0.5,
        0.0
      ]
    },
    {
      "orbit_id": 5,
      "representative_formal_class": [
        0.0,
        0.5,
        0.5
      ],
      "target_reduced_polarization": [
        0.0,
        0.5,
        0.5
      ]
    },
    {
      "orbit_id": 6,
      "representative_formal_class": [
        0.5,
        0.0,
        0.5
      ],
      "target_reduced_polarization": [
        -0.5,
        0.0,
        0.5
      ]
    },
    {
      "orbit_id": 7,
      "representative_formal_class": [
        0.5,
        0.5,
        0.5
      ],
      "target_reduced_polarization": [
        -0.5,
        0.5,
        0.5
      ]
    }
  ],
  "parent_candidates": [
    {
      "candidate_id": "inversion_parent_endpoint_00",
      "source": "same_species_inversion_center_projection_from_endpoint",
      "spacegroup": "P2_1/m",
      "spacegroup_number": 11,
      "pointgroup": "2/m",
      "has_inversion": true,
      "is_polar_point_group": false,
      "nonpolar_parent_hypothesis": true,
      "symmetry_tolerance_A": null,
      "target_reduced_polarization": [
        0.0,
        0.0,
        0.0
      ],
      "formal_class": [
        0.0,
        0.0,
        0.0
      ],
      "target_residual": 6.082913838725621e-16,
      "parent_symmetrization_rmsd_A": 0.09580572242523867,
      "parent_cell_rmsd_A": 0.0,
      "energy_eV": -207.10602703676398,
      "reduced_polarization": [
        3.2020422059086627e-16,
        4.424776754713125e-16,
        2.677707443297278e-16
      ],
      "cartesian_polarization_e_A2": [
        3.1128580250809977e-18,
        5.504748604646367e-18,
        3.91371698837172e-18
      ],
      "ranking_score": 0.0958057224252399
    },
    {
      "candidate_id": "bec_projection_00",
      "source": "MACEField_BEC_backprojection",
      "spacegroup": "P2_1",
      "spacegroup_number": 4,
      "pointgroup": "2",
      "has_inversion": false,
      "is_polar_point_group": true,
      "nonpolar_parent_hypothesis": false,
      "symmetry_tolerance_A": null,
      "target_reduced_polarization": [
        0.0,
        0.0,
        0.0
      ],
      "formal_class": [
        0.0,
        0.0,
        0.0
      ],
      "target_residual": 4.9766934793917265e-05,
      "parent_symmetrization_rmsd_A": 0.01516095695878261,
      "parent_cell_rmsd_A": 0.0027828594685327676,
      "energy_eV": -207.02197346677255,
      "reduced_polarization": [
        -2.697699736592049e-12,
        4.976693479391719e-05,
        -8.86638803053095e-14
      ],
      "cartesian_polarization_e_A2": [
        -4.418980050007144e-14,
        6.190543442379345e-07,
        -1.2860536097859035e-15
      ],
      "ranking_score": 0.5159562056955036
    },
    {
      "candidate_id": "inversion_parent_bec_00_00",
      "source": "same_species_inversion_center_projection_after_BEC",
      "spacegroup": "P2_1/m",
      "spacegroup_number": 11,
      "pointgroup": "2/m",
      "has_inversion": true,
      "is_polar_point_group": false,
      "nonpolar_parent_hypothesis": true,
      "symmetry_tolerance_A": null,
      "target_reduced_polarization": [
        0.0,
        0.0,
        0.0
      ],
      "formal_class": [
        0.0,
        0.0,
        0.0
      ],
      "target_residual": 1.5838622413389958e-15,
      "parent_symmetrization_rmsd_A": 0.09580810722408352,
      "parent_cell_rmsd_A": 0.0027828594685327676,
      "energy_eV": -207.10458883945674,
      "reduced_polarization": [
        -5.828157654272939e-16,
        1.245957379200647e-15,
        -7.8519780458445e-16
      ],
      "cartesian_polarization_e_A2": [
        -3.192007620013169e-18,
        1.5498550021628087e-17,
        -1.1470711693090803e-17
      ],
      "ranking_score": 0.09650382209121988
    },
    {
      "candidate_id": "bec_projection_01",
      "source": "MACEField_BEC_backprojection",
      "spacegroup": "P2_1",
      "spacegroup_number": 4,
      "pointgroup": "2",
      "has_inversion": false,
      "is_polar_point_group": true,
      "nonpolar_parent_hypothesis": false,
      "symmetry_tolerance_A": null,
      "target_reduced_polarization": [
        0.0,
        0.5,
        0.0
      ],
      "formal_class": [
        0.0,
        0.5,
        0.0
      ],
      "target_residual": 7.958032455235298e-06,
      "parent_symmetrization_rmsd_A": 0.05744700446843624,
      "parent_cell_rmsd_A": 0.010492830129244173,
      "energy_eV": -206.55443646514036,
      "reduced_polarization": [
        -3.926430872154838e-14,
        0.5000079580324552,
        -2.33263370178915e-14
      ],
      "cartesian_polarization_e_A2": [
        -3.219096483753067e-14,
        0.006223621099053913,
        1.2215443488453445e-13
      ],
      "ranking_score": 0.5600861280656577
    },
    {
      "candidate_id": "bec_projection_02",
      "source": "MACEField_BEC_backprojection",
      "spacegroup": "P1",
      "spacegroup_number": 1,
      "pointgroup": "1",
      "has_inversion": false,
      "is_polar_point_group": true,
      "nonpolar_parent_hypothesis": false,
      "symmetry_tolerance_A": null,
      "target_reduced_polarization": [
        -0.5,
        0.0,
        0.0
      ],
      "formal_class": [
        0.5,
        0.0,
        0.0
      ],
      "target_residual": 6.931004274024144e-06,
      "parent_symmetrization_rmsd_A": 0.11805443892907622,
      "parent_cell_rmsd_A": 0.061327744048695586,
      "energy_eV": -204.89988522241575,
      "reduced_polarization": [
        -0.49999865102662866,
        6.762873249015527e-06,
        6.947204529207777e-07
      ],
      "cartesian_polarization_e_A2": [
        -0.008322387972110282,
        -5.523404898046193e-05,
        1.577534782549983e-07
      ],
      "ranking_score": 0.6334002369497982
    },
    {
      "candidate_id": "bec_projection_03",
      "source": "MACEField_BEC_backprojection",
      "spacegroup": "P1",
      "spacegroup_number": 1,
      "pointgroup": "1",
      "has_inversion": false,
      "is_polar_point_group": true,
      "nonpolar_parent_hypothesis": false,
      "symmetry_tolerance_A": null,
      "target_reduced_polarization": [
        0.0,
        0.0,
        0.5
      ],
      "formal_class": [
        0.0,
        0.0,
        0.5
      ],
      "target_residual": 1.2143130508247523e-05,
      "parent_symmetrization_rmsd_A": 0.10744526153423732,
      "parent_cell_rmsd_A": 0.08495218886401529,
      "energy_eV": -205.12245713076447,
      "reduced_polarization": [
        -5.793734511618371e-06,
        6.254111182672724e-06,
        0.499991352783554
      ],
      "cartesian_polarization_e_A2": [
        -0.004144766972049045,
        -9.50058486470466e-05,
        0.007304508145931221
      ],
      "ranking_score": 0.6287075950112576
    },
    {
      "candidate_id": "bec_projection_04",
      "source": "MACEField_BEC_backprojection",
      "spacegroup": "P1",
      "spacegroup_number": 1,
      "pointgroup": "1",
      "has_inversion": false,
      "is_polar_point_group": true,
      "nonpolar_parent_hypothesis": false,
      "symmetry_tolerance_A": null,
      "target_reduced_polarization": [
        -0.5,
        0.5,
        0.0
      ],
      "formal_class": [
        0.5,
        0.5,
        0.0
      ],
      "target_residual": 1.598159254259029e-05,
      "parent_symmetrization_rmsd_A": 0.131556693082125,
      "parent_cell_rmsd_A": 0.06227262532447545,
      "energy_eV": -204.33558170696932,
      "reduced_polarization": [
        -0.5000049326481907,
        0.5000150898887037,
        -1.8372645249400304e-06
      ],
      "cartesian_polarization_e_A2": [
        -0.008315940840688185,
        0.006168156613081754,
        -1.3478237313887176e-05
      ],
      "ranking_score": 0.647156812598329
    },
    {
      "candidate_id": "bec_projection_05",
      "source": "MACEField_BEC_backprojection",
      "spacegroup": "P1",
      "spacegroup_number": 1,
      "pointgroup": "1",
      "has_inversion": false,
      "is_polar_point_group": true,
      "nonpolar_parent_hypothesis": false,
      "symmetry_tolerance_A": null,
      "target_reduced_polarization": [
        0.0,
        0.5,
        0.5
      ],
      "formal_class": [
        0.0,
        0.5,
        0.5
      ],
      "target_residual": 1.0264854205156426e-05,
      "parent_symmetrization_rmsd_A": 0.12197825524938662,
      "parent_cell_rmsd_A": 0.08506408546730292,
      "energy_eV": -204.4949204617253,
      "reduced_polarization": [
        4.272841579187377e-06,
        0.500008869217408,
        0.5000029063790639
      ],
      "cartesian_polarization_e_A2": [
        -0.004146969872721671,
        0.0061289473074150665,
        0.007249503936026567
      ],
      "ranking_score": 0.6432648063246227
    },
    {
      "candidate_id": "bec_projection_06",
      "source": "MACEField_BEC_backprojection",
      "spacegroup": "P1",
      "spacegroup_number": 1,
      "pointgroup": "1",
      "has_inversion": false,
      "is_polar_point_group": true,
      "nonpolar_parent_hypothesis": false,
      "symmetry_tolerance_A": null,
      "target_reduced_polarization": [
        -0.5,
        0.0,
        0.5
      ],
      "formal_class": [
        0.5,
        0.0,
        0.5
      ],
      "target_residual": 4.985052039214179e-06,
      "parent_symmetrization_rmsd_A": 0.19923640807025955,
      "parent_cell_rmsd_A": 0.1399334671599225,
      "energy_eV": -198.5981545641019,
      "reduced_polarization": [
        -0.5000034312238999,
        -2.691426148789447e-06,
        0.4999975847005014
      ],
      "cartesian_polarization_e_A2": [
        -0.012465914848356723,
        -0.00021626807416253566,
        0.007305111889064243
      ],
      "ranking_score": 0.7342297449643186
    },
    {
      "candidate_id": "bec_projection_07",
      "source": "MACEField_BEC_backprojection",
      "spacegroup": "P1",
      "spacegroup_number": 1,
      "pointgroup": "1",
      "has_inversion": false,
      "is_polar_point_group": true,
      "nonpolar_parent_hypothesis": false,
      "symmetry_tolerance_A": null,
      "target_reduced_polarization": [
        -0.5,
        0.5,
        0.5
      ],
      "formal_class": [
        0.5,
        0.5,
        0.5
      ],
      "target_residual": 0.0009371959031980508,
      "parent_symmetrization_rmsd_A": 0.209490775295405,
      "parent_cell_rmsd_A": 0.14010486530365038,
      "energy_eV": -197.66330082311345,
      "reduced_polarization": [
        -0.5005807922607016,
        0.5007295699126327,
        0.49990648928691656
      ],
      "cartesian_polarization_e_A2": [
        -0.012472691408892803,
        0.006015878076033359,
        0.007233169032069438
      ],
      "ranking_score": 0.7463913834277137
    }
  ],
  "formal_branches": [
    {
      "orbit_id": 0,
      "formal_class": [
        0.0,
        0.0,
        0.0
      ],
      "formal_classes_in_orbit": [
        [
          0.0,
          0.0,
          0.0
        ]
      ],
      "target_reduced_polarization": [
        0.0,
        0.0,
        0.0
      ],
      "bec_backprojection": {
        "converged_to_target": true,
        "history": [
          {
            "iteration": 0,
            "reduced_polarization": [
              -1.9811285888463236e-09,
              0.10540820570608662,
              2.945421047622473e-10
            ],
            "branch_aligned_reduced_polarization": [
              -1.9811285888463236e-09,
              0.10540820570608662,
              2.945421047622473e-10
            ],
            "target_residual": 0.10540820570608664,
            "energy_eV": -207.05334624718208,
            "max_atomic_step_A": 0.01998482891956573,
            "max_log_strain_component": 0.0006082346684966572,
            "step_scale": 1.0,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 0.762665009945683,
            "cell_principal_stretches": [
              1.000608419680711,
              1.0002504730902522,
              0.9998836752791145
            ],
            "cell_volume_ratio": 1.000742620514647,
            "cell_rmsd_from_input_A": 0.0027828594685327676
          },
          {
            "iteration": 1,
            "reduced_polarization": [
              -2.697699736592049e-12,
              4.976693479391719e-05,
              -8.86638803053095e-14
            ],
            "branch_aligned_reduced_polarization": [
              -2.697699736592049e-12,
              4.976693479391719e-05,
              -8.86638803053095e-14
            ],
            "target_residual": 4.9766934793917265e-05,
            "energy_eV": -207.02197346677255
          }
        ],
        "iterations": 1
      },
      "parent": {
        "candidate_id": "inversion_parent_endpoint_00",
        "source": "same_species_inversion_center_projection_from_endpoint",
        "spacegroup": "P2_1/m",
        "spacegroup_number": 11,
        "pointgroup": "2/m",
        "has_inversion": true,
        "is_polar_point_group": false,
        "nonpolar_parent_hypothesis": true,
        "symmetry_tolerance_A": null,
        "target_reduced_polarization": [
          0.0,
          0.0,
          0.0
        ],
        "formal_class": [
          0.0,
          0.0,
          0.0
        ],
        "target_residual": 6.082913838725621e-16,
        "parent_symmetrization_rmsd_A": 0.09580572242523867,
        "parent_cell_rmsd_A": 0.0,
        "energy_eV": -207.10602703676398,
        "reduced_polarization": [
          3.2020422059086627e-16,
          4.424776754713125e-16,
          2.677707443297278e-16
        ],
        "cartesian_polarization_e_A2": [
          3.1128580250809977e-18,
          5.504748604646367e-18,
          3.91371698837172e-18
        ],
        "ranking_score": 0.0958057224252399
      },
      "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": [
          -207.0533462471821,
          -207.06660798083806,
          -207.07771634958007,
          -207.0867661029607,
          -207.09390255257188,
          -207.09927714594926,
          -207.10302954375047,
          -207.10527303337403,
          -207.10602703676403
        ],
        "cartesian_polarizations_e_A2": [
          [
            -3.544888684645265e-11,
            0.0013113558162246232,
            4.305010591382928e-12
          ],
          [
            -3.098341484622221e-11,
            0.0011613329403152414,
            3.8011712596373165e-12
          ],
          [
            -2.6534887919624768e-11,
            0.0010054943698238382,
            3.28598731609052e-12
          ],
          [
            -2.2099432004645076e-11,
            0.0008448468635910371,
            2.759253009054565e-12
          ],
          [
            -1.7672990195844874e-11,
            0.0006805245456716278,
            2.2218410770378487e-12
          ],
          [
            -1.3251950548347084e-11,
            0.000513401432151677,
            1.6755582193659767e-12
          ],
          [
            -8.83369476812574e-12,
            0.0003439528605624671,
            1.1219776147789404e-12
          ],
          [
            -4.416706700089923e-12,
            0.0001725664601774393,
            5.626222732222019e-13
          ],
          [
            -5.653868028871655e-17,
            1.5310741278251484e-18,
            -3.575559763532659e-17
          ]
        ],
        "raw_reduced_polarization": [
          [
            -1.9811288079634268e-09,
            0.1054082057060865,
            2.9454247556146514e-10
          ],
          [
            -1.7302568942451992e-09,
            0.09334920389374692,
            2.6007053155402556e-10
          ],
          [
            -1.4807886611719251e-09,
            0.08082273023033461,
            2.2482240593837035e-10
          ],
          [
            -1.2324985791964324e-09,
            0.06790970908561704,
            1.887840214874544e-10
          ],
          [
            -9.851133953664237e-10,
            0.05470130258369848,
            1.52015089682893e-10
          ],
          [
            -7.38354741875046e-10,
            0.041267765087468586,
            1.1463922222799398e-10
          ],
          [
            -4.920118516642886e-10,
            0.02764730474429466,
            7.67640536919975e-11
          ],
          [
            -2.4594182292483545e-10,
            0.01387107961645624,
            3.8493786169211784e-11
          ],
          [
            -4.612058617361431e-15,
            1.23069402385154e-16,
            -2.4463452572611776e-15
          ]
        ],
        "unwrapped_reduced_polarization": [
          [
            -1.9811288079634268e-09,
            0.1054082057060865,
            2.9454247556146514e-10
          ],
          [
            -1.7302568942451992e-09,
            0.09334920389374692,
            2.6007053155402556e-10
          ],
          [
            -1.4807886611719251e-09,
            0.08082273023033461,
            2.2482240593837035e-10
          ],
          [
            -1.2324985791964324e-09,
            0.06790970908561704,
            1.887840214874544e-10
          ],
          [
            -9.851133953664237e-10,
            0.05470130258369848,
            1.52015089682893e-10
          ],
          [
            -7.38354741875046e-10,
            0.041267765087468586,
            1.1463922222799398e-10
          ],
          [
            -4.920118516642886e-10,
            0.02764730474429466,
            7.67640536919975e-11
          ],
          [
            -2.4594182292483545e-10,
            0.01387107961645624,
            3.8493786169211784e-11
          ],
          [
            -4.612058617378486e-15,
            1.231653667943533e-16,
            -2.4463452572615767e-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": [
          [
            -1.9811288165527685e-09,
            0.10540820570608656,
            2.945425014999614e-10
          ],
          [
            -1.7302568822152864e-09,
            0.0933492038937469,
            2.6007052067456016e-10
          ],
          [
            -1.480788658358989e-09,
            0.0808227302303346,
            2.2482238293264345e-10
          ],
          [
            -1.232498603176424e-09,
            0.067909709085617,
            1.8878398844179856e-10
          ],
          [
            -9.851133797589284e-10,
            0.05470130258369843,
            1.520150672007503e-10
          ],
          [
            -7.383547662165313e-10,
            0.041267765087468544,
            1.1463918703213949e-10
          ],
          [
            -4.92011875685705e-10,
            0.027647304744294665,
            7.676403956935474e-11
          ],
          [
            -2.459418224631804e-10,
            0.013871079616456283,
            3.849376373210589e-11
          ],
          [
            -4.6074255521944e-15,
            1.1102230246251565e-16,
            -2.4424906541753444e-15
          ]
        ]
      },
      "reflected": {
        "reached": true,
        "construction": "reflect_displacements_about_reconstructed_parent",
        "energies_eV": [
          -207.10602703676403,
          -207.1052730333741,
          -207.10302954375044,
          -207.0992771459492,
          -207.09390255257188,
          -207.08676610296072,
          -207.07771634958004,
          -207.0666079808381,
          -207.05334624718213
        ],
        "cartesian_polarizations_e_A2": [
          [
            -5.653868028871655e-17,
            1.5310741278251484e-18,
            -3.575559763532659e-17
          ],
          [
            4.41668653142687e-12,
            -0.0001725664601774659,
            -5.626293096098135e-13
          ],
          [
            8.833700616434171e-12,
            -0.00034395286056251493,
            -1.1219919192824402e-12
          ],
          [
            1.3251912762296468e-11,
            -0.0005134014321516991,
            -1.6755928423633532e-12
          ],
          [
            1.7672994591888795e-11,
            -0.0006805245456716595,
            -2.2218479552916685e-12
          ],
          [
            2.2099428644207656e-11,
            -0.0008448468635910848,
            -2.759272016811788e-12
          ],
          [
            2.6534843433834135e-11,
            -0.0010054943698238478,
            -3.2860097178744427e-12
          ],
          [
            3.098339100613786e-11,
            -0.0011613329403152518,
            -3.801201699448666e-12
          ],
          [
            3.544888481147078e-11,
            -0.001311355816224643,
            -4.304984476285461e-12
          ]
        ],
        "raw_reduced_polarization": [
          [
            -4.612058617361431e-15,
            1.23069402385154e-16,
            -2.4463452572611776e-15
          ],
          [
            2.459403725459753e-10,
            -0.01387107961645838,
            -3.849426758847478e-11
          ],
          [
            4.920117153000045e-10,
            -0.027647304744298502,
            -7.676503238503045e-11
          ],
          [
            7.383512940336139e-10,
            -0.04126776508747037,
            -1.1464159108241191e-10
          ],
          [
            9.851134248704984e-10,
            -0.054701302583701025,
            -1.520155602828752e-10
          ],
          [
            1.2324977298202076e-09,
            -0.06790970908562088,
            -1.8878532197017065e-10
          ],
          [
            1.4807852276020837e-09,
            -0.08082273023033537,
            -2.2482393863538784e-10
          ],
          [
            1.7302544260463378e-09,
            -0.09334920389374775,
            -2.6007261420102493e-10
          ],
          [
            1.9811295756539856e-09,
            -0.1054082057060881,
            -2.9454068880501143e-10
          ]
        ],
        "unwrapped_reduced_polarization": [
          [
            -4.612058617361431e-15,
            1.23069402385154e-16,
            -2.4463452572611776e-15
          ],
          [
            2.459403725459753e-10,
            -0.01387107961645838,
            -3.849426758847478e-11
          ],
          [
            4.920117153000045e-10,
            -0.027647304744298502,
            -7.676503238503045e-11
          ],
          [
            7.383512940336139e-10,
            -0.04126776508747037,
            -1.1464159108241191e-10
          ],
          [
            9.851134248704984e-10,
            -0.054701302583701025,
            -1.520155602828752e-10
          ],
          [
            1.2324977298202076e-09,
            -0.06790970908562088,
            -1.8878532197017065e-10
          ],
          [
            1.4807852276020837e-09,
            -0.08082273023033537,
            -2.2482393863538784e-10
          ],
          [
            1.7302544260463378e-09,
            -0.09334920389374775,
            -2.6007261420102493e-10
          ],
          [
            1.9811295756539856e-09,
            -0.1054082057060881,
            -2.9454068880501143e-10
          ]
        ],
        "gauge_integer_shift": [
          0,
          0,
          0
        ],
        "expected_opposite_endpoint_reduced_polarization": [
          1.9811195838461922e-09,
          -0.10540820570608625,
          -2.945473682519797e-10
        ],
        "actual_opposite_endpoint_branch_residual": 1.215968800009587e-14
      },
      "pnp_branch": {
        "construction": "incoming_path_concatenated_with_parent_reflection",
        "reduced_polarization": [
          [
            -1.9811288079634268e-09,
            0.1054082057060865,
            2.9454247556146514e-10
          ],
          [
            -1.7302568942451992e-09,
            0.09334920389374692,
            2.6007053155402556e-10
          ],
          [
            -1.4807886611719251e-09,
            0.08082273023033461,
            2.2482240593837035e-10
          ],
          [
            -1.2324985791964324e-09,
            0.06790970908561704,
            1.887840214874544e-10
          ],
          [
            -9.851133953664237e-10,
            0.05470130258369848,
            1.52015089682893e-10
          ],
          [
            -7.38354741875046e-10,
            0.041267765087468586,
            1.1463922222799398e-10
          ],
          [
            -4.920118516642886e-10,
            0.02764730474429466,
            7.67640536919975e-11
          ],
          [
            -2.4594182292483545e-10,
            0.01387107961645624,
            3.8493786169211784e-11
          ],
          [
            -4.612058617361431e-15,
            1.23069402385154e-16,
            -2.4463452572611776e-15
          ],
          [
            2.459403725459753e-10,
            -0.01387107961645838,
            -3.849426758847478e-11
          ],
          [
            4.920117153000045e-10,
            -0.027647304744298502,
            -7.676503238503045e-11
          ],
          [
            7.383512940336139e-10,
            -0.04126776508747037,
            -1.1464159108241191e-10
          ],
          [
            9.851134248704984e-10,
            -0.054701302583701025,
            -1.520155602828752e-10
          ],
          [
            1.2324977298202076e-09,
            -0.06790970908562088,
            -1.8878532197017065e-10
          ],
          [
            1.4807852276020837e-09,
            -0.08082273023033537,
            -2.2482393863538784e-10
          ],
          [
            1.7302544260463378e-09,
            -0.09334920389374775,
            -2.6007261420102493e-10
          ],
          [
            1.9811295756539856e-09,
            -0.1054082057060881,
            -2.9454068880501143e-10
          ]
        ],
        "unwrapped_reduced_polarization": [
          [
            -1.9811288079634268e-09,
            0.1054082057060865,
            2.9454247556146514e-10
          ],
          [
            -1.7302568942451992e-09,
            0.09334920389374692,
            2.6007053155402556e-10
          ],
          [
            -1.4807886611719251e-09,
            0.08082273023033461,
            2.2482240593837035e-10
          ],
          [
            -1.2324985791964324e-09,
            0.06790970908561704,
            1.887840214874544e-10
          ],
          [
            -9.851133953664237e-10,
            0.05470130258369848,
            1.52015089682893e-10
          ],
          [
            -7.38354741875046e-10,
            0.041267765087468586,
            1.1463922222799398e-10
          ],
          [
            -4.920118516642886e-10,
            0.02764730474429466,
            7.67640536919975e-11
          ],
          [
            -2.4594182292483545e-10,
            0.01387107961645624,
            3.8493786169211784e-11
          ],
          [
            -4.612058617378486e-15,
            1.231653667943533e-16,
            -2.4463452572615767e-15
          ],
          [
            2.459403725459753e-10,
            -0.01387107961645838,
            -3.849426758847478e-11
          ],
          [
            4.920117153000045e-10,
            -0.027647304744298502,
            -7.676503238503045e-11
          ],
          [
            7.383512940336139e-10,
            -0.04126776508747037,
            -1.1464159108241191e-10
          ],
          [
            9.851134248704984e-10,
            -0.054701302583701025,
            -1.520155602828752e-10
          ],
          [
            1.2324977298202076e-09,
            -0.06790970908562088,
            -1.8878532197017065e-10
          ],
          [
            1.4807852276020837e-09,
            -0.08082273023033537,
            -2.2482393863538784e-10
          ],
          [
            1.7302544260463378e-09,
            -0.09334920389374775,
            -2.6007261420102493e-10
          ],
          [
            1.9811295756539856e-09,
            -0.1054082057060881,
            -2.9454068880501143e-10
          ]
        ],
        "berry_integer_shifts": [
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ]
        ],
        "folded_reduced_polarization": [
          [
            -1.9811288165527685e-09,
            0.10540820570608656,
            2.945425014999614e-10
          ],
          [
            -1.7302568822152864e-09,
            0.0933492038937469,
            2.6007052067456016e-10
          ],
          [
            -1.480788658358989e-09,
            0.0808227302303346,
            2.2482238293264345e-10
          ],
          [
            -1.232498603176424e-09,
            0.067909709085617,
            1.8878398844179856e-10
          ],
          [
            -9.851133797589284e-10,
            0.05470130258369843,
            1.520150672007503e-10
          ],
          [
            -7.383547662165313e-10,
            0.041267765087468544,
            1.1463918703213949e-10
          ],
          [
            -4.92011875685705e-10,
            0.027647304744294665,
            7.676403956935474e-11
          ],
          [
            -2.459418224631804e-10,
            0.013871079616456283,
            3.849376373210589e-11
          ],
          [
            -4.6074255521944e-15,
            1.1102230246251565e-16,
            -2.4424906541753444e-15
          ],
          [
            2.459403791732484e-10,
            -0.013871079616458393,
            -3.849426333246697e-11
          ],
          [
            4.920117646634026e-10,
            -0.027647304744298495,
            -7.67650387700769e-11
          ],
          [
            7.383512690140037e-10,
            -0.041267765087470376,
            -1.1464157401164243e-10
          ],
          [
            9.851134352700797e-10,
            -0.05470130258370104,
            -1.520155668011114e-10
          ],
          [
            1.2324977705091555e-09,
            -0.06790970908562088,
            -1.887853207094281e-10
          ],
          [
            1.480785272178764e-09,
            -0.08082273023033537,
            -2.2482393724487792e-10
          ],
          [
            1.730254384213481e-09,
            -0.09334920389374773,
            -2.6007263009830695e-10
          ],
          [
            1.9811295937088857e-09,
            -0.10540820570608811,
            -2.945406696319708e-10
          ]
        ]
      },
      "incoming_structure_ids": [
        "incoming_00_000",
        "incoming_00_001",
        "incoming_00_002",
        "incoming_00_003",
        "incoming_00_004",
        "incoming_00_005",
        "incoming_00_006",
        "incoming_00_007",
        "incoming_00_008"
      ],
      "reflected_structure_ids": [
        "reflected_00_001",
        "reflected_00_002",
        "reflected_00_003",
        "reflected_00_004",
        "reflected_00_005",
        "reflected_00_006",
        "reflected_00_007",
        "reflected_00_008"
      ]
    },
    {
      "orbit_id": 1,
      "formal_class": [
        0.0,
        0.5,
        0.0
      ],
      "formal_classes_in_orbit": [
        [
          0.0,
          0.5,
          0.0
        ]
      ],
      "target_reduced_polarization": [
        0.0,
        0.5,
        0.0
      ],
      "bec_backprojection": {
        "converged_to_target": true,
        "history": [
          {
            "iteration": 0,
            "reduced_polarization": [
              -1.9811285888463236e-09,
              0.10540820570608662,
              2.945421047622473e-10
            ],
            "branch_aligned_reduced_polarization": [
              -1.9811285888463236e-09,
              0.10540820570608661,
              2.945421047622473e-10
            ],
            "target_residual": 0.3945917942939134,
            "energy_eV": -207.05334624718208,
            "max_atomic_step_A": 0.07481248190055287,
            "max_log_strain_component": 0.0022769044173190107,
            "step_scale": 1.0,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 0.762665009945683,
            "cell_principal_stretches": [
              1.0004355775384126,
              0.9990629198136759,
              0.9977256857633061
            ],
            "cell_volume_ratio": 0.9972249164472355,
            "cell_rmsd_from_input_A": 0.010394322292130184
          },
          {
            "iteration": 1,
            "reduced_polarization": [
              -5.756138149257517e-12,
              0.4964649355134137,
              5.242951094057263e-12
            ],
            "branch_aligned_reduced_polarization": [
              -5.756138149257517e-12,
              0.4964649355134137,
              5.242951094057263e-12
            ],
            "target_residual": 0.0035350644865863035,
            "energy_eV": -206.56377219253406,
            "max_atomic_step_A": 0.0006603320227046612,
            "max_log_strain_component": 2.1616782055399953e-05,
            "step_scale": 1.0,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 0.762665009945683,
            "cell_principal_stretches": [
              1.000439713792209,
              0.9990540274447773,
              0.9977041183777158
            ],
            "cell_volume_ratio": 0.9971986069227008,
            "cell_rmsd_from_input_A": 0.010492830129244173
          },
          {
            "iteration": 2,
            "reduced_polarization": [
              -3.926430872154838e-14,
              0.5000079580324552,
              -2.33263370178915e-14
            ],
            "branch_aligned_reduced_polarization": [
              -3.926430872154838e-14,
              0.5000079580324552,
              -2.33263370178915e-14
            ],
            "target_residual": 7.958032455235298e-06,
            "energy_eV": -206.55443646514036
          }
        ],
        "iterations": 2
      },
      "parent": {
        "candidate_id": "bec_projection_01",
        "source": "MACEField_BEC_backprojection",
        "spacegroup": "P2_1",
        "spacegroup_number": 4,
        "pointgroup": "2",
        "has_inversion": false,
        "is_polar_point_group": true,
        "nonpolar_parent_hypothesis": false,
        "symmetry_tolerance_A": null,
        "target_reduced_polarization": [
          0.0,
          0.5,
          0.0
        ],
        "formal_class": [
          0.0,
          0.5,
          0.0
        ],
        "target_residual": 7.958032455235298e-06,
        "parent_symmetrization_rmsd_A": 0.05744700446843624,
        "parent_cell_rmsd_A": 0.010492830129244173,
        "energy_eV": -206.55443646514036,
        "reduced_polarization": [
          -3.926430872154838e-14,
          0.5000079580324552,
          -2.33263370178915e-14
        ],
        "cartesian_polarization_e_A2": [
          -3.219096483753067e-14,
          0.006223621099053913,
          1.2215443488453445e-13
        ],
        "ranking_score": 0.5600861280656577
      },
      "branch_status": "awaiting_branch_sampling"
    },
    {
      "orbit_id": 2,
      "formal_class": [
        0.5,
        0.0,
        0.0
      ],
      "formal_classes_in_orbit": [
        [
          0.5,
          0.0,
          0.0
        ]
      ],
      "target_reduced_polarization": [
        -0.5,
        0.0,
        0.0
      ],
      "bec_backprojection": {
        "converged_to_target": true,
        "history": [
          {
            "iteration": 0,
            "reduced_polarization": [
              -1.9811285888463236e-09,
              0.10540820570608662,
              2.945421047622473e-10
            ],
            "branch_aligned_reduced_polarization": [
              -1.9811285945081636e-09,
              0.10540820570608662,
              2.945421047622473e-10
            ],
            "target_residual": 0.5109901054316494,
            "energy_eV": -207.05334624718208,
            "max_atomic_step_A": 0.12,
            "max_log_strain_component": 0.005313990268096103,
            "step_scale": 0.8184836500083104,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 0.762665009945683,
            "cell_principal_stretches": [
              1.0058502086607217,
              1.000169321152315,
              0.9946196538531953
            ],
            "cell_volume_ratio": 1.0006077817466907,
            "cell_rmsd_from_input_A": 0.04940801877824281
          },
          {
            "iteration": 1,
            "reduced_polarization": [
              -0.4032715282376302,
              0.023069038260752312,
              0.0020438312168534244
            ],
            "branch_aligned_reduced_polarization": [
              -0.4032715282376302,
              0.023069038260752312,
              0.0020438312168534244
            ],
            "target_residual": 0.09946232966205151,
            "energy_eV": -205.717327654366,
            "max_atomic_step_A": 0.03038403492388817,
            "max_log_strain_component": 0.0013208756210211436,
            "step_scale": 1.0,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 0.762665009945683,
            "cell_principal_stretches": [
              1.0072849010821399,
              1.0002235081901065,
              0.9933290169372238
            ],
            "cell_volume_ratio": 1.0007889551115141,
            "cell_rmsd_from_input_A": 0.061269806517178955
          },
          {
            "iteration": 2,
            "reduced_polarization": [
              -0.49922359800857175,
              0.00082340917934824,
              0.00033734278093270075
            ],
            "branch_aligned_reduced_polarization": [
              -0.49922359800857175,
              0.00082340917934824,
              0.00033734278093270075
            ],
            "target_residual": 0.0011809330551627853,
            "energy_eV": -204.90642514857288,
            "max_atomic_step_A": 0.0002567829145432573,
            "max_log_strain_component": 9.454170970818254e-06,
            "step_scale": 1.0,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 0.762665009945683,
            "cell_principal_stretches": [
              1.0072947297034993,
              1.0002254968478168,
              0.9933233999140463
            ],
            "cell_volume_ratio": 1.0007950508760797,
            "cell_rmsd_from_input_A": 0.061327744048695586
          },
          {
            "iteration": 3,
            "reduced_polarization": [
              -0.49999865102662866,
              6.762873249015527e-06,
              6.947204529207777e-07
            ],
            "branch_aligned_reduced_polarization": [
              -0.49999865102662866,
              6.762873249015527e-06,
              6.947204529207777e-07
            ],
            "target_residual": 6.931004274024144e-06,
            "energy_eV": -204.89988522241575
          }
        ],
        "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": [
          -0.5,
          0.0,
          0.0
        ],
        "formal_class": [
          0.5,
          0.0,
          0.0
        ],
        "target_residual": 6.931004274024144e-06,
        "parent_symmetrization_rmsd_A": 0.11805443892907622,
        "parent_cell_rmsd_A": 0.061327744048695586,
        "energy_eV": -204.89988522241575,
        "reduced_polarization": [
          -0.49999865102662866,
          6.762873249015527e-06,
          6.947204529207777e-07
        ],
        "cartesian_polarization_e_A2": [
          -0.008322387972110282,
          -5.523404898046193e-05,
          1.577534782549983e-07
        ],
        "ranking_score": 0.6334002369497982
      },
      "branch_status": "awaiting_branch_sampling"
    },
    {
      "orbit_id": 3,
      "formal_class": [
        0.0,
        0.0,
        0.5
      ],
      "formal_classes_in_orbit": [
        [
          0.0,
          0.0,
          0.5
        ]
      ],
      "target_reduced_polarization": [
        0.0,
        0.0,
        0.5
      ],
      "bec_backprojection": {
        "converged_to_target": true,
        "history": [
          {
            "iteration": 0,
            "reduced_polarization": [
              -1.9811285888463236e-09,
              0.10540820570608662,
              2.945421047622473e-10
            ],
            "branch_aligned_reduced_polarization": [
              -1.9811285888463236e-09,
              0.10540820570608662,
              2.945421129219028e-10
            ],
            "target_residual": 0.5109901070819616,
            "energy_eV": -207.05334624718208,
            "max_atomic_step_A": 0.12,
            "max_log_strain_component": 0.009044697812175479,
            "step_scale": 0.8041526867990948,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 0.762665009945683,
            "cell_principal_stretches": [
              1.00962407905618,
              0.9999154884065795,
              0.9911428687500871
            ],
            "cell_volume_ratio": 1.0005971368694198,
            "cell_rmsd_from_input_A": 0.06601245608517527
          },
          {
            "iteration": 1,
            "reduced_polarization": [
              -0.0021741893803655134,
              0.02537533944434266,
              0.39400930380835825
            ],
            "branch_aligned_reduced_polarization": [
              -0.0021741893803655134,
              0.02537533944434266,
              0.39400930380835825
            ],
            "target_residual": 0.10900762647891298,
            "energy_eV": -205.91606744155783,
            "max_atomic_step_A": 0.03155463898136309,
            "max_log_strain_component": 0.002601723755469713,
            "step_scale": 1.0,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 0.762665009945683,
            "cell_principal_stretches": [
              1.0124166763425544,
              0.9998854776900203,
              0.988642960800605
            ],
            "cell_volume_ratio": 1.0008039929506936,
            "cell_rmsd_from_input_A": 0.08469855537224602
          },
          {
            "iteration": 2,
            "reduced_polarization": [
              -0.0006732003641704546,
              0.0009923273308114643,
              0.4982982224694936
            ],
            "branch_aligned_reduced_polarization": [
              -0.0006732003641704546,
              0.0009923273308114643,
              0.4982982224694936
            ],
            "target_residual": 0.0020818162803501704,
            "energy_eV": -205.1347507481734,
            "max_atomic_step_A": 0.0005098031797694378,
            "max_log_strain_component": 4.084866356163062e-05,
            "step_scale": 1.0,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 0.762665009945683,
            "cell_principal_stretches": [
              1.0124616402108875,
              0.9998842703643883,
              0.9886079380764465
            ],
            "cell_volume_ratio": 1.0008117775222816,
            "cell_rmsd_from_input_A": 0.08495218886401529
          },
          {
            "iteration": 3,
            "reduced_polarization": [
              -5.793734511618371e-06,
              6.254111182672724e-06,
              0.499991352783554
            ],
            "branch_aligned_reduced_polarization": [
              -5.793734511618371e-06,
              6.254111182672724e-06,
              0.499991352783554
            ],
            "target_residual": 1.2143130508247523e-05,
            "energy_eV": -205.12245713076447
          }
        ],
        "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": [
          0.0,
          0.0,
          0.5
        ],
        "formal_class": [
          0.0,
          0.0,
          0.5
        ],
        "target_residual": 1.2143130508247523e-05,
        "parent_symmetrization_rmsd_A": 0.10744526153423732,
        "parent_cell_rmsd_A": 0.08495218886401529,
        "energy_eV": -205.12245713076447,
        "reduced_polarization": [
          -5.793734511618371e-06,
          6.254111182672724e-06,
          0.499991352783554
        ],
        "cartesian_polarization_e_A2": [
          -0.004144766972049045,
          -9.50058486470466e-05,
          0.007304508145931221
        ],
        "ranking_score": 0.6287075950112576
      },
      "branch_status": "awaiting_branch_sampling"
    },
    {
      "orbit_id": 4,
      "formal_class": [
        0.5,
        0.5,
        0.0
      ],
      "formal_classes_in_orbit": [
        [
          0.5,
          0.5,
          0.0
        ]
      ],
      "target_reduced_polarization": [
        -0.5,
        0.5,
        0.0
      ],
      "bec_backprojection": {
        "converged_to_target": true,
        "history": [
          {
            "iteration": 0,
            "reduced_polarization": [
              -1.9811285888463236e-09,
              0.10540820570608662,
              2.945421047622473e-10
            ],
            "branch_aligned_reduced_polarization": [
              -1.9811285945081636e-09,
              0.10540820570608661,
              2.945421047622473e-10
            ],
            "target_residual": 0.6369479430400584,
            "energy_eV": -207.05334624718208,
            "max_atomic_step_A": 0.12,
            "max_log_strain_component": 0.004580759267074898,
            "step_scale": 0.7055482527341084,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 0.762665009945683,
            "cell_principal_stretches": [
              1.0042294546788568,
              0.9994498174654927,
              0.9943849447750778
            ],
            "cell_volume_ratio": 0.9980412436971314,
            "cell_rmsd_from_input_A": 0.043082987747914206
          },
          {
            "iteration": 1,
            "reduced_polarization": [
              -0.348757259587461,
              0.3830937130014818,
              0.0010852760978700964
            ],
            "branch_aligned_reduced_polarization": [
              -0.348757259587461,
              0.3830937130014818,
              0.0010852760978700964
            ],
            "target_residual": 0.19116125206611084,
            "energy_eV": -205.82762418727762,
            "max_atomic_step_A": 0.05123700361979848,
            "max_log_strain_component": 0.0020758597830083645,
            "step_scale": 1.0,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 0.762665009945683,
            "cell_principal_stretches": [
              1.0061266363960872,
              0.9991896271867812,
              0.9918934322906513
            ],
            "cell_volume_ratio": 0.9971616746112231,
            "cell_rmsd_from_input_A": 0.062133187138379876
          },
          {
            "iteration": 2,
            "reduced_polarization": [
              -0.4980746616803419,
              0.49974309461592215,
              0.000834133916189228
            ],
            "branch_aligned_reduced_polarization": [
              -0.4980746616803419,
              0.49974309461592215,
              0.000834133916189228
            ],
            "target_residual": 0.0021139317424290582,
            "energy_eV": -204.35207258520552,
            "max_atomic_step_A": 0.0005341477045154324,
            "max_log_strain_component": 2.3422436623629484e-05,
            "step_scale": 1.0,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 0.762665009945683,
            "cell_principal_stretches": [
              1.0061455829874784,
              0.9991867081676665,
              0.9918751379342078
            ],
            "cell_volume_ratio": 0.9971591474160731,
            "cell_rmsd_from_input_A": 0.06227262532447545
          },
          {
            "iteration": 3,
            "reduced_polarization": [
              -0.5000049326481907,
              0.5000150898887037,
              -1.8372645249400304e-06
            ],
            "branch_aligned_reduced_polarization": [
              -0.5000049326481907,
              0.5000150898887037,
              -1.8372645249400304e-06
            ],
            "target_residual": 1.598159254259029e-05,
            "energy_eV": -204.33558170696932
          }
        ],
        "iterations": 3
      },
      "parent": {
        "candidate_id": "bec_projection_04",
        "source": "MACEField_BEC_backprojection",
        "spacegroup": "P1",
        "spacegroup_number": 1,
        "pointgroup": "1",
        "has_inversion": false,
        "is_polar_point_group": true,
        "nonpolar_parent_hypothesis": false,
        "symmetry_tolerance_A": null,
        "target_reduced_polarization": [
          -0.5,
          0.5,
          0.0
        ],
        "formal_class": [
          0.5,
          0.5,
          0.0
        ],
        "target_residual": 1.598159254259029e-05,
        "parent_symmetrization_rmsd_A": 0.131556693082125,
        "parent_cell_rmsd_A": 0.06227262532447545,
        "energy_eV": -204.33558170696932,
        "reduced_polarization": [
          -0.5000049326481907,
          0.5000150898887037,
          -1.8372645249400304e-06
        ],
        "cartesian_polarization_e_A2": [
          -0.008315940840688185,
          0.006168156613081754,
          -1.3478237313887176e-05
        ],
        "ranking_score": 0.647156812598329
      },
      "branch_status": "awaiting_branch_sampling"
    },
    {
      "orbit_id": 5,
      "formal_class": [
        0.0,
        0.5,
        0.5
      ],
      "formal_classes_in_orbit": [
        [
          0.0,
          0.5,
          0.5
        ]
      ],
      "target_reduced_polarization": [
        0.0,
        0.5,
        0.5
      ],
      "bec_backprojection": {
        "converged_to_target": true,
        "history": [
          {
            "iteration": 0,
            "reduced_polarization": [
              -1.9811285888463236e-09,
              0.10540820570608662,
              2.945421047622473e-10
            ],
            "branch_aligned_reduced_polarization": [
              -1.9811285888463236e-09,
              0.10540820570608661,
              2.945421129219028e-10
            ],
            "target_residual": 0.6369479443640178,
            "energy_eV": -207.05334624718208,
            "max_atomic_step_A": 0.12,
            "max_log_strain_component": 0.0077938668296066395,
            "step_scale": 0.6929428804265386,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 0.762665009945683,
            "cell_principal_stretches": [
              1.0068997682157481,
              1.000271914867969,
              0.990967441685385
            ],
            "cell_volume_ratio": 0.9980762053265678,
            "cell_rmsd_from_input_A": 0.05709025702400355
          },
          {
            "iteration": 1,
            "reduced_polarization": [
              -0.00016441086348382002,
              0.37868362406221057,
              0.3428141899124547
            ],
            "branch_aligned_reduced_polarization": [
              -0.00016441086348382002,
              0.37868362406221057,
              0.3428141899124547
            ],
            "target_residual": 0.19855747025606704,
            "energy_eV": -205.95518105057343,
            "max_atomic_step_A": 0.050967612581073504,
            "max_log_strain_component": 0.003796105693135077,
            "step_scale": 1.0,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 0.762665009945683,
            "cell_principal_stretches": [
              1.0102944969855496,
              1.0003996323032347,
              0.9866279382158438
            ],
            "cell_volume_ratio": 0.9971831239477487,
            "cell_rmsd_from_input_A": 0.08461728845857272
          },
          {
            "iteration": 2,
            "reduced_polarization": [
              -9.70064219545747e-05,
              0.4999184554113667,
              0.4975214380774067
            ],
            "branch_aligned_reduced_polarization": [
              -9.70064219545747e-05,
              0.4999184554113667,
              0.4975214380774067
            ],
            "target_residual": 0.002481799542663614,
            "energy_eV": -204.51867283050376,
            "max_atomic_step_A": 0.0007384279989442402,
            "max_log_strain_component": 6.365157442792004e-05,
            "step_scale": 1.0,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 0.762665009945683,
            "cell_principal_stretches": [
              1.010358977032457,
              1.0003998638677483,
              0.9865638368281983
            ],
            "cell_volume_ratio": 0.9971822067121362,
            "cell_rmsd_from_input_A": 0.08506408546730292
          },
          {
            "iteration": 3,
            "reduced_polarization": [
              4.272841579187377e-06,
              0.500008869217408,
              0.5000029063790639
            ],
            "branch_aligned_reduced_polarization": [
              4.272841579187377e-06,
              0.500008869217408,
              0.5000029063790639
            ],
            "target_residual": 1.0264854205156426e-05,
            "energy_eV": -204.4949204617253
          }
        ],
        "iterations": 3
      },
      "parent": {
        "candidate_id": "bec_projection_05",
        "source": "MACEField_BEC_backprojection",
        "spacegroup": "P1",
        "spacegroup_number": 1,
        "pointgroup": "1",
        "has_inversion": false,
        "is_polar_point_group": true,
        "nonpolar_parent_hypothesis": false,
        "symmetry_tolerance_A": null,
        "target_reduced_polarization": [
          0.0,
          0.5,
          0.5
        ],
        "formal_class": [
          0.0,
          0.5,
          0.5
        ],
        "target_residual": 1.0264854205156426e-05,
        "parent_symmetrization_rmsd_A": 0.12197825524938662,
        "parent_cell_rmsd_A": 0.08506408546730292,
        "energy_eV": -204.4949204617253,
        "reduced_polarization": [
          4.272841579187377e-06,
          0.500008869217408,
          0.5000029063790639
        ],
        "cartesian_polarization_e_A2": [
          -0.004146969872721671,
          0.0061289473074150665,
          0.007249503936026567
        ],
        "ranking_score": 0.6432648063246227
      },
      "branch_status": "awaiting_branch_sampling"
    },
    {
      "orbit_id": 6,
      "formal_class": [
        0.5,
        0.0,
        0.5
      ],
      "formal_classes_in_orbit": [
        [
          0.5,
          0.0,
          0.5
        ]
      ],
      "target_reduced_polarization": [
        -0.5,
        0.0,
        0.5
      ],
      "bec_backprojection": {
        "converged_to_target": true,
        "history": [
          {
            "iteration": 0,
            "reduced_polarization": [
              -1.9811285888463236e-09,
              0.10540820570608662,
              2.945421047622473e-10
            ],
            "branch_aligned_reduced_polarization": [
              -1.9811285945081636e-09,
              0.10540820570608662,
              2.945421129219028e-10
            ],
            "target_residual": 0.7149201966335166,
            "energy_eV": -207.05334624718208,
            "max_atomic_step_A": 0.12,
            "max_log_strain_component": 0.006232844901411985,
            "step_scale": 0.4640921503084028,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 0.762665009945683,
            "cell_principal_stretches": [
              1.007662373001588,
              0.9999929769800595,
              0.9927448201528589
            ],
            "cell_volume_ratio": 1.0003445757710214,
            "cell_rmsd_from_input_A": 0.06222736396304553
          },
          {
            "iteration": 1,
            "reduced_polarization": [
              -0.23089173350819847,
              0.06010817195123375,
              0.22906016561458625
            ],
            "branch_aligned_reduced_polarization": [
              -0.23089173350819847,
              0.06010817195123375,
              0.22906016561458625
            ],
            "target_residual": 0.3865755363267792,
            "energy_eV": -205.7957265910138,
            "max_atomic_step_A": 0.12,
            "max_log_strain_component": 0.0062428409548971504,
            "step_scale": 0.8172954394414327,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 0.762665009945683,
            "cell_principal_stretches": [
              1.015359841027543,
              0.9999824329084028,
              0.9856283194236057
            ],
            "cell_volume_ratio": 1.0007498331493725,
            "cell_rmsd_from_input_A": 0.1238238993736418
          },
          {
            "iteration": 2,
            "reduced_polarization": [
              -0.44975771831784395,
              0.018098522481361203,
              0.44277410119530486
            ],
            "branch_aligned_reduced_polarization": [
              -0.44975771831784395,
              0.018098522481361203,
              0.44277410119530486
            ],
            "target_residual": 0.07827290002703784,
            "energy_eV": -201.1204137235304,
            "max_atomic_step_A": 0.0418544691875304,
            "max_log_strain_component": 0.0017265977391561949,
            "step_scale": 1.0,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 0.762665009945683,
            "cell_principal_stretches": [
              1.0174540491592132,
              0.9999749867511711,
              0.9837808411477592
            ],
            "cell_volume_ratio": 1.0009267632545973,
            "cell_rmsd_from_input_A": 0.1399187611671927
          },
          {
            "iteration": 3,
            "reduced_polarization": [
              -0.5006728207442177,
              0.0012411034543379513,
              0.4995486035441038
            ],
            "branch_aligned_reduced_polarization": [
              -0.5006728207442177,
              0.0012411034543379513,
              0.4995486035441038
            ],
            "target_residual": 0.0014821552882930032,
            "energy_eV": -198.59309231746693,
            "max_atomic_step_A": 0.0003440800304305417,
            "max_log_strain_component": 1.0237505854352066e-05,
            "step_scale": 1.0,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 0.762665009945683,
            "cell_principal_stretches": [
              1.017464250152233,
              0.9999744595956783,
              0.9837808277846173
            ],
            "cell_volume_ratio": 1.000936257286368,
            "cell_rmsd_from_input_A": 0.1399334671599225
          },
          {
            "iteration": 4,
            "reduced_polarization": [
              -0.5000034312238999,
              -2.691426148789447e-06,
              0.4999975847005014
            ],
            "branch_aligned_reduced_polarization": [
              -0.5000034312238999,
              -2.691426148789447e-06,
              0.4999975847005014
            ],
            "target_residual": 4.985052039214179e-06,
            "energy_eV": -198.5981545641019
          }
        ],
        "iterations": 4
      },
      "parent": {
        "candidate_id": "bec_projection_06",
        "source": "MACEField_BEC_backprojection",
        "spacegroup": "P1",
        "spacegroup_number": 1,
        "pointgroup": "1",
        "has_inversion": false,
        "is_polar_point_group": true,
        "nonpolar_parent_hypothesis": false,
        "symmetry_tolerance_A": null,
        "target_reduced_polarization": [
          -0.5,
          0.0,
          0.5
        ],
        "formal_class": [
          0.5,
          0.0,
          0.5
        ],
        "target_residual": 4.985052039214179e-06,
        "parent_symmetrization_rmsd_A": 0.19923640807025955,
        "parent_cell_rmsd_A": 0.1399334671599225,
        "energy_eV": -198.5981545641019,
        "reduced_polarization": [
          -0.5000034312238999,
          -2.691426148789447e-06,
          0.4999975847005014
        ],
        "cartesian_polarization_e_A2": [
          -0.012465914848356723,
          -0.00021626807416253566,
          0.007305111889064243
        ],
        "ranking_score": 0.7342297449643186
      },
      "branch_status": "awaiting_branch_sampling"
    },
    {
      "orbit_id": 7,
      "formal_class": [
        0.5,
        0.5,
        0.5
      ],
      "formal_classes_in_orbit": [
        [
          0.5,
          0.5,
          0.5
        ]
      ],
      "target_reduced_polarization": [
        -0.5,
        0.5,
        0.5
      ],
      "bec_backprojection": {
        "converged_to_target": true,
        "history": [
          {
            "iteration": 0,
            "reduced_polarization": [
              -1.9811285888463236e-09,
              0.10540820570608662,
              2.945421047622473e-10
            ],
            "branch_aligned_reduced_polarization": [
              -1.9811285945081636e-09,
              0.10540820570608661,
              2.945421129219028e-10
            ],
            "target_residual": 0.8097547047399103,
            "energy_eV": -207.05334624718208,
            "max_atomic_step_A": 0.12,
            "max_log_strain_component": 0.005814916326741749,
            "step_scale": 0.43297355632932344,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 0.762665009945683,
            "cell_principal_stretches": [
              1.0063784287597208,
              1.000023153557017,
              0.9924441559438467
            ],
            "cell_volume_ratio": 0.9987975154703287,
            "cell_rmsd_from_input_A": 0.058108321007032705
          },
          {
            "iteration": 1,
            "reduced_polarization": [
              -0.21519171101851853,
              0.2776090009342234,
              0.21463415085786267
            ],
            "branch_aligned_reduced_polarization": [
              -0.21519171101851853,
              0.2776090009342234,
              0.21463415085786264
            ],
            "target_residual": 0.4604423805370726,
            "energy_eV": -205.8600601301571,
            "max_atomic_step_A": 0.12,
            "max_log_strain_component": 0.006222665291173897,
            "step_scale": 0.7778160086093242,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 0.762665009945683,
            "cell_principal_stretches": [
              1.013222909228747,
              1.0000517019836763,
              0.9844694952781579
            ],
            "cell_volume_ratio": 0.9975386181116636,
            "cell_rmsd_from_input_A": 0.11968505169196149
          },
          {
            "iteration": 2,
            "reduced_polarization": [
              -0.4335307952619001,
              0.4505862839912485,
              0.430001527880421
            ],
            "branch_aligned_reduced_polarization": [
              -0.4335307952619001,
              0.4505862839912485,
              0.430001527880421
            ],
            "target_residual": 0.10844195040381958,
            "energy_eV": -201.03687119404702,
            "max_atomic_step_A": 0.05180967937712659,
            "max_log_strain_component": 0.002141877740490962,
            "step_scale": 1.0,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 0.762665009945683,
            "cell_principal_stretches": [
              1.0155339082289965,
              1.0000681759643417,
              0.9818061701658363
            ],
            "cell_volume_ratio": 0.997125432465498,
            "cell_rmsd_from_input_A": 0.14010486530365038
          },
          {
            "iteration": 3,
            "reduced_polarization": [
              -0.5005807922607016,
              0.5007295699126327,
              0.49990648928691656
            ],
            "branch_aligned_reduced_polarization": [
              -0.5005807922607016,
              0.5007295699126327,
              0.49990648928691656
            ],
            "target_residual": 0.0009371959031980508,
            "energy_eV": -197.66330082311345
          }
        ],
        "iterations": 3
      },
      "parent": {
        "candidate_id": "bec_projection_07",
        "source": "MACEField_BEC_backprojection",
        "spacegroup": "P1",
        "spacegroup_number": 1,
        "pointgroup": "1",
        "has_inversion": false,
        "is_polar_point_group": true,
        "nonpolar_parent_hypothesis": false,
        "symmetry_tolerance_A": null,
        "target_reduced_polarization": [
          -0.5,
          0.5,
          0.5
        ],
        "formal_class": [
          0.5,
          0.5,
          0.5
        ],
        "target_residual": 0.0009371959031980508,
        "parent_symmetrization_rmsd_A": 0.209490775295405,
        "parent_cell_rmsd_A": 0.14010486530365038,
        "energy_eV": -197.66330082311345,
        "reduced_polarization": [
          -0.5005807922607016,
          0.5007295699126327,
          0.49990648928691656
        ],
        "cartesian_polarization_e_A2": [
          -0.012472691408892803,
          0.006015878076033359,
          0.007233169032069438
        ],
        "ranking_score": 0.7463913834277137
      },
      "branch_status": "awaiting_branch_sampling"
    }
  ],
  "sampled_polarization_branches": [
    {
      "orbit_id": 0,
      "candidate_id": "inversion_parent_endpoint_00",
      "formal_class": [
        0.0,
        0.0,
        0.0
      ],
      "construction": "MACEField-BEC-parent plus variable-cell P-N-P path and symmetric log-strain continuation beyond both polar endpoints",
      "geometry_diagnostics": {
        "collision_aware": false,
        "permutations_tested": 1,
        "selected_order": [
          0,
          1,
          2,
          3,
          4,
          5,
          6,
          7,
          8,
          9,
          10,
          11,
          12,
          13,
          14,
          15,
          16,
          17,
          18,
          19,
          20,
          21,
          22,
          23,
          24,
          25,
          26,
          27,
          28,
          29,
          30,
          31,
          32,
          33,
          34,
          35,
          36,
          37,
          38,
          39,
          40,
          41
        ],
        "endpoint_rmsd_A": 0.09580572242523867,
        "minimum_distance_A_by_image": [
          1.5327968451978016,
          1.5327693524970998,
          1.5327455251684348,
          1.5327253633827487,
          1.5327088672846898,
          1.5326960369926215,
          1.532686872598608,
          1.5326813741684011,
          1.532679541741461
        ],
        "minimum_distance_A": 1.532679541741461,
        "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": [
          574.5523532784798,
          574.5523532784798,
          574.5523532784798,
          574.5523532784798,
          574.5523532784798,
          574.5523532784798,
          574.5523532784798,
          574.5523532784798,
          574.5523532784798
        ],
        "cell_deformation_log_strain_norm": 0.0
      },
      "parent_reduced_polarization": [
        -4.612058617361431e-15,
        1.23069402385154e-16,
        -2.4463452572611776e-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": [
          -207.0533462471821,
          -207.06660798083806,
          -207.07771634958007,
          -207.0867661029607,
          -207.09390255257188,
          -207.09927714594926,
          -207.10302954375047,
          -207.10527303337403,
          -207.10602703676403
        ],
        "cartesian_polarizations_e_A2": [
          [
            -3.544888684645265e-11,
            0.0013113558162246232,
            4.305010591382928e-12
          ],
          [
            -3.098341484622221e-11,
            0.0011613329403152414,
            3.8011712596373165e-12
          ],
          [
            -2.6534887919624768e-11,
            0.0010054943698238382,
            3.28598731609052e-12
          ],
          [
            -2.2099432004645076e-11,
            0.0008448468635910371,
            2.759253009054565e-12
          ],
          [
            -1.7672990195844874e-11,
            0.0006805245456716278,
            2.2218410770378487e-12
          ],
          [
            -1.3251950548347084e-11,
            0.000513401432151677,
            1.6755582193659767e-12
          ],
          [
            -8.83369476812574e-12,
            0.0003439528605624671,
            1.1219776147789404e-12
          ],
          [
            -4.416706700089923e-12,
            0.0001725664601774393,
            5.626222732222019e-13
          ],
          [
            -5.653868028871655e-17,
            1.5310741278251484e-18,
            -3.575559763532659e-17
          ]
        ],
        "raw_reduced_polarization": [
          [
            -1.9811288079634268e-09,
            0.1054082057060865,
            2.9454247556146514e-10
          ],
          [
            -1.7302568942451992e-09,
            0.09334920389374692,
            2.6007053155402556e-10
          ],
          [
            -1.4807886611719251e-09,
            0.08082273023033461,
            2.2482240593837035e-10
          ],
          [
            -1.2324985791964324e-09,
            0.06790970908561704,
            1.887840214874544e-10
          ],
          [
            -9.851133953664237e-10,
            0.05470130258369848,
            1.52015089682893e-10
          ],
          [
            -7.38354741875046e-10,
            0.041267765087468586,
            1.1463922222799398e-10
          ],
          [
            -4.920118516642886e-10,
            0.02764730474429466,
            7.67640536919975e-11
          ],
          [
            -2.4594182292483545e-10,
            0.01387107961645624,
            3.8493786169211784e-11
          ],
          [
            -4.612058617361431e-15,
            1.23069402385154e-16,
            -2.4463452572611776e-15
          ]
        ],
        "unwrapped_reduced_polarization": [
          [
            -1.9811288079634268e-09,
            0.1054082057060865,
            2.9454247556146514e-10
          ],
          [
            -1.7302568942451992e-09,
            0.09334920389374692,
            2.6007053155402556e-10
          ],
          [
            -1.4807886611719251e-09,
            0.08082273023033461,
            2.2482240593837035e-10
          ],
          [
            -1.2324985791964324e-09,
            0.06790970908561704,
            1.887840214874544e-10
          ],
          [
            -9.851133953664237e-10,
            0.05470130258369848,
            1.52015089682893e-10
          ],
          [
            -7.38354741875046e-10,
            0.041267765087468586,
            1.1463922222799398e-10
          ],
          [
            -4.920118516642886e-10,
            0.02764730474429466,
            7.67640536919975e-11
          ],
          [
            -2.4594182292483545e-10,
            0.01387107961645624,
            3.8493786169211784e-11
          ],
          [
            -4.612058617378486e-15,
            1.231653667943533e-16,
            -2.4463452572615767e-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": [
          [
            -1.9811288165527685e-09,
            0.10540820570608656,
            2.945425014999614e-10
          ],
          [
            -1.7302568822152864e-09,
            0.0933492038937469,
            2.6007052067456016e-10
          ],
          [
            -1.480788658358989e-09,
            0.0808227302303346,
            2.2482238293264345e-10
          ],
          [
            -1.232498603176424e-09,
            0.067909709085617,
            1.8878398844179856e-10
          ],
          [
            -9.851133797589284e-10,
            0.05470130258369843,
            1.520150672007503e-10
          ],
          [
            -7.383547662165313e-10,
            0.041267765087468544,
            1.1463918703213949e-10
          ],
          [
            -4.92011875685705e-10,
            0.027647304744294665,
            7.676403956935474e-11
          ],
          [
            -2.459418224631804e-10,
            0.013871079616456283,
            3.849376373210589e-11
          ],
          [
            -4.6074255521944e-15,
            1.1102230246251565e-16,
            -2.4424906541753444e-15
          ]
        ]
      },
      "reflected": {
        "reached": true,
        "construction": "reflect_displacements_about_reconstructed_parent",
        "energies_eV": [
          -207.10602703676403,
          -207.1052730333741,
          -207.10302954375044,
          -207.0992771459492,
          -207.09390255257188,
          -207.08676610296072,
          -207.07771634958004,
          -207.0666079808381,
          -207.05334624718213
        ],
        "cartesian_polarizations_e_A2": [
          [
            -5.653868028871655e-17,
            1.5310741278251484e-18,
            -3.575559763532659e-17
          ],
          [
            4.41668653142687e-12,
            -0.0001725664601774659,
            -5.626293096098135e-13
          ],
          [
            8.833700616434171e-12,
            -0.00034395286056251493,
            -1.1219919192824402e-12
          ],
          [
            1.3251912762296468e-11,
            -0.0005134014321516991,
            -1.6755928423633532e-12
          ],
          [
            1.7672994591888795e-11,
            -0.0006805245456716595,
            -2.2218479552916685e-12
          ],
          [
            2.2099428644207656e-11,
            -0.0008448468635910848,
            -2.759272016811788e-12
          ],
          [
            2.6534843433834135e-11,
            -0.0010054943698238478,
            -3.2860097178744427e-12
          ],
          [
            3.098339100613786e-11,
            -0.0011613329403152518,
            -3.801201699448666e-12
          ],
          [
            3.544888481147078e-11,
            -0.001311355816224643,
            -4.304984476285461e-12
          ]
        ],
        "raw_reduced_polarization": [
          [
            -4.612058617361431e-15,
            1.23069402385154e-16,
            -2.4463452572611776e-15
          ],
          [
            2.459403725459753e-10,
            -0.01387107961645838,
            -3.849426758847478e-11
          ],
          [
            4.920117153000045e-10,
            -0.027647304744298502,
            -7.676503238503045e-11
          ],
          [
            7.383512940336139e-10,
            -0.04126776508747037,
            -1.1464159108241191e-10
          ],
          [
            9.851134248704984e-10,
            -0.054701302583701025,
            -1.520155602828752e-10
          ],
          [
            1.2324977298202076e-09,
            -0.06790970908562088,
            -1.8878532197017065e-10
          ],
          [
            1.4807852276020837e-09,
            -0.08082273023033537,
            -2.2482393863538784e-10
          ],
          [
            1.7302544260463378e-09,
            -0.09334920389374775,
            -2.6007261420102493e-10
          ],
          [
            1.9811295756539856e-09,
            -0.1054082057060881,
            -2.9454068880501143e-10
          ]
        ],
        "unwrapped_reduced_polarization": [
          [
            -4.612058617361431e-15,
            1.23069402385154e-16,
            -2.4463452572611776e-15
          ],
          [
            2.459403725459753e-10,
            -0.01387107961645838,
            -3.849426758847478e-11
          ],
          [
            4.920117153000045e-10,
            -0.027647304744298502,
            -7.676503238503045e-11
          ],
          [
            7.383512940336139e-10,
            -0.04126776508747037,
            -1.1464159108241191e-10
          ],
          [
            9.851134248704984e-10,
            -0.054701302583701025,
            -1.520155602828752e-10
          ],
          [
            1.2324977298202076e-09,
            -0.06790970908562088,
            -1.8878532197017065e-10
          ],
          [
            1.4807852276020837e-09,
            -0.08082273023033537,
            -2.2482393863538784e-10
          ],
          [
            1.7302544260463378e-09,
            -0.09334920389374775,
            -2.6007261420102493e-10
          ],
          [
            1.9811295756539856e-09,
            -0.1054082057060881,
            -2.9454068880501143e-10
          ]
        ],
        "gauge_integer_shift": [
          0,
          0,
          0
        ],
        "expected_opposite_endpoint_reduced_polarization": [
          1.9811195838461922e-09,
          -0.10540820570608625,
          -2.945473682519797e-10
        ],
        "actual_opposite_endpoint_branch_residual": 1.215968800009587e-14
      },
      "pnp_branch": {
        "construction": "incoming_path_concatenated_with_parent_reflection",
        "reduced_polarization": [
          [
            -1.9811288079634268e-09,
            0.1054082057060865,
            2.9454247556146514e-10
          ],
          [
            -1.7302568942451992e-09,
            0.09334920389374692,
            2.6007053155402556e-10
          ],
          [
            -1.4807886611719251e-09,
            0.08082273023033461,
            2.2482240593837035e-10
          ],
          [
            -1.2324985791964324e-09,
            0.06790970908561704,
            1.887840214874544e-10
          ],
          [
            -9.851133953664237e-10,
            0.05470130258369848,
            1.52015089682893e-10
          ],
          [
            -7.38354741875046e-10,
            0.041267765087468586,
            1.1463922222799398e-10
          ],
          [
            -4.920118516642886e-10,
            0.02764730474429466,
            7.67640536919975e-11
          ],
          [
            -2.4594182292483545e-10,
            0.01387107961645624,
            3.8493786169211784e-11
          ],
          [
            -4.612058617361431e-15,
            1.23069402385154e-16,
            -2.4463452572611776e-15
          ],
          [
            2.459403725459753e-10,
            -0.01387107961645838,
            -3.849426758847478e-11
          ],
          [
            4.920117153000045e-10,
            -0.027647304744298502,
            -7.676503238503045e-11
          ],
          [
            7.383512940336139e-10,
            -0.04126776508747037,
            -1.1464159108241191e-10
          ],
          [
            9.851134248704984e-10,
            -0.054701302583701025,
            -1.520155602828752e-10
          ],
          [
            1.2324977298202076e-09,
            -0.06790970908562088,
            -1.8878532197017065e-10
          ],
          [
            1.4807852276020837e-09,
            -0.08082273023033537,
            -2.2482393863538784e-10
          ],
          [
            1.7302544260463378e-09,
            -0.09334920389374775,
            -2.6007261420102493e-10
          ],
          [
            1.9811295756539856e-09,
            -0.1054082057060881,
            -2.9454068880501143e-10
          ]
        ],
        "unwrapped_reduced_polarization": [
          [
            -1.9811288079634268e-09,
            0.1054082057060865,
            2.9454247556146514e-10
          ],
          [
            -1.7302568942451992e-09,
            0.09334920389374692,
            2.6007053155402556e-10
          ],
          [
            -1.4807886611719251e-09,
            0.08082273023033461,
            2.2482240593837035e-10
          ],
          [
            -1.2324985791964324e-09,
            0.06790970908561704,
            1.887840214874544e-10
          ],
          [
            -9.851133953664237e-10,
            0.05470130258369848,
            1.52015089682893e-10
          ],
          [
            -7.38354741875046e-10,
            0.041267765087468586,
            1.1463922222799398e-10
          ],
          [
            -4.920118516642886e-10,
            0.02764730474429466,
            7.67640536919975e-11
          ],
          [
            -2.4594182292483545e-10,
            0.01387107961645624,
            3.8493786169211784e-11
          ],
          [
            -4.612058617378486e-15,
            1.231653667943533e-16,
            -2.4463452572615767e-15
          ],
          [
            2.459403725459753e-10,
            -0.01387107961645838,
            -3.849426758847478e-11
          ],
          [
            4.920117153000045e-10,
            -0.027647304744298502,
            -7.676503238503045e-11
          ],
          [
            7.383512940336139e-10,
            -0.04126776508747037,
            -1.1464159108241191e-10
          ],
          [
            9.851134248704984e-10,
            -0.054701302583701025,
            -1.520155602828752e-10
          ],
          [
            1.2324977298202076e-09,
            -0.06790970908562088,
            -1.8878532197017065e-10
          ],
          [
            1.4807852276020837e-09,
            -0.08082273023033537,
            -2.2482393863538784e-10
          ],
          [
            1.7302544260463378e-09,
            -0.09334920389374775,
            -2.6007261420102493e-10
          ],
          [
            1.9811295756539856e-09,
            -0.1054082057060881,
            -2.9454068880501143e-10
          ]
        ],
        "berry_integer_shifts": [
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ]
        ],
        "folded_reduced_polarization": [
          [
            -1.9811288165527685e-09,
            0.10540820570608656,
            2.945425014999614e-10
          ],
          [
            -1.7302568822152864e-09,
            0.0933492038937469,
            2.6007052067456016e-10
          ],
          [
            -1.480788658358989e-09,
            0.0808227302303346,
            2.2482238293264345e-10
          ],
          [
            -1.232498603176424e-09,
            0.067909709085617,
            1.8878398844179856e-10
          ],
          [
            -9.851133797589284e-10,
            0.05470130258369843,
            1.520150672007503e-10
          ],
          [
            -7.383547662165313e-10,
            0.041267765087468544,
            1.1463918703213949e-10
          ],
          [
            -4.92011875685705e-10,
            0.027647304744294665,
            7.676403956935474e-11
          ],
          [
            -2.459418224631804e-10,
            0.013871079616456283,
            3.849376373210589e-11
          ],
          [
            -4.6074255521944e-15,
            1.1102230246251565e-16,
            -2.4424906541753444e-15
          ],
          [
            2.459403791732484e-10,
            -0.013871079616458393,
            -3.849426333246697e-11
          ],
          [
            4.920117646634026e-10,
            -0.027647304744298495,
            -7.67650387700769e-11
          ],
          [
            7.383512690140037e-10,
            -0.041267765087470376,
            -1.1464157401164243e-10
          ],
          [
            9.851134352700797e-10,
            -0.05470130258370104,
            -1.520155668011114e-10
          ],
          [
            1.2324977705091555e-09,
            -0.06790970908562088,
            -1.887853207094281e-10
          ],
          [
            1.480785272178764e-09,
            -0.08082273023033537,
            -2.2482393724487792e-10
          ],
          [
            1.730254384213481e-09,
            -0.09334920389374773,
            -2.6007263009830695e-10
          ],
          [
            1.9811295937088857e-09,
            -0.10540820570608811,
            -2.945406696319708e-10
          ]
        ]
      },
      "incoming_structure_ids": [
        "incoming_00_000",
        "incoming_00_001",
        "incoming_00_002",
        "incoming_00_003",
        "incoming_00_004",
        "incoming_00_005",
        "incoming_00_006",
        "incoming_00_007",
        "incoming_00_008"
      ],
      "reflected_structure_ids": [
        "reflected_00_001",
        "reflected_00_002",
        "reflected_00_003",
        "reflected_00_004",
        "reflected_00_005",
        "reflected_00_006",
        "reflected_00_007",
        "reflected_00_008"
      ],
      "positive_extension_structure_ids": [
        "extension_plus_00_000",
        "extension_plus_00_001",
        "extension_plus_00_002",
        "extension_plus_00_003"
      ],
      "negative_extension_structure_ids": [
        "extension_minus_00_000",
        "extension_minus_00_001",
        "extension_minus_00_002",
        "extension_minus_00_003"
      ],
      "extension": {
        "enabled": true,
        "fraction_beyond_polar_endpoint": 0.35,
        "images_per_side": 4,
        "construction": "continue fractional atomic displacements and symmetric log strain beyond +P; reflect these structures about N for the -P side",
        "positive_path_coordinates": [
          1.35,
          1.2625,
          1.175,
          1.0875
        ],
        "negative_path_coordinates": [
          -1.0875,
          -1.175,
          -1.2625,
          -1.35
        ]
      },
      "branch_coordinates": [
        1.35,
        1.2625,
        1.175,
        1.0875,
        1.0,
        0.875,
        0.75,
        0.625,
        0.5,
        0.375,
        0.25,
        0.125,
        0.0,
        -0.125,
        -0.25,
        -0.375,
        -0.5,
        -0.625,
        -0.75,
        -0.875,
        -1.0,
        -1.0875,
        -1.175,
        -1.2625,
        -1.35
      ],
      "parent": {
        "candidate_id": "inversion_parent_endpoint_00",
        "source": "same_species_inversion_center_projection_from_endpoint",
        "spacegroup": "P2_1/m",
        "spacegroup_number": 11,
        "pointgroup": "2/m",
        "has_inversion": true,
        "is_polar_point_group": false,
        "nonpolar_parent_hypothesis": true,
        "symmetry_tolerance_A": null,
        "target_reduced_polarization": [
          0.0,
          0.0,
          0.0
        ],
        "formal_class": [
          0.0,
          0.0,
          0.0
        ],
        "target_residual": 6.082913838725621e-16,
        "parent_symmetrization_rmsd_A": 0.09580572242523867,
        "parent_cell_rmsd_A": 0.0,
        "energy_eV": -207.10602703676398,
        "reduced_polarization": [
          3.2020422059086627e-16,
          4.424776754713125e-16,
          2.677707443297278e-16
        ],
        "cartesian_polarization_e_A2": [
          3.1128580250809977e-18,
          5.504748604646367e-18,
          3.91371698837172e-18
        ],
        "ranking_score": 0.0958057224252399
      }
    }
  ],
  "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": 55,
      "full_response": 23,
      "energy_polarization": 32
    },
    "model_evaluations_for_recovery_and_path_properties": {
      "total": 80,
      "full_response": 48,
      "energy_polarization": 32
    },
    "elapsed_seconds": 1048.2628271799767
  }
}