{
  "schema": "ferrofinder.endpoint_parent_recovery.v4_variable_cell",
  "status": "complete",
  "input_atom_count": 16,
  "input_formula": "SbTe6Tl9",
  "input_spacegroup": "I4",
  "input_pointgroup": "4",
  "input_is_polar_point_group": true,
  "input_energy_eV": -45.45166591437446,
  "input_cartesian_polarization_e_A2": [
    -3.152080528220921e-08,
    1.7638002798155857e-08,
    0.0041409312275381685
  ],
  "input_reduced_polarization": [
    0.16556534589751254,
    0.16556832918015013,
    0.3311345174761283
  ],
  "input_formal_targets": [
    {
      "orbit_id": 0,
      "representative_formal_class": [
        0.0,
        0.0,
        0.5
      ],
      "target_reduced_polarization": [
        0.0,
        0.0,
        0.5
      ]
    },
    {
      "orbit_id": 1,
      "representative_formal_class": [
        0.0,
        0.0,
        0.0
      ],
      "target_reduced_polarization": [
        0.0,
        0.0,
        0.0
      ]
    },
    {
      "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,
        0.5,
        0.0
      ],
      "target_reduced_polarization": [
        0.5,
        0.5,
        0.0
      ]
    }
  ],
  "parent_candidates": [
    {
      "candidate_id": "inversion_parent_endpoint_00",
      "source": "same_species_inversion_center_projection_from_endpoint",
      "spacegroup": "I4/m",
      "spacegroup_number": 87,
      "pointgroup": "4/m",
      "has_inversion": true,
      "is_polar_point_group": false,
      "nonpolar_parent_hypothesis": true,
      "symmetry_tolerance_A": null,
      "target_reduced_polarization": [
        0.0,
        0.0,
        0.0
      ],
      "formal_class": [
        0.0,
        0.0,
        0.0
      ],
      "target_residual": 2.176258483341343e-15,
      "parent_symmetrization_rmsd_A": 0.05602721497198772,
      "parent_cell_rmsd_A": 0.0,
      "energy_eV": -45.36263815454786,
      "reduced_polarization": [
        -5.415228569076092e-17,
        -2.1736757749045504e-15,
        9.111609003206217e-17
      ],
      "cartesian_polarization_e_A2": [
        -1.6430360803985487e-18,
        -3.6568740777742016e-17,
        1.1394325950092037e-18
      ],
      "ranking_score": 0.05602721497199207
    },
    {
      "candidate_id": "inversion_parent_endpoint_01",
      "source": "same_species_inversion_center_projection_from_endpoint",
      "spacegroup": "P-1",
      "spacegroup_number": 2,
      "pointgroup": "-1",
      "has_inversion": true,
      "is_polar_point_group": false,
      "nonpolar_parent_hypothesis": true,
      "symmetry_tolerance_A": null,
      "target_reduced_polarization": [
        0.0,
        0.0,
        0.0
      ],
      "formal_class": [
        0.0,
        0.0,
        0.0
      ],
      "target_residual": 0.0004684084356048213,
      "parent_symmetrization_rmsd_A": 1.1680508458252203,
      "parent_cell_rmsd_A": 0.0,
      "energy_eV": "Infinity",
      "reduced_polarization": [
        0.00032795827990091044,
        0.00033443953082038777,
        1.7150752468499776e-07
      ],
      "cartesian_polarization_e_A2": [
        5.40271390459296e-06,
        5.5095125585522125e-06,
        2.1447503272656532e-09
      ],
      "ranking_score": 1.16898766269643
    },
    {
      "candidate_id": "inversion_parent_endpoint_02",
      "source": "same_species_inversion_center_projection_from_endpoint",
      "spacegroup": "P-1",
      "spacegroup_number": 2,
      "pointgroup": "-1",
      "has_inversion": true,
      "is_polar_point_group": false,
      "nonpolar_parent_hypothesis": true,
      "symmetry_tolerance_A": null,
      "target_reduced_polarization": [
        0.0,
        0.0,
        0.0
      ],
      "formal_class": [
        0.0,
        0.0,
        0.0
      ],
      "target_residual": 7.888911868478723e-15,
      "parent_symmetrization_rmsd_A": 1.1680508761095172,
      "parent_cell_rmsd_A": 0.0,
      "energy_eV": -17.8728929780435,
      "reduced_polarization": [
        5.054592743061574e-15,
        2.6987906880540455e-15,
        5.422411962631251e-15
      ],
      "cartesian_polarization_e_A2": [
        3.86145444576157e-17,
        -2.0458036798736793e-19,
        6.780880228306306e-17
      ],
      "ranking_score": 1.168050876109533
    },
    {
      "candidate_id": "bec_projection_00",
      "source": "MACEField_BEC_backprojection",
      "spacegroup": "P1",
      "spacegroup_number": 1,
      "pointgroup": "1",
      "has_inversion": false,
      "is_polar_point_group": true,
      "nonpolar_parent_hypothesis": false,
      "symmetry_tolerance_A": null,
      "target_reduced_polarization": [
        0.0,
        0.0,
        0.5
      ],
      "formal_class": [
        0.0,
        0.0,
        0.5
      ],
      "target_residual": 0.0002509143114036164,
      "parent_symmetrization_rmsd_A": 0.07375724307726404,
      "parent_cell_rmsd_A": 0.01601395225432733,
      "energy_eV": -45.58058326544612,
      "reduced_polarization": [
        0.00019918800635622424,
        0.00015182398039676056,
        0.5000152186979557
      ],
      "cartesian_polarization_e_A2": [
        -0.004124664420299323,
        -0.0041230900720189406,
        0.006236040385172085
      ],
      "ranking_score": 0.5782625597636532
    },
    {
      "candidate_id": "inversion_parent_bec_00_00",
      "source": "same_species_inversion_center_projection_after_BEC",
      "spacegroup": "P-1",
      "spacegroup_number": 2,
      "pointgroup": "-1",
      "has_inversion": true,
      "is_polar_point_group": false,
      "nonpolar_parent_hypothesis": true,
      "symmetry_tolerance_A": null,
      "target_reduced_polarization": [
        0.0,
        0.0,
        0.5
      ],
      "formal_class": [
        0.0,
        0.0,
        0.5
      ],
      "target_residual": 0.4999999999999988,
      "parent_symmetrization_rmsd_A": 0.05619748780095909,
      "parent_cell_rmsd_A": 0.01601395225432733,
      "energy_eV": -45.37138889864099,
      "reduced_polarization": [
        -5.794997165782264e-16,
        -3.0100884748675884e-15,
        -1.2650450604649994e-15
      ],
      "cartesian_polarization_e_A2": [
        8.707710628204067e-19,
        -3.9287141481367766e-17,
        -1.5815139326160522e-17
      ],
      "ranking_score": 1.0602009758645385
    },
    {
      "candidate_id": "bec_projection_01",
      "source": "MACEField_BEC_backprojection",
      "spacegroup": "I4",
      "spacegroup_number": 79,
      "pointgroup": "4",
      "has_inversion": false,
      "is_polar_point_group": true,
      "nonpolar_parent_hypothesis": false,
      "symmetry_tolerance_A": null,
      "target_reduced_polarization": [
        0.0,
        0.0,
        0.0
      ],
      "formal_class": [
        0.0,
        0.0,
        0.0
      ],
      "target_residual": 2.3148725747483214e-05,
      "parent_symmetrization_rmsd_A": 0.04997742655401655,
      "parent_cell_rmsd_A": 0.023691319723670716,
      "energy_eV": -45.34585603473807,
      "reduced_polarization": [
        -9.45046929772629e-06,
        -9.450406259919116e-06,
        -1.890084535959719e-05
      ],
      "cartesian_polarization_e_A2": [
        -7.550686463776594e-13,
        2.6607484716816436e-13,
        -2.3718743822920436e-07
      ],
      "ranking_score": 0.5559465539364292
    },
    {
      "candidate_id": "bec_projection_02",
      "source": "MACEField_BEC_backprojection",
      "spacegroup": "P1",
      "spacegroup_number": 1,
      "pointgroup": "1",
      "has_inversion": false,
      "is_polar_point_group": true,
      "nonpolar_parent_hypothesis": false,
      "symmetry_tolerance_A": null,
      "target_reduced_polarization": [
        0.0,
        0.5,
        0.0
      ],
      "formal_class": [
        0.0,
        0.5,
        0.0
      ],
      "target_residual": 4.482840033493618e-05,
      "parent_symmetrization_rmsd_A": 0.10443993008435462,
      "parent_cell_rmsd_A": 0.02488734243168261,
      "energy_eV": -45.47511576694958,
      "reduced_polarization": [
        1.5600447364273667e-05,
        0.5000282301250755,
        3.1133126358386626e-05
      ],
      "cartesian_polarization_e_A2": [
        -6.38756401147178e-10,
        0.008204219991761656,
        -7.670401520017506e-06
      ],
      "ranking_score": 0.6107514224929451
    },
    {
      "candidate_id": "bec_projection_03",
      "source": "MACEField_BEC_backprojection",
      "spacegroup": "P1",
      "spacegroup_number": 1,
      "pointgroup": "1",
      "has_inversion": false,
      "is_polar_point_group": true,
      "nonpolar_parent_hypothesis": false,
      "symmetry_tolerance_A": null,
      "target_reduced_polarization": [
        0.5,
        0.5,
        0.0
      ],
      "formal_class": [
        0.5,
        0.5,
        0.0
      ],
      "target_residual": 0.0002662583880590696,
      "parent_symmetrization_rmsd_A": 0.14359832847378415,
      "parent_cell_rmsd_A": 0.027905209640821868,
      "energy_eV": -45.54232210981151,
      "reduced_polarization": [
        0.5001227066941737,
        0.5001054806246154,
        0.00021144841982746968
      ],
      "cartesian_polarization_e_A2": [
        0.008205631744107742,
        0.008205353033550166,
        -1.4455850966340033e-05
      ],
      "ranking_score": 0.6511071476601078
    }
  ],
  "formal_branches": [
    {
      "orbit_id": 0,
      "formal_class": [
        0.0,
        0.0,
        0.5
      ],
      "formal_classes_in_orbit": [
        [
          0.0,
          0.0,
          0.5
        ],
        [
          0.0,
          0.5,
          0.5
        ],
        [
          0.5,
          0.0,
          0.5
        ],
        [
          0.5,
          0.5,
          0.5
        ]
      ],
      "target_reduced_polarization": [
        0.0,
        0.0,
        0.5
      ],
      "bec_backprojection": {
        "converged_to_target": true,
        "history": [
          {
            "iteration": 0,
            "reduced_polarization": [
              0.16556534589751254,
              0.16556832918015013,
              0.3311345174761283
            ],
            "branch_aligned_reduced_polarization": [
              0.16556534589751254,
              0.16556832918015013,
              0.3311345174761283
            ],
            "target_residual": 0.2886872123556732,
            "energy_eV": -45.45166591437446,
            "max_atomic_step_A": 0.0952636046658071,
            "max_log_strain_component": 0.0031173126523114988,
            "step_scale": 1.0,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 2.23902380192908,
            "cell_principal_stretches": [
              1.0010235028723944,
              1.0008936606166046,
              0.9967581815878678
            ],
            "cell_volume_ratio": 0.9986700416800021,
            "cell_rmsd_from_input_A": 0.014440199785312146
          },
          {
            "iteration": 1,
            "reduced_polarization": [
              0.003488669407229435,
              0.000945669057516392,
              0.48330612238826015
            ],
            "branch_aligned_reduced_polarization": [
              0.003488669407229435,
              0.000945669057516392,
              0.48330612238826015
            ],
            "target_residual": 0.01708070999446544,
            "energy_eV": -45.57186208155734,
            "max_atomic_step_A": 0.00519899971141888,
            "max_log_strain_component": 0.00039441133582750334,
            "step_scale": 1.0,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 2.23902380192908,
            "cell_principal_stretches": [
              1.0011353356217028,
              1.0010067883705451,
              0.9963664244259995
            ],
            "cell_volume_ratio": 0.9985019037382017,
            "cell_rmsd_from_input_A": 0.01601395225432733
          },
          {
            "iteration": 2,
            "reduced_polarization": [
              0.00019918800635622424,
              0.00015182398039676056,
              0.5000152186979557
            ],
            "branch_aligned_reduced_polarization": [
              0.00019918800635622424,
              0.00015182398039676056,
              0.5000152186979557
            ],
            "target_residual": 0.0002509143114036164,
            "energy_eV": -45.58058326544612
          }
        ],
        "iterations": 2
      },
      "parent": {
        "candidate_id": "bec_projection_00",
        "source": "MACEField_BEC_backprojection",
        "spacegroup": "P1",
        "spacegroup_number": 1,
        "pointgroup": "1",
        "has_inversion": false,
        "is_polar_point_group": true,
        "nonpolar_parent_hypothesis": false,
        "symmetry_tolerance_A": null,
        "target_reduced_polarization": [
          0.0,
          0.0,
          0.5
        ],
        "formal_class": [
          0.0,
          0.0,
          0.5
        ],
        "target_residual": 0.0002509143114036164,
        "parent_symmetrization_rmsd_A": 0.07375724307726404,
        "parent_cell_rmsd_A": 0.01601395225432733,
        "energy_eV": -45.58058326544612,
        "reduced_polarization": [
          0.00019918800635622424,
          0.00015182398039676056,
          0.5000152186979557
        ],
        "cartesian_polarization_e_A2": [
          -0.004124664420299323,
          -0.0041230900720189406,
          0.006236040385172085
        ],
        "ranking_score": 0.5782625597636532
      },
      "branch_status": "awaiting_branch_sampling"
    },
    {
      "orbit_id": 1,
      "formal_class": [
        0.0,
        0.0,
        0.0
      ],
      "formal_classes_in_orbit": [
        [
          0.0,
          0.0,
          0.0
        ]
      ],
      "target_reduced_polarization": [
        0.0,
        0.0,
        0.0
      ],
      "bec_backprojection": {
        "converged_to_target": true,
        "history": [
          {
            "iteration": 0,
            "reduced_polarization": [
              0.16556534589751254,
              0.16556832918015013,
              0.3311345174761283
            ],
            "branch_aligned_reduced_polarization": [
              0.16556534589751254,
              0.16556832918015013,
              0.3311345174761283
            ],
            "target_residual": 0.4055549581176611,
            "energy_eV": -45.45166591437446,
            "max_atomic_step_A": 0.08085140828745446,
            "max_log_strain_component": 0.0061128240795417805,
            "step_scale": 1.0,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 2.23902380192908,
            "cell_principal_stretches": [
              1.0061315455164117,
              0.9982499052517997,
              0.9982498645600291
            ],
            "cell_volume_ratio": 1.0026129351906938,
            "cell_rmsd_from_input_A": 0.02376290687384518
          },
          {
            "iteration": 1,
            "reduced_polarization": [
              -0.0005156201675128618,
              -0.0005157970740552877,
              -0.0010314891908215652
            ],
            "branch_aligned_reduced_polarization": [
              -0.0005156201675128618,
              -0.0005157970740552877,
              -0.0010314891908215652
            ],
            "target_residual": 0.0012632817300712122,
            "energy_eV": -45.345578456516115,
            "max_atomic_step_A": 0.00024007834717831687,
            "max_log_strain_component": 1.8363581178112316e-05,
            "step_scale": 1.0,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 2.23902380192908,
            "cell_principal_stretches": [
              1.0061130695077396,
              0.998255158135298,
              0.9982551175655648
            ],
            "cell_volume_ratio": 1.0026050754368285,
            "cell_rmsd_from_input_A": 0.023691319723670716
          },
          {
            "iteration": 2,
            "reduced_polarization": [
              -9.45046929772629e-06,
              -9.450406259919116e-06,
              -1.890084535959719e-05
            ],
            "branch_aligned_reduced_polarization": [
              -9.45046929772629e-06,
              -9.450406259919116e-06,
              -1.890084535959719e-05
            ],
            "target_residual": 2.3148725747483214e-05,
            "energy_eV": -45.34585603473807
          }
        ],
        "iterations": 2
      },
      "parent": {
        "candidate_id": "inversion_parent_endpoint_00",
        "source": "same_species_inversion_center_projection_from_endpoint",
        "spacegroup": "I4/m",
        "spacegroup_number": 87,
        "pointgroup": "4/m",
        "has_inversion": true,
        "is_polar_point_group": false,
        "nonpolar_parent_hypothesis": true,
        "symmetry_tolerance_A": null,
        "target_reduced_polarization": [
          0.0,
          0.0,
          0.0
        ],
        "formal_class": [
          0.0,
          0.0,
          0.0
        ],
        "target_residual": 2.176258483341343e-15,
        "parent_symmetrization_rmsd_A": 0.05602721497198772,
        "parent_cell_rmsd_A": 0.0,
        "energy_eV": -45.36263815454786,
        "reduced_polarization": [
          -5.415228569076092e-17,
          -2.1736757749045504e-15,
          9.111609003206217e-17
        ],
        "cartesian_polarization_e_A2": [
          -1.6430360803985487e-18,
          -3.6568740777742016e-17,
          1.1394325950092037e-18
        ],
        "ranking_score": 0.05602721497199207
      },
      "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": [
          -45.451665914374466,
          -45.43467286570153,
          -45.4181406901011,
          -45.402756997280946,
          -45.38916637166352,
          -45.37794290444908,
          -45.36956411801891,
          -45.36438846466285,
          -45.36263815454786
        ],
        "cartesian_polarizations_e_A2": [
          [
            -3.152080520114903e-08,
            1.7638002850068124e-08,
            0.004140931227538125
          ],
          [
            -2.7689335626942353e-08,
            1.5478776380607645e-08,
            0.0036646545038147987
          ],
          [
            -2.3816398869371705e-08,
            1.3298720655547803e-08,
            0.003172330174283603
          ],
          [
            -1.990672960005625e-08,
            1.1103164406329017e-08,
            0.002665897652942355
          ],
          [
            -1.5965352218643672e-08,
            8.895774977503442e-09,
            0.002147464963135075
          ],
          [
            -1.1997758404744787e-08,
            6.679352058004698e-09,
            0.0016192747552363613
          ],
          [
            -8.00997192846349e-09,
            4.456410001059997e-09,
            0.001083674512512086
          ],
          [
            -4.0084586546649546e-09,
            2.229243231551336e-09,
            0.0005430900330104972
          ],
          [
            -2.2011568968140868e-17,
            -4.920157850096199e-17,
            -1.3115825060304863e-17
          ]
        ],
        "raw_reduced_polarization": [
          [
            0.16556534589751576,
            0.16556832918015155,
            0.3311345174761249
          ],
          [
            0.1465225595304397,
            0.1465251792578919,
            0.2930484797157257
          ],
          [
            0.12683814268532073,
            0.1268403950770282,
            0.2536791759666287
          ],
          [
            0.1065896388546278,
            0.10659152074074332,
            0.21318169378838664
          ],
          [
            0.08586133303724815,
            0.08586284177539723,
            0.17172460378854973
          ],
          [
            0.06474289300945893,
            0.06474402646044236,
            0.12948724218616017
          ],
          [
            0.04332817805900457,
            0.04332893460177312,
            0.08665732828777356
          ],
          [
            0.021714178714413265,
            0.021714557259550186,
            0.04342884393516965
          ],
          [
            -1.8602193671164122e-15,
            -3.510289548267107e-15,
            -1.0488226352958263e-15
          ]
        ],
        "unwrapped_reduced_polarization": [
          [
            0.16556534589751576,
            0.16556832918015155,
            0.3311345174761249
          ],
          [
            0.1465225595304397,
            0.1465251792578919,
            0.2930484797157257
          ],
          [
            0.12683814268532073,
            0.1268403950770282,
            0.2536791759666287
          ],
          [
            0.1065896388546278,
            0.10659152074074332,
            0.21318169378838664
          ],
          [
            0.08586133303724815,
            0.08586284177539723,
            0.17172460378854973
          ],
          [
            0.06474289300945893,
            0.06474402646044236,
            0.12948724218616017
          ],
          [
            0.04332817805900457,
            0.04332893460177312,
            0.08665732828777356
          ],
          [
            0.021714178714413265,
            0.021714557259550186,
            0.04342884393516965
          ],
          [
            -1.8596235662471372e-15,
            -3.5110803153770576e-15,
            -1.0477729794899915e-15
          ]
        ],
        "berry_integer_shifts": [
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ]
        ],
        "folded_reduced_polarization": [
          [
            0.1655653458975157,
            0.16556832918015152,
            0.3311345174761249
          ],
          [
            0.1465225595304397,
            0.14652517925789188,
            0.2930484797157257
          ],
          [
            0.12683814268532068,
            0.12684039507702827,
            0.2536791759666287
          ],
          [
            0.1065896388546278,
            0.1065915207407433,
            0.21318169378838658
          ],
          [
            0.08586133303724819,
            0.08586284177539727,
            0.1717246037885497
          ],
          [
            0.0647428930094589,
            0.06474402646044242,
            0.12948724218616015
          ],
          [
            0.043328178059004574,
            0.04332893460177312,
            0.08665732828777362
          ],
          [
            0.02171417871441328,
            0.021714557259550182,
            0.04342884393516966
          ],
          [
            -1.887379141862766e-15,
            -3.497202527569243e-15,
            -1.0547118733938987e-15
          ]
        ]
      },
      "reflected": {
        "reached": true,
        "construction": "reflect_displacements_about_reconstructed_parent",
        "energies_eV": [
          -45.36263815454786,
          -45.364388464662866,
          -45.369564118018914,
          -45.377942904449085,
          -45.38916637166352,
          -45.402756997280946,
          -45.418140690101104,
          -45.434672865701515,
          -45.451665914374445
        ],
        "cartesian_polarizations_e_A2": [
          [
            -1.5503356011542727e-17,
            -1.774734692290417e-17,
            -1.3101735108775062e-18
          ],
          [
            4.0084586354280075e-09,
            -2.2292432356940886e-09,
            -0.0005430900330104664
          ],
          [
            8.009971907807266e-09,
            -4.4564099770729484e-09,
            -0.0010836745125121145
          ],
          [
            1.199775836873225e-08,
            -6.6793520414848335e-09,
            -0.0016192747552363212
          ],
          [
            1.5965352169857645e-08,
            -8.895774980879017e-09,
            -0.002147464963135065
          ],
          [
            1.99067295399288e-08,
            -1.1103164425968733e-08,
            -0.002665897652942346
          ],
          [
            2.381639883642148e-08,
            -1.3298720638209616e-08,
            -0.003172330174283635
          ],
          [
            2.7689335679663354e-08,
            -1.547877623203115e-08,
            -0.003664654503814842
          ],
          [
            3.1520805223925384e-08,
            -1.763800286346814e-08,
            -0.004140931227538096
          ]
        ],
        "raw_reduced_polarization": [
          [
            -9.932313016187064e-16,
            -1.1294115587510585e-15,
            -1.0476959154725037e-16
          ],
          [
            -0.021714178714413206,
            -0.02171455725954921,
            -0.043428843935167195
          ],
          [
            -0.04332817805900697,
            -0.0433289346017728,
            -0.08665732828777584
          ],
          [
            -0.0647428930094595,
            -0.06474402646043977,
            -0.12948724218615695
          ],
          [
            -0.0858613330372507,
            -0.08586284177539703,
            -0.17172460378854892
          ],
          [
            -0.10658963885463107,
            -0.10659152074074414,
            -0.2131816937883859
          ],
          [
            -0.126838142685324,
            -0.12684039507702843,
            -0.2536791759666313
          ],
          [
            -0.14652255953043822,
            -0.1465251792578847,
            -0.2930484797157291
          ],
          [
            -0.1655653458975132,
            -0.16556832918015116,
            -0.3311345174761225
          ]
        ],
        "unwrapped_reduced_polarization": [
          [
            -9.932313016187064e-16,
            -1.1294115587510585e-15,
            -1.0476959154725037e-16
          ],
          [
            -0.021714178714413206,
            -0.02171455725954921,
            -0.043428843935167195
          ],
          [
            -0.04332817805900697,
            -0.0433289346017728,
            -0.08665732828777584
          ],
          [
            -0.0647428930094595,
            -0.06474402646043977,
            -0.12948724218615695
          ],
          [
            -0.0858613330372507,
            -0.08586284177539703,
            -0.17172460378854892
          ],
          [
            -0.10658963885463107,
            -0.10659152074074414,
            -0.2131816937883859
          ],
          [
            -0.126838142685324,
            -0.12684039507702843,
            -0.2536791759666313
          ],
          [
            -0.14652255953043822,
            -0.1465251792578847,
            -0.2930484797157291
          ],
          [
            -0.1655653458975132,
            -0.16556832918015116,
            -0.3311345174761225
          ]
        ],
        "gauge_integer_shift": [
          0,
          0,
          0
        ],
        "expected_opposite_endpoint_reduced_polarization": [
          -0.16556534589751948,
          -0.16556832918015854,
          -0.331134517476127
        ],
        "actual_opposite_endpoint_branch_residual": 1.0680524377484176e-14
      },
      "pnp_branch": {
        "construction": "incoming_path_concatenated_with_parent_reflection",
        "reduced_polarization": [
          [
            0.16556534589751576,
            0.16556832918015155,
            0.3311345174761249
          ],
          [
            0.1465225595304397,
            0.1465251792578919,
            0.2930484797157257
          ],
          [
            0.12683814268532073,
            0.1268403950770282,
            0.2536791759666287
          ],
          [
            0.1065896388546278,
            0.10659152074074332,
            0.21318169378838664
          ],
          [
            0.08586133303724815,
            0.08586284177539723,
            0.17172460378854973
          ],
          [
            0.06474289300945893,
            0.06474402646044236,
            0.12948724218616017
          ],
          [
            0.04332817805900457,
            0.04332893460177312,
            0.08665732828777356
          ],
          [
            0.021714178714413265,
            0.021714557259550186,
            0.04342884393516965
          ],
          [
            -1.8602193671164122e-15,
            -3.510289548267107e-15,
            -1.0488226352958263e-15
          ],
          [
            -0.021714178714413206,
            -0.02171455725954921,
            -0.043428843935167195
          ],
          [
            -0.04332817805900697,
            -0.0433289346017728,
            -0.08665732828777584
          ],
          [
            -0.0647428930094595,
            -0.06474402646043977,
            -0.12948724218615695
          ],
          [
            -0.0858613330372507,
            -0.08586284177539703,
            -0.17172460378854892
          ],
          [
            -0.10658963885463107,
            -0.10659152074074414,
            -0.2131816937883859
          ],
          [
            -0.126838142685324,
            -0.12684039507702843,
            -0.2536791759666313
          ],
          [
            -0.14652255953043822,
            -0.1465251792578847,
            -0.2930484797157291
          ],
          [
            -0.1655653458975132,
            -0.16556832918015116,
            -0.3311345174761225
          ]
        ],
        "unwrapped_reduced_polarization": [
          [
            0.16556534589751576,
            0.16556832918015155,
            0.3311345174761249
          ],
          [
            0.1465225595304397,
            0.1465251792578919,
            0.2930484797157257
          ],
          [
            0.12683814268532073,
            0.1268403950770282,
            0.2536791759666287
          ],
          [
            0.1065896388546278,
            0.10659152074074332,
            0.21318169378838664
          ],
          [
            0.08586133303724815,
            0.08586284177539723,
            0.17172460378854973
          ],
          [
            0.06474289300945893,
            0.06474402646044236,
            0.12948724218616017
          ],
          [
            0.04332817805900457,
            0.04332893460177312,
            0.08665732828777356
          ],
          [
            0.021714178714413265,
            0.021714557259550186,
            0.04342884393516965
          ],
          [
            -1.8596235662471372e-15,
            -3.5110803153770576e-15,
            -1.0477729794899915e-15
          ],
          [
            -0.021714178714413206,
            -0.02171455725954921,
            -0.043428843935167195
          ],
          [
            -0.04332817805900697,
            -0.0433289346017728,
            -0.08665732828777584
          ],
          [
            -0.0647428930094595,
            -0.06474402646043977,
            -0.12948724218615695
          ],
          [
            -0.0858613330372507,
            -0.08586284177539703,
            -0.17172460378854892
          ],
          [
            -0.10658963885463107,
            -0.10659152074074414,
            -0.2131816937883859
          ],
          [
            -0.126838142685324,
            -0.12684039507702843,
            -0.2536791759666313
          ],
          [
            -0.14652255953043822,
            -0.1465251792578847,
            -0.2930484797157291
          ],
          [
            -0.1655653458975132,
            -0.16556832918015116,
            -0.3311345174761225
          ]
        ],
        "berry_integer_shifts": [
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ]
        ],
        "folded_reduced_polarization": [
          [
            0.1655653458975157,
            0.16556832918015152,
            0.3311345174761249
          ],
          [
            0.1465225595304397,
            0.14652517925789188,
            0.2930484797157257
          ],
          [
            0.12683814268532068,
            0.12684039507702827,
            0.2536791759666287
          ],
          [
            0.1065896388546278,
            0.1065915207407433,
            0.21318169378838658
          ],
          [
            0.08586133303724819,
            0.08586284177539727,
            0.1717246037885497
          ],
          [
            0.0647428930094589,
            0.06474402646044242,
            0.12948724218616015
          ],
          [
            0.043328178059004574,
            0.04332893460177312,
            0.08665732828777362
          ],
          [
            0.02171417871441328,
            0.021714557259550182,
            0.04342884393516966
          ],
          [
            -1.887379141862766e-15,
            -3.497202527569243e-15,
            -1.0547118733938987e-15
          ],
          [
            -0.021714178714413224,
            -0.021714557259549183,
            -0.043428843935167216
          ],
          [
            -0.04332817805900696,
            -0.043328934601772784,
            -0.08665732828777584
          ],
          [
            -0.06474289300945951,
            -0.06474402646043975,
            -0.12948724218615693
          ],
          [
            -0.08586133303725069,
            -0.08586284177539705,
            -0.17172460378854892
          ],
          [
            -0.10658963885463107,
            -0.10659152074074413,
            -0.21318169378838592
          ],
          [
            -0.126838142685324,
            -0.12684039507702843,
            -0.2536791759666313
          ],
          [
            -0.14652255953043825,
            -0.14652517925788466,
            -0.2930484797157291
          ],
          [
            -0.1655653458975132,
            -0.16556832918015119,
            -0.3311345174761225
          ]
        ]
      },
      "incoming_structure_ids": [
        "incoming_01_000",
        "incoming_01_001",
        "incoming_01_002",
        "incoming_01_003",
        "incoming_01_004",
        "incoming_01_005",
        "incoming_01_006",
        "incoming_01_007",
        "incoming_01_008"
      ],
      "reflected_structure_ids": [
        "reflected_01_001",
        "reflected_01_002",
        "reflected_01_003",
        "reflected_01_004",
        "reflected_01_005",
        "reflected_01_006",
        "reflected_01_007",
        "reflected_01_008"
      ]
    },
    {
      "orbit_id": 2,
      "formal_class": [
        0.0,
        0.5,
        0.0
      ],
      "formal_classes_in_orbit": [
        [
          0.0,
          0.5,
          0.0
        ],
        [
          0.5,
          0.0,
          0.0
        ]
      ],
      "target_reduced_polarization": [
        0.0,
        0.5,
        0.0
      ],
      "bec_backprojection": {
        "converged_to_target": true,
        "history": [
          {
            "iteration": 0,
            "reduced_polarization": [
              0.16556534589751254,
              0.16556832918015013,
              0.3311345174761283
            ],
            "branch_aligned_reduced_polarization": [
              0.16556534589751254,
              0.16556832918015013,
              0.3311345174761283
            ],
            "target_residual": 0.49890529649791027,
            "energy_eV": -45.45166591437446,
            "max_atomic_step_A": 0.11999999999999998,
            "max_log_strain_component": 0.005148896691424013,
            "step_scale": 0.8423114234081246,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 2.23902380192908,
            "cell_principal_stretches": [
              1.0052759214402822,
              0.9985257038666583,
              0.9984127155000477
            ],
            "cell_volume_ratio": 1.0022005406218126,
            "cell_rmsd_from_input_A": 0.021377569753646762
          },
          {
            "iteration": 1,
            "reduced_polarization": [
              0.024695332904031683,
              0.44501551687657276,
              0.04567320820256053
            ],
            "branch_aligned_reduced_polarization": [
              0.024695332904031683,
              0.44501551687657276,
              0.04567320820256053
            ],
            "target_residual": 0.07562535817505824,
            "energy_eV": -45.45948558016866,
            "max_atomic_step_A": 0.021490471661284895,
            "max_log_strain_component": 0.0007962818011004594,
            "step_scale": 1.0,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 2.23902380192908,
            "cell_principal_stretches": [
              1.0061044082747745,
              0.9982978986791943,
              0.9981574676201003
            ],
            "cell_volume_ratio": 1.002541292004076,
            "cell_rmsd_from_input_A": 0.02477833755134208
          },
          {
            "iteration": 2,
            "reduced_polarization": [
              0.0008305547367333781,
              0.5000164113317411,
              0.0014624776401470532
            ],
            "branch_aligned_reduced_polarization": [
              0.0008305547367333781,
              0.5000164113317411,
              0.0014624776401470532
            ],
            "target_residual": 0.0016819427310256025,
            "energy_eV": -45.47524740591374,
            "max_atomic_step_A": 0.00039501520163105373,
            "max_log_strain_component": 2.8182765312886146e-05,
            "step_scale": 1.0,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 2.23902380192908,
            "cell_principal_stretches": [
              1.0061325510542873,
              0.9982898366771498,
              0.998149617492842
            ],
            "cell_volume_ratio": 1.0025533538576823,
            "cell_rmsd_from_input_A": 0.02488734243168261
          },
          {
            "iteration": 3,
            "reduced_polarization": [
              1.5600447364273667e-05,
              0.5000282301250755,
              3.1133126358386626e-05
            ],
            "branch_aligned_reduced_polarization": [
              1.5600447364273667e-05,
              0.5000282301250755,
              3.1133126358386626e-05
            ],
            "target_residual": 4.482840033493618e-05,
            "energy_eV": -45.47511576694958
          }
        ],
        "iterations": 3
      },
      "parent": {
        "candidate_id": "bec_projection_02",
        "source": "MACEField_BEC_backprojection",
        "spacegroup": "P1",
        "spacegroup_number": 1,
        "pointgroup": "1",
        "has_inversion": false,
        "is_polar_point_group": true,
        "nonpolar_parent_hypothesis": false,
        "symmetry_tolerance_A": null,
        "target_reduced_polarization": [
          0.0,
          0.5,
          0.0
        ],
        "formal_class": [
          0.0,
          0.5,
          0.0
        ],
        "target_residual": 4.482840033493618e-05,
        "parent_symmetrization_rmsd_A": 0.10443993008435462,
        "parent_cell_rmsd_A": 0.02488734243168261,
        "energy_eV": -45.47511576694958,
        "reduced_polarization": [
          1.5600447364273667e-05,
          0.5000282301250755,
          3.1133126358386626e-05
        ],
        "cartesian_polarization_e_A2": [
          -6.38756401147178e-10,
          0.008204219991761656,
          -7.670401520017506e-06
        ],
        "ranking_score": 0.6107514224929451
      },
      "branch_status": "awaiting_branch_sampling"
    },
    {
      "orbit_id": 3,
      "formal_class": [
        0.5,
        0.5,
        0.0
      ],
      "formal_classes_in_orbit": [
        [
          0.5,
          0.5,
          0.0
        ]
      ],
      "target_reduced_polarization": [
        0.5,
        0.5,
        0.0
      ],
      "bec_backprojection": {
        "converged_to_target": true,
        "history": [
          {
            "iteration": 0,
            "reduced_polarization": [
              0.16556534589751254,
              0.16556832918015013,
              0.3311345174761283
            ],
            "branch_aligned_reduced_polarization": [
              0.16556534589751254,
              0.16556832918015013,
              0.3311345174761283
            ],
            "target_residual": 0.5773570376951814,
            "energy_eV": -45.45166591437446,
            "max_atomic_step_A": 0.12,
            "max_log_strain_component": 0.0038596358251803587,
            "step_scale": 0.6313967722953198,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 2.23902380192908,
            "cell_principal_stretches": [
              1.0040346898434365,
              0.9988946387617196,
              0.9987279682244775
            ],
            "cell_volume_ratio": 1.0016491165138,
            "cell_rmsd_from_input_A": 0.018067460806864586
          },
          {
            "iteration": 1,
            "reduced_polarization": [
              0.36871428452907284,
              0.37087906441146024,
              0.11200610510432282
            ],
            "branch_aligned_reduced_polarization": [
              0.36871428452907284,
              0.37087906441146024,
              0.11200610510432282
            ],
            "target_residual": 0.2155307928687075,
            "energy_eV": -45.488975414857336,
            "max_atomic_step_A": 0.06813064629076837,
            "max_log_strain_component": 0.001752548227287724,
            "step_scale": 1.0,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 2.23902380192908,
            "cell_principal_stretches": [
              1.0059387079012008,
              0.9983931335367348,
              0.9980848283827386
            ],
            "cell_volume_ratio": 1.002398849166268,
            "cell_rmsd_from_input_A": 0.027256231345982738
          },
          {
            "iteration": 2,
            "reduced_polarization": [
              0.4941401438244439,
              0.4945390058020586,
              0.006755334981730306
            ],
            "branch_aligned_reduced_polarization": [
              0.4941401438244439,
              0.4945390058020586,
              0.006755334981730306
            ],
            "target_residual": 0.0104783072460938,
            "energy_eV": -45.540868149895736,
            "max_atomic_step_A": 0.0037260738970517036,
            "max_log_strain_component": 0.00013226583467191593,
            "step_scale": 1.0,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 2.23902380192908,
            "cell_principal_stretches": [
              1.006079236594114,
              0.998355294526313,
              0.9980395949905301
            ],
            "cell_volume_ratio": 1.0024554536814463,
            "cell_rmsd_from_input_A": 0.027905209640821868
          },
          {
            "iteration": 3,
            "reduced_polarization": [
              0.5001227066941737,
              0.5001054806246154,
              0.00021144841982746968
            ],
            "branch_aligned_reduced_polarization": [
              0.5001227066941737,
              0.5001054806246154,
              0.00021144841982746968
            ],
            "target_residual": 0.0002662583880590696,
            "energy_eV": -45.54232210981151
          }
        ],
        "iterations": 3
      },
      "parent": {
        "candidate_id": "bec_projection_03",
        "source": "MACEField_BEC_backprojection",
        "spacegroup": "P1",
        "spacegroup_number": 1,
        "pointgroup": "1",
        "has_inversion": false,
        "is_polar_point_group": true,
        "nonpolar_parent_hypothesis": false,
        "symmetry_tolerance_A": null,
        "target_reduced_polarization": [
          0.5,
          0.5,
          0.0
        ],
        "formal_class": [
          0.5,
          0.5,
          0.0
        ],
        "target_residual": 0.0002662583880590696,
        "parent_symmetrization_rmsd_A": 0.14359832847378415,
        "parent_cell_rmsd_A": 0.027905209640821868,
        "energy_eV": -45.54232210981151,
        "reduced_polarization": [
          0.5001227066941737,
          0.5001054806246154,
          0.00021144841982746968
        ],
        "cartesian_polarization_e_A2": [
          0.008205631744107742,
          0.008205353033550166,
          -1.4455850966340033e-05
        ],
        "ranking_score": 0.6511071476601078
      },
      "branch_status": "awaiting_branch_sampling"
    }
  ],
  "sampled_polarization_branches": [
    {
      "orbit_id": 1,
      "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
        ],
        "endpoint_rmsd_A": 0.05602721497198772,
        "minimum_distance_A_by_image": [
          2.98286975,
          3.010036581460048,
          3.0372034129200967,
          3.0643702443801453,
          3.091537075840194,
          3.1187039073002407,
          3.1458707387602898,
          3.1678412607951443,
          3.1678079784765867
        ],
        "minimum_distance_A": 2.98286975,
        "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": [
          542.6830714732648,
          542.6830714732648,
          542.6830714732648,
          542.6830714732648,
          542.6830714732648,
          542.6830714732648,
          542.6830714732648,
          542.6830714732648,
          542.6830714732648
        ],
        "cell_deformation_log_strain_norm": 0.0
      },
      "parent_reduced_polarization": [
        -1.8602193671164122e-15,
        -3.510289548267107e-15,
        -1.0488226352958263e-15
      ],
      "incoming": {
        "reached": true,
        "construction": "variable_cell_linear_interpolation",
        "continuation_fractions": [
          0.0,
          0.125,
          0.25,
          0.375,
          0.5,
          0.625,
          0.75,
          0.875,
          1.0
        ],
        "energies_eV": [
          -45.451665914374466,
          -45.43467286570153,
          -45.4181406901011,
          -45.402756997280946,
          -45.38916637166352,
          -45.37794290444908,
          -45.36956411801891,
          -45.36438846466285,
          -45.36263815454786
        ],
        "cartesian_polarizations_e_A2": [
          [
            -3.152080520114903e-08,
            1.7638002850068124e-08,
            0.004140931227538125
          ],
          [
            -2.7689335626942353e-08,
            1.5478776380607645e-08,
            0.0036646545038147987
          ],
          [
            -2.3816398869371705e-08,
            1.3298720655547803e-08,
            0.003172330174283603
          ],
          [
            -1.990672960005625e-08,
            1.1103164406329017e-08,
            0.002665897652942355
          ],
          [
            -1.5965352218643672e-08,
            8.895774977503442e-09,
            0.002147464963135075
          ],
          [
            -1.1997758404744787e-08,
            6.679352058004698e-09,
            0.0016192747552363613
          ],
          [
            -8.00997192846349e-09,
            4.456410001059997e-09,
            0.001083674512512086
          ],
          [
            -4.0084586546649546e-09,
            2.229243231551336e-09,
            0.0005430900330104972
          ],
          [
            -2.2011568968140868e-17,
            -4.920157850096199e-17,
            -1.3115825060304863e-17
          ]
        ],
        "raw_reduced_polarization": [
          [
            0.16556534589751576,
            0.16556832918015155,
            0.3311345174761249
          ],
          [
            0.1465225595304397,
            0.1465251792578919,
            0.2930484797157257
          ],
          [
            0.12683814268532073,
            0.1268403950770282,
            0.2536791759666287
          ],
          [
            0.1065896388546278,
            0.10659152074074332,
            0.21318169378838664
          ],
          [
            0.08586133303724815,
            0.08586284177539723,
            0.17172460378854973
          ],
          [
            0.06474289300945893,
            0.06474402646044236,
            0.12948724218616017
          ],
          [
            0.04332817805900457,
            0.04332893460177312,
            0.08665732828777356
          ],
          [
            0.021714178714413265,
            0.021714557259550186,
            0.04342884393516965
          ],
          [
            -1.8602193671164122e-15,
            -3.510289548267107e-15,
            -1.0488226352958263e-15
          ]
        ],
        "unwrapped_reduced_polarization": [
          [
            0.16556534589751576,
            0.16556832918015155,
            0.3311345174761249
          ],
          [
            0.1465225595304397,
            0.1465251792578919,
            0.2930484797157257
          ],
          [
            0.12683814268532073,
            0.1268403950770282,
            0.2536791759666287
          ],
          [
            0.1065896388546278,
            0.10659152074074332,
            0.21318169378838664
          ],
          [
            0.08586133303724815,
            0.08586284177539723,
            0.17172460378854973
          ],
          [
            0.06474289300945893,
            0.06474402646044236,
            0.12948724218616017
          ],
          [
            0.04332817805900457,
            0.04332893460177312,
            0.08665732828777356
          ],
          [
            0.021714178714413265,
            0.021714557259550186,
            0.04342884393516965
          ],
          [
            -1.8596235662471372e-15,
            -3.5110803153770576e-15,
            -1.0477729794899915e-15
          ]
        ],
        "berry_integer_shifts": [
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ]
        ],
        "folded_reduced_polarization": [
          [
            0.1655653458975157,
            0.16556832918015152,
            0.3311345174761249
          ],
          [
            0.1465225595304397,
            0.14652517925789188,
            0.2930484797157257
          ],
          [
            0.12683814268532068,
            0.12684039507702827,
            0.2536791759666287
          ],
          [
            0.1065896388546278,
            0.1065915207407433,
            0.21318169378838658
          ],
          [
            0.08586133303724819,
            0.08586284177539727,
            0.1717246037885497
          ],
          [
            0.0647428930094589,
            0.06474402646044242,
            0.12948724218616015
          ],
          [
            0.043328178059004574,
            0.04332893460177312,
            0.08665732828777362
          ],
          [
            0.02171417871441328,
            0.021714557259550182,
            0.04342884393516966
          ],
          [
            -1.887379141862766e-15,
            -3.497202527569243e-15,
            -1.0547118733938987e-15
          ]
        ]
      },
      "reflected": {
        "reached": true,
        "construction": "reflect_displacements_about_reconstructed_parent",
        "energies_eV": [
          -45.36263815454786,
          -45.364388464662866,
          -45.369564118018914,
          -45.377942904449085,
          -45.38916637166352,
          -45.402756997280946,
          -45.418140690101104,
          -45.434672865701515,
          -45.451665914374445
        ],
        "cartesian_polarizations_e_A2": [
          [
            -1.5503356011542727e-17,
            -1.774734692290417e-17,
            -1.3101735108775062e-18
          ],
          [
            4.0084586354280075e-09,
            -2.2292432356940886e-09,
            -0.0005430900330104664
          ],
          [
            8.009971907807266e-09,
            -4.4564099770729484e-09,
            -0.0010836745125121145
          ],
          [
            1.199775836873225e-08,
            -6.6793520414848335e-09,
            -0.0016192747552363212
          ],
          [
            1.5965352169857645e-08,
            -8.895774980879017e-09,
            -0.002147464963135065
          ],
          [
            1.99067295399288e-08,
            -1.1103164425968733e-08,
            -0.002665897652942346
          ],
          [
            2.381639883642148e-08,
            -1.3298720638209616e-08,
            -0.003172330174283635
          ],
          [
            2.7689335679663354e-08,
            -1.547877623203115e-08,
            -0.003664654503814842
          ],
          [
            3.1520805223925384e-08,
            -1.763800286346814e-08,
            -0.004140931227538096
          ]
        ],
        "raw_reduced_polarization": [
          [
            -9.932313016187064e-16,
            -1.1294115587510585e-15,
            -1.0476959154725037e-16
          ],
          [
            -0.021714178714413206,
            -0.02171455725954921,
            -0.043428843935167195
          ],
          [
            -0.04332817805900697,
            -0.0433289346017728,
            -0.08665732828777584
          ],
          [
            -0.0647428930094595,
            -0.06474402646043977,
            -0.12948724218615695
          ],
          [
            -0.0858613330372507,
            -0.08586284177539703,
            -0.17172460378854892
          ],
          [
            -0.10658963885463107,
            -0.10659152074074414,
            -0.2131816937883859
          ],
          [
            -0.126838142685324,
            -0.12684039507702843,
            -0.2536791759666313
          ],
          [
            -0.14652255953043822,
            -0.1465251792578847,
            -0.2930484797157291
          ],
          [
            -0.1655653458975132,
            -0.16556832918015116,
            -0.3311345174761225
          ]
        ],
        "unwrapped_reduced_polarization": [
          [
            -9.932313016187064e-16,
            -1.1294115587510585e-15,
            -1.0476959154725037e-16
          ],
          [
            -0.021714178714413206,
            -0.02171455725954921,
            -0.043428843935167195
          ],
          [
            -0.04332817805900697,
            -0.0433289346017728,
            -0.08665732828777584
          ],
          [
            -0.0647428930094595,
            -0.06474402646043977,
            -0.12948724218615695
          ],
          [
            -0.0858613330372507,
            -0.08586284177539703,
            -0.17172460378854892
          ],
          [
            -0.10658963885463107,
            -0.10659152074074414,
            -0.2131816937883859
          ],
          [
            -0.126838142685324,
            -0.12684039507702843,
            -0.2536791759666313
          ],
          [
            -0.14652255953043822,
            -0.1465251792578847,
            -0.2930484797157291
          ],
          [
            -0.1655653458975132,
            -0.16556832918015116,
            -0.3311345174761225
          ]
        ],
        "gauge_integer_shift": [
          0,
          0,
          0
        ],
        "expected_opposite_endpoint_reduced_polarization": [
          -0.16556534589751948,
          -0.16556832918015854,
          -0.331134517476127
        ],
        "actual_opposite_endpoint_branch_residual": 1.0680524377484176e-14
      },
      "pnp_branch": {
        "construction": "incoming_path_concatenated_with_parent_reflection",
        "reduced_polarization": [
          [
            0.16556534589751576,
            0.16556832918015155,
            0.3311345174761249
          ],
          [
            0.1465225595304397,
            0.1465251792578919,
            0.2930484797157257
          ],
          [
            0.12683814268532073,
            0.1268403950770282,
            0.2536791759666287
          ],
          [
            0.1065896388546278,
            0.10659152074074332,
            0.21318169378838664
          ],
          [
            0.08586133303724815,
            0.08586284177539723,
            0.17172460378854973
          ],
          [
            0.06474289300945893,
            0.06474402646044236,
            0.12948724218616017
          ],
          [
            0.04332817805900457,
            0.04332893460177312,
            0.08665732828777356
          ],
          [
            0.021714178714413265,
            0.021714557259550186,
            0.04342884393516965
          ],
          [
            -1.8602193671164122e-15,
            -3.510289548267107e-15,
            -1.0488226352958263e-15
          ],
          [
            -0.021714178714413206,
            -0.02171455725954921,
            -0.043428843935167195
          ],
          [
            -0.04332817805900697,
            -0.0433289346017728,
            -0.08665732828777584
          ],
          [
            -0.0647428930094595,
            -0.06474402646043977,
            -0.12948724218615695
          ],
          [
            -0.0858613330372507,
            -0.08586284177539703,
            -0.17172460378854892
          ],
          [
            -0.10658963885463107,
            -0.10659152074074414,
            -0.2131816937883859
          ],
          [
            -0.126838142685324,
            -0.12684039507702843,
            -0.2536791759666313
          ],
          [
            -0.14652255953043822,
            -0.1465251792578847,
            -0.2930484797157291
          ],
          [
            -0.1655653458975132,
            -0.16556832918015116,
            -0.3311345174761225
          ]
        ],
        "unwrapped_reduced_polarization": [
          [
            0.16556534589751576,
            0.16556832918015155,
            0.3311345174761249
          ],
          [
            0.1465225595304397,
            0.1465251792578919,
            0.2930484797157257
          ],
          [
            0.12683814268532073,
            0.1268403950770282,
            0.2536791759666287
          ],
          [
            0.1065896388546278,
            0.10659152074074332,
            0.21318169378838664
          ],
          [
            0.08586133303724815,
            0.08586284177539723,
            0.17172460378854973
          ],
          [
            0.06474289300945893,
            0.06474402646044236,
            0.12948724218616017
          ],
          [
            0.04332817805900457,
            0.04332893460177312,
            0.08665732828777356
          ],
          [
            0.021714178714413265,
            0.021714557259550186,
            0.04342884393516965
          ],
          [
            -1.8596235662471372e-15,
            -3.5110803153770576e-15,
            -1.0477729794899915e-15
          ],
          [
            -0.021714178714413206,
            -0.02171455725954921,
            -0.043428843935167195
          ],
          [
            -0.04332817805900697,
            -0.0433289346017728,
            -0.08665732828777584
          ],
          [
            -0.0647428930094595,
            -0.06474402646043977,
            -0.12948724218615695
          ],
          [
            -0.0858613330372507,
            -0.08586284177539703,
            -0.17172460378854892
          ],
          [
            -0.10658963885463107,
            -0.10659152074074414,
            -0.2131816937883859
          ],
          [
            -0.126838142685324,
            -0.12684039507702843,
            -0.2536791759666313
          ],
          [
            -0.14652255953043822,
            -0.1465251792578847,
            -0.2930484797157291
          ],
          [
            -0.1655653458975132,
            -0.16556832918015116,
            -0.3311345174761225
          ]
        ],
        "berry_integer_shifts": [
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ]
        ],
        "folded_reduced_polarization": [
          [
            0.1655653458975157,
            0.16556832918015152,
            0.3311345174761249
          ],
          [
            0.1465225595304397,
            0.14652517925789188,
            0.2930484797157257
          ],
          [
            0.12683814268532068,
            0.12684039507702827,
            0.2536791759666287
          ],
          [
            0.1065896388546278,
            0.1065915207407433,
            0.21318169378838658
          ],
          [
            0.08586133303724819,
            0.08586284177539727,
            0.1717246037885497
          ],
          [
            0.0647428930094589,
            0.06474402646044242,
            0.12948724218616015
          ],
          [
            0.043328178059004574,
            0.04332893460177312,
            0.08665732828777362
          ],
          [
            0.02171417871441328,
            0.021714557259550182,
            0.04342884393516966
          ],
          [
            -1.887379141862766e-15,
            -3.497202527569243e-15,
            -1.0547118733938987e-15
          ],
          [
            -0.021714178714413224,
            -0.021714557259549183,
            -0.043428843935167216
          ],
          [
            -0.04332817805900696,
            -0.043328934601772784,
            -0.08665732828777584
          ],
          [
            -0.06474289300945951,
            -0.06474402646043975,
            -0.12948724218615693
          ],
          [
            -0.08586133303725069,
            -0.08586284177539705,
            -0.17172460378854892
          ],
          [
            -0.10658963885463107,
            -0.10659152074074413,
            -0.21318169378838592
          ],
          [
            -0.126838142685324,
            -0.12684039507702843,
            -0.2536791759666313
          ],
          [
            -0.14652255953043825,
            -0.14652517925788466,
            -0.2930484797157291
          ],
          [
            -0.1655653458975132,
            -0.16556832918015119,
            -0.3311345174761225
          ]
        ]
      },
      "incoming_structure_ids": [
        "incoming_01_000",
        "incoming_01_001",
        "incoming_01_002",
        "incoming_01_003",
        "incoming_01_004",
        "incoming_01_005",
        "incoming_01_006",
        "incoming_01_007",
        "incoming_01_008"
      ],
      "reflected_structure_ids": [
        "reflected_01_001",
        "reflected_01_002",
        "reflected_01_003",
        "reflected_01_004",
        "reflected_01_005",
        "reflected_01_006",
        "reflected_01_007",
        "reflected_01_008"
      ],
      "positive_extension_structure_ids": [
        "extension_plus_01_000",
        "extension_plus_01_001",
        "extension_plus_01_002",
        "extension_plus_01_003"
      ],
      "negative_extension_structure_ids": [
        "extension_minus_01_000",
        "extension_minus_01_001",
        "extension_minus_01_002",
        "extension_minus_01_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": "I4/m",
        "spacegroup_number": 87,
        "pointgroup": "4/m",
        "has_inversion": true,
        "is_polar_point_group": false,
        "nonpolar_parent_hypothesis": true,
        "symmetry_tolerance_A": null,
        "target_reduced_polarization": [
          0.0,
          0.0,
          0.0
        ],
        "formal_class": [
          0.0,
          0.0,
          0.0
        ],
        "target_residual": 2.176258483341343e-15,
        "parent_symmetrization_rmsd_A": 0.05602721497198772,
        "parent_cell_rmsd_A": 0.0,
        "energy_eV": -45.36263815454786,
        "reduced_polarization": [
          -5.415228569076092e-17,
          -2.1736757749045504e-15,
          9.111609003206217e-17
        ],
        "cartesian_polarization_e_A2": [
          -1.6430360803985487e-18,
          -3.6568740777742016e-17,
          1.1394325950092037e-18
        ],
        "ranking_score": 0.05602721497199207
      }
    }
  ],
  "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": 45,
      "full_response": 11,
      "energy_polarization": 34
    },
    "model_evaluations_for_recovery_and_path_properties": {
      "total": 70,
      "full_response": 36,
      "energy_polarization": 34
    },
    "elapsed_seconds": 98.71639180800412
  }
}