{
  "schema": "ferrofinder.endpoint_parent_recovery.v4_variable_cell",
  "status": "complete",
  "input_atom_count": 28,
  "input_formula": "Cl16Rb8Zn4",
  "input_spacegroup": "Pna2_1",
  "input_pointgroup": "mm2",
  "input_is_polar_point_group": true,
  "input_energy_eV": -87.21865335418946,
  "input_cartesian_polarization_e_A2": [
    2.5757253818176647e-18,
    2.8279477485831927e-18,
    -0.00016021581329722867
  ],
  "input_reduced_polarization": [
    2.487399225611893e-16,
    1.9738089541055647e-16,
    -0.019591463905136525
  ],
  "input_formal_targets": [
    {
      "orbit_id": 0,
      "representative_formal_class": [
        0.0,
        0.0,
        0.0
      ],
      "target_reduced_polarization": [
        0.0,
        0.0,
        0.0
      ]
    },
    {
      "orbit_id": 1,
      "representative_formal_class": [
        0.0,
        0.0,
        0.5
      ],
      "target_reduced_polarization": [
        0.0,
        0.0,
        -0.5
      ]
    },
    {
      "orbit_id": 2,
      "representative_formal_class": [
        0.0,
        0.5,
        0.0
      ],
      "target_reduced_polarization": [
        0.0,
        0.5,
        0.0
      ]
    },
    {
      "orbit_id": 3,
      "representative_formal_class": [
        0.5,
        0.0,
        0.0
      ],
      "target_reduced_polarization": [
        0.5,
        0.0,
        0.0
      ]
    },
    {
      "orbit_id": 4,
      "representative_formal_class": [
        0.0,
        0.5,
        0.5
      ],
      "target_reduced_polarization": [
        0.0,
        0.5,
        -0.5
      ]
    },
    {
      "orbit_id": 5,
      "representative_formal_class": [
        0.5,
        0.0,
        0.5
      ],
      "target_reduced_polarization": [
        0.5,
        0.0,
        -0.5
      ]
    },
    {
      "orbit_id": 6,
      "representative_formal_class": [
        0.5,
        0.5,
        0.0
      ],
      "target_reduced_polarization": [
        0.5,
        0.5,
        0.0
      ]
    },
    {
      "orbit_id": 7,
      "representative_formal_class": [
        0.5,
        0.5,
        0.5
      ],
      "target_reduced_polarization": [
        0.5,
        0.5,
        -0.5
      ]
    }
  ],
  "parent_candidates": [
    {
      "candidate_id": "inversion_parent_endpoint_00",
      "source": "same_species_inversion_center_projection_from_endpoint",
      "spacegroup": "Pnma",
      "spacegroup_number": 62,
      "pointgroup": "mmm",
      "has_inversion": true,
      "is_polar_point_group": false,
      "nonpolar_parent_hypothesis": true,
      "symmetry_tolerance_A": null,
      "target_reduced_polarization": [
        0.0,
        0.0,
        0.0
      ],
      "formal_class": [
        0.0,
        0.0,
        0.0
      ],
      "target_residual": 1.3687204386215149e-15,
      "parent_symmetrization_rmsd_A": 0.039667121705951686,
      "parent_cell_rmsd_A": 0.0,
      "energy_eV": -87.21865939833181,
      "reduced_polarization": [
        -4.90836939178608e-16,
        2.9553788123634674e-16,
        1.2430334263375134e-15
      ],
      "cartesian_polarization_e_A2": [
        -5.082662845426549e-18,
        4.234278520851592e-18,
        1.0165325690853099e-17
      ],
      "ranking_score": 0.039667121705954426
    },
    {
      "candidate_id": "symmetry_projection_00",
      "source": "spglib_refine_cell_from_polar_endpoint",
      "spacegroup": "Pnma",
      "spacegroup_number": 62,
      "pointgroup": "mmm",
      "has_inversion": true,
      "is_polar_point_group": false,
      "nonpolar_parent_hypothesis": true,
      "symmetry_tolerance_A": null,
      "target_reduced_polarization": [
        0.0,
        0.0,
        0.0
      ],
      "formal_class": [
        0.0,
        0.0,
        0.0
      ],
      "target_residual": 1.0096246961832314e-15,
      "parent_symmetrization_rmsd_A": 2.320063014508228,
      "parent_cell_rmsd_A": 5.266998298330985,
      "energy_eV": -87.20484800344802,
      "reduced_polarization": [
        3.5871692096361465e-16,
        1.3832251661500164e-16,
        -9.335582891039844e-16
      ],
      "cartesian_polarization_e_A2": [
        3.71454758327414e-18,
        1.131179099433277e-18,
        -1.3375428540596182e-17
      ],
      "ranking_score": 3.6368125890909764
    },
    {
      "candidate_id": "bec_projection_00",
      "source": "MACEField_BEC_backprojection",
      "spacegroup": "Pna2_1",
      "spacegroup_number": 33,
      "pointgroup": "mm2",
      "has_inversion": false,
      "is_polar_point_group": true,
      "nonpolar_parent_hypothesis": false,
      "symmetry_tolerance_A": null,
      "target_reduced_polarization": [
        0.0,
        0.0,
        0.0
      ],
      "formal_class": [
        0.0,
        0.0,
        0.0
      ],
      "target_residual": 8.68218998112643e-07,
      "parent_symmetrization_rmsd_A": 0.005181280844651851,
      "parent_cell_rmsd_A": 0.0019251288011364388,
      "energy_eV": -87.21703844182487,
      "reduced_polarization": [
        -6.709381737945221e-16,
        2.30415091536189e-16,
        -8.68218998112643e-07
      ],
      "cartesian_polarization_e_A2": [
        -6.946171618067356e-18,
        3.3011508679924066e-18,
        -7.098978178318791e-09
      ],
      "ranking_score": 0.5056642994829322
    },
    {
      "candidate_id": "inversion_parent_bec_00_00",
      "source": "same_species_inversion_center_projection_after_BEC",
      "spacegroup": "Pnma",
      "spacegroup_number": 62,
      "pointgroup": "mmm",
      "has_inversion": true,
      "is_polar_point_group": false,
      "nonpolar_parent_hypothesis": true,
      "symmetry_tolerance_A": null,
      "target_reduced_polarization": [
        0.0,
        0.0,
        0.0
      ],
      "formal_class": [
        0.0,
        0.0,
        0.0
      ],
      "target_residual": 1.2268667550827974e-15,
      "parent_symmetrization_rmsd_A": 0.039667153805313125,
      "parent_cell_rmsd_A": 0.0019251288011364388,
      "energy_eV": -87.21853705269008,
      "reduced_polarization": [
        1.163994187992339e-15,
        -3.0508718172453154e-16,
        -2.392517013415597e-16
      ],
      "cartesian_polarization_e_A2": [
        1.2050728978759318e-17,
        -4.370968278915871e-18,
        -1.9562375514029075e-18
      ],
      "ranking_score": 0.04014843600559969
    },
    {
      "candidate_id": "symmetry_parent_00_00",
      "source": "spglib_refine_cell_after_MACEField_BEC_backprojection",
      "spacegroup": "Pnma",
      "spacegroup_number": 62,
      "pointgroup": "mmm",
      "has_inversion": true,
      "is_polar_point_group": false,
      "nonpolar_parent_hypothesis": true,
      "symmetry_tolerance_A": null,
      "target_reduced_polarization": [
        0.0,
        0.0,
        0.0
      ],
      "formal_class": [
        0.0,
        0.0,
        0.0
      ],
      "target_residual": 8.638418530427998e-16,
      "parent_symmetrization_rmsd_A": 2.370856623346051,
      "parent_cell_rmsd_A": 5.26826175445123,
      "energy_eV": -87.19033405659563,
      "reduced_polarization": [
        1.623834631314614e-16,
        -4.504660939321514e-16,
        -7.189816800081638e-16
      ],
      "cartesian_polarization_e_A2": [
        1.6811416457368736e-18,
        -3.6832285147507865e-18,
        -1.0300813356605935e-17
      ],
      "ranking_score": 3.6879220619588606
    },
    {
      "candidate_id": "bec_projection_01",
      "source": "MACEField_BEC_backprojection",
      "spacegroup": "Pna2_1",
      "spacegroup_number": 33,
      "pointgroup": "mm2",
      "has_inversion": false,
      "is_polar_point_group": true,
      "nonpolar_parent_hypothesis": false,
      "symmetry_tolerance_A": null,
      "target_reduced_polarization": [
        0.0,
        0.0,
        -0.5
      ],
      "formal_class": [
        0.0,
        0.0,
        0.5
      ],
      "target_residual": 0.00029354853282337334,
      "parent_symmetrization_rmsd_A": 0.13153482463665409,
      "parent_cell_rmsd_A": 0.04890001719216529,
      "energy_eV": -86.67201537150926,
      "reduced_polarization": [
        3.713280882379016e-15,
        2.3885705192437632e-15,
        -0.4997064514671766
      ],
      "cartesian_polarization_e_A2": [
        1.5658187229783399e-16,
        -4.975340783086075e-17,
        -0.0041038268335652625
      ],
      "ranking_score": 0.6443469260003422
    },
    {
      "candidate_id": "bec_projection_02",
      "source": "MACEField_BEC_backprojection",
      "spacegroup": "Pc",
      "spacegroup_number": 7,
      "pointgroup": "m",
      "has_inversion": false,
      "is_polar_point_group": true,
      "nonpolar_parent_hypothesis": false,
      "symmetry_tolerance_A": null,
      "target_reduced_polarization": [
        0.0,
        0.5,
        0.0
      ],
      "formal_class": [
        0.0,
        0.5,
        0.0
      ],
      "target_residual": 6.447310282727387e-05,
      "parent_symmetrization_rmsd_A": 0.2978768030206429,
      "parent_cell_rmsd_A": 0.20026133289423118,
      "energy_eV": -84.50314704799592,
      "reduced_polarization": [
        6.634213820259253e-16,
        0.49993606930307705,
        -8.34547656648073e-06
      ],
      "cartesian_polarization_e_A2": [
        1.220977496263918e-16,
        0.007164107534260544,
        0.0001604178256594405
      ],
      "ranking_score": 0.8480710824498552
    },
    {
      "candidate_id": "bec_projection_03",
      "source": "MACEField_BEC_backprojection",
      "spacegroup": "Pc",
      "spacegroup_number": 7,
      "pointgroup": "m",
      "has_inversion": false,
      "is_polar_point_group": true,
      "nonpolar_parent_hypothesis": false,
      "symmetry_tolerance_A": null,
      "target_reduced_polarization": [
        0.5,
        0.0,
        0.0
      ],
      "formal_class": [
        0.5,
        0.0,
        0.0
      ],
      "target_residual": 6.324756450468685e-07,
      "parent_symmetrization_rmsd_A": 0.17191013822483936,
      "parent_cell_rmsd_A": 0.0035000755737574123,
      "energy_eV": -86.39353344725754,
      "reduced_polarization": [
        0.4999998192818196,
        1.2096766537468057e-15,
        -6.061075654065235e-07
      ],
      "cartesian_polarization_e_A2": [
        0.005176499749651214,
        4.8004638985607084e-17,
        -2.3934739735982123e-06
      ],
      "ranking_score": 0.6727864220695688
    },
    {
      "candidate_id": "bec_projection_04",
      "source": "MACEField_BEC_backprojection",
      "spacegroup": "Pc",
      "spacegroup_number": 7,
      "pointgroup": "m",
      "has_inversion": false,
      "is_polar_point_group": true,
      "nonpolar_parent_hypothesis": false,
      "symmetry_tolerance_A": null,
      "target_reduced_polarization": [
        0.0,
        0.5,
        -0.5
      ],
      "formal_class": [
        0.0,
        0.5,
        0.5
      ],
      "target_residual": 0.0001189852802245788,
      "parent_symmetrization_rmsd_A": 0.3418955901292876,
      "parent_cell_rmsd_A": 0.2075323272705776,
      "energy_eV": -83.77902653970631,
      "reduced_polarization": [
        1.2421842324741592e-16,
        0.5001130590854931,
        -0.5000370828814629
      ],
      "cartesian_polarization_e_A2": [
        7.334511494843447e-16,
        0.0070808003533899665,
        -0.003948758674853481
      ],
      "ranking_score": 0.8940166425073812
    },
    {
      "candidate_id": "bec_projection_05",
      "source": "MACEField_BEC_backprojection",
      "spacegroup": "Pc",
      "spacegroup_number": 7,
      "pointgroup": "m",
      "has_inversion": false,
      "is_polar_point_group": true,
      "nonpolar_parent_hypothesis": false,
      "symmetry_tolerance_A": null,
      "target_reduced_polarization": [
        0.5,
        0.0,
        -0.5
      ],
      "formal_class": [
        0.5,
        0.0,
        0.5
      ],
      "target_residual": 2.905437289363874e-05,
      "parent_symmetrization_rmsd_A": 0.22491190539164918,
      "parent_cell_rmsd_A": 0.052730444725410164,
      "energy_eV": -85.83376957599631,
      "reduced_polarization": [
        0.4999793945785889,
        -2.595186122543606e-15,
        -0.4999795165141464
      ],
      "cartesian_polarization_e_A2": [
        0.005209390792772553,
        4.6084004220346385e-17,
        -0.0041099081637267455
      ],
      "ranking_score": 0.738152625318789
    },
    {
      "candidate_id": "bec_projection_06",
      "source": "MACEField_BEC_backprojection",
      "spacegroup": "P1",
      "spacegroup_number": 1,
      "pointgroup": "1",
      "has_inversion": false,
      "is_polar_point_group": true,
      "nonpolar_parent_hypothesis": false,
      "symmetry_tolerance_A": null,
      "target_reduced_polarization": [
        0.5,
        0.5,
        0.0
      ],
      "formal_class": [
        0.5,
        0.5,
        0.0
      ],
      "target_residual": 0.00041771436301739573,
      "parent_symmetrization_rmsd_A": 0.3692386374321328,
      "parent_cell_rmsd_A": 0.21451700105472205,
      "energy_eV": -83.5828458322207,
      "reduced_polarization": [
        0.4998193241578134,
        0.49968814009127893,
        -0.0002111514301482995
      ],
      "cartesian_polarization_e_A2": [
        0.005172731092094109,
        0.007160645469743718,
        0.00016713038285791763
      ],
      "ranking_score": 0.9237033164218481
    },
    {
      "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": 0.00034598303036439433,
      "parent_symmetrization_rmsd_A": 0.4081087771289357,
      "parent_cell_rmsd_A": 0.21970389053504086,
      "energy_eV": -82.73256642726068,
      "reduced_polarization": [
        0.5000922595206408,
        0.5003205818471221,
        -0.5000917590183416
      ],
      "cartesian_polarization_e_A2": [
        0.005217311169529498,
        0.007079016100850431,
        -0.0039442895615632535
      ],
      "ranking_score": 0.9637267158234246
    }
  ],
  "formal_branches": [
    {
      "orbit_id": 0,
      "formal_class": [
        0.0,
        0.0,
        0.0
      ],
      "formal_classes_in_orbit": [
        [
          0.0,
          0.0,
          0.0
        ]
      ],
      "target_reduced_polarization": [
        0.0,
        0.0,
        0.0
      ],
      "bec_backprojection": {
        "converged_to_target": true,
        "history": [
          {
            "iteration": 0,
            "reduced_polarization": [
              2.487399225611893e-16,
              1.9738089541055647e-16,
              -0.019591463905136525
            ],
            "branch_aligned_reduced_polarization": [
              2.487399225611893e-16,
              1.9738089541055647e-16,
              -0.019591463905136525
            ],
            "target_residual": 0.019591463905136525,
            "energy_eV": -87.21865335418946,
            "max_atomic_step_A": 0.005234779579179312,
            "max_log_strain_component": 0.00017374947355016003,
            "step_scale": 1.0,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 0.33523308942343616,
            "cell_principal_stretches": [
              1.0001737645688644,
              1.0000370653098614,
              0.9999918843996499
            ],
            "cell_volume_ratio": 1.0002027190079497,
            "cell_rmsd_from_input_A": 0.0019251288011364388
          },
          {
            "iteration": 1,
            "reduced_polarization": [
              -6.709381737945221e-16,
              2.30415091536189e-16,
              -8.68218998112643e-07
            ],
            "branch_aligned_reduced_polarization": [
              -6.709381737945221e-16,
              2.30415091536189e-16,
              -8.68218998112643e-07
            ],
            "target_residual": 8.68218998112643e-07,
            "energy_eV": -87.21703844182487
          }
        ],
        "iterations": 1
      },
      "parent": {
        "candidate_id": "inversion_parent_endpoint_00",
        "source": "same_species_inversion_center_projection_from_endpoint",
        "spacegroup": "Pnma",
        "spacegroup_number": 62,
        "pointgroup": "mmm",
        "has_inversion": true,
        "is_polar_point_group": false,
        "nonpolar_parent_hypothesis": true,
        "symmetry_tolerance_A": null,
        "target_reduced_polarization": [
          0.0,
          0.0,
          0.0
        ],
        "formal_class": [
          0.0,
          0.0,
          0.0
        ],
        "target_residual": 1.3687204386215149e-15,
        "parent_symmetrization_rmsd_A": 0.039667121705951686,
        "parent_cell_rmsd_A": 0.0,
        "energy_eV": -87.21865939833181,
        "reduced_polarization": [
          -4.90836939178608e-16,
          2.9553788123634674e-16,
          1.2430334263375134e-15
        ],
        "cartesian_polarization_e_A2": [
          -5.082662845426549e-18,
          4.234278520851592e-18,
          1.0165325690853099e-17
        ],
        "ranking_score": 0.039667121705954426
      },
      "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": [
          -87.21865335418947,
          -87.21865621035408,
          -87.21865780486601,
          -87.21865861412688,
          -87.21865904143112,
          -87.2186592600648,
          -87.21865935648367,
          -87.21865939078619,
          -87.2186593983318
        ],
        "cartesian_polarizations_e_A2": [
          [
            -3.722190685297338e-18,
            -2.3693616271913238e-18,
            -0.00016021581329722225
          ],
          [
            1.5286204046395637e-20,
            -7.352664146316301e-18,
            -0.0001403323197559236
          ],
          [
            5.04444733531056e-19,
            -1.0058322262528329e-17,
            -0.00012039205137253866
          ],
          [
            -4.891585294846604e-18,
            -6.557781535903728e-18,
            -0.000100402691758812
          ],
          [
            -4.425356071431537e-18,
            -1.6509100370107288e-18,
            -8.037204775788418e-05
          ],
          [
            1.3834014661988052e-18,
            1.871031375278826e-17,
            -6.030820549795474e-05
          ],
          [
            -1.3375428540596182e-18,
            6.664784964228498e-18,
            -4.021938502214149e-05
          ],
          [
            2.231785790773763e-18,
            -7.245660717991531e-18,
            -2.011387198071294e-05
          ],
          [
            6.611283250066113e-18,
            -3.2253890537894794e-18,
            -2.1400685664953892e-19
          ]
        ],
        "raw_reduced_polarization": [
          [
            -3.594550216240333e-16,
            -1.6537318264127708e-16,
            -0.01959146390513574
          ],
          [
            1.476201320837919e-18,
            -5.131903280674469e-16,
            -0.017160076278624183
          ],
          [
            4.8714643587651325e-17,
            -7.020358334061955e-16,
            -0.014721746127235948
          ],
          [
            -4.723844226681341e-16,
            -4.577102926006959e-16,
            -0.012277413016167853
          ],
          [
            -4.2736028238257757e-16,
            -1.1522776596940596e-16,
            -0.009828031579562775
          ],
          [
            1.3359621953583166e-16,
            1.3059146809866008e-15,
            -0.007374590603018672
          ],
          [
            -1.291676155733179e-16,
            4.651787589135277e-16,
            -0.004918095247478941
          ],
          [
            2.1552539284233616e-16,
            -5.05721861754615e-16,
            -0.0024595586964416744
          ],
          [
            6.384570712624e-16,
            -2.25120913143932e-16,
            -2.6169124765000283e-17
          ]
        ],
        "unwrapped_reduced_polarization": [
          [
            -3.594550216240333e-16,
            -1.6537318264127708e-16,
            -0.01959146390513574
          ],
          [
            1.4762013208379047e-18,
            -5.131903280674469e-16,
            -0.017160076278624183
          ],
          [
            4.8714643587651325e-17,
            -7.020358334061955e-16,
            -0.014721746127235948
          ],
          [
            -4.723844226681341e-16,
            -4.577102926006959e-16,
            -0.012277413016167853
          ],
          [
            -4.2736028238257757e-16,
            -1.1522776596940593e-16,
            -0.009828031579562775
          ],
          [
            1.3359621953583166e-16,
            1.3059146809866006e-15,
            -0.007374590603018672
          ],
          [
            -1.291676155733179e-16,
            4.651787589135277e-16,
            -0.004918095247478941
          ],
          [
            2.1552539284233616e-16,
            -5.057218617546149e-16,
            -0.0024595586964416744
          ],
          [
            6.384570712624e-16,
            -2.25120913143932e-16,
            -2.6020852139652106e-17
          ]
        ],
        "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": [
          [
            -3.3306690738754696e-16,
            -1.6653345369377348e-16,
            -0.01959146390513572
          ],
          [
            0.0,
            -4.996003610813204e-16,
            -0.017160076278624203
          ],
          [
            0.0,
            -7.216449660063518e-16,
            -0.014721746127235924
          ],
          [
            -4.996003610813204e-16,
            -4.440892098500626e-16,
            -0.01227741301616786
          ],
          [
            -4.440892098500626e-16,
            -1.1102230246251565e-16,
            -0.009828031579562801
          ],
          [
            1.1102230246251565e-16,
            1.3322676295501878e-15,
            -0.007374590603018649
          ],
          [
            -1.1102230246251565e-16,
            4.440892098500626e-16,
            -0.0049180952474789374
          ],
          [
            2.220446049250313e-16,
            -4.996003610813204e-16,
            -0.002459558696441655
          ],
          [
            6.661338147750939e-16,
            -2.220446049250313e-16,
            0.0
          ]
        ]
      },
      "reflected": {
        "reached": true,
        "construction": "reflect_displacements_about_reconstructed_parent",
        "energies_eV": [
          -87.2186593983318,
          -87.21865939078621,
          -87.21865935648367,
          -87.21865926006481,
          -87.21865904143115,
          -87.2186586141269,
          -87.21865780486598,
          -87.21865621035406,
          -87.21865335418944
        ],
        "cartesian_polarizations_e_A2": [
          [
            3.3782510942534357e-18,
            3.668688971134953e-19,
            5.136164559588934e-18
          ],
          [
            6.12976782260465e-18,
            1.941347913892246e-18,
            2.0113871980698387e-05
          ],
          [
            -6.038050598326277e-18,
            -6.664784964228498e-18,
            4.0219385022135745e-05
          ],
          [
            -5.510676558725627e-18,
            -1.559192812732355e-18,
            6.0308205497936504e-05
          ],
          [
            -2.8508770546527862e-18,
            -2.1156106400211562e-17,
            8.037204775786028e-05
          ],
          [
            5.7093972113287704e-18,
            7.031653861341993e-19,
            0.00010040269175880351
          ],
          [
            -1.7044117511731136e-18,
            -1.2641690746369191e-17,
            0.000120392051372517
          ],
          [
            1.6425026247852112e-17,
            -1.6906541675313575e-17,
            0.00014033231975591894
          ],
          [
            1.3986876702452008e-18,
            -1.2779266582786753e-17,
            0.00016021581329719528
          ]
        ],
        "raw_reduced_polarization": [
          [
            3.262404919051801e-16,
            2.5606170215423545e-17,
            6.280589943600069e-16
          ],
          [
            5.919567296560055e-16,
            1.354993173899496e-16,
            0.002459558696439895
          ],
          [
            -5.83099521730978e-16,
            -4.651787589135277e-16,
            0.004918095247478238
          ],
          [
            -5.321705761620697e-16,
            -1.0882622341555008e-16,
            0.007374590603016442
          ],
          [
            -2.7531154633627185e-16,
            -1.4766224824227578e-15,
            0.009828031579559852
          ],
          [
            5.513611933329627e-16,
            4.907849291289513e-17,
            0.012277413016166814
          ],
          [
            -1.6459644727342798e-16,
            -8.823459486731362e-16,
            0.014721746127233296
          ],
          [
            1.5861783192403439e-15,
            -1.180017677427435e-15,
            0.01716007627862361
          ],
          [
            1.350724208566696e-16,
            -8.919482625039202e-16,
            0.019591463905132445
          ]
        ],
        "unwrapped_reduced_polarization": [
          [
            3.262404919051801e-16,
            2.5606170215423545e-17,
            6.280589943600069e-16
          ],
          [
            5.919567296560055e-16,
            1.354993173899496e-16,
            0.002459558696439895
          ],
          [
            -5.830995217309781e-16,
            -4.651787589135277e-16,
            0.004918095247478238
          ],
          [
            -5.321705761620697e-16,
            -1.0882622341555007e-16,
            0.007374590603016442
          ],
          [
            -2.7531154633627185e-16,
            -1.4766224824227578e-15,
            0.009828031579559852
          ],
          [
            5.513611933329627e-16,
            4.90784929128952e-17,
            0.012277413016166814
          ],
          [
            -1.64596447273428e-16,
            -8.823459486731361e-16,
            0.014721746127233296
          ],
          [
            1.5861783192403439e-15,
            -1.180017677427435e-15,
            0.01716007627862361
          ],
          [
            1.3507242085666962e-16,
            -8.919482625039202e-16,
            0.019591463905132445
          ]
        ],
        "gauge_integer_shift": [
          0,
          0,
          0
        ],
        "expected_opposite_endpoint_reduced_polarization": [
          1.636369164148833e-15,
          -2.8486864364658697e-16,
          0.01959146390513569
        ],
        "actual_opposite_endpoint_branch_residual": 3.625677624286417e-15
      },
      "pnp_branch": {
        "construction": "incoming_path_concatenated_with_parent_reflection",
        "reduced_polarization": [
          [
            -3.594550216240333e-16,
            -1.6537318264127708e-16,
            -0.01959146390513574
          ],
          [
            1.476201320837919e-18,
            -5.131903280674469e-16,
            -0.017160076278624183
          ],
          [
            4.8714643587651325e-17,
            -7.020358334061955e-16,
            -0.014721746127235948
          ],
          [
            -4.723844226681341e-16,
            -4.577102926006959e-16,
            -0.012277413016167853
          ],
          [
            -4.2736028238257757e-16,
            -1.1522776596940596e-16,
            -0.009828031579562775
          ],
          [
            1.3359621953583166e-16,
            1.3059146809866008e-15,
            -0.007374590603018672
          ],
          [
            -1.291676155733179e-16,
            4.651787589135277e-16,
            -0.004918095247478941
          ],
          [
            2.1552539284233616e-16,
            -5.05721861754615e-16,
            -0.0024595586964416744
          ],
          [
            6.384570712624e-16,
            -2.25120913143932e-16,
            -2.6169124765000283e-17
          ],
          [
            5.919567296560055e-16,
            1.354993173899496e-16,
            0.002459558696439895
          ],
          [
            -5.83099521730978e-16,
            -4.651787589135277e-16,
            0.004918095247478238
          ],
          [
            -5.321705761620697e-16,
            -1.0882622341555008e-16,
            0.007374590603016442
          ],
          [
            -2.7531154633627185e-16,
            -1.4766224824227578e-15,
            0.009828031579559852
          ],
          [
            5.513611933329627e-16,
            4.907849291289513e-17,
            0.012277413016166814
          ],
          [
            -1.6459644727342798e-16,
            -8.823459486731362e-16,
            0.014721746127233296
          ],
          [
            1.5861783192403439e-15,
            -1.180017677427435e-15,
            0.01716007627862361
          ],
          [
            1.350724208566696e-16,
            -8.919482625039202e-16,
            0.019591463905132445
          ]
        ],
        "unwrapped_reduced_polarization": [
          [
            -3.594550216240333e-16,
            -1.6537318264127708e-16,
            -0.01959146390513574
          ],
          [
            1.4762013208379047e-18,
            -5.131903280674469e-16,
            -0.017160076278624183
          ],
          [
            4.8714643587651325e-17,
            -7.020358334061955e-16,
            -0.014721746127235948
          ],
          [
            -4.723844226681341e-16,
            -4.577102926006959e-16,
            -0.012277413016167853
          ],
          [
            -4.2736028238257757e-16,
            -1.1522776596940593e-16,
            -0.009828031579562775
          ],
          [
            1.3359621953583166e-16,
            1.3059146809866006e-15,
            -0.007374590603018672
          ],
          [
            -1.291676155733179e-16,
            4.651787589135277e-16,
            -0.004918095247478941
          ],
          [
            2.1552539284233616e-16,
            -5.057218617546149e-16,
            -0.0024595586964416744
          ],
          [
            6.384570712624e-16,
            -2.25120913143932e-16,
            -2.6020852139652106e-17
          ],
          [
            5.919567296560055e-16,
            1.3549931738994962e-16,
            0.002459558696439895
          ],
          [
            -5.830995217309781e-16,
            -4.651787589135277e-16,
            0.004918095247478238
          ],
          [
            -5.321705761620697e-16,
            -1.0882622341555007e-16,
            0.007374590603016442
          ],
          [
            -2.7531154633627185e-16,
            -1.4766224824227578e-15,
            0.009828031579559852
          ],
          [
            5.513611933329627e-16,
            4.90784929128952e-17,
            0.012277413016166814
          ],
          [
            -1.64596447273428e-16,
            -8.823459486731361e-16,
            0.014721746127233296
          ],
          [
            1.5861783192403439e-15,
            -1.180017677427435e-15,
            0.01716007627862361
          ],
          [
            1.3507242085666962e-16,
            -8.919482625039202e-16,
            0.019591463905132445
          ]
        ],
        "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": [
          [
            -3.3306690738754696e-16,
            -1.6653345369377348e-16,
            -0.01959146390513572
          ],
          [
            0.0,
            -4.996003610813204e-16,
            -0.017160076278624203
          ],
          [
            0.0,
            -7.216449660063518e-16,
            -0.014721746127235924
          ],
          [
            -4.996003610813204e-16,
            -4.440892098500626e-16,
            -0.01227741301616786
          ],
          [
            -4.440892098500626e-16,
            -1.1102230246251565e-16,
            -0.009828031579562801
          ],
          [
            1.1102230246251565e-16,
            1.3322676295501878e-15,
            -0.007374590603018649
          ],
          [
            -1.1102230246251565e-16,
            4.440892098500626e-16,
            -0.0049180952474789374
          ],
          [
            2.220446049250313e-16,
            -4.996003610813204e-16,
            -0.002459558696441655
          ],
          [
            6.661338147750939e-16,
            -2.220446049250313e-16,
            0.0
          ],
          [
            5.551115123125783e-16,
            1.1102230246251565e-16,
            0.0024595586964398786
          ],
          [
            -6.106226635438361e-16,
            -4.440892098500626e-16,
            0.004918095247478216
          ],
          [
            -5.551115123125783e-16,
            -1.1102230246251565e-16,
            0.007374590603016484
          ],
          [
            -2.7755575615628914e-16,
            -1.4988010832439613e-15,
            0.009828031579559804
          ],
          [
            5.551115123125783e-16,
            0.0,
            0.012277413016166805
          ],
          [
            -1.6653345369377348e-16,
            -8.881784197001252e-16,
            0.014721746127233315
          ],
          [
            1.5543122344752192e-15,
            -1.1657341758564144e-15,
            0.017160076278623593
          ],
          [
            1.1102230246251565e-16,
            -8.881784197001252e-16,
            0.019591463905132445
          ]
        ]
      },
      "incoming_structure_ids": [
        "incoming_00_000",
        "incoming_00_001",
        "incoming_00_002",
        "incoming_00_003",
        "incoming_00_004",
        "incoming_00_005",
        "incoming_00_006",
        "incoming_00_007",
        "incoming_00_008"
      ],
      "reflected_structure_ids": [
        "reflected_00_001",
        "reflected_00_002",
        "reflected_00_003",
        "reflected_00_004",
        "reflected_00_005",
        "reflected_00_006",
        "reflected_00_007",
        "reflected_00_008"
      ]
    },
    {
      "orbit_id": 1,
      "formal_class": [
        0.0,
        0.0,
        0.5
      ],
      "formal_classes_in_orbit": [
        [
          0.0,
          0.0,
          0.5
        ]
      ],
      "target_reduced_polarization": [
        0.0,
        0.0,
        -0.5
      ],
      "bec_backprojection": {
        "converged_to_target": true,
        "history": [
          {
            "iteration": 0,
            "reduced_polarization": [
              2.487399225611893e-16,
              1.9738089541055647e-16,
              -0.019591463905136525
            ],
            "branch_aligned_reduced_polarization": [
              2.487399225611893e-16,
              1.9738089541055647e-16,
              -0.019591463905136552
            ],
            "target_residual": 0.48040853609486345,
            "energy_eV": -87.21865335418946,
            "max_atomic_step_A": 0.12,
            "max_log_strain_component": 0.003982963658861061,
            "step_scale": 0.9348437295073947,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 0.33523308942343616,
            "cell_principal_stretches": [
              1.0001860568481282,
              0.9991507062149965,
              0.9960249578204149
            ],
            "cell_volume_ratio": 0.9953641998895377,
            "cell_rmsd_from_input_A": 0.04394874789939957
          },
          {
            "iteration": 1,
            "reduced_polarization": [
              -8.305775937144547e-15,
              -2.5012740039259735e-16,
              -0.45646548661713593
            ],
            "branch_aligned_reduced_polarization": [
              -8.305775937144547e-15,
              -2.5012740039259735e-16,
              -0.45646548661713593
            ],
            "target_residual": 0.04353451338286407,
            "energy_eV": -86.76230499206991,
            "max_atomic_step_A": 0.011765925304362771,
            "max_log_strain_component": 0.00045070719231475576,
            "step_scale": 1.0,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 0.33523308942343616,
            "cell_principal_stretches": [
              1.0002071129887808,
              0.9990546466313788,
              0.995576143357751
            ],
            "cell_volume_ratio": 0.994840973918726,
            "cell_rmsd_from_input_A": 0.04890001719216529
          },
          {
            "iteration": 2,
            "reduced_polarization": [
              3.713280882379016e-15,
              2.3885705192437632e-15,
              -0.4997064514671766
            ],
            "branch_aligned_reduced_polarization": [
              3.713280882379016e-15,
              2.3885705192437632e-15,
              -0.4997064514671766
            ],
            "target_residual": 0.00029354853282337334,
            "energy_eV": -86.67201537150926
          }
        ],
        "iterations": 2
      },
      "parent": {
        "candidate_id": "bec_projection_01",
        "source": "MACEField_BEC_backprojection",
        "spacegroup": "Pna2_1",
        "spacegroup_number": 33,
        "pointgroup": "mm2",
        "has_inversion": false,
        "is_polar_point_group": true,
        "nonpolar_parent_hypothesis": false,
        "symmetry_tolerance_A": null,
        "target_reduced_polarization": [
          0.0,
          0.0,
          -0.5
        ],
        "formal_class": [
          0.0,
          0.0,
          0.5
        ],
        "target_residual": 0.00029354853282337334,
        "parent_symmetrization_rmsd_A": 0.13153482463665409,
        "parent_cell_rmsd_A": 0.04890001719216529,
        "energy_eV": -86.67201537150926,
        "reduced_polarization": [
          3.713280882379016e-15,
          2.3885705192437632e-15,
          -0.4997064514671766
        ],
        "cartesian_polarization_e_A2": [
          1.5658187229783399e-16,
          -4.975340783086075e-17,
          -0.0041038268335652625
        ],
        "ranking_score": 0.6443469260003422
      },
      "branch_status": "awaiting_branch_sampling"
    },
    {
      "orbit_id": 2,
      "formal_class": [
        0.0,
        0.5,
        0.0
      ],
      "formal_classes_in_orbit": [
        [
          0.0,
          0.5,
          0.0
        ]
      ],
      "target_reduced_polarization": [
        0.0,
        0.5,
        0.0
      ],
      "bec_backprojection": {
        "converged_to_target": true,
        "history": [
          {
            "iteration": 0,
            "reduced_polarization": [
              2.487399225611893e-16,
              1.9738089541055647e-16,
              -0.019591463905136525
            ],
            "branch_aligned_reduced_polarization": [
              2.487399225611893e-16,
              2.220446049250313e-16,
              -0.019591463905136525
            ],
            "target_residual": 0.5003836782489473,
            "energy_eV": -87.21865335418946,
            "max_atomic_step_A": 0.12,
            "max_log_strain_component": 0.008458530117385274,
            "step_scale": 0.46349779014128656,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 0.33523308942343616,
            "cell_principal_stretches": [
              1.0085437365195997,
              0.9999962384289416,
              0.991625529392572
            ],
            "cell_volume_ratio": 1.000093954703184,
            "cell_rmsd_from_input_A": 0.0754645692768265
          },
          {
            "iteration": 1,
            "reduced_polarization": [
              -1.4531453842949952e-15,
              0.22617642160111495,
              -0.010090672790847277
            ],
            "branch_aligned_reduced_polarization": [
              -1.4531453842949952e-15,
              0.22617642160111495,
              -0.010090672790847277
            ],
            "target_residual": 0.2740094410135211,
            "energy_eV": -86.69703820271637,
            "max_atomic_step_A": 0.12,
            "max_log_strain_component": 0.009829254357833394,
            "step_scale": 0.8613611548288939,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 0.33523308942343616,
            "cell_principal_stretches": [
              1.0185652038204625,
              0.9999917572968693,
              0.9819834164307457
            ],
            "cell_volume_ratio": 1.0002058942368837,
            "cell_rmsd_from_input_A": 0.16326717524000453
          },
          {
            "iteration": 2,
            "reduced_polarization": [
              2.148629388136809e-15,
              0.43691572327315475,
              -0.006218132248837376
            ],
            "branch_aligned_reduced_polarization": [
              2.148629388136809e-15,
              0.43691572327315475,
              -0.006218132248837376
            ],
            "target_residual": 0.06338999241846635,
            "energy_eV": -85.11505590642095,
            "max_atomic_step_A": 0.047939138560851066,
            "max_log_strain_component": 0.003949179678206194,
            "step_scale": 1.0,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 0.33523308942343616,
            "cell_principal_stretches": [
              1.0227101249540091,
              0.9999831638053945,
              0.9782218997357811
            ],
            "cell_volume_ratio": 1.0004205977520768,
            "cell_rmsd_from_input_A": 0.19869969352066583
          },
          {
            "iteration": 3,
            "reduced_polarization": [
              -9.813783001141928e-17,
              0.4975306901686651,
              -0.0011020949716831628
            ],
            "branch_aligned_reduced_polarization": [
              -9.813783001141928e-17,
              0.4975306901686651,
              -0.0011020949716831628
            ],
            "target_residual": 0.0027040903035469442,
            "energy_eV": -84.52652569397517,
            "max_atomic_step_A": 0.0020844383630262467,
            "max_log_strain_component": 0.0001727575615039554,
            "step_scale": 1.0,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 0.33523308942343616,
            "cell_principal_stretches": [
              1.0228997305656418,
              0.999982195944079,
              0.9780651657426346
            ],
            "cell_volume_ratio": 1.000444782221801,
            "cell_rmsd_from_input_A": 0.20026133289423118
          },
          {
            "iteration": 4,
            "reduced_polarization": [
              6.634213820259253e-16,
              0.49993606930307705,
              -8.34547656648073e-06
            ],
            "branch_aligned_reduced_polarization": [
              6.634213820259253e-16,
              0.49993606930307705,
              -8.34547656648073e-06
            ],
            "target_residual": 6.447310282727387e-05,
            "energy_eV": -84.50314704799592
          }
        ],
        "iterations": 4
      },
      "parent": {
        "candidate_id": "bec_projection_02",
        "source": "MACEField_BEC_backprojection",
        "spacegroup": "Pc",
        "spacegroup_number": 7,
        "pointgroup": "m",
        "has_inversion": false,
        "is_polar_point_group": true,
        "nonpolar_parent_hypothesis": false,
        "symmetry_tolerance_A": null,
        "target_reduced_polarization": [
          0.0,
          0.5,
          0.0
        ],
        "formal_class": [
          0.0,
          0.5,
          0.0
        ],
        "target_residual": 6.447310282727387e-05,
        "parent_symmetrization_rmsd_A": 0.2978768030206429,
        "parent_cell_rmsd_A": 0.20026133289423118,
        "energy_eV": -84.50314704799592,
        "reduced_polarization": [
          6.634213820259253e-16,
          0.49993606930307705,
          -8.34547656648073e-06
        ],
        "cartesian_polarization_e_A2": [
          1.220977496263918e-16,
          0.007164107534260544,
          0.0001604178256594405
        ],
        "ranking_score": 0.8480710824498552
      },
      "branch_status": "awaiting_branch_sampling"
    },
    {
      "orbit_id": 3,
      "formal_class": [
        0.5,
        0.0,
        0.0
      ],
      "formal_classes_in_orbit": [
        [
          0.5,
          0.0,
          0.0
        ]
      ],
      "target_reduced_polarization": [
        0.5,
        0.0,
        0.0
      ],
      "bec_backprojection": {
        "converged_to_target": true,
        "history": [
          {
            "iteration": 0,
            "reduced_polarization": [
              2.487399225611893e-16,
              1.9738089541055647e-16,
              -0.019591463905136525
            ],
            "branch_aligned_reduced_polarization": [
              2.220446049250313e-16,
              1.9738089541055647e-16,
              -0.019591463905136525
            ],
            "target_residual": 0.5003836782489473,
            "energy_eV": -87.21865335418946,
            "max_atomic_step_A": 0.12,
            "max_log_strain_component": 0.00037225107120023563,
            "step_scale": 0.8373533724171713,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 0.33523308942343616,
            "cell_principal_stretches": [
              1.0003849256990982,
              1.0001455002917776,
              0.9996394539123256
            ],
            "cell_volume_ratio": 1.0001697446467948,
            "cell_rmsd_from_input_A": 0.0028906306361747725
          },
          {
            "iteration": 1,
            "reduced_polarization": [
              0.4107314259434284,
              5.182718658777105e-16,
              -0.0025261957029429783
            ],
            "branch_aligned_reduced_polarization": [
              0.4107314259434284,
              5.182718658777105e-16,
              -0.0025261957029429783
            ],
            "target_residual": 0.08930431108755714,
            "energy_eV": -86.65479254233698,
            "max_atomic_step_A": 0.028669419327406614,
            "max_log_strain_component": 8.802441267282459e-05,
            "step_scale": 1.0,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 0.33523308942343616,
            "cell_principal_stretches": [
              1.000474762783146,
              1.0001664611622991,
              0.9995531820852321
            ],
            "cell_volume_ratio": 1.0001941985145846,
            "cell_rmsd_from_input_A": 0.003493309501123964
          },
          {
            "iteration": 2,
            "reduced_polarization": [
              0.49890945513938717,
              -1.564948808098274e-15,
              -1.4187941973391671e-05
            ],
            "branch_aligned_reduced_polarization": [
              0.49890945513938717,
              -1.564948808098274e-15,
              -1.4187941973391671e-05
            ],
            "target_residual": 0.0010906371489668306,
            "energy_eV": -86.39697093659234,
            "max_atomic_step_A": 0.000368631096042463,
            "max_log_strain_component": 1.1308992423896053e-06,
            "step_scale": 1.0,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 0.33523308942343616,
            "cell_principal_stretches": [
              1.0004759017481233,
              1.0001665592713158,
              0.9995520605069345
            ],
            "cell_volume_ratio": 1.0001943129730526,
            "cell_rmsd_from_input_A": 0.0035000755737574123
          },
          {
            "iteration": 3,
            "reduced_polarization": [
              0.4999998192818196,
              1.2096766537468057e-15,
              -6.061075654065235e-07
            ],
            "branch_aligned_reduced_polarization": [
              0.4999998192818196,
              1.2096766537468057e-15,
              -6.061075654065235e-07
            ],
            "target_residual": 6.324756450468685e-07,
            "energy_eV": -86.39353344725754
          }
        ],
        "iterations": 3
      },
      "parent": {
        "candidate_id": "bec_projection_03",
        "source": "MACEField_BEC_backprojection",
        "spacegroup": "Pc",
        "spacegroup_number": 7,
        "pointgroup": "m",
        "has_inversion": false,
        "is_polar_point_group": true,
        "nonpolar_parent_hypothesis": false,
        "symmetry_tolerance_A": null,
        "target_reduced_polarization": [
          0.5,
          0.0,
          0.0
        ],
        "formal_class": [
          0.5,
          0.0,
          0.0
        ],
        "target_residual": 6.324756450468685e-07,
        "parent_symmetrization_rmsd_A": 0.17191013822483936,
        "parent_cell_rmsd_A": 0.0035000755737574123,
        "energy_eV": -86.39353344725754,
        "reduced_polarization": [
          0.4999998192818196,
          1.2096766537468057e-15,
          -6.061075654065235e-07
        ],
        "cartesian_polarization_e_A2": [
          0.005176499749651214,
          4.8004638985607084e-17,
          -2.3934739735982123e-06
        ],
        "ranking_score": 0.6727864220695688
      },
      "branch_status": "awaiting_branch_sampling"
    },
    {
      "orbit_id": 4,
      "formal_class": [
        0.0,
        0.5,
        0.5
      ],
      "formal_classes_in_orbit": [
        [
          0.0,
          0.5,
          0.5
        ]
      ],
      "target_reduced_polarization": [
        0.0,
        0.5,
        -0.5
      ],
      "bec_backprojection": {
        "converged_to_target": true,
        "history": [
          {
            "iteration": 0,
            "reduced_polarization": [
              2.487399225611893e-16,
              1.9738089541055647e-16,
              -0.019591463905136525
            ],
            "branch_aligned_reduced_polarization": [
              2.487399225611893e-16,
              2.220446049250313e-16,
              -0.019591463905136552
            ],
            "target_residual": 0.6933919249261629,
            "energy_eV": -87.21865335418946,
            "max_atomic_step_A": 0.12,
            "max_log_strain_component": 0.007573606425161358,
            "step_scale": 0.41500707483953697,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 0.33523308942343616,
            "cell_principal_stretches": [
              1.0065541811258882,
              1.000082592321981,
              0.9913593965287993
            ],
            "cell_volume_ratio": 0.9979393608966403,
            "cell_rmsd_from_input_A": 0.07000249768870859
          },
          {
            "iteration": 1,
            "reduced_polarization": [
              -6.224525459878708e-15,
              0.20303454442738963,
              -0.21421185330000497
            ],
            "branch_aligned_reduced_polarization": [
              -6.224525459878708e-15,
              0.20303454442738966,
              -0.21421185330000497
            ],
            "target_residual": 0.412144812654079,
            "energy_eV": -86.68071080022153,
            "max_atomic_step_A": 0.12000000000000001,
            "max_log_strain_component": 0.008829321224267831,
            "step_scale": 0.7221051524021003,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 0.33523308942343616,
            "cell_principal_stretches": [
              1.0142531721134314,
              1.000178575146923,
              0.981384590024563
            ],
            "cell_volume_ratio": 0.995550182274207,
            "cell_rmsd_from_input_A": 0.15081117320076254
          },
          {
            "iteration": 2,
            "reduced_polarization": [
              -9.359020377957723e-15,
              0.400342333206102,
              -0.40245122475314626
            ],
            "branch_aligned_reduced_polarization": [
              -9.359020377957723e-15,
              0.400342333206102,
              -0.40245122475314626
            ],
            "target_residual": 0.13945398561161593,
            "energy_eV": -85.0121292675107,
            "max_atomic_step_A": 0.07687756169965829,
            "max_log_strain_component": 0.005977547153294354,
            "step_scale": 1.0,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 0.33523308942343616,
            "cell_principal_stretches": [
              1.0194683362981987,
              1.0002460145915104,
              0.9746556844543557
            ],
            "cell_volume_ratio": 0.9938750567226728,
            "cell_rmsd_from_input_A": 0.2052043779067194
          },
          {
            "iteration": 3,
            "reduced_polarization": [
              -2.8458211020028113e-15,
              0.49711702657896745,
              -0.492279293742811
            ],
            "branch_aligned_reduced_polarization": [
              -2.8458211020028113e-15,
              0.49711702657896745,
              -0.492279293742811
            ],
            "target_residual": 0.008241410125468683,
            "energy_eV": -83.82948156537653,
            "max_atomic_step_A": 0.0034669652603965787,
            "max_log_strain_component": 0.00023792632894659233,
            "step_scale": 1.0,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 0.33523308942343616,
            "cell_principal_stretches": [
              1.0196381213273558,
              1.0002517808475189,
              0.9743474714789919
            ],
            "cell_volume_ratio": 0.9937319650348772,
            "cell_rmsd_from_input_A": 0.2075323272705776
          },
          {
            "iteration": 4,
            "reduced_polarization": [
              1.2421842324741592e-16,
              0.5001130590854931,
              -0.5000370828814629
            ],
            "branch_aligned_reduced_polarization": [
              1.2421842324741592e-16,
              0.5001130590854931,
              -0.5000370828814629
            ],
            "target_residual": 0.0001189852802245788,
            "energy_eV": -83.77902653970631
          }
        ],
        "iterations": 4
      },
      "parent": {
        "candidate_id": "bec_projection_04",
        "source": "MACEField_BEC_backprojection",
        "spacegroup": "Pc",
        "spacegroup_number": 7,
        "pointgroup": "m",
        "has_inversion": false,
        "is_polar_point_group": true,
        "nonpolar_parent_hypothesis": false,
        "symmetry_tolerance_A": null,
        "target_reduced_polarization": [
          0.0,
          0.5,
          -0.5
        ],
        "formal_class": [
          0.0,
          0.5,
          0.5
        ],
        "target_residual": 0.0001189852802245788,
        "parent_symmetrization_rmsd_A": 0.3418955901292876,
        "parent_cell_rmsd_A": 0.2075323272705776,
        "energy_eV": -83.77902653970631,
        "reduced_polarization": [
          1.2421842324741592e-16,
          0.5001130590854931,
          -0.5000370828814629
        ],
        "cartesian_polarization_e_A2": [
          7.334511494843447e-16,
          0.0070808003533899665,
          -0.003948758674853481
        ],
        "ranking_score": 0.8940166425073812
      },
      "branch_status": "awaiting_branch_sampling"
    },
    {
      "orbit_id": 5,
      "formal_class": [
        0.5,
        0.0,
        0.5
      ],
      "formal_classes_in_orbit": [
        [
          0.5,
          0.0,
          0.5
        ]
      ],
      "target_reduced_polarization": [
        0.5,
        0.0,
        -0.5
      ],
      "bec_backprojection": {
        "converged_to_target": true,
        "history": [
          {
            "iteration": 0,
            "reduced_polarization": [
              2.487399225611893e-16,
              1.9738089541055647e-16,
              -0.019591463905136525
            ],
            "branch_aligned_reduced_polarization": [
              2.220446049250313e-16,
              1.9738089541055647e-16,
              -0.019591463905136552
            ],
            "target_residual": 0.6933919249261629,
            "energy_eV": -87.21865335418946,
            "max_atomic_step_A": 0.12,
            "max_log_strain_component": 0.002721636481556929,
            "step_scale": 0.6387968901309777,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 0.33523308942343616,
            "cell_principal_stretches": [
              1.0002270118825376,
              0.99931978423818,
              0.9972820638132981
            ],
            "cell_volume_ratio": 0.9968299377158742,
            "cell_rmsd_from_input_A": 0.030124328996209343
          },
          {
            "iteration": 1,
            "reduced_polarization": [
              0.31281895818963473,
              -3.5277802149819713e-16,
              -0.31763147090273114
            ],
            "branch_aligned_reduced_polarization": [
              0.31281895818963473,
              -3.5277802149819713e-16,
              -0.31763147090273114
            ],
            "target_residual": 0.26133316440573534,
            "energy_eV": -86.6942142634424,
            "max_atomic_step_A": 0.0747573941259634,
            "max_log_strain_component": 0.0018997181028309713,
            "step_scale": 1.0,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 0.33523308942343616,
            "cell_principal_stretches": [
              1.0003785554746847,
              0.9988521958140403,
              0.9953893074440481
            ],
            "cell_volume_ratio": 0.9946231729979027,
            "cell_rmsd_from_input_A": 0.05105071521701914
          },
          {
            "iteration": 2,
            "reduced_polarization": [
              0.4919873636903708,
              1.9623542905912387e-15,
              -0.4884636049853022
            ],
            "branch_aligned_reduced_polarization": [
              0.4919873636903708,
              1.9623542905912387e-15,
              -0.4884636049853022
            ],
            "target_residual": 0.014046022588816078,
            "energy_eV": -85.88658381311795,
            "max_atomic_step_A": 0.004553057097575808,
            "max_log_strain_component": 0.00015296464316214071,
            "step_scale": 1.0,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 0.33523308942343616,
            "cell_principal_stretches": [
              1.00038780835386,
              0.998817500992409,
              0.9952370597183838
            ],
            "cell_volume_ratio": 0.994445697729989,
            "cell_rmsd_from_input_A": 0.052730444725410164
          },
          {
            "iteration": 3,
            "reduced_polarization": [
              0.4999793945785889,
              -2.595186122543606e-15,
              -0.4999795165141464
            ],
            "branch_aligned_reduced_polarization": [
              0.4999793945785889,
              -2.595186122543606e-15,
              -0.4999795165141464
            ],
            "target_residual": 2.905437289363874e-05,
            "energy_eV": -85.83376957599631
          }
        ],
        "iterations": 3
      },
      "parent": {
        "candidate_id": "bec_projection_05",
        "source": "MACEField_BEC_backprojection",
        "spacegroup": "Pc",
        "spacegroup_number": 7,
        "pointgroup": "m",
        "has_inversion": false,
        "is_polar_point_group": true,
        "nonpolar_parent_hypothesis": false,
        "symmetry_tolerance_A": null,
        "target_reduced_polarization": [
          0.5,
          0.0,
          -0.5
        ],
        "formal_class": [
          0.5,
          0.0,
          0.5
        ],
        "target_residual": 2.905437289363874e-05,
        "parent_symmetrization_rmsd_A": 0.22491190539164918,
        "parent_cell_rmsd_A": 0.052730444725410164,
        "energy_eV": -85.83376957599631,
        "reduced_polarization": [
          0.4999793945785889,
          -2.595186122543606e-15,
          -0.4999795165141464
        ],
        "cartesian_polarization_e_A2": [
          0.005209390792772553,
          4.6084004220346385e-17,
          -0.0041099081637267455
        ],
        "ranking_score": 0.738152625318789
      },
      "branch_status": "awaiting_branch_sampling"
    },
    {
      "orbit_id": 6,
      "formal_class": [
        0.5,
        0.5,
        0.0
      ],
      "formal_classes_in_orbit": [
        [
          0.5,
          0.5,
          0.0
        ]
      ],
      "target_reduced_polarization": [
        0.5,
        0.5,
        0.0
      ],
      "bec_backprojection": {
        "converged_to_target": true,
        "history": [
          {
            "iteration": 0,
            "reduced_polarization": [
              2.487399225611893e-16,
              1.9738089541055647e-16,
              -0.019591463905136525
            ],
            "branch_aligned_reduced_polarization": [
              2.220446049250313e-16,
              2.220446049250313e-16,
              -0.019591463905136525
            ],
            "target_residual": 0.7073781347044491,
            "energy_eV": -87.21865335418946,
            "max_atomic_step_A": 0.12,
            "max_log_strain_component": 0.0073776200069609575,
            "step_scale": 0.4042677063594353,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 0.33523308942343616,
            "cell_principal_stretches": [
              1.0074500660743662,
              0.9999967627212566,
              0.9926895823748034
            ],
            "cell_volume_ratio": 1.0000819478003191,
            "cell_rmsd_from_input_A": 0.06582760728956204
          },
          {
            "iteration": 1,
            "reduced_polarization": [
              0.19768797312032377,
              0.19731067570637725,
              -0.01113609638039603
            ],
            "branch_aligned_reduced_polarization": [
              0.19768797312032377,
              0.19731067570637728,
              -0.01113609638039603
            ],
            "target_residual": 0.4279455587805784,
            "energy_eV": -86.69550710034136,
            "max_atomic_step_A": 0.12,
            "max_log_strain_component": 0.00823154506220697,
            "step_scale": 0.6522590833291485,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 0.33523308942343616,
            "cell_principal_stretches": [
              1.0158251942816745,
              0.9999933512790196,
              0.9845935419719596
            ],
            "cell_volume_ratio": 1.0001682761781325,
            "cell_rmsd_from_input_A": 0.13934214681774285
          },
          {
            "iteration": 2,
            "reduced_polarization": [
              0.3798183743840789,
              0.37569650015726447,
              -0.007201929736094547
            ],
            "branch_aligned_reduced_polarization": [
              0.3798183743840789,
              0.37569650015726447,
              -0.007201929736094547
            ],
            "target_residual": 0.17305158479702523,
            "energy_eV": -85.17191887417451,
            "max_atomic_step_A": 0.10359946950607035,
            "max_log_strain_component": 0.007585399397505853,
            "step_scale": 1.0,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 0.33523308942343616,
            "cell_principal_stretches": [
              1.0237084242217618,
              0.9999824690532463,
              0.9772908689652896
            ],
            "cell_volume_ratio": 1.0004433564480852,
            "cell_rmsd_from_input_A": 0.20731156557662725
          },
          {
            "iteration": 3,
            "reduced_polarization": [
              0.4927956242100245,
              0.48983629850949995,
              -0.003877697783582251
            ],
            "branch_aligned_reduced_polarization": [
              0.4927956242100245,
              0.48983629850949995,
              -0.003877697783582251
            ],
            "target_residual": 0.013047620419523901,
            "energy_eV": -83.69659813979159,
            "max_atomic_step_A": 0.010225318515610548,
            "max_log_strain_component": 0.0007974941690608175,
            "step_scale": 1.0,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 0.33523308942343616,
            "cell_principal_stretches": [
              1.0245764938027533,
              0.9999786748342603,
              0.9765601327026281
            ],
            "cell_volume_ratio": 1.000539219632305,
            "cell_rmsd_from_input_A": 0.21451700105472205
          },
          {
            "iteration": 4,
            "reduced_polarization": [
              0.4998193241578134,
              0.49968814009127893,
              -0.0002111514301482995
            ],
            "branch_aligned_reduced_polarization": [
              0.4998193241578134,
              0.49968814009127893,
              -0.0002111514301482995
            ],
            "target_residual": 0.00041771436301739573,
            "energy_eV": -83.5828458322207
          }
        ],
        "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,
          0.5,
          0.0
        ],
        "formal_class": [
          0.5,
          0.5,
          0.0
        ],
        "target_residual": 0.00041771436301739573,
        "parent_symmetrization_rmsd_A": 0.3692386374321328,
        "parent_cell_rmsd_A": 0.21451700105472205,
        "energy_eV": -83.5828458322207,
        "reduced_polarization": [
          0.4998193241578134,
          0.49968814009127893,
          -0.0002111514301482995
        ],
        "cartesian_polarization_e_A2": [
          0.005172731092094109,
          0.007160645469743718,
          0.00016713038285791763
        ],
        "ranking_score": 0.9237033164218481
      },
      "branch_status": "awaiting_branch_sampling"
    },
    {
      "orbit_id": 7,
      "formal_class": [
        0.5,
        0.5,
        0.5
      ],
      "formal_classes_in_orbit": [
        [
          0.5,
          0.5,
          0.5
        ]
      ],
      "target_reduced_polarization": [
        0.5,
        0.5,
        -0.5
      ],
      "bec_backprojection": {
        "converged_to_target": true,
        "history": [
          {
            "iteration": 0,
            "reduced_polarization": [
              2.487399225611893e-16,
              1.9738089541055647e-16,
              -0.019591463905136525
            ],
            "branch_aligned_reduced_polarization": [
              2.220446049250313e-16,
              2.220446049250313e-16,
              -0.019591463905136552
            ],
            "target_residual": 0.8548639432990546,
            "energy_eV": -87.21865335418946,
            "max_atomic_step_A": 0.11999999999999998,
            "max_log_strain_component": 0.006753406559379211,
            "step_scale": 0.3700629982696227,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 0.33523308942343616,
            "cell_principal_stretches": [
              1.0058448951297787,
              1.0000726539752534,
              0.9922899710107655
            ],
            "cell_volume_ratio": 0.9981623170214169,
            "cell_rmsd_from_input_A": 0.06246108499983474
          },
          {
            "iteration": 1,
            "reduced_polarization": [
              0.18111489628452931,
              0.1810219136292405,
              -0.19282472997815686
            ],
            "branch_aligned_reduced_polarization": [
              0.18111489628452931,
              0.18102191362924047,
              -0.19282472997815686
            ],
            "target_residual": 0.5457026438174645,
            "energy_eV": -86.68958217486971,
            "max_atomic_step_A": 0.12000000000000001,
            "max_log_strain_component": 0.007880688601998852,
            "step_scale": 0.5974800315212132,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 0.33523308942343616,
            "cell_principal_stretches": [
              1.0127044604068387,
              1.0001577893923095,
              0.9833636256229795
            ],
            "cell_volume_ratio": 0.9960138654984653,
            "cell_rmsd_from_input_A": 0.13474054548692121
          },
          {
            "iteration": 2,
            "reduced_polarization": [
              0.3574241070895245,
              0.3561970725500371,
              -0.35921032142451276
            ],
            "branch_aligned_reduced_polarization": [
              0.3574241070895245,
              0.3561970725500371,
              -0.35921032142451276
            ],
            "target_residual": 0.24663515721767587,
            "energy_eV": -85.01507362354735,
            "max_atomic_step_A": 0.12,
            "max_log_strain_component": 0.00828263405640178,
            "step_scale": 0.9719591272855144,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 0.33523308942343616,
            "cell_principal_stretches": [
              1.0199191527808922,
              1.0002509507651367,
              0.9740204146574357
            ],
            "cell_volume_ratio": 0.9936713761388078,
            "cell_rmsd_from_input_A": 0.21021458244930338
          },
          {
            "iteration": 3,
            "reduced_polarization": [
              0.48976242754913846,
              0.4873967965961,
              -0.4815848841947306
            ],
            "branch_aligned_reduced_polarization": [
              0.48976242754913846,
              0.4873967965961,
              -0.4815848841947306
            ],
            "target_residual": 0.02455127523873653,
            "energy_eV": -82.95077705742337,
            "max_atomic_step_A": 0.014754541617165346,
            "max_log_strain_component": 0.0010172835084980506,
            "step_scale": 1.0,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 0.33523308942343616,
            "cell_principal_stretches": [
              1.0207484857479163,
              1.0002672129673802,
              0.9728142151508582
            ],
            "cell_volume_ratio": 0.9932639791416917,
            "cell_rmsd_from_input_A": 0.21970389053504086
          },
          {
            "iteration": 4,
            "reduced_polarization": [
              0.5000922595206408,
              0.5003205818471221,
              -0.5000917590183416
            ],
            "branch_aligned_reduced_polarization": [
              0.5000922595206408,
              0.5003205818471221,
              -0.5000917590183416
            ],
            "target_residual": 0.00034598303036439433,
            "energy_eV": -82.73256642726068
          }
        ],
        "iterations": 4
      },
      "parent": {
        "candidate_id": "bec_projection_07",
        "source": "MACEField_BEC_backprojection",
        "spacegroup": "P1",
        "spacegroup_number": 1,
        "pointgroup": "1",
        "has_inversion": false,
        "is_polar_point_group": true,
        "nonpolar_parent_hypothesis": false,
        "symmetry_tolerance_A": null,
        "target_reduced_polarization": [
          0.5,
          0.5,
          -0.5
        ],
        "formal_class": [
          0.5,
          0.5,
          0.5
        ],
        "target_residual": 0.00034598303036439433,
        "parent_symmetrization_rmsd_A": 0.4081087771289357,
        "parent_cell_rmsd_A": 0.21970389053504086,
        "energy_eV": -82.73256642726068,
        "reduced_polarization": [
          0.5000922595206408,
          0.5003205818471221,
          -0.5000917590183416
        ],
        "cartesian_polarization_e_A2": [
          0.005217311169529498,
          0.007079016100850431,
          -0.0039442895615632535
        ],
        "ranking_score": 0.9637267158234246
      },
      "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
        ],
        "endpoint_rmsd_A": 0.039667121705951686,
        "minimum_distance_A_by_image": [
          2.270420302940599,
          2.2703941997104287,
          2.2703715766681856,
          2.270352433917907,
          2.2703367715476244,
          2.27032458962937,
          2.2703158882191685,
          2.2703106673570397,
          2.2703089270669956
        ],
        "minimum_distance_A": 2.2703089270669956,
        "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": [
          907.8635719956072,
          907.8635719956072,
          907.8635719956072,
          907.8635719956072,
          907.8635719956072,
          907.8635719956072,
          907.8635719956072,
          907.8635719956072,
          907.8635719956072
        ],
        "cell_deformation_log_strain_norm": 0.0
      },
      "parent_reduced_polarization": [
        6.384570712624e-16,
        -2.25120913143932e-16,
        -2.6169124765000283e-17
      ],
      "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": [
          -87.21865335418947,
          -87.21865621035408,
          -87.21865780486601,
          -87.21865861412688,
          -87.21865904143112,
          -87.2186592600648,
          -87.21865935648367,
          -87.21865939078619,
          -87.2186593983318
        ],
        "cartesian_polarizations_e_A2": [
          [
            -3.722190685297338e-18,
            -2.3693616271913238e-18,
            -0.00016021581329722225
          ],
          [
            1.5286204046395637e-20,
            -7.352664146316301e-18,
            -0.0001403323197559236
          ],
          [
            5.04444733531056e-19,
            -1.0058322262528329e-17,
            -0.00012039205137253866
          ],
          [
            -4.891585294846604e-18,
            -6.557781535903728e-18,
            -0.000100402691758812
          ],
          [
            -4.425356071431537e-18,
            -1.6509100370107288e-18,
            -8.037204775788418e-05
          ],
          [
            1.3834014661988052e-18,
            1.871031375278826e-17,
            -6.030820549795474e-05
          ],
          [
            -1.3375428540596182e-18,
            6.664784964228498e-18,
            -4.021938502214149e-05
          ],
          [
            2.231785790773763e-18,
            -7.245660717991531e-18,
            -2.011387198071294e-05
          ],
          [
            6.611283250066113e-18,
            -3.2253890537894794e-18,
            -2.1400685664953892e-19
          ]
        ],
        "raw_reduced_polarization": [
          [
            -3.594550216240333e-16,
            -1.6537318264127708e-16,
            -0.01959146390513574
          ],
          [
            1.476201320837919e-18,
            -5.131903280674469e-16,
            -0.017160076278624183
          ],
          [
            4.8714643587651325e-17,
            -7.020358334061955e-16,
            -0.014721746127235948
          ],
          [
            -4.723844226681341e-16,
            -4.577102926006959e-16,
            -0.012277413016167853
          ],
          [
            -4.2736028238257757e-16,
            -1.1522776596940596e-16,
            -0.009828031579562775
          ],
          [
            1.3359621953583166e-16,
            1.3059146809866008e-15,
            -0.007374590603018672
          ],
          [
            -1.291676155733179e-16,
            4.651787589135277e-16,
            -0.004918095247478941
          ],
          [
            2.1552539284233616e-16,
            -5.05721861754615e-16,
            -0.0024595586964416744
          ],
          [
            6.384570712624e-16,
            -2.25120913143932e-16,
            -2.6169124765000283e-17
          ]
        ],
        "unwrapped_reduced_polarization": [
          [
            -3.594550216240333e-16,
            -1.6537318264127708e-16,
            -0.01959146390513574
          ],
          [
            1.4762013208379047e-18,
            -5.131903280674469e-16,
            -0.017160076278624183
          ],
          [
            4.8714643587651325e-17,
            -7.020358334061955e-16,
            -0.014721746127235948
          ],
          [
            -4.723844226681341e-16,
            -4.577102926006959e-16,
            -0.012277413016167853
          ],
          [
            -4.2736028238257757e-16,
            -1.1522776596940593e-16,
            -0.009828031579562775
          ],
          [
            1.3359621953583166e-16,
            1.3059146809866006e-15,
            -0.007374590603018672
          ],
          [
            -1.291676155733179e-16,
            4.651787589135277e-16,
            -0.004918095247478941
          ],
          [
            2.1552539284233616e-16,
            -5.057218617546149e-16,
            -0.0024595586964416744
          ],
          [
            6.384570712624e-16,
            -2.25120913143932e-16,
            -2.6020852139652106e-17
          ]
        ],
        "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": [
          [
            -3.3306690738754696e-16,
            -1.6653345369377348e-16,
            -0.01959146390513572
          ],
          [
            0.0,
            -4.996003610813204e-16,
            -0.017160076278624203
          ],
          [
            0.0,
            -7.216449660063518e-16,
            -0.014721746127235924
          ],
          [
            -4.996003610813204e-16,
            -4.440892098500626e-16,
            -0.01227741301616786
          ],
          [
            -4.440892098500626e-16,
            -1.1102230246251565e-16,
            -0.009828031579562801
          ],
          [
            1.1102230246251565e-16,
            1.3322676295501878e-15,
            -0.007374590603018649
          ],
          [
            -1.1102230246251565e-16,
            4.440892098500626e-16,
            -0.0049180952474789374
          ],
          [
            2.220446049250313e-16,
            -4.996003610813204e-16,
            -0.002459558696441655
          ],
          [
            6.661338147750939e-16,
            -2.220446049250313e-16,
            0.0
          ]
        ]
      },
      "reflected": {
        "reached": true,
        "construction": "reflect_displacements_about_reconstructed_parent",
        "energies_eV": [
          -87.2186593983318,
          -87.21865939078621,
          -87.21865935648367,
          -87.21865926006481,
          -87.21865904143115,
          -87.2186586141269,
          -87.21865780486598,
          -87.21865621035406,
          -87.21865335418944
        ],
        "cartesian_polarizations_e_A2": [
          [
            3.3782510942534357e-18,
            3.668688971134953e-19,
            5.136164559588934e-18
          ],
          [
            6.12976782260465e-18,
            1.941347913892246e-18,
            2.0113871980698387e-05
          ],
          [
            -6.038050598326277e-18,
            -6.664784964228498e-18,
            4.0219385022135745e-05
          ],
          [
            -5.510676558725627e-18,
            -1.559192812732355e-18,
            6.0308205497936504e-05
          ],
          [
            -2.8508770546527862e-18,
            -2.1156106400211562e-17,
            8.037204775786028e-05
          ],
          [
            5.7093972113287704e-18,
            7.031653861341993e-19,
            0.00010040269175880351
          ],
          [
            -1.7044117511731136e-18,
            -1.2641690746369191e-17,
            0.000120392051372517
          ],
          [
            1.6425026247852112e-17,
            -1.6906541675313575e-17,
            0.00014033231975591894
          ],
          [
            1.3986876702452008e-18,
            -1.2779266582786753e-17,
            0.00016021581329719528
          ]
        ],
        "raw_reduced_polarization": [
          [
            3.262404919051801e-16,
            2.5606170215423545e-17,
            6.280589943600069e-16
          ],
          [
            5.919567296560055e-16,
            1.354993173899496e-16,
            0.002459558696439895
          ],
          [
            -5.83099521730978e-16,
            -4.651787589135277e-16,
            0.004918095247478238
          ],
          [
            -5.321705761620697e-16,
            -1.0882622341555008e-16,
            0.007374590603016442
          ],
          [
            -2.7531154633627185e-16,
            -1.4766224824227578e-15,
            0.009828031579559852
          ],
          [
            5.513611933329627e-16,
            4.907849291289513e-17,
            0.012277413016166814
          ],
          [
            -1.6459644727342798e-16,
            -8.823459486731362e-16,
            0.014721746127233296
          ],
          [
            1.5861783192403439e-15,
            -1.180017677427435e-15,
            0.01716007627862361
          ],
          [
            1.350724208566696e-16,
            -8.919482625039202e-16,
            0.019591463905132445
          ]
        ],
        "unwrapped_reduced_polarization": [
          [
            3.262404919051801e-16,
            2.5606170215423545e-17,
            6.280589943600069e-16
          ],
          [
            5.919567296560055e-16,
            1.354993173899496e-16,
            0.002459558696439895
          ],
          [
            -5.830995217309781e-16,
            -4.651787589135277e-16,
            0.004918095247478238
          ],
          [
            -5.321705761620697e-16,
            -1.0882622341555007e-16,
            0.007374590603016442
          ],
          [
            -2.7531154633627185e-16,
            -1.4766224824227578e-15,
            0.009828031579559852
          ],
          [
            5.513611933329627e-16,
            4.90784929128952e-17,
            0.012277413016166814
          ],
          [
            -1.64596447273428e-16,
            -8.823459486731361e-16,
            0.014721746127233296
          ],
          [
            1.5861783192403439e-15,
            -1.180017677427435e-15,
            0.01716007627862361
          ],
          [
            1.3507242085666962e-16,
            -8.919482625039202e-16,
            0.019591463905132445
          ]
        ],
        "gauge_integer_shift": [
          0,
          0,
          0
        ],
        "expected_opposite_endpoint_reduced_polarization": [
          1.636369164148833e-15,
          -2.8486864364658697e-16,
          0.01959146390513569
        ],
        "actual_opposite_endpoint_branch_residual": 3.625677624286417e-15
      },
      "pnp_branch": {
        "construction": "incoming_path_concatenated_with_parent_reflection",
        "reduced_polarization": [
          [
            -3.594550216240333e-16,
            -1.6537318264127708e-16,
            -0.01959146390513574
          ],
          [
            1.476201320837919e-18,
            -5.131903280674469e-16,
            -0.017160076278624183
          ],
          [
            4.8714643587651325e-17,
            -7.020358334061955e-16,
            -0.014721746127235948
          ],
          [
            -4.723844226681341e-16,
            -4.577102926006959e-16,
            -0.012277413016167853
          ],
          [
            -4.2736028238257757e-16,
            -1.1522776596940596e-16,
            -0.009828031579562775
          ],
          [
            1.3359621953583166e-16,
            1.3059146809866008e-15,
            -0.007374590603018672
          ],
          [
            -1.291676155733179e-16,
            4.651787589135277e-16,
            -0.004918095247478941
          ],
          [
            2.1552539284233616e-16,
            -5.05721861754615e-16,
            -0.0024595586964416744
          ],
          [
            6.384570712624e-16,
            -2.25120913143932e-16,
            -2.6169124765000283e-17
          ],
          [
            5.919567296560055e-16,
            1.354993173899496e-16,
            0.002459558696439895
          ],
          [
            -5.83099521730978e-16,
            -4.651787589135277e-16,
            0.004918095247478238
          ],
          [
            -5.321705761620697e-16,
            -1.0882622341555008e-16,
            0.007374590603016442
          ],
          [
            -2.7531154633627185e-16,
            -1.4766224824227578e-15,
            0.009828031579559852
          ],
          [
            5.513611933329627e-16,
            4.907849291289513e-17,
            0.012277413016166814
          ],
          [
            -1.6459644727342798e-16,
            -8.823459486731362e-16,
            0.014721746127233296
          ],
          [
            1.5861783192403439e-15,
            -1.180017677427435e-15,
            0.01716007627862361
          ],
          [
            1.350724208566696e-16,
            -8.919482625039202e-16,
            0.019591463905132445
          ]
        ],
        "unwrapped_reduced_polarization": [
          [
            -3.594550216240333e-16,
            -1.6537318264127708e-16,
            -0.01959146390513574
          ],
          [
            1.4762013208379047e-18,
            -5.131903280674469e-16,
            -0.017160076278624183
          ],
          [
            4.8714643587651325e-17,
            -7.020358334061955e-16,
            -0.014721746127235948
          ],
          [
            -4.723844226681341e-16,
            -4.577102926006959e-16,
            -0.012277413016167853
          ],
          [
            -4.2736028238257757e-16,
            -1.1522776596940593e-16,
            -0.009828031579562775
          ],
          [
            1.3359621953583166e-16,
            1.3059146809866006e-15,
            -0.007374590603018672
          ],
          [
            -1.291676155733179e-16,
            4.651787589135277e-16,
            -0.004918095247478941
          ],
          [
            2.1552539284233616e-16,
            -5.057218617546149e-16,
            -0.0024595586964416744
          ],
          [
            6.384570712624e-16,
            -2.25120913143932e-16,
            -2.6020852139652106e-17
          ],
          [
            5.919567296560055e-16,
            1.3549931738994962e-16,
            0.002459558696439895
          ],
          [
            -5.830995217309781e-16,
            -4.651787589135277e-16,
            0.004918095247478238
          ],
          [
            -5.321705761620697e-16,
            -1.0882622341555007e-16,
            0.007374590603016442
          ],
          [
            -2.7531154633627185e-16,
            -1.4766224824227578e-15,
            0.009828031579559852
          ],
          [
            5.513611933329627e-16,
            4.90784929128952e-17,
            0.012277413016166814
          ],
          [
            -1.64596447273428e-16,
            -8.823459486731361e-16,
            0.014721746127233296
          ],
          [
            1.5861783192403439e-15,
            -1.180017677427435e-15,
            0.01716007627862361
          ],
          [
            1.3507242085666962e-16,
            -8.919482625039202e-16,
            0.019591463905132445
          ]
        ],
        "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": [
          [
            -3.3306690738754696e-16,
            -1.6653345369377348e-16,
            -0.01959146390513572
          ],
          [
            0.0,
            -4.996003610813204e-16,
            -0.017160076278624203
          ],
          [
            0.0,
            -7.216449660063518e-16,
            -0.014721746127235924
          ],
          [
            -4.996003610813204e-16,
            -4.440892098500626e-16,
            -0.01227741301616786
          ],
          [
            -4.440892098500626e-16,
            -1.1102230246251565e-16,
            -0.009828031579562801
          ],
          [
            1.1102230246251565e-16,
            1.3322676295501878e-15,
            -0.007374590603018649
          ],
          [
            -1.1102230246251565e-16,
            4.440892098500626e-16,
            -0.0049180952474789374
          ],
          [
            2.220446049250313e-16,
            -4.996003610813204e-16,
            -0.002459558696441655
          ],
          [
            6.661338147750939e-16,
            -2.220446049250313e-16,
            0.0
          ],
          [
            5.551115123125783e-16,
            1.1102230246251565e-16,
            0.0024595586964398786
          ],
          [
            -6.106226635438361e-16,
            -4.440892098500626e-16,
            0.004918095247478216
          ],
          [
            -5.551115123125783e-16,
            -1.1102230246251565e-16,
            0.007374590603016484
          ],
          [
            -2.7755575615628914e-16,
            -1.4988010832439613e-15,
            0.009828031579559804
          ],
          [
            5.551115123125783e-16,
            0.0,
            0.012277413016166805
          ],
          [
            -1.6653345369377348e-16,
            -8.881784197001252e-16,
            0.014721746127233315
          ],
          [
            1.5543122344752192e-15,
            -1.1657341758564144e-15,
            0.017160076278623593
          ],
          [
            1.1102230246251565e-16,
            -8.881784197001252e-16,
            0.019591463905132445
          ]
        ]
      },
      "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": "Pnma",
        "spacegroup_number": 62,
        "pointgroup": "mmm",
        "has_inversion": true,
        "is_polar_point_group": false,
        "nonpolar_parent_hypothesis": true,
        "symmetry_tolerance_A": null,
        "target_reduced_polarization": [
          0.0,
          0.0,
          0.0
        ],
        "formal_class": [
          0.0,
          0.0,
          0.0
        ],
        "target_residual": 1.3687204386215149e-15,
        "parent_symmetrization_rmsd_A": 0.039667121705951686,
        "parent_cell_rmsd_A": 0.0,
        "energy_eV": -87.21865939833181,
        "reduced_polarization": [
          -4.90836939178608e-16,
          2.9553788123634674e-16,
          1.2430334263375134e-15
        ],
        "cartesian_polarization_e_A2": [
          -5.082662845426549e-18,
          4.234278520851592e-18,
          1.0165325690853099e-17
        ],
        "ranking_score": 0.039667121705954426
      }
    }
  ],
  "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": 60,
      "full_response": 26,
      "energy_polarization": 34
    },
    "model_evaluations_for_recovery_and_path_properties": {
      "total": 85,
      "full_response": 51,
      "energy_polarization": 34
    },
    "elapsed_seconds": 222.67989279405447
  }
}