{
  "schema": "ferrofinder.endpoint_parent_recovery.v4_variable_cell",
  "status": "complete",
  "input_atom_count": 48,
  "input_formula": "Ba10I2O30Re6",
  "input_spacegroup": "P6_3cm",
  "input_pointgroup": "6mm",
  "input_is_polar_point_group": true,
  "input_energy_eV": -341.1330771981926,
  "input_cartesian_polarization_e_A2": [
    5.965047885620801e-11,
    -0.007280236097421792,
    8.650196509818244e-11
  ],
  "input_reduced_polarization": [
    8.526537959834896e-09,
    -0.795680178263078,
    7.771191179419945e-09
  ],
  "input_formal_targets": [
    {
      "orbit_id": 0,
      "representative_formal_class": [
        0.0,
        0.0,
        0.0
      ],
      "target_reduced_polarization": [
        0.0,
        -1.0,
        0.0
      ]
    },
    {
      "orbit_id": 1,
      "representative_formal_class": [
        0.0,
        0.5,
        0.0
      ],
      "target_reduced_polarization": [
        0.0,
        -0.5,
        0.0
      ]
    },
    {
      "orbit_id": 2,
      "representative_formal_class": [
        0.5,
        0.0,
        0.0
      ],
      "target_reduced_polarization": [
        0.5,
        -1.0,
        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": "Cmcm",
      "spacegroup_number": 63,
      "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": 1.2438278453420975e-14,
      "parent_symmetrization_rmsd_A": 0.5228457192728673,
      "parent_cell_rmsd_A": 0.0,
      "energy_eV": -217.4238760626131,
      "reduced_polarization": [
        6.6931693818781366e-15,
        -1.5437607632178164e-15,
        1.0369621845384463e-14
      ],
      "cartesian_polarization_e_A2": [
        1.9387080897284753e-17,
        -1.4124950125935898e-17,
        1.1542537639869903e-16
      ],
      "ranking_score": 0.5228457192728921
    },
    {
      "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": 6.301684553488548e-15,
      "parent_symmetrization_rmsd_A": 0.6297182799245272,
      "parent_cell_rmsd_A": 0.0,
      "energy_eV": -313.4529352412875,
      "reduced_polarization": [
        -2.1583960142152475e-15,
        3.323216323092279e-15,
        -4.899876337973125e-15
      ],
      "cartesian_polarization_e_A2": [
        3.7472162913670775e-18,
        3.0406437279525226e-17,
        -5.4541050681550477e-17
      ],
      "ranking_score": 0.6297182799245399
    },
    {
      "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": 5.9965038705938754e-15,
      "parent_symmetrization_rmsd_A": 0.6297182800722523,
      "parent_cell_rmsd_A": 0.0,
      "energy_eV": -313.4529354700211,
      "reduced_polarization": [
        -3.0802946925513467e-15,
        -4.9501172645539044e-15,
        1.4022062416965304e-15
      ],
      "cartesian_polarization_e_A2": [
        -4.8602665541841634e-17,
        -4.5292095216629614e-17,
        1.5608108535651853e-17
      ],
      "ranking_score": 0.6297182800722643
    },
    {
      "candidate_id": "bec_projection_00",
      "source": "MACEField_BEC_backprojection",
      "spacegroup": "P6_3cm",
      "spacegroup_number": 185,
      "pointgroup": "6mm",
      "has_inversion": false,
      "is_polar_point_group": true,
      "nonpolar_parent_hypothesis": false,
      "symmetry_tolerance_A": null,
      "target_reduced_polarization": [
        0.0,
        -1.0,
        0.0
      ],
      "formal_class": [
        0.0,
        0.0,
        0.0
      ],
      "target_residual": 0.0005550649008700951,
      "parent_symmetrization_rmsd_A": 0.016465302498625923,
      "parent_cell_rmsd_A": 0.01453701414113342,
      "energy_eV": -341.1057687718085,
      "reduced_polarization": [
        -1.1702306754159965e-11,
        -0.9994449350991299,
        -1.1922980882744818e-11
      ],
      "cartesian_polarization_e_A2": [
        -5.966743849970424e-14,
        -0.009131980411362933,
        2.850366832850303e-13
      ],
      "ranking_score": 0.5212096858356494
    },
    {
      "candidate_id": "inversion_parent_bec_00_00",
      "source": "same_species_inversion_center_projection_after_BEC",
      "spacegroup": "Cmcm",
      "spacegroup_number": 63,
      "pointgroup": "mmm",
      "has_inversion": true,
      "is_polar_point_group": false,
      "nonpolar_parent_hypothesis": true,
      "symmetry_tolerance_A": null,
      "target_reduced_polarization": [
        0.0,
        -1.0,
        0.0
      ],
      "formal_class": [
        0.0,
        0.0,
        0.0
      ],
      "target_residual": 8.480123590502628e-15,
      "parent_symmetrization_rmsd_A": 0.522851548352034,
      "parent_cell_rmsd_A": 0.01453701414113342,
      "energy_eV": -217.47590670018167,
      "reduced_polarization": [
        -4.585617357770669e-15,
        5.266711766319045e-16,
        -7.119508011934974e-15
      ],
      "cartesian_polarization_e_A2": [
        -1.3212868621622805e-17,
        4.8122219673825296e-18,
        -7.941236140877869e-17
      ],
      "ranking_score": 0.5264858018873343
    },
    {
      "candidate_id": "inversion_parent_bec_00_01",
      "source": "same_species_inversion_center_projection_after_BEC",
      "spacegroup": "P2_1/m",
      "spacegroup_number": 11,
      "pointgroup": "2/m",
      "has_inversion": true,
      "is_polar_point_group": false,
      "nonpolar_parent_hypothesis": true,
      "symmetry_tolerance_A": null,
      "target_reduced_polarization": [
        0.0,
        -1.0,
        0.0
      ],
      "formal_class": [
        0.0,
        0.0,
        0.0
      ],
      "target_residual": 3.0389514675723306e-15,
      "parent_symmetrization_rmsd_A": 0.5550993692000966,
      "parent_cell_rmsd_A": 0.01453701414113342,
      "energy_eV": -317.15767821370287,
      "reduced_polarization": [
        -1.9087711224190454e-15,
        1.7744294034628343e-15,
        -1.560889234889879e-15
      ],
      "cartesian_polarization_e_A2": [
        -1.4532565487561062e-17,
        1.6213053851714444e-17,
        -1.741045865304088e-17
      ],
      "ranking_score": 0.5587336227353861
    },
    {
      "candidate_id": "bec_projection_01",
      "source": "MACEField_BEC_backprojection",
      "spacegroup": "P6_3cm",
      "spacegroup_number": 185,
      "pointgroup": "6mm",
      "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": 4.952956306203564e-07,
      "parent_symmetrization_rmsd_A": 0.02356911550132669,
      "parent_cell_rmsd_A": 0.021014629615352897,
      "energy_eV": -340.6232008067801,
      "reduced_polarization": [
        -8.104965595389782e-14,
        -0.5000004952956306,
        -9.627726673281185e-14
      ],
      "cartesian_polarization_e_A2": [
        1.3790404971754931e-13,
        -0.004583981193748593,
        -8.658304217512314e-14
      ],
      "ranking_score": 0.5288237634964261
    },
    {
      "candidate_id": "bec_projection_02",
      "source": "MACEField_BEC_backprojection",
      "spacegroup": "Cm",
      "spacegroup_number": 8,
      "pointgroup": "m",
      "has_inversion": false,
      "is_polar_point_group": true,
      "nonpolar_parent_hypothesis": false,
      "symmetry_tolerance_A": null,
      "target_reduced_polarization": [
        0.5,
        -1.0,
        0.0
      ],
      "formal_class": [
        0.5,
        0.0,
        0.0
      ],
      "target_residual": 1.3839706048803078e-05,
      "parent_symmetrization_rmsd_A": 0.04818129601298596,
      "parent_cell_rmsd_A": 0.020023210280483834,
      "energy_eV": -339.84187964391634,
      "reduced_polarization": [
        0.5000135252088715,
        -1.0000029336306,
        -3.3063565975905796e-11
      ],
      "cartesian_polarization_e_A2": [
        0.006427285612549355,
        -0.009127423021595313,
        -1.3277955029403651e-10
      ],
      "ranking_score": 0.5532147779952046
    },
    {
      "candidate_id": "bec_projection_03",
      "source": "MACEField_BEC_backprojection",
      "spacegroup": "Cm",
      "spacegroup_number": 8,
      "pointgroup": "m",
      "has_inversion": false,
      "is_polar_point_group": true,
      "nonpolar_parent_hypothesis": false,
      "symmetry_tolerance_A": null,
      "target_reduced_polarization": [
        0.5,
        -0.5,
        0.0
      ],
      "formal_class": [
        0.5,
        0.5,
        0.0
      ],
      "target_residual": 1.4539498979449718e-05,
      "parent_symmetrization_rmsd_A": 0.05091626679646265,
      "parent_cell_rmsd_A": 0.02465554863570104,
      "energy_eV": -339.37741198174126,
      "reduced_polarization": [
        0.5000143705814656,
        -0.5000022098459027,
        2.663238252230593e-11
      ],
      "cartesian_polarization_e_A2": [
        0.00640124881569144,
        -0.00457454944202407,
        -4.074174956602553e-11
      ],
      "ranking_score": 0.5571092329533468
    }
  ],
  "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,
        -1.0,
        0.0
      ],
      "bec_backprojection": {
        "converged_to_target": true,
        "history": [
          {
            "iteration": 0,
            "reduced_polarization": [
              8.526537959834896e-09,
              -0.795680178263078,
              7.771191179419945e-09
            ],
            "branch_aligned_reduced_polarization": [
              8.526537959834896e-09,
              -0.795680178263078,
              7.771191179419945e-09
            ],
            "target_residual": 0.2043198217369223,
            "energy_eV": -341.1330771981926,
            "max_atomic_step_A": 0.019658844620849002,
            "max_log_strain_component": 0.002763468422420152,
            "step_scale": 1.0,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 2.421156015657218,
            "cell_principal_stretches": [
              1.0006919665138052,
              1.0006919620871146,
              0.9972403464415461
            ],
            "cell_volume_ratio": 0.9986209333722086,
            "cell_rmsd_from_input_A": 0.01453701414113342
          },
          {
            "iteration": 1,
            "reduced_polarization": [
              -1.1702306754159965e-11,
              -0.9994449350991299,
              -1.1922980882744818e-11
            ],
            "branch_aligned_reduced_polarization": [
              -1.1702306754159965e-11,
              -0.9994449350991299,
              -1.1922980882744818e-11
            ],
            "target_residual": 0.0005550649008700951,
            "energy_eV": -341.1057687718085
          }
        ],
        "iterations": 1
      },
      "parent": {
        "candidate_id": "bec_projection_00",
        "source": "MACEField_BEC_backprojection",
        "spacegroup": "P6_3cm",
        "spacegroup_number": 185,
        "pointgroup": "6mm",
        "has_inversion": false,
        "is_polar_point_group": true,
        "nonpolar_parent_hypothesis": false,
        "symmetry_tolerance_A": null,
        "target_reduced_polarization": [
          0.0,
          -1.0,
          0.0
        ],
        "formal_class": [
          0.0,
          0.0,
          0.0
        ],
        "target_residual": 0.0005550649008700951,
        "parent_symmetrization_rmsd_A": 0.016465302498625923,
        "parent_cell_rmsd_A": 0.01453701414113342,
        "energy_eV": -341.1057687718085,
        "reduced_polarization": [
          -1.1702306754159965e-11,
          -0.9994449350991299,
          -1.1922980882744818e-11
        ],
        "cartesian_polarization_e_A2": [
          -5.966743849970424e-14,
          -0.009131980411362933,
          2.850366832850303e-13
        ],
        "ranking_score": 0.5212096858356494
      },
      "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": [
          -341.13307719819267,
          -341.14719474992944,
          -341.15634991964197,
          -341.16052068231375,
          -341.1596840220691,
          -341.1538159432499,
          -341.1428914814027,
          -341.12688471413486,
          -341.1057687718086
        ],
        "cartesian_polarizations_e_A2": [
          [
            5.96504713458974e-11,
            -0.007280236097421806,
            8.650201774974695e-11
          ],
          [
            5.221111484129297e-11,
            -0.0075129978860452445,
            7.574492337921967e-11
          ],
          [
            4.4764095749757846e-11,
            -0.007745375480152768,
            6.498142283373836e-11
          ],
          [
            3.730967728579341e-11,
            -0.007977375757474505,
            5.421174423646172e-11
          ],
          [
            2.9848315055923997e-11,
            -0.008209005936283688,
            4.343634603687234e-11
          ],
          [
            2.238042312340939e-11,
            -0.008440273548515164,
            3.265560554065767e-11
          ],
          [
            1.4906183238542743e-11,
            -0.008671186411638065,
            2.186986655480166e-11
          ],
          [
            7.426066591551393e-12,
            -0.008901752599374688,
            1.1079573403933156e-11
          ],
          [
            -5.958182515302178e-14,
            -0.009131980411362933,
            2.850017987678753e-13
          ]
        ],
        "raw_reduced_polarization": [
          [
            8.526539740579504e-09,
            -0.7956801782630795,
            7.771195909548022e-09
          ],
          [
            7.460566856959987e-09,
            -0.8212614645854297,
            6.799179362625265e-09
          ],
          [
            6.394134794238562e-09,
            -0.8468095711145434,
            5.826850307163848e-09
          ],
          [
            5.3272750506701655e-09,
            -0.8723252304232346,
            4.854230085169881e-09
          ],
          [
            4.260044372909045e-09,
            -0.8978092128423765,
            3.881360673042778e-09
          ],
          [
            3.1924925728495848e-09,
            -0.9232623235528225,
            2.9082767082825433e-09
          ],
          [
            2.124649853760227e-09,
            -0.9486853995380025,
            1.9350097719378955e-09
          ],
          [
            1.0565733643340967e-09,
            -0.9740793064070705,
            9.616004098934385e-10
          ],
          [
            -1.1697223366811207e-11,
            -0.9994449350991299,
            -1.192610836307169e-11
          ]
        ],
        "unwrapped_reduced_polarization": [
          [
            8.526539740579504e-09,
            -0.7956801782630795,
            7.771195909548022e-09
          ],
          [
            7.460566856959987e-09,
            -0.8212614645854297,
            6.799179362625265e-09
          ],
          [
            6.394134794238562e-09,
            -0.8468095711145434,
            5.826850307163848e-09
          ],
          [
            5.3272750506701655e-09,
            -0.8723252304232346,
            4.854230085169881e-09
          ],
          [
            4.260044372909045e-09,
            -0.8978092128423765,
            3.881360673042778e-09
          ],
          [
            3.1924925728495848e-09,
            -0.9232623235528225,
            2.9082767082825433e-09
          ],
          [
            2.124649853760227e-09,
            -0.9486853995380025,
            1.9350097719378955e-09
          ],
          [
            1.0565733643340967e-09,
            -0.9740793064070705,
            9.616004098934385e-10
          ],
          [
            -1.1697223366811306e-11,
            -0.9994449350991299,
            -1.1926108363071627e-11
          ]
        ],
        "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": [
          [
            8.526539696518398e-09,
            0.20431982173692054,
            7.771195909000994e-09
          ],
          [
            7.460566830985726e-09,
            0.1787385354145703,
            6.7991793306632076e-09
          ],
          [
            6.39413477721007e-09,
            0.15319042888545664,
            5.8268503355662915e-09
          ],
          [
            5.327275065525328e-09,
            0.12767476957676538,
            4.854230128970016e-09
          ],
          [
            4.260044428328058e-09,
            0.10219078715762353,
            3.881360677304713e-09
          ],
          [
            3.1924926036097645e-09,
            0.07673767644717755,
            2.9082767305510515e-09
          ],
          [
            2.124649900459019e-09,
            0.05131460046199754,
            1.935009819042932e-09
          ],
          [
            1.0565733843392877e-09,
            0.025920693592929478,
            9.616003548984509e-10
          ],
          [
            -1.1697198765148187e-11,
            0.0005550649008700947,
            -1.1926126752825894e-11
          ]
        ]
      },
      "reflected": {
        "reached": true,
        "construction": "reflect_displacements_about_reconstructed_parent",
        "energies_eV": [
          -341.1057687718087,
          -341.08129148738385,
          -341.052312707561,
          -341.01881447115585,
          -340.98077795387997,
          -340.93818347708543,
          -340.89101050728686,
          -340.8392376641459,
          -340.7828427392584
        ],
        "cartesian_polarizations_e_A2": [
          [
            -5.957761166302812e-14,
            -0.009131980411362895,
            2.85017666930191e-13
          ],
          [
            -7.567583156426105e-12,
            -0.00934933102407725,
            -1.0598837410617085e-11
          ],
          [
            -1.5069216352603655e-11,
            -0.009566450335381074,
            -2.1477533134138552e-11
          ],
          [
            -2.2564381497396123e-11,
            -0.009783343093030937,
            -3.2350759294857217e-11
          ],
          [
            -3.005238614053542e-11,
            -0.010000014283218521,
            -4.321796667401487e-11
          ],
          [
            -3.7533129017044886e-11,
            -0.010216469106437696,
            -5.407857736069435e-11
          ],
          [
            -4.500606321770983e-11,
            -0.010432712954645582,
            -6.493225908501649e-11
          ],
          [
            -5.247074377729044e-11,
            -0.010648751383064035,
            -7.577841019939966e-11
          ],
          [
            -5.9926861661028e-11,
            -0.010864590075613117,
            -8.661669276196133e-11
          ]
        ],
        "raw_reduced_polarization": [
          [
            -1.1696184916895596e-11,
            -0.9994449350991257,
            -1.1924685744391513e-11
          ],
          [
            -1.0807173300985477e-09,
            -1.0230558283481168,
            -9.840316118566717e-10
          ],
          [
            -2.1494482891328735e-09,
            -1.0466332203861592,
            -1.9559573640277676e-09
          ],
          [
            -3.2178674881390007e-09,
            -1.0701776458151926,
            -2.927674184920394e-09
          ],
          [
            -4.2858962728472284e-09,
            -1.093689664950277,
            -3.899132929772104e-09
          ],
          [
            -5.353500574259706e-09,
            -1.1171698611582674,
            -4.87028181710728e-09
          ],
          [
            -6.420622656656336e-09,
            -1.1406188383407225,
            -5.841091057664961e-09
          ],
          [
            -7.487200551065405e-09,
            -1.1640372178335288,
            -6.811506625981797e-09
          ],
          [
            -8.553194639488444e-09,
            -1.1874256346137653,
            -7.78149811993606e-09
          ]
        ],
        "unwrapped_reduced_polarization": [
          [
            -1.1696184916895596e-11,
            -0.9994449350991257,
            -1.1924685744391513e-11
          ],
          [
            -1.0807173300985477e-09,
            -1.0230558283481168,
            -9.840316118566717e-10
          ],
          [
            -2.1494482891328735e-09,
            -1.0466332203861592,
            -1.9559573640277676e-09
          ],
          [
            -3.2178674881390007e-09,
            -1.0701776458151926,
            -2.927674184920394e-09
          ],
          [
            -4.2858962728472284e-09,
            -1.093689664950277,
            -3.899132929772104e-09
          ],
          [
            -5.353500574259706e-09,
            -1.1171698611582674,
            -4.87028181710728e-09
          ],
          [
            -6.420622656656336e-09,
            -1.1406188383407225,
            -5.841091057664961e-09
          ],
          [
            -7.487200551065405e-09,
            -1.1640372178335288,
            -6.811506625981797e-09
          ],
          [
            -8.553194639488444e-09,
            -1.1874256346137653,
            -7.78149811993606e-09
          ]
        ],
        "gauge_integer_shift": [
          0,
          0,
          0
        ],
        "expected_opposite_endpoint_reduced_polarization": [
          -8.510206862797063e-09,
          -1.2004462397198234,
          -7.71998774422623e-09
        ],
        "actual_opposite_endpoint_branch_residual": 0.01302060510605818
      },
      "pnp_branch": {
        "construction": "incoming_path_concatenated_with_parent_reflection",
        "reduced_polarization": [
          [
            8.526539740579504e-09,
            -0.7956801782630795,
            7.771195909548022e-09
          ],
          [
            7.460566856959987e-09,
            -0.8212614645854297,
            6.799179362625265e-09
          ],
          [
            6.394134794238562e-09,
            -0.8468095711145434,
            5.826850307163848e-09
          ],
          [
            5.3272750506701655e-09,
            -0.8723252304232346,
            4.854230085169881e-09
          ],
          [
            4.260044372909045e-09,
            -0.8978092128423765,
            3.881360673042778e-09
          ],
          [
            3.1924925728495848e-09,
            -0.9232623235528225,
            2.9082767082825433e-09
          ],
          [
            2.124649853760227e-09,
            -0.9486853995380025,
            1.9350097719378955e-09
          ],
          [
            1.0565733643340967e-09,
            -0.9740793064070705,
            9.616004098934385e-10
          ],
          [
            -1.1697223366811207e-11,
            -0.9994449350991299,
            -1.192610836307169e-11
          ],
          [
            -1.0807173300985477e-09,
            -1.0230558283481168,
            -9.840316118566717e-10
          ],
          [
            -2.1494482891328735e-09,
            -1.0466332203861592,
            -1.9559573640277676e-09
          ],
          [
            -3.2178674881390007e-09,
            -1.0701776458151926,
            -2.927674184920394e-09
          ],
          [
            -4.2858962728472284e-09,
            -1.093689664950277,
            -3.899132929772104e-09
          ],
          [
            -5.353500574259706e-09,
            -1.1171698611582674,
            -4.87028181710728e-09
          ],
          [
            -6.420622656656336e-09,
            -1.1406188383407225,
            -5.841091057664961e-09
          ],
          [
            -7.487200551065405e-09,
            -1.1640372178335288,
            -6.811506625981797e-09
          ],
          [
            -8.553194639488444e-09,
            -1.1874256346137653,
            -7.78149811993606e-09
          ]
        ],
        "unwrapped_reduced_polarization": [
          [
            8.526539740579504e-09,
            -0.7956801782630795,
            7.771195909548022e-09
          ],
          [
            7.460566856959987e-09,
            -0.8212614645854297,
            6.799179362625265e-09
          ],
          [
            6.394134794238562e-09,
            -0.8468095711145434,
            5.826850307163848e-09
          ],
          [
            5.3272750506701655e-09,
            -0.8723252304232346,
            4.854230085169881e-09
          ],
          [
            4.260044372909045e-09,
            -0.8978092128423765,
            3.881360673042778e-09
          ],
          [
            3.1924925728495848e-09,
            -0.9232623235528225,
            2.9082767082825433e-09
          ],
          [
            2.124649853760227e-09,
            -0.9486853995380025,
            1.9350097719378955e-09
          ],
          [
            1.0565733643340967e-09,
            -0.9740793064070705,
            9.616004098934385e-10
          ],
          [
            -1.1697223366811306e-11,
            -0.9994449350991299,
            -1.1926108363071627e-11
          ],
          [
            -1.0807173300985477e-09,
            -1.0230558283481168,
            -9.840316118566717e-10
          ],
          [
            -2.1494482891328735e-09,
            -1.0466332203861592,
            -1.9559573640277676e-09
          ],
          [
            -3.2178674881390007e-09,
            -1.0701776458151926,
            -2.927674184920394e-09
          ],
          [
            -4.2858962728472284e-09,
            -1.093689664950277,
            -3.899132929772104e-09
          ],
          [
            -5.353500574259706e-09,
            -1.1171698611582674,
            -4.87028181710728e-09
          ],
          [
            -6.420622656656336e-09,
            -1.1406188383407225,
            -5.841091057664961e-09
          ],
          [
            -7.487200551065405e-09,
            -1.1640372178335288,
            -6.811506625981797e-09
          ],
          [
            -8.553194639488444e-09,
            -1.1874256346137653,
            -7.78149811993606e-09
          ]
        ],
        "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": [
          [
            8.526539696518398e-09,
            0.20431982173692054,
            7.771195909000994e-09
          ],
          [
            7.460566830985726e-09,
            0.1787385354145703,
            6.7991793306632076e-09
          ],
          [
            6.39413477721007e-09,
            0.15319042888545664,
            5.8268503355662915e-09
          ],
          [
            5.327275065525328e-09,
            0.12767476957676538,
            4.854230128970016e-09
          ],
          [
            4.260044428328058e-09,
            0.10219078715762353,
            3.881360677304713e-09
          ],
          [
            3.1924926036097645e-09,
            0.07673767644717755,
            2.9082767305510515e-09
          ],
          [
            2.124649900459019e-09,
            0.05131460046199754,
            1.935009819042932e-09
          ],
          [
            1.0565733843392877e-09,
            0.025920693592929478,
            9.616003548984509e-10
          ],
          [
            -1.1697198765148187e-11,
            0.0005550649008700947,
            -1.1926126752825894e-11
          ],
          [
            -1.0807173489446598e-09,
            -0.023055828348116814,
            -9.84031633954885e-10
          ],
          [
            -2.1494482860262565e-09,
            -0.046633220386159246,
            -1.955957340538106e-09
          ],
          [
            -3.2178674724825385e-09,
            -0.07017764581519259,
            -2.9276741586592436e-09
          ],
          [
            -4.285896249012211e-09,
            -0.09368966495027697,
            -3.899132905438307e-09
          ],
          [
            -5.353500587279569e-09,
            -0.11716986115826744,
            -4.870281844482349e-09
          ],
          [
            -6.4206226446650305e-09,
            -0.14061883834072253,
            -5.841091055280856e-09
          ],
          [
            -7.487200526234972e-09,
            -0.16403721783352876,
            -6.811506636505982e-09
          ],
          [
            -8.553194652538565e-09,
            -0.18742563461376527,
            -7.7814981125357e-09
          ]
        ]
      },
      "incoming_structure_ids": [
        "incoming_00_000",
        "incoming_00_001",
        "incoming_00_002",
        "incoming_00_003",
        "incoming_00_004",
        "incoming_00_005",
        "incoming_00_006",
        "incoming_00_007",
        "incoming_00_008"
      ],
      "reflected_structure_ids": [
        "reflected_00_001",
        "reflected_00_002",
        "reflected_00_003",
        "reflected_00_004",
        "reflected_00_005",
        "reflected_00_006",
        "reflected_00_007",
        "reflected_00_008"
      ]
    },
    {
      "orbit_id": 1,
      "formal_class": [
        0.0,
        0.5,
        0.0
      ],
      "formal_classes_in_orbit": [
        [
          0.0,
          0.5,
          0.0
        ]
      ],
      "target_reduced_polarization": [
        0.0,
        -0.5,
        0.0
      ],
      "bec_backprojection": {
        "converged_to_target": true,
        "history": [
          {
            "iteration": 0,
            "reduced_polarization": [
              8.526537959834896e-09,
              -0.795680178263078,
              7.771191179419945e-09
            ],
            "branch_aligned_reduced_polarization": [
              8.526537959834896e-09,
              -0.795680178263078,
              7.771191179419945e-09
            ],
            "target_residual": 0.29568017826307824,
            "energy_eV": -341.1330771981926,
            "max_atomic_step_A": 0.02844917649051413,
            "max_log_strain_component": 0.003999136397141451,
            "step_scale": 1.0,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 2.421156015657218,
            "cell_principal_stretches": [
              1.0040071436135285,
              0.9989994784555642,
              0.9989994720603409
            ],
            "cell_volume_ratio": 1.0019990806978825,
            "cell_rmsd_from_input_A": 0.021112242555163918
          },
          {
            "iteration": 1,
            "reduced_polarization": [
              3.238641236771295e-11,
              -0.49859931633144705,
              2.8936641552995823e-11
            ],
            "branch_aligned_reduced_polarization": [
              3.238641236771295e-11,
              -0.49859931633144705,
              2.8936641552995823e-11
            ],
            "target_residual": 0.0014006836685529496,
            "energy_eV": -340.619261864784,
            "max_atomic_step_A": 0.00013519941205322785,
            "max_log_strain_component": 1.8451165083254812e-05,
            "step_scale": 1.0,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 2.421156015657218,
            "cell_principal_stretches": [
              1.0039886186828804,
              0.9990040923498335,
              0.9990040859840869
            ],
            "cell_volume_ratio": 1.0019898481941432,
            "cell_rmsd_from_input_A": 0.021014629615352897
          },
          {
            "iteration": 2,
            "reduced_polarization": [
              -8.104965595389782e-14,
              -0.5000004952956306,
              -9.627726673281185e-14
            ],
            "branch_aligned_reduced_polarization": [
              -8.104965595389782e-14,
              -0.5000004952956306,
              -9.627726673281185e-14
            ],
            "target_residual": 4.952956306203564e-07,
            "energy_eV": -340.6232008067801
          }
        ],
        "iterations": 2
      },
      "parent": {
        "candidate_id": "bec_projection_01",
        "source": "MACEField_BEC_backprojection",
        "spacegroup": "P6_3cm",
        "spacegroup_number": 185,
        "pointgroup": "6mm",
        "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": 4.952956306203564e-07,
        "parent_symmetrization_rmsd_A": 0.02356911550132669,
        "parent_cell_rmsd_A": 0.021014629615352897,
        "energy_eV": -340.6232008067801,
        "reduced_polarization": [
          -8.104965595389782e-14,
          -0.5000004952956306,
          -9.627726673281185e-14
        ],
        "cartesian_polarization_e_A2": [
          1.3790404971754931e-13,
          -0.004583981193748593,
          -8.658304217512314e-14
        ],
        "ranking_score": 0.5288237634964261
      },
      "branch_status": "awaiting_branch_sampling"
    },
    {
      "orbit_id": 2,
      "formal_class": [
        0.5,
        0.0,
        0.0
      ],
      "formal_classes_in_orbit": [
        [
          0.5,
          0.0,
          0.0
        ],
        [
          0.0,
          0.0,
          0.5
        ],
        [
          0.5,
          0.0,
          0.5
        ]
      ],
      "target_reduced_polarization": [
        0.5,
        -1.0,
        0.0
      ],
      "bec_backprojection": {
        "converged_to_target": true,
        "history": [
          {
            "iteration": 0,
            "reduced_polarization": [
              8.526537959834896e-09,
              -0.795680178263078,
              7.771191179419945e-09
            ],
            "branch_aligned_reduced_polarization": [
              8.52653797567271e-09,
              -0.795680178263078,
              7.771191179419945e-09
            ],
            "target_residual": 0.5401357061221465,
            "energy_eV": -341.1330771981926,
            "max_atomic_step_A": 0.07551794799401464,
            "max_log_strain_component": 0.0027634684406053146,
            "step_scale": 1.0,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 2.421156015657218,
            "cell_principal_stretches": [
              1.0012090104932294,
              1.0006919650233326,
              0.996725349023998
            ],
            "cell_volume_ratio": 0.9986209333626532,
            "cell_rmsd_from_input_A": 0.0196269037809678
          },
          {
            "iteration": 1,
            "reduced_polarization": [
              0.4971022609654499,
              -0.9937236053905465,
              2.2152903017865667e-08
            ],
            "branch_aligned_reduced_polarization": [
              0.4971022609654499,
              -0.9937236053905465,
              2.2152903017865667e-08
            ],
            "target_residual": 0.006913032677951342,
            "energy_eV": -339.8627044221436,
            "max_atomic_step_A": 0.0008581961070214892,
            "max_log_strain_component": 8.737459477849961e-05,
            "step_scale": 1.0,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 2.421156015657218,
            "cell_principal_stretches": [
              1.0012242055042382,
              1.0007138511926765,
              0.9966449360769285
            ],
            "cell_volume_ratio": 0.9985773614383053,
            "cell_rmsd_from_input_A": 0.020023210280483834
          },
          {
            "iteration": 2,
            "reduced_polarization": [
              0.5000135252088715,
              -1.0000029336306,
              -3.3063565975905796e-11
            ],
            "branch_aligned_reduced_polarization": [
              0.5000135252088715,
              -1.0000029336306,
              -3.3063565975905796e-11
            ],
            "target_residual": 1.3839706048803078e-05,
            "energy_eV": -339.84187964391634
          }
        ],
        "iterations": 2
      },
      "parent": {
        "candidate_id": "bec_projection_02",
        "source": "MACEField_BEC_backprojection",
        "spacegroup": "Cm",
        "spacegroup_number": 8,
        "pointgroup": "m",
        "has_inversion": false,
        "is_polar_point_group": true,
        "nonpolar_parent_hypothesis": false,
        "symmetry_tolerance_A": null,
        "target_reduced_polarization": [
          0.5,
          -1.0,
          0.0
        ],
        "formal_class": [
          0.5,
          0.0,
          0.0
        ],
        "target_residual": 1.3839706048803078e-05,
        "parent_symmetrization_rmsd_A": 0.04818129601298596,
        "parent_cell_rmsd_A": 0.020023210280483834,
        "energy_eV": -339.84187964391634,
        "reduced_polarization": [
          0.5000135252088715,
          -1.0000029336306,
          -3.3063565975905796e-11
        ],
        "cartesian_polarization_e_A2": [
          0.006427285612549355,
          -0.009127423021595313,
          -1.3277955029403651e-10
        ],
        "ranking_score": 0.5532147779952046
      },
      "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
        ],
        [
          0.0,
          0.5,
          0.5
        ],
        [
          0.5,
          0.5,
          0.5
        ]
      ],
      "target_reduced_polarization": [
        0.5,
        -0.5,
        0.0
      ],
      "bec_backprojection": {
        "converged_to_target": true,
        "history": [
          {
            "iteration": 0,
            "reduced_polarization": [
              8.526537959834896e-09,
              -0.795680178263078,
              7.771191179419945e-09
            ],
            "branch_aligned_reduced_polarization": [
              8.52653797567271e-09,
              -0.795680178263078,
              7.771191179419945e-09
            ],
            "target_residual": 0.5808844629452123,
            "energy_eV": -341.1330771981926,
            "max_atomic_step_A": 0.08088460203141225,
            "max_log_strain_component": 0.0039991363789562894,
            "step_scale": 1.0,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 2.421156015657218,
            "cell_principal_stretches": [
              1.0043899886062615,
              0.9989994742237467,
              0.9986186860003623
            ],
            "cell_volume_ratio": 1.0019990806882946,
            "cell_rmsd_from_input_A": 0.0249209252871796
          },
          {
            "iteration": 1,
            "reduced_polarization": [
              0.49418811587358485,
              -0.4940679418162453,
              -2.210658538299849e-08
            ],
            "branch_aligned_reduced_polarization": [
              0.49418811587358485,
              -0.4940679418162453,
              -2.210658538299849e-08
            ],
            "target_residual": 0.00830465600701294,
            "energy_eV": -339.38936484545826,
            "max_atomic_step_A": 0.0011277361470027874,
            "max_log_strain_component": 7.902672980651555e-05,
            "step_scale": 1.0,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 2.421156015657218,
            "cell_principal_stretches": [
              1.0043262576034166,
              0.9990192358638008,
              0.9986228891212342
            ],
            "cell_volume_ratio": 1.0019595382778357,
            "cell_rmsd_from_input_A": 0.02465554863570104
          },
          {
            "iteration": 2,
            "reduced_polarization": [
              0.5000143705814656,
              -0.5000022098459027,
              2.663238252230593e-11
            ],
            "branch_aligned_reduced_polarization": [
              0.5000143705814656,
              -0.5000022098459027,
              2.663238252230593e-11
            ],
            "target_residual": 1.4539498979449718e-05,
            "energy_eV": -339.37741198174126
          }
        ],
        "iterations": 2
      },
      "parent": {
        "candidate_id": "bec_projection_03",
        "source": "MACEField_BEC_backprojection",
        "spacegroup": "Cm",
        "spacegroup_number": 8,
        "pointgroup": "m",
        "has_inversion": false,
        "is_polar_point_group": true,
        "nonpolar_parent_hypothesis": false,
        "symmetry_tolerance_A": null,
        "target_reduced_polarization": [
          0.5,
          -0.5,
          0.0
        ],
        "formal_class": [
          0.5,
          0.5,
          0.0
        ],
        "target_residual": 1.4539498979449718e-05,
        "parent_symmetrization_rmsd_A": 0.05091626679646265,
        "parent_cell_rmsd_A": 0.02465554863570104,
        "energy_eV": -339.37741198174126,
        "reduced_polarization": [
          0.5000143705814656,
          -0.5000022098459027,
          2.663238252230593e-11
        ],
        "cartesian_polarization_e_A2": [
          0.00640124881569144,
          -0.00457454944202407,
          -4.074174956602553e-11
        ],
        "ranking_score": 0.5571092329533468
      },
      "branch_status": "awaiting_branch_sampling"
    }
  ],
  "sampled_polarization_branches": [
    {
      "orbit_id": 0,
      "candidate_id": "bec_projection_00",
      "formal_class": [
        0.0,
        0.0,
        0.0
      ],
      "construction": "MACEField-BEC-parent plus variable-cell P-N-P path and symmetric log-strain continuation beyond both polar endpoints",
      "geometry_diagnostics": {
        "collision_aware": false,
        "permutations_tested": 1,
        "selected_order": [
          0,
          1,
          2,
          3,
          4,
          5,
          6,
          7,
          8,
          9,
          10,
          11,
          12,
          13,
          14,
          15,
          16,
          17,
          18,
          19,
          20,
          21,
          22,
          23,
          24,
          25,
          26,
          27,
          28,
          29,
          30,
          31,
          32,
          33,
          34,
          35,
          36,
          37,
          38,
          39,
          40,
          41,
          42,
          43,
          44,
          45,
          46,
          47
        ],
        "endpoint_rmsd_A": 0.016465302498625923,
        "minimum_distance_A_by_image": [
          1.7576120142787717,
          1.7543154437359545,
          1.7510243110015609,
          1.7477386249773634,
          1.7444583986864952,
          1.7411836436476824,
          1.7379143711273097,
          1.734650592449954,
          1.7313923189985334
        ],
        "minimum_distance_A": 1.7313923189985334,
        "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": [
          874.0242537345905,
          873.8734955423341,
          873.7227633539677,
          873.5720571650082,
          873.4213769709727,
          873.2707227673741,
          873.1200945497318,
          872.9694923135628,
          872.8189160543848
        ],
        "cell_deformation_log_strain_norm": 0.0029315055317679093
      },
      "parent_reduced_polarization": [
        -1.1697223366811207e-11,
        -0.9994449350991299,
        -1.192610836307169e-11
      ],
      "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": [
          -341.13307719819267,
          -341.14719474992944,
          -341.15634991964197,
          -341.16052068231375,
          -341.1596840220691,
          -341.1538159432499,
          -341.1428914814027,
          -341.12688471413486,
          -341.1057687718086
        ],
        "cartesian_polarizations_e_A2": [
          [
            5.96504713458974e-11,
            -0.007280236097421806,
            8.650201774974695e-11
          ],
          [
            5.221111484129297e-11,
            -0.0075129978860452445,
            7.574492337921967e-11
          ],
          [
            4.4764095749757846e-11,
            -0.007745375480152768,
            6.498142283373836e-11
          ],
          [
            3.730967728579341e-11,
            -0.007977375757474505,
            5.421174423646172e-11
          ],
          [
            2.9848315055923997e-11,
            -0.008209005936283688,
            4.343634603687234e-11
          ],
          [
            2.238042312340939e-11,
            -0.008440273548515164,
            3.265560554065767e-11
          ],
          [
            1.4906183238542743e-11,
            -0.008671186411638065,
            2.186986655480166e-11
          ],
          [
            7.426066591551393e-12,
            -0.008901752599374688,
            1.1079573403933156e-11
          ],
          [
            -5.958182515302178e-14,
            -0.009131980411362933,
            2.850017987678753e-13
          ]
        ],
        "raw_reduced_polarization": [
          [
            8.526539740579504e-09,
            -0.7956801782630795,
            7.771195909548022e-09
          ],
          [
            7.460566856959987e-09,
            -0.8212614645854297,
            6.799179362625265e-09
          ],
          [
            6.394134794238562e-09,
            -0.8468095711145434,
            5.826850307163848e-09
          ],
          [
            5.3272750506701655e-09,
            -0.8723252304232346,
            4.854230085169881e-09
          ],
          [
            4.260044372909045e-09,
            -0.8978092128423765,
            3.881360673042778e-09
          ],
          [
            3.1924925728495848e-09,
            -0.9232623235528225,
            2.9082767082825433e-09
          ],
          [
            2.124649853760227e-09,
            -0.9486853995380025,
            1.9350097719378955e-09
          ],
          [
            1.0565733643340967e-09,
            -0.9740793064070705,
            9.616004098934385e-10
          ],
          [
            -1.1697223366811207e-11,
            -0.9994449350991299,
            -1.192610836307169e-11
          ]
        ],
        "unwrapped_reduced_polarization": [
          [
            8.526539740579504e-09,
            -0.7956801782630795,
            7.771195909548022e-09
          ],
          [
            7.460566856959987e-09,
            -0.8212614645854297,
            6.799179362625265e-09
          ],
          [
            6.394134794238562e-09,
            -0.8468095711145434,
            5.826850307163848e-09
          ],
          [
            5.3272750506701655e-09,
            -0.8723252304232346,
            4.854230085169881e-09
          ],
          [
            4.260044372909045e-09,
            -0.8978092128423765,
            3.881360673042778e-09
          ],
          [
            3.1924925728495848e-09,
            -0.9232623235528225,
            2.9082767082825433e-09
          ],
          [
            2.124649853760227e-09,
            -0.9486853995380025,
            1.9350097719378955e-09
          ],
          [
            1.0565733643340967e-09,
            -0.9740793064070705,
            9.616004098934385e-10
          ],
          [
            -1.1697223366811306e-11,
            -0.9994449350991299,
            -1.1926108363071627e-11
          ]
        ],
        "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": [
          [
            8.526539696518398e-09,
            0.20431982173692054,
            7.771195909000994e-09
          ],
          [
            7.460566830985726e-09,
            0.1787385354145703,
            6.7991793306632076e-09
          ],
          [
            6.39413477721007e-09,
            0.15319042888545664,
            5.8268503355662915e-09
          ],
          [
            5.327275065525328e-09,
            0.12767476957676538,
            4.854230128970016e-09
          ],
          [
            4.260044428328058e-09,
            0.10219078715762353,
            3.881360677304713e-09
          ],
          [
            3.1924926036097645e-09,
            0.07673767644717755,
            2.9082767305510515e-09
          ],
          [
            2.124649900459019e-09,
            0.05131460046199754,
            1.935009819042932e-09
          ],
          [
            1.0565733843392877e-09,
            0.025920693592929478,
            9.616003548984509e-10
          ],
          [
            -1.1697198765148187e-11,
            0.0005550649008700947,
            -1.1926126752825894e-11
          ]
        ]
      },
      "reflected": {
        "reached": true,
        "construction": "reflect_displacements_about_reconstructed_parent",
        "energies_eV": [
          -341.1057687718087,
          -341.08129148738385,
          -341.052312707561,
          -341.01881447115585,
          -340.98077795387997,
          -340.93818347708543,
          -340.89101050728686,
          -340.8392376641459,
          -340.7828427392584
        ],
        "cartesian_polarizations_e_A2": [
          [
            -5.957761166302812e-14,
            -0.009131980411362895,
            2.85017666930191e-13
          ],
          [
            -7.567583156426105e-12,
            -0.00934933102407725,
            -1.0598837410617085e-11
          ],
          [
            -1.5069216352603655e-11,
            -0.009566450335381074,
            -2.1477533134138552e-11
          ],
          [
            -2.2564381497396123e-11,
            -0.009783343093030937,
            -3.2350759294857217e-11
          ],
          [
            -3.005238614053542e-11,
            -0.010000014283218521,
            -4.321796667401487e-11
          ],
          [
            -3.7533129017044886e-11,
            -0.010216469106437696,
            -5.407857736069435e-11
          ],
          [
            -4.500606321770983e-11,
            -0.010432712954645582,
            -6.493225908501649e-11
          ],
          [
            -5.247074377729044e-11,
            -0.010648751383064035,
            -7.577841019939966e-11
          ],
          [
            -5.9926861661028e-11,
            -0.010864590075613117,
            -8.661669276196133e-11
          ]
        ],
        "raw_reduced_polarization": [
          [
            -1.1696184916895596e-11,
            -0.9994449350991257,
            -1.1924685744391513e-11
          ],
          [
            -1.0807173300985477e-09,
            -1.0230558283481168,
            -9.840316118566717e-10
          ],
          [
            -2.1494482891328735e-09,
            -1.0466332203861592,
            -1.9559573640277676e-09
          ],
          [
            -3.2178674881390007e-09,
            -1.0701776458151926,
            -2.927674184920394e-09
          ],
          [
            -4.2858962728472284e-09,
            -1.093689664950277,
            -3.899132929772104e-09
          ],
          [
            -5.353500574259706e-09,
            -1.1171698611582674,
            -4.87028181710728e-09
          ],
          [
            -6.420622656656336e-09,
            -1.1406188383407225,
            -5.841091057664961e-09
          ],
          [
            -7.487200551065405e-09,
            -1.1640372178335288,
            -6.811506625981797e-09
          ],
          [
            -8.553194639488444e-09,
            -1.1874256346137653,
            -7.78149811993606e-09
          ]
        ],
        "unwrapped_reduced_polarization": [
          [
            -1.1696184916895596e-11,
            -0.9994449350991257,
            -1.1924685744391513e-11
          ],
          [
            -1.0807173300985477e-09,
            -1.0230558283481168,
            -9.840316118566717e-10
          ],
          [
            -2.1494482891328735e-09,
            -1.0466332203861592,
            -1.9559573640277676e-09
          ],
          [
            -3.2178674881390007e-09,
            -1.0701776458151926,
            -2.927674184920394e-09
          ],
          [
            -4.2858962728472284e-09,
            -1.093689664950277,
            -3.899132929772104e-09
          ],
          [
            -5.353500574259706e-09,
            -1.1171698611582674,
            -4.87028181710728e-09
          ],
          [
            -6.420622656656336e-09,
            -1.1406188383407225,
            -5.841091057664961e-09
          ],
          [
            -7.487200551065405e-09,
            -1.1640372178335288,
            -6.811506625981797e-09
          ],
          [
            -8.553194639488444e-09,
            -1.1874256346137653,
            -7.78149811993606e-09
          ]
        ],
        "gauge_integer_shift": [
          0,
          0,
          0
        ],
        "expected_opposite_endpoint_reduced_polarization": [
          -8.510206862797063e-09,
          -1.2004462397198234,
          -7.71998774422623e-09
        ],
        "actual_opposite_endpoint_branch_residual": 0.01302060510605818
      },
      "pnp_branch": {
        "construction": "incoming_path_concatenated_with_parent_reflection",
        "reduced_polarization": [
          [
            8.526539740579504e-09,
            -0.7956801782630795,
            7.771195909548022e-09
          ],
          [
            7.460566856959987e-09,
            -0.8212614645854297,
            6.799179362625265e-09
          ],
          [
            6.394134794238562e-09,
            -0.8468095711145434,
            5.826850307163848e-09
          ],
          [
            5.3272750506701655e-09,
            -0.8723252304232346,
            4.854230085169881e-09
          ],
          [
            4.260044372909045e-09,
            -0.8978092128423765,
            3.881360673042778e-09
          ],
          [
            3.1924925728495848e-09,
            -0.9232623235528225,
            2.9082767082825433e-09
          ],
          [
            2.124649853760227e-09,
            -0.9486853995380025,
            1.9350097719378955e-09
          ],
          [
            1.0565733643340967e-09,
            -0.9740793064070705,
            9.616004098934385e-10
          ],
          [
            -1.1697223366811207e-11,
            -0.9994449350991299,
            -1.192610836307169e-11
          ],
          [
            -1.0807173300985477e-09,
            -1.0230558283481168,
            -9.840316118566717e-10
          ],
          [
            -2.1494482891328735e-09,
            -1.0466332203861592,
            -1.9559573640277676e-09
          ],
          [
            -3.2178674881390007e-09,
            -1.0701776458151926,
            -2.927674184920394e-09
          ],
          [
            -4.2858962728472284e-09,
            -1.093689664950277,
            -3.899132929772104e-09
          ],
          [
            -5.353500574259706e-09,
            -1.1171698611582674,
            -4.87028181710728e-09
          ],
          [
            -6.420622656656336e-09,
            -1.1406188383407225,
            -5.841091057664961e-09
          ],
          [
            -7.487200551065405e-09,
            -1.1640372178335288,
            -6.811506625981797e-09
          ],
          [
            -8.553194639488444e-09,
            -1.1874256346137653,
            -7.78149811993606e-09
          ]
        ],
        "unwrapped_reduced_polarization": [
          [
            8.526539740579504e-09,
            -0.7956801782630795,
            7.771195909548022e-09
          ],
          [
            7.460566856959987e-09,
            -0.8212614645854297,
            6.799179362625265e-09
          ],
          [
            6.394134794238562e-09,
            -0.8468095711145434,
            5.826850307163848e-09
          ],
          [
            5.3272750506701655e-09,
            -0.8723252304232346,
            4.854230085169881e-09
          ],
          [
            4.260044372909045e-09,
            -0.8978092128423765,
            3.881360673042778e-09
          ],
          [
            3.1924925728495848e-09,
            -0.9232623235528225,
            2.9082767082825433e-09
          ],
          [
            2.124649853760227e-09,
            -0.9486853995380025,
            1.9350097719378955e-09
          ],
          [
            1.0565733643340967e-09,
            -0.9740793064070705,
            9.616004098934385e-10
          ],
          [
            -1.1697223366811306e-11,
            -0.9994449350991299,
            -1.1926108363071627e-11
          ],
          [
            -1.0807173300985477e-09,
            -1.0230558283481168,
            -9.840316118566717e-10
          ],
          [
            -2.1494482891328735e-09,
            -1.0466332203861592,
            -1.9559573640277676e-09
          ],
          [
            -3.2178674881390007e-09,
            -1.0701776458151926,
            -2.927674184920394e-09
          ],
          [
            -4.2858962728472284e-09,
            -1.093689664950277,
            -3.899132929772104e-09
          ],
          [
            -5.353500574259706e-09,
            -1.1171698611582674,
            -4.87028181710728e-09
          ],
          [
            -6.420622656656336e-09,
            -1.1406188383407225,
            -5.841091057664961e-09
          ],
          [
            -7.487200551065405e-09,
            -1.1640372178335288,
            -6.811506625981797e-09
          ],
          [
            -8.553194639488444e-09,
            -1.1874256346137653,
            -7.78149811993606e-09
          ]
        ],
        "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": [
          [
            8.526539696518398e-09,
            0.20431982173692054,
            7.771195909000994e-09
          ],
          [
            7.460566830985726e-09,
            0.1787385354145703,
            6.7991793306632076e-09
          ],
          [
            6.39413477721007e-09,
            0.15319042888545664,
            5.8268503355662915e-09
          ],
          [
            5.327275065525328e-09,
            0.12767476957676538,
            4.854230128970016e-09
          ],
          [
            4.260044428328058e-09,
            0.10219078715762353,
            3.881360677304713e-09
          ],
          [
            3.1924926036097645e-09,
            0.07673767644717755,
            2.9082767305510515e-09
          ],
          [
            2.124649900459019e-09,
            0.05131460046199754,
            1.935009819042932e-09
          ],
          [
            1.0565733843392877e-09,
            0.025920693592929478,
            9.616003548984509e-10
          ],
          [
            -1.1697198765148187e-11,
            0.0005550649008700947,
            -1.1926126752825894e-11
          ],
          [
            -1.0807173489446598e-09,
            -0.023055828348116814,
            -9.84031633954885e-10
          ],
          [
            -2.1494482860262565e-09,
            -0.046633220386159246,
            -1.955957340538106e-09
          ],
          [
            -3.2178674724825385e-09,
            -0.07017764581519259,
            -2.9276741586592436e-09
          ],
          [
            -4.285896249012211e-09,
            -0.09368966495027697,
            -3.899132905438307e-09
          ],
          [
            -5.353500587279569e-09,
            -0.11716986115826744,
            -4.870281844482349e-09
          ],
          [
            -6.4206226446650305e-09,
            -0.14061883834072253,
            -5.841091055280856e-09
          ],
          [
            -7.487200526234972e-09,
            -0.16403721783352876,
            -6.811506636505982e-09
          ],
          [
            -8.553194652538565e-09,
            -0.18742563461376527,
            -7.7814981125357e-09
          ]
        ]
      },
      "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": "bec_projection_00",
        "source": "MACEField_BEC_backprojection",
        "spacegroup": "P6_3cm",
        "spacegroup_number": 185,
        "pointgroup": "6mm",
        "has_inversion": false,
        "is_polar_point_group": true,
        "nonpolar_parent_hypothesis": false,
        "symmetry_tolerance_A": null,
        "target_reduced_polarization": [
          0.0,
          -1.0,
          0.0
        ],
        "formal_class": [
          0.0,
          0.0,
          0.0
        ],
        "target_residual": 0.0005550649008700951,
        "parent_symmetrization_rmsd_A": 0.016465302498625923,
        "parent_cell_rmsd_A": 0.01453701414113342,
        "energy_eV": -341.1057687718085,
        "reduced_polarization": [
          -1.1702306754159965e-11,
          -0.9994449350991299,
          -1.1922980882744818e-11
        ],
        "cartesian_polarization_e_A2": [
          -5.966743849970424e-14,
          -0.009131980411362933,
          2.850366832850303e-13
        ],
        "ranking_score": 0.5212096858356494
      }
    }
  ],
  "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": 43,
      "full_response": 8,
      "energy_polarization": 35
    },
    "model_evaluations_for_recovery_and_path_properties": {
      "total": 68,
      "full_response": 33,
      "energy_polarization": 35
    },
    "elapsed_seconds": 452.4302283300203
  }
}
