{
  "schema": "ferrofinder.endpoint_parent_recovery.v4_variable_cell",
  "status": "complete",
  "input_atom_count": 20,
  "input_formula": "Cs4O12S4",
  "input_spacegroup": "P6_3mc",
  "input_pointgroup": "6mm",
  "input_is_polar_point_group": true,
  "input_energy_eV": -109.2025273333989,
  "input_cartesian_polarization_e_A2": [
    -5.42140969639967e-11,
    -0.0019395551657580214,
    2.7961204613224896e-11
  ],
  "input_reduced_polarization": [
    -2.5866510952592177e-09,
    -0.06952051018296006,
    2.1936751333612826e-09
  ],
  "input_formal_targets": [
    {
      "orbit_id": 0,
      "representative_formal_class": [
        0.0,
        0.0,
        0.0
      ],
      "target_reduced_polarization": [
        0.0,
        0.0,
        0.0
      ]
    },
    {
      "orbit_id": 1,
      "representative_formal_class": [
        0.0,
        0.5,
        0.0
      ],
      "target_reduced_polarization": [
        0.0,
        -0.5,
        0.0
      ]
    },
    {
      "orbit_id": 2,
      "representative_formal_class": [
        0.5,
        0.0,
        0.0
      ],
      "target_reduced_polarization": [
        -0.5,
        0.0,
        0.0
      ]
    },
    {
      "orbit_id": 3,
      "representative_formal_class": [
        0.5,
        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": "P6_3/mmc",
      "spacegroup_number": 194,
      "pointgroup": "6/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": 5.634470476570451e-15,
      "parent_symmetrization_rmsd_A": 0.7224615238348843,
      "parent_cell_rmsd_A": 0.0,
      "energy_eV": -81.97129402879503,
      "reduced_polarization": [
        -4.8853629216095985e-15,
        5.633202501093305e-18,
        -2.8072148016380496e-15
      ],
      "cartesian_polarization_e_A2": [
        -5.124496563511084e-17,
        1.5716091527525264e-19,
        -3.57815550115678e-17
      ],
      "ranking_score": 0.7224615238348956
    },
    {
      "candidate_id": "inversion_parent_endpoint_01",
      "source": "same_species_inversion_center_projection_from_endpoint",
      "spacegroup": "P-31c",
      "spacegroup_number": 163,
      "pointgroup": "-3m",
      "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": 1.364491206214902e-15,
      "parent_symmetrization_rmsd_A": 0.8730211368454227,
      "parent_cell_rmsd_A": 0.0,
      "energy_eV": -93.19499792209054,
      "reduced_polarization": [
        -1.3449050238021844e-15,
        -2.298768600523254e-16,
        -1.4945166507188238e-17
      ],
      "cartesian_polarization_e_A2": [
        -1.9684516973764205e-17,
        -6.4133426269360794e-18,
        -1.904953255525568e-19
      ],
      "ranking_score": 0.8730211368454255
    },
    {
      "candidate_id": "inversion_parent_endpoint_02",
      "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": 0.00030072919826761827,
      "parent_symmetrization_rmsd_A": 0.9551022174789126,
      "parent_cell_rmsd_A": 0.0,
      "energy_eV": "Infinity",
      "reduced_polarization": [
        2.891268645976459e-05,
        -0.000297936561289598,
        -2.891215487115052e-05
      ],
      "cartesian_polarization_e_A2": [
        6.383074783536257e-07,
        -8.312142632391954e-06,
        -3.6852251542040245e-07
      ],
      "ranking_score": 0.9557036758754478
    },
    {
      "candidate_id": "bec_projection_00",
      "source": "MACEField_BEC_backprojection",
      "spacegroup": "P6_3mc",
      "spacegroup_number": 186,
      "pointgroup": "6mm",
      "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": 0.000654884670964318,
      "parent_symmetrization_rmsd_A": 0.032720020661631544,
      "parent_cell_rmsd_A": 0.061298904763691126,
      "energy_eV": -109.02148238198552,
      "reduced_polarization": [
        3.712705661942782e-11,
        -0.0006548846709643169,
        -6.375327953778243e-12
      ],
      "cartesian_polarization_e_A2": [
        5.890948504701358e-13,
        -1.8231740731196692e-05,
        -8.067116884652355e-14
      ],
      "ranking_score": 0.549354516194483
    },
    {
      "candidate_id": "inversion_parent_bec_00_00",
      "source": "same_species_inversion_center_projection_after_BEC",
      "spacegroup": "P6_3/mmc",
      "spacegroup_number": 194,
      "pointgroup": "6/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": 6.6775535651166835e-15,
      "parent_symmetrization_rmsd_A": 0.7224919809088206,
      "parent_cell_rmsd_A": 0.061298904763691126,
      "energy_eV": -82.00179744919416,
      "reduced_polarization": [
        -4.438092420335592e-15,
        3.6790145414232795e-16,
        -4.975711587662839e-15
      ],
      "cartesian_polarization_e_A2": [
        -2.8519378164718296e-17,
        1.024223687564626e-17,
        -6.301421654707978e-17
      ],
      "ranking_score": 0.7378167070997567
    },
    {
      "candidate_id": "inversion_parent_bec_00_01",
      "source": "same_species_inversion_center_projection_after_BEC",
      "spacegroup": "P-31c",
      "spacegroup_number": 163,
      "pointgroup": "-3m",
      "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": 2.0731907337966747e-15,
      "parent_symmetrization_rmsd_A": 0.8730327275019651,
      "parent_cell_rmsd_A": 0.061298904763691126,
      "energy_eV": -93.01303745041187,
      "reduced_polarization": [
        3.8346459853702337e-16,
        1.567676196314351e-15,
        1.3013324186688816e-15
      ],
      "cartesian_polarization_e_A2": [
        -3.907433423944423e-18,
        4.3643510420669564e-17,
        1.648054581228172e-17
      ],
      "ranking_score": 0.888357453692892
    },
    {
      "candidate_id": "bec_projection_01",
      "source": "MACEField_BEC_backprojection",
      "spacegroup": "P6_3mc",
      "spacegroup_number": 186,
      "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": 1.5654679120791217e-06,
      "parent_symmetrization_rmsd_A": 0.2005087274729299,
      "parent_cell_rmsd_A": 0.3334055925190513,
      "energy_eV": -101.99668109381956,
      "reduced_polarization": [
        -5.204874602319409e-16,
        -0.4999984345320879,
        -1.9745372045669586e-14
      ],
      "cartesian_polarization_e_A2": [
        -2.110638545795806e-12,
        -0.014116716194170736,
        1.9138185994196722e-12
      ],
      "ranking_score": 0.7838632565385169
    },
    {
      "candidate_id": "bec_projection_02",
      "source": "MACEField_BEC_backprojection",
      "spacegroup": "Cc",
      "spacegroup_number": 9,
      "pointgroup": "m",
      "has_inversion": false,
      "is_polar_point_group": true,
      "nonpolar_parent_hypothesis": false,
      "symmetry_tolerance_A": null,
      "target_reduced_polarization": [
        -0.5,
        0.0,
        0.0
      ],
      "formal_class": [
        0.5,
        0.0,
        0.0
      ],
      "target_residual": 1.5087374955372282e-05,
      "parent_symmetrization_rmsd_A": 0.1285347020382321,
      "parent_cell_rmsd_A": 0.09340618046546452,
      "energy_eV": -99.7404839737381,
      "reduced_polarization": [
        -0.5000143467956877,
        4.668868871570487e-06,
        4.220728030955188e-12
      ],
      "cartesian_polarization_e_A2": [
        -0.007303963368076855,
        4.56628617048045e-05,
        -9.09828805417196e-12
      ],
      "ranking_score": 0.651916421904509
    },
    {
      "candidate_id": "bec_projection_03",
      "source": "MACEField_BEC_backprojection",
      "spacegroup": "Cc",
      "spacegroup_number": 9,
      "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": 8.497923670278674e-06,
      "parent_symmetrization_rmsd_A": 0.24418315550731262,
      "parent_cell_rmsd_A": 0.34973496541193827,
      "energy_eV": -98.62429507778661,
      "reduced_polarization": [
        -0.4999995633070184,
        -0.49999151330417974,
        -8.987665222587203e-13
      ],
      "cartesian_polarization_e_A2": [
        -0.007555070537252732,
        -0.014077583905550507,
        5.0228621405053165e-11
      ],
      "ranking_score": 0.8316338927076377
    }
  ],
  "formal_branches": [
    {
      "orbit_id": 0,
      "formal_class": [
        0.0,
        0.0,
        0.0
      ],
      "formal_classes_in_orbit": [
        [
          0.0,
          0.0,
          0.0
        ]
      ],
      "target_reduced_polarization": [
        0.0,
        0.0,
        0.0
      ],
      "bec_backprojection": {
        "converged_to_target": true,
        "history": [
          {
            "iteration": 0,
            "reduced_polarization": [
              -2.5866510952592177e-09,
              -0.06952051018296006,
              2.1936751333612826e-09
            ],
            "branch_aligned_reduced_polarization": [
              -2.5866510952592177e-09,
              -0.06952051018296006,
              2.1936751333612826e-09
            ],
            "target_residual": 0.06952051018296014,
            "energy_eV": -109.2025273333989,
            "max_atomic_step_A": 0.04834403191753361,
            "max_log_strain_component": 0.005381823565070221,
            "step_scale": 1.0,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 0.8879598758982391,
            "cell_principal_stretches": [
              1.0053963315923837,
              1.0010665444823172,
              1.0010664973397647
            ],
            "cell_volume_ratio": 1.0075420276204397,
            "cell_rmsd_from_input_A": 0.061298904763691126
          },
          {
            "iteration": 1,
            "reduced_polarization": [
              3.712705661942782e-11,
              -0.0006548846709643169,
              -6.375327953778243e-12
            ],
            "branch_aligned_reduced_polarization": [
              3.712705661942782e-11,
              -0.0006548846709643169,
              -6.375327953778243e-12
            ],
            "target_residual": 0.000654884670964318,
            "energy_eV": -109.02148238198552
          }
        ],
        "iterations": 1
      },
      "parent": {
        "candidate_id": "bec_projection_00",
        "source": "MACEField_BEC_backprojection",
        "spacegroup": "P6_3mc",
        "spacegroup_number": 186,
        "pointgroup": "6mm",
        "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": 0.000654884670964318,
        "parent_symmetrization_rmsd_A": 0.032720020661631544,
        "parent_cell_rmsd_A": 0.061298904763691126,
        "energy_eV": -109.02148238198552,
        "reduced_polarization": [
          3.712705661942782e-11,
          -0.0006548846709643169,
          -6.375327953778243e-12
        ],
        "cartesian_polarization_e_A2": [
          5.890948504701358e-13,
          -1.8231740731196692e-05,
          -8.067116884652355e-14
        ],
        "ranking_score": 0.549354516194483
      },
      "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": [
          -109.20252733339888,
          -109.20428367622485,
          -109.19901170449107,
          -109.18673212458275,
          -109.16747315867416,
          -109.14127069094947,
          -109.10816852861855,
          -109.0682187843627,
          -109.0214823819855
        ],
        "cartesian_polarizations_e_A2": [
          [
            -5.421411519153226e-11,
            -0.0019395551657579908,
            2.7961175848430736e-11
          ],
          [
            -4.7406227917782074e-11,
            -0.0016979275660096288,
            2.4450683156735226e-11
          ],
          [
            -4.058392274581167e-11,
            -0.0014566674826022039,
            2.0942090333491786e-11
          ],
          [
            -3.374809709120089e-11,
            -0.001215810152044219,
            1.7435066103056457e-11
          ],
          [
            -2.6899873535296896e-11,
            -0.0009753855127551905,
            1.3929450162785454e-11
          ],
          [
            -2.004048972195592e-11,
            -0.000735414588299538,
            1.042512898357727e-11
          ],
          [
            -1.3171432134493675e-11,
            -0.0004959061123401785,
            6.9220495776047135e-12
          ],
          [
            -6.294352644382845e-12,
            -0.000256853433270648,
            3.4201075594025974e-12
          ],
          [
            5.890595065645531e-13,
            -1.8231740731221398e-05,
            -8.068815357729376e-14
          ]
        ],
        "raw_reduced_polarization": [
          [
            -2.5866534620593444e-09,
            -0.06952051018295896,
            2.1936728766411396e-09
          ],
          [
            -2.263307816880919e-09,
            -0.06087594381967386,
            1.919743971713906e-09
          ],
          [
            -1.9384758291028225e-09,
            -0.05223994466215635,
            1.645539015592332e-09
          ],
          [
            -1.612228376437387e-09,
            -0.04361378541510243,
            1.3710317640780796e-09
          ],
          [
            -1.2846451671395734e-09,
            -0.03499855003096158,
            1.0962093413432733e-09
          ],
          [
            -9.55812164387127e-10,
            -0.026395003646973864,
            8.210625123253572e-10
          ],
          [
            -6.258302140657502e-10,
            -0.017803470992371447,
            5.455867852582532e-10
          ],
          [
            -2.94813834010488e-10,
            -0.009223724644861172,
            2.697736021564068e-10
          ],
          [
            3.712396912989498e-11,
            -0.0006548846709652044,
            -6.376669097510447e-12
          ]
        ],
        "unwrapped_reduced_polarization": [
          [
            -2.5866534620593444e-09,
            -0.06952051018295896,
            2.1936728766411396e-09
          ],
          [
            -2.263307816880919e-09,
            -0.06087594381967386,
            1.919743971713906e-09
          ],
          [
            -1.9384758291028225e-09,
            -0.05223994466215635,
            1.645539015592332e-09
          ],
          [
            -1.612228376437387e-09,
            -0.04361378541510243,
            1.3710317640780796e-09
          ],
          [
            -1.2846451671395734e-09,
            -0.03499855003096158,
            1.0962093413432733e-09
          ],
          [
            -9.55812164387127e-10,
            -0.026395003646973864,
            8.210625123253572e-10
          ],
          [
            -6.258302140657502e-10,
            -0.017803470992371447,
            5.455867852582532e-10
          ],
          [
            -2.94813834010488e-10,
            -0.009223724644861172,
            2.697736021564068e-10
          ],
          [
            3.7123969129894996e-11,
            -0.000654884670965205,
            -6.376669097510472e-12
          ]
        ],
        "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": [
          [
            -2.5866534469898284e-09,
            -0.06952051018295896,
            2.193672909989175e-09
          ],
          [
            -2.263307818939353e-09,
            -0.06087594381967387,
            1.919743919387429e-09
          ],
          [
            -1.9384758243035094e-09,
            -0.05223994466215637,
            1.6455390383640633e-09
          ],
          [
            -1.61222835082242e-09,
            -0.04361378541510241,
            1.37103173258879e-09
          ],
          [
            -1.284645168020404e-09,
            -0.034998550030961584,
            1.096209345519128e-09
          ],
          [
            -9.558121516484164e-10,
            -0.02639500364697389,
            8.210625512816705e-10
          ],
          [
            -6.258302209793953e-10,
            -0.01780347099237145,
            5.455867979620166e-10
          ],
          [
            -2.948138400071798e-10,
            -0.009223724644861153,
            2.697736478651791e-10
          ],
          [
            3.712397056432337e-11,
            -0.0006548846709651945,
            -6.376676964237049e-12
          ]
        ]
      },
      "reflected": {
        "reached": true,
        "construction": "reflect_displacements_about_reconstructed_parent",
        "energies_eV": [
          -109.02148238198554,
          -108.97034003280771,
          -108.91258513239323,
          -108.84831441201273,
          -108.77763541221772,
          -108.7006664379631,
          -108.61753631695969,
          -108.5283839181386,
          -108.43335738933186
        ],
        "cartesian_polarizations_e_A2": [
          [
            5.890866818032463e-13,
            -1.8231740731289998e-05,
            -8.067167303148148e-14
          ],
          [
            7.455300136822265e-12,
            0.00019786797265203507,
            -3.645438055930516e-12
          ],
          [
            1.4330894942814804e-11,
            0.0004143171914052895,
            -7.217688251201576e-12
          ],
          [
            2.1214019556980945e-11,
            0.0006312285389652258,
            -1.079807198973673e-11
          ],
          [
            2.8102721288216776e-11,
            0.0008487400957305465,
            -1.4387516915464789e-11
          ],
          [
            3.499484413800177e-11,
            0.0010670143017685366,
            -1.798670334976873e-11
          ],
          [
            4.188824540066078e-11,
            0.0012862354529975786,
            -2.1596090501203777e-11
          ],
          [
            4.878062173642888e-11,
            0.001506605534871801,
            -2.5216245588096676e-11
          ],
          [
            5.5669399711775626e-11,
            0.0017283381536794408,
            -2.8847308732661776e-11
          ]
        ],
        "raw_reduced_polarization": [
          [
            3.712647811687265e-11,
            -0.0006548846709676685,
            -6.375367765094404e-12
          ],
          [
            3.653290203078758e-10,
            0.007105529688817493,
            -2.875670113946163e-10
          ],
          [
            6.934306011606176e-10,
            0.014874356083284059,
            -5.689114073992877e-10
          ],
          [
            1.0212790874533072e-09,
            0.022655628339636493,
            -8.504588495192444e-10
          ],
          [
            1.3487050713324165e-09,
            0.030454289422242167,
            -1.1322813552383561e-09
          ],
          [
            1.6755356616433271e-09,
            0.03827615085622823,
            -1.414431275817282e-09
          ],
          [
            2.0016082339774288e-09,
            0.046127801773307366,
            -1.696943439322209e-09
          ],
          [
            2.3267456646624976e-09,
            0.054016458496407564,
            -1.979861066962789e-09
          ],
          [
            2.650769960937107e-09,
            0.061949746175696284,
            -2.2631937610193447e-09
          ]
        ],
        "unwrapped_reduced_polarization": [
          [
            3.712647811687265e-11,
            -0.0006548846709676685,
            -6.375367765094404e-12
          ],
          [
            3.653290203078758e-10,
            0.007105529688817493,
            -2.875670113946163e-10
          ],
          [
            6.934306011606176e-10,
            0.014874356083284059,
            -5.689114073992877e-10
          ],
          [
            1.0212790874533072e-09,
            0.022655628339636493,
            -8.504588495192444e-10
          ],
          [
            1.3487050713324165e-09,
            0.030454289422242167,
            -1.1322813552383561e-09
          ],
          [
            1.6755356616433271e-09,
            0.03827615085622823,
            -1.414431275817282e-09
          ],
          [
            2.0016082339774288e-09,
            0.046127801773307366,
            -1.696943439322209e-09
          ],
          [
            2.3267456646624976e-09,
            0.054016458496407564,
            -1.979861066962789e-09
          ],
          [
            2.650769960937107e-09,
            0.061949746175696284,
            -2.2631937610193447e-09
          ]
        ],
        "gauge_integer_shift": [
          0,
          0,
          0
        ],
        "expected_opposite_endpoint_reduced_polarization": [
          2.66036851226316e-09,
          0.06821353017070177,
          -2.2063335326112785e-09
        ],
        "actual_opposite_endpoint_branch_residual": 0.006263783995005483
      },
      "pnp_branch": {
        "construction": "incoming_path_concatenated_with_parent_reflection",
        "reduced_polarization": [
          [
            -2.5866534620593444e-09,
            -0.06952051018295896,
            2.1936728766411396e-09
          ],
          [
            -2.263307816880919e-09,
            -0.06087594381967386,
            1.919743971713906e-09
          ],
          [
            -1.9384758291028225e-09,
            -0.05223994466215635,
            1.645539015592332e-09
          ],
          [
            -1.612228376437387e-09,
            -0.04361378541510243,
            1.3710317640780796e-09
          ],
          [
            -1.2846451671395734e-09,
            -0.03499855003096158,
            1.0962093413432733e-09
          ],
          [
            -9.55812164387127e-10,
            -0.026395003646973864,
            8.210625123253572e-10
          ],
          [
            -6.258302140657502e-10,
            -0.017803470992371447,
            5.455867852582532e-10
          ],
          [
            -2.94813834010488e-10,
            -0.009223724644861172,
            2.697736021564068e-10
          ],
          [
            3.712396912989498e-11,
            -0.0006548846709652044,
            -6.376669097510447e-12
          ],
          [
            3.653290203078758e-10,
            0.007105529688817493,
            -2.875670113946163e-10
          ],
          [
            6.934306011606176e-10,
            0.014874356083284059,
            -5.689114073992877e-10
          ],
          [
            1.0212790874533072e-09,
            0.022655628339636493,
            -8.504588495192444e-10
          ],
          [
            1.3487050713324165e-09,
            0.030454289422242167,
            -1.1322813552383561e-09
          ],
          [
            1.6755356616433271e-09,
            0.03827615085622823,
            -1.414431275817282e-09
          ],
          [
            2.0016082339774288e-09,
            0.046127801773307366,
            -1.696943439322209e-09
          ],
          [
            2.3267456646624976e-09,
            0.054016458496407564,
            -1.979861066962789e-09
          ],
          [
            2.650769960937107e-09,
            0.061949746175696284,
            -2.2631937610193447e-09
          ]
        ],
        "unwrapped_reduced_polarization": [
          [
            -2.5866534620593444e-09,
            -0.06952051018295896,
            2.1936728766411396e-09
          ],
          [
            -2.263307816880919e-09,
            -0.06087594381967386,
            1.919743971713906e-09
          ],
          [
            -1.9384758291028225e-09,
            -0.05223994466215635,
            1.645539015592332e-09
          ],
          [
            -1.612228376437387e-09,
            -0.04361378541510243,
            1.3710317640780796e-09
          ],
          [
            -1.2846451671395734e-09,
            -0.03499855003096158,
            1.0962093413432733e-09
          ],
          [
            -9.55812164387127e-10,
            -0.026395003646973864,
            8.210625123253572e-10
          ],
          [
            -6.258302140657502e-10,
            -0.017803470992371447,
            5.455867852582532e-10
          ],
          [
            -2.94813834010488e-10,
            -0.009223724644861172,
            2.697736021564068e-10
          ],
          [
            3.7123969129894996e-11,
            -0.000654884670965205,
            -6.376669097510472e-12
          ],
          [
            3.653290203078758e-10,
            0.007105529688817493,
            -2.875670113946163e-10
          ],
          [
            6.934306011606176e-10,
            0.014874356083284059,
            -5.689114073992877e-10
          ],
          [
            1.0212790874533072e-09,
            0.022655628339636493,
            -8.504588495192444e-10
          ],
          [
            1.3487050713324165e-09,
            0.030454289422242167,
            -1.1322813552383561e-09
          ],
          [
            1.6755356616433271e-09,
            0.03827615085622823,
            -1.414431275817282e-09
          ],
          [
            2.0016082339774288e-09,
            0.046127801773307366,
            -1.696943439322209e-09
          ],
          [
            2.3267456646624976e-09,
            0.054016458496407564,
            -1.979861066962789e-09
          ],
          [
            2.650769960937107e-09,
            0.061949746175696284,
            -2.2631937610193447e-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": [
          [
            -2.5866534469898284e-09,
            -0.06952051018295896,
            2.193672909989175e-09
          ],
          [
            -2.263307818939353e-09,
            -0.06087594381967387,
            1.919743919387429e-09
          ],
          [
            -1.9384758243035094e-09,
            -0.05223994466215637,
            1.6455390383640633e-09
          ],
          [
            -1.61222835082242e-09,
            -0.04361378541510241,
            1.37103173258879e-09
          ],
          [
            -1.284645168020404e-09,
            -0.034998550030961584,
            1.096209345519128e-09
          ],
          [
            -9.558121516484164e-10,
            -0.02639500364697389,
            8.210625512816705e-10
          ],
          [
            -6.258302209793953e-10,
            -0.01780347099237145,
            5.455867979620166e-10
          ],
          [
            -2.948138400071798e-10,
            -0.009223724644861153,
            2.697736478651791e-10
          ],
          [
            3.712397056432337e-11,
            -0.0006548846709651945,
            -6.376676964237049e-12
          ],
          [
            3.6532898928243185e-10,
            0.007105529688817502,
            -2.875670257473928e-10
          ],
          [
            6.934306462369477e-10,
            0.014874356083284024,
            -5.689114179752153e-10
          ],
          [
            1.0212790613195466e-09,
            0.022655628339636524,
            -8.504588699942417e-10
          ],
          [
            1.3487050365412756e-09,
            0.030454289422242153,
            -1.132281379767619e-09
          ],
          [
            1.6755357101772006e-09,
            0.038276150856228264,
            -1.4144312943109583e-09
          ],
          [
            2.001608212509609e-09,
            0.04612780177330733,
            -1.6969434191160815e-09
          ],
          [
            2.3267456850106782e-09,
            0.05401645849640757,
            -1.979861052880949e-09
          ],
          [
            2.6507699368849558e-09,
            0.06194974617569626,
            -2.2631937435235727e-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": [
              -2.5866510952592177e-09,
              -0.06952051018296006,
              2.1936751333612826e-09
            ],
            "branch_aligned_reduced_polarization": [
              -2.5866510952592177e-09,
              -0.06952051018296007,
              2.1936751333612826e-09
            ],
            "target_residual": 0.43047948981703993,
            "energy_eV": -109.2025273333989,
            "max_atomic_step_A": 0.12,
            "max_log_strain_component": 0.013358811877959334,
            "step_scale": 0.4008656693515812,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 0.8879598758982391,
            "cell_principal_stretches": [
              0.9973576383584187,
              0.9973575217742909,
              0.9867300210420469
            ],
            "cell_volume_ratio": 0.9815222006156176,
            "cell_rmsd_from_input_A": 0.14935246701244853
          },
          {
            "iteration": 1,
            "reduced_polarization": [
              -1.3795284162609495e-09,
              -0.24771596232453458,
              1.4208663009421456e-09
            ],
            "branch_aligned_reduced_polarization": [
              -1.3795284162609495e-09,
              -0.24771596232453458,
              1.4208663009421456e-09
            ],
            "target_residual": 0.2522840376754654,
            "energy_eV": -107.70868282019578,
            "max_atomic_step_A": 0.12,
            "max_log_strain_component": 0.010336449881436663,
            "step_scale": 0.6711861285355347,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 0.8879598758982391,
            "cell_principal_stretches": [
              0.995317889590228,
              0.9953176832214583,
              0.9765832666836122
            ],
            "cell_volume_ratio": 0.967459533545607,
            "cell_rmsd_from_input_A": 0.26222402489913094
          },
          {
            "iteration": 2,
            "reduced_polarization": [
              -4.137674016614342e-10,
              -0.4176230123855286,
              5.587340509834424e-10
            ],
            "branch_aligned_reduced_polarization": [
              -4.137674016614342e-10,
              -0.4176230123855286,
              5.587340509834424e-10
            ],
            "target_residual": 0.08237698761447138,
            "energy_eV": -104.31580217504047,
            "max_atomic_step_A": 0.04545233290785503,
            "max_log_strain_component": 0.005522479740327283,
            "step_scale": 1.0,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 0.8879598758982391,
            "cell_principal_stretches": [
              0.9942298184621755,
              0.994229564274744,
              0.9712049698151926
            ],
            "cell_volume_ratio": 0.9600290026636219,
            "cell_rmsd_from_input_A": 0.3215846710141156
          },
          {
            "iteration": 3,
            "reduced_polarization": [
              -3.74708226997825e-11,
              -0.48793408462867244,
              -1.2230307207153883e-11
            ],
            "branch_aligned_reduced_polarization": [
              -3.74708226997825e-11,
              -0.48793408462867244,
              -1.2230307207153883e-11
            ],
            "target_residual": 0.012065915371327562,
            "energy_eV": -102.30956602550664,
            "max_atomic_step_A": 0.007981203245972795,
            "max_log_strain_component": 0.0011487959844266257,
            "step_scale": 1.0,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 0.8879598758982391,
            "cell_principal_stretches": [
              0.99400362548207,
              0.99400336136049,
              0.9700898940657192
            ],
            "cell_volume_ratio": 0.9584904757831054,
            "cell_rmsd_from_input_A": 0.3338513480717683
          },
          {
            "iteration": 4,
            "reduced_polarization": [
              -8.762037729516758e-12,
              -0.4988159101572883,
              2.4467932903713287e-12
            ],
            "branch_aligned_reduced_polarization": [
              -8.762037729516758e-12,
              -0.4988159101572883,
              2.4467932903713287e-12
            ],
            "target_residual": 0.0011840898427116775,
            "energy_eV": -102.02306025665267,
            "max_atomic_step_A": 0.0008200896032763722,
            "max_log_strain_component": 5.563717491208669e-05,
            "step_scale": 1.0,
            "strain_jacobian_refreshed": true,
            "strain_jacobian_frobenius_norm": 0.8431051460735994,
            "cell_principal_stretches": [
              0.9940589305766279,
              0.9940586655549566,
              0.970128548842661
            ],
            "cell_volume_ratio": 0.9586353331025274,
            "cell_rmsd_from_input_A": 0.3334055925190513
          },
          {
            "iteration": 5,
            "reduced_polarization": [
              -5.204874602319409e-16,
              -0.4999984345320879,
              -1.9745372045669586e-14
            ],
            "branch_aligned_reduced_polarization": [
              -5.204874602319409e-16,
              -0.4999984345320879,
              -1.9745372045669586e-14
            ],
            "target_residual": 1.5654679120791217e-06,
            "energy_eV": -101.99668109381956
          }
        ],
        "iterations": 5
      },
      "parent": {
        "candidate_id": "bec_projection_01",
        "source": "MACEField_BEC_backprojection",
        "spacegroup": "P6_3mc",
        "spacegroup_number": 186,
        "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": 1.5654679120791217e-06,
        "parent_symmetrization_rmsd_A": 0.2005087274729299,
        "parent_cell_rmsd_A": 0.3334055925190513,
        "energy_eV": -101.99668109381956,
        "reduced_polarization": [
          -5.204874602319409e-16,
          -0.4999984345320879,
          -1.9745372045669586e-14
        ],
        "cartesian_polarization_e_A2": [
          -2.110638545795806e-12,
          -0.014116716194170736,
          1.9138185994196722e-12
        ],
        "ranking_score": 0.7838632565385169
      },
      "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,
        0.0,
        0.0
      ],
      "bec_backprojection": {
        "converged_to_target": true,
        "history": [
          {
            "iteration": 0,
            "reduced_polarization": [
              -2.5866510952592177e-09,
              -0.06952051018296006,
              2.1936751333612826e-09
            ],
            "branch_aligned_reduced_polarization": [
              -2.5866511155214766e-09,
              -0.06952051018296006,
              2.1936751333612826e-09
            ],
            "target_residual": 0.5048099630053352,
            "energy_eV": -109.2025273333989,
            "max_atomic_step_A": 0.12,
            "max_log_strain_component": 0.00433749720207565,
            "step_scale": 0.7296538021370574,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 0.8879598758982391,
            "cell_principal_stretches": [
              1.0069910830283573,
              1.0007780960081514,
              0.9977404252104041
            ],
            "cell_volume_ratio": 1.005497476648138,
            "cell_rmsd_from_input_A": 0.06080748339893266
          },
          {
            "iteration": 1,
            "reduced_polarization": [
              -0.3606381836735815,
              -0.02600792575484057,
              3.1800080862298928e-09
            ],
            "branch_aligned_reduced_polarization": [
              -0.3606381836735815,
              -0.02600792575484057,
              3.1800080862298928e-09
            ],
            "target_residual": 0.14176786678181946,
            "energy_eV": -104.5075643846234,
            "max_atomic_step_A": 0.04720779804084963,
            "max_log_strain_component": 0.0023053417571920654,
            "step_scale": 1.0,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 0.8879598758982391,
            "cell_principal_stretches": [
              1.010432422178264,
              1.0012351739382697,
              0.997092422381088
            ],
            "cell_volume_ratio": 1.0087389424456468,
            "cell_rmsd_from_input_A": 0.09231070655823886
          },
          {
            "iteration": 2,
            "reduced_polarization": [
              -0.49613227735098553,
              -0.0009436388611724835,
              -1.0591259839480395e-09
            ],
            "branch_aligned_reduced_polarization": [
              -0.49613227735098553,
              -0.0009436388611724835,
              -1.0591259839480395e-09
            ],
            "target_residual": 0.003981172288411485,
            "energy_eV": -99.89042244975522,
            "max_atomic_step_A": 0.0015336378814513221,
            "max_log_strain_component": 8.173984250954665e-05,
            "step_scale": 1.0,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 0.8879598758982391,
            "cell_principal_stretches": [
              1.0105503437275964,
              1.0012513842512119,
              0.9970737092050579
            ],
            "cell_volume_ratio": 1.008854065795449,
            "cell_rmsd_from_input_A": 0.09340618046546452
          },
          {
            "iteration": 3,
            "reduced_polarization": [
              -0.5000143467956877,
              4.668868871570487e-06,
              4.220728030955188e-12
            ],
            "branch_aligned_reduced_polarization": [
              -0.5000143467956877,
              4.668868871570487e-06,
              4.220728030955188e-12
            ],
            "target_residual": 1.5087374955372282e-05,
            "energy_eV": -99.7404839737381
          }
        ],
        "iterations": 3
      },
      "parent": {
        "candidate_id": "bec_projection_02",
        "source": "MACEField_BEC_backprojection",
        "spacegroup": "Cc",
        "spacegroup_number": 9,
        "pointgroup": "m",
        "has_inversion": false,
        "is_polar_point_group": true,
        "nonpolar_parent_hypothesis": false,
        "symmetry_tolerance_A": null,
        "target_reduced_polarization": [
          -0.5,
          0.0,
          0.0
        ],
        "formal_class": [
          0.5,
          0.0,
          0.0
        ],
        "target_residual": 1.5087374955372282e-05,
        "parent_symmetrization_rmsd_A": 0.1285347020382321,
        "parent_cell_rmsd_A": 0.09340618046546452,
        "energy_eV": -99.7404839737381,
        "reduced_polarization": [
          -0.5000143467956877,
          4.668868871570487e-06,
          4.220728030955188e-12
        ],
        "cartesian_polarization_e_A2": [
          -0.007303963368076855,
          4.56628617048045e-05,
          -9.09828805417196e-12
        ],
        "ranking_score": 0.651916421904509
      },
      "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": [
              -2.5866510952592177e-09,
              -0.06952051018296006,
              2.1936751333612826e-09
            ],
            "branch_aligned_reduced_polarization": [
              -2.5866511155214766e-09,
              -0.06952051018296007,
              2.1936751333612826e-09
            ],
            "target_residual": 0.659782228137806,
            "energy_eV": -109.2025273333989,
            "max_atomic_step_A": 0.12000000000000001,
            "max_log_strain_component": 0.011827283054903756,
            "step_scale": 0.354908189416304,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 0.8879598758982391,
            "cell_principal_stretches": [
              0.9981073975127178,
              0.9976601155328808,
              0.987799625328263
            ],
            "cell_volume_ratio": 0.9836231507426534,
            "cell_rmsd_from_input_A": 0.133820543096002
          },
          {
            "iteration": 1,
            "reduced_polarization": [
              -0.17636029393856653,
              -0.2260202829780516,
              1.4471876058735667e-09
            ],
            "branch_aligned_reduced_polarization": [
              -0.17636029393856656,
              -0.2260202829780516,
              1.4471876058735667e-09
            ],
            "target_residual": 0.42403719728221717,
            "energy_eV": -107.00973338575872,
            "max_atomic_step_A": 0.12,
            "max_log_strain_component": 0.009931402451791688,
            "step_scale": 0.5655514787194551,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 0.8879598758982391,
            "cell_principal_stretches": [
              0.9966915567838461,
              0.9956995375111788,
              0.9775026236629096
            ],
            "cell_volume_ratio": 0.9700788061200603,
            "cell_rmsd_from_input_A": 0.24423167854680305
          },
          {
            "iteration": 2,
            "reduced_polarization": [
              -0.36375828222340517,
              -0.3844921124480011,
              3.205864059278775e-09
            ],
            "branch_aligned_reduced_polarization": [
              -0.36375828222340517,
              -0.3844921124480011,
              3.205864059278775e-09
            ],
            "target_residual": 0.17861656627939793,
            "energy_eV": -101.96677936111718,
            "max_atomic_step_A": 0.07737423537261348,
            "max_log_strain_component": 0.006895817791715295,
            "step_scale": 1.0,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 0.8879598758982391,
            "cell_principal_stretches": [
              0.9957457167812629,
              0.9943404871611962,
              0.9703810177310868
            ],
            "cell_volume_ratio": 0.9607842222524023,
            "cell_rmsd_from_input_A": 0.3196688248215565
          },
          {
            "iteration": 3,
            "reduced_polarization": [
              -0.49416038810933766,
              -0.47659614934119865,
              2.054510360074451e-09
            ],
            "branch_aligned_reduced_polarization": [
              -0.49416038810933766,
              -0.47659614934119865,
              2.054510360074451e-09
            ],
            "target_residual": 0.024121386624591998,
            "energy_eV": -98.58797669890896,
            "max_atomic_step_A": 0.015439511023119313,
            "max_log_strain_component": 0.002781573935582425,
            "step_scale": 1.0,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 0.8879598758982391,
            "cell_principal_stretches": [
              0.9951413891945726,
              0.9937928106496737,
              0.9677399406759608
            ],
            "cell_volume_ratio": 0.9570603092978454,
            "cell_rmsd_from_input_A": 0.34911645558620935
          },
          {
            "iteration": 4,
            "reduced_polarization": [
              -0.49835689064217065,
              -0.49780322868702503,
              5.703289328589118e-11
            ],
            "branch_aligned_reduced_polarization": [
              -0.49835689064217065,
              -0.49780322868702503,
              5.703289328589118e-11
            ],
            "target_residual": 0.002743284994909597,
            "energy_eV": -98.63027252657085,
            "max_atomic_step_A": 0.0018181357250976408,
            "max_log_strain_component": 6.39786764038591e-05,
            "step_scale": 1.0,
            "strain_jacobian_refreshed": true,
            "strain_jacobian_frobenius_norm": 0.817651086340293,
            "cell_principal_stretches": [
              0.9951732275922123,
              0.9938563942322921,
              0.9676709406226423
            ],
            "cell_volume_ratio": 0.957083919562344,
            "cell_rmsd_from_input_A": 0.34973496541193827
          },
          {
            "iteration": 5,
            "reduced_polarization": [
              -0.4999995633070184,
              -0.49999151330417974,
              -8.987665222587203e-13
            ],
            "branch_aligned_reduced_polarization": [
              -0.4999995633070184,
              -0.49999151330417974,
              -8.987665222587203e-13
            ],
            "target_residual": 8.497923670278674e-06,
            "energy_eV": -98.62429507778661
          }
        ],
        "iterations": 5
      },
      "parent": {
        "candidate_id": "bec_projection_03",
        "source": "MACEField_BEC_backprojection",
        "spacegroup": "Cc",
        "spacegroup_number": 9,
        "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": 8.497923670278674e-06,
        "parent_symmetrization_rmsd_A": 0.24418315550731262,
        "parent_cell_rmsd_A": 0.34973496541193827,
        "energy_eV": -98.62429507778661,
        "reduced_polarization": [
          -0.4999995633070184,
          -0.49999151330417974,
          -8.987665222587203e-13
        ],
        "cartesian_polarization_e_A2": [
          -0.007555070537252732,
          -0.014077583905550507,
          5.0228621405053165e-11
        ],
        "ranking_score": 0.8316338927076377
      },
      "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
        ],
        "endpoint_rmsd_A": 0.032720020661631544,
        "minimum_distance_A_by_image": [
          1.4715287724408768,
          1.468352637612021,
          1.4652146503485166,
          1.4621152474414836,
          1.459054866879335,
          1.4560339477449784,
          1.4530529301099577,
          1.4501122549255205,
          1.4472123638807923
        ],
        "minimum_distance_A": 1.4472123638807923,
        "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": [
          437.1064046078854,
          437.5171348286172,
          437.928250994997,
          438.3397534696806,
          438.7516426156647,
          439.1639187962894,
          439.57658237523333,
          439.98963371651865,
          440.403073184509
        ],
        "cell_deformation_log_strain_norm": 0.005588965440882664
      },
      "parent_reduced_polarization": [
        3.712396912989498e-11,
        -0.0006548846709652044,
        -6.376669097510447e-12
      ],
      "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": [
          -109.20252733339888,
          -109.20428367622485,
          -109.19901170449107,
          -109.18673212458275,
          -109.16747315867416,
          -109.14127069094947,
          -109.10816852861855,
          -109.0682187843627,
          -109.0214823819855
        ],
        "cartesian_polarizations_e_A2": [
          [
            -5.421411519153226e-11,
            -0.0019395551657579908,
            2.7961175848430736e-11
          ],
          [
            -4.7406227917782074e-11,
            -0.0016979275660096288,
            2.4450683156735226e-11
          ],
          [
            -4.058392274581167e-11,
            -0.0014566674826022039,
            2.0942090333491786e-11
          ],
          [
            -3.374809709120089e-11,
            -0.001215810152044219,
            1.7435066103056457e-11
          ],
          [
            -2.6899873535296896e-11,
            -0.0009753855127551905,
            1.3929450162785454e-11
          ],
          [
            -2.004048972195592e-11,
            -0.000735414588299538,
            1.042512898357727e-11
          ],
          [
            -1.3171432134493675e-11,
            -0.0004959061123401785,
            6.9220495776047135e-12
          ],
          [
            -6.294352644382845e-12,
            -0.000256853433270648,
            3.4201075594025974e-12
          ],
          [
            5.890595065645531e-13,
            -1.8231740731221398e-05,
            -8.068815357729376e-14
          ]
        ],
        "raw_reduced_polarization": [
          [
            -2.5866534620593444e-09,
            -0.06952051018295896,
            2.1936728766411396e-09
          ],
          [
            -2.263307816880919e-09,
            -0.06087594381967386,
            1.919743971713906e-09
          ],
          [
            -1.9384758291028225e-09,
            -0.05223994466215635,
            1.645539015592332e-09
          ],
          [
            -1.612228376437387e-09,
            -0.04361378541510243,
            1.3710317640780796e-09
          ],
          [
            -1.2846451671395734e-09,
            -0.03499855003096158,
            1.0962093413432733e-09
          ],
          [
            -9.55812164387127e-10,
            -0.026395003646973864,
            8.210625123253572e-10
          ],
          [
            -6.258302140657502e-10,
            -0.017803470992371447,
            5.455867852582532e-10
          ],
          [
            -2.94813834010488e-10,
            -0.009223724644861172,
            2.697736021564068e-10
          ],
          [
            3.712396912989498e-11,
            -0.0006548846709652044,
            -6.376669097510447e-12
          ]
        ],
        "unwrapped_reduced_polarization": [
          [
            -2.5866534620593444e-09,
            -0.06952051018295896,
            2.1936728766411396e-09
          ],
          [
            -2.263307816880919e-09,
            -0.06087594381967386,
            1.919743971713906e-09
          ],
          [
            -1.9384758291028225e-09,
            -0.05223994466215635,
            1.645539015592332e-09
          ],
          [
            -1.612228376437387e-09,
            -0.04361378541510243,
            1.3710317640780796e-09
          ],
          [
            -1.2846451671395734e-09,
            -0.03499855003096158,
            1.0962093413432733e-09
          ],
          [
            -9.55812164387127e-10,
            -0.026395003646973864,
            8.210625123253572e-10
          ],
          [
            -6.258302140657502e-10,
            -0.017803470992371447,
            5.455867852582532e-10
          ],
          [
            -2.94813834010488e-10,
            -0.009223724644861172,
            2.697736021564068e-10
          ],
          [
            3.7123969129894996e-11,
            -0.000654884670965205,
            -6.376669097510472e-12
          ]
        ],
        "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": [
          [
            -2.5866534469898284e-09,
            -0.06952051018295896,
            2.193672909989175e-09
          ],
          [
            -2.263307818939353e-09,
            -0.06087594381967387,
            1.919743919387429e-09
          ],
          [
            -1.9384758243035094e-09,
            -0.05223994466215637,
            1.6455390383640633e-09
          ],
          [
            -1.61222835082242e-09,
            -0.04361378541510241,
            1.37103173258879e-09
          ],
          [
            -1.284645168020404e-09,
            -0.034998550030961584,
            1.096209345519128e-09
          ],
          [
            -9.558121516484164e-10,
            -0.02639500364697389,
            8.210625512816705e-10
          ],
          [
            -6.258302209793953e-10,
            -0.01780347099237145,
            5.455867979620166e-10
          ],
          [
            -2.948138400071798e-10,
            -0.009223724644861153,
            2.697736478651791e-10
          ],
          [
            3.712397056432337e-11,
            -0.0006548846709651945,
            -6.376676964237049e-12
          ]
        ]
      },
      "reflected": {
        "reached": true,
        "construction": "reflect_displacements_about_reconstructed_parent",
        "energies_eV": [
          -109.02148238198554,
          -108.97034003280771,
          -108.91258513239323,
          -108.84831441201273,
          -108.77763541221772,
          -108.7006664379631,
          -108.61753631695969,
          -108.5283839181386,
          -108.43335738933186
        ],
        "cartesian_polarizations_e_A2": [
          [
            5.890866818032463e-13,
            -1.8231740731289998e-05,
            -8.067167303148148e-14
          ],
          [
            7.455300136822265e-12,
            0.00019786797265203507,
            -3.645438055930516e-12
          ],
          [
            1.4330894942814804e-11,
            0.0004143171914052895,
            -7.217688251201576e-12
          ],
          [
            2.1214019556980945e-11,
            0.0006312285389652258,
            -1.079807198973673e-11
          ],
          [
            2.8102721288216776e-11,
            0.0008487400957305465,
            -1.4387516915464789e-11
          ],
          [
            3.499484413800177e-11,
            0.0010670143017685366,
            -1.798670334976873e-11
          ],
          [
            4.188824540066078e-11,
            0.0012862354529975786,
            -2.1596090501203777e-11
          ],
          [
            4.878062173642888e-11,
            0.001506605534871801,
            -2.5216245588096676e-11
          ],
          [
            5.5669399711775626e-11,
            0.0017283381536794408,
            -2.8847308732661776e-11
          ]
        ],
        "raw_reduced_polarization": [
          [
            3.712647811687265e-11,
            -0.0006548846709676685,
            -6.375367765094404e-12
          ],
          [
            3.653290203078758e-10,
            0.007105529688817493,
            -2.875670113946163e-10
          ],
          [
            6.934306011606176e-10,
            0.014874356083284059,
            -5.689114073992877e-10
          ],
          [
            1.0212790874533072e-09,
            0.022655628339636493,
            -8.504588495192444e-10
          ],
          [
            1.3487050713324165e-09,
            0.030454289422242167,
            -1.1322813552383561e-09
          ],
          [
            1.6755356616433271e-09,
            0.03827615085622823,
            -1.414431275817282e-09
          ],
          [
            2.0016082339774288e-09,
            0.046127801773307366,
            -1.696943439322209e-09
          ],
          [
            2.3267456646624976e-09,
            0.054016458496407564,
            -1.979861066962789e-09
          ],
          [
            2.650769960937107e-09,
            0.061949746175696284,
            -2.2631937610193447e-09
          ]
        ],
        "unwrapped_reduced_polarization": [
          [
            3.712647811687265e-11,
            -0.0006548846709676685,
            -6.375367765094404e-12
          ],
          [
            3.653290203078758e-10,
            0.007105529688817493,
            -2.875670113946163e-10
          ],
          [
            6.934306011606176e-10,
            0.014874356083284059,
            -5.689114073992877e-10
          ],
          [
            1.0212790874533072e-09,
            0.022655628339636493,
            -8.504588495192444e-10
          ],
          [
            1.3487050713324165e-09,
            0.030454289422242167,
            -1.1322813552383561e-09
          ],
          [
            1.6755356616433271e-09,
            0.03827615085622823,
            -1.414431275817282e-09
          ],
          [
            2.0016082339774288e-09,
            0.046127801773307366,
            -1.696943439322209e-09
          ],
          [
            2.3267456646624976e-09,
            0.054016458496407564,
            -1.979861066962789e-09
          ],
          [
            2.650769960937107e-09,
            0.061949746175696284,
            -2.2631937610193447e-09
          ]
        ],
        "gauge_integer_shift": [
          0,
          0,
          0
        ],
        "expected_opposite_endpoint_reduced_polarization": [
          2.66036851226316e-09,
          0.06821353017070177,
          -2.2063335326112785e-09
        ],
        "actual_opposite_endpoint_branch_residual": 0.006263783995005483
      },
      "pnp_branch": {
        "construction": "incoming_path_concatenated_with_parent_reflection",
        "reduced_polarization": [
          [
            -2.5866534620593444e-09,
            -0.06952051018295896,
            2.1936728766411396e-09
          ],
          [
            -2.263307816880919e-09,
            -0.06087594381967386,
            1.919743971713906e-09
          ],
          [
            -1.9384758291028225e-09,
            -0.05223994466215635,
            1.645539015592332e-09
          ],
          [
            -1.612228376437387e-09,
            -0.04361378541510243,
            1.3710317640780796e-09
          ],
          [
            -1.2846451671395734e-09,
            -0.03499855003096158,
            1.0962093413432733e-09
          ],
          [
            -9.55812164387127e-10,
            -0.026395003646973864,
            8.210625123253572e-10
          ],
          [
            -6.258302140657502e-10,
            -0.017803470992371447,
            5.455867852582532e-10
          ],
          [
            -2.94813834010488e-10,
            -0.009223724644861172,
            2.697736021564068e-10
          ],
          [
            3.712396912989498e-11,
            -0.0006548846709652044,
            -6.376669097510447e-12
          ],
          [
            3.653290203078758e-10,
            0.007105529688817493,
            -2.875670113946163e-10
          ],
          [
            6.934306011606176e-10,
            0.014874356083284059,
            -5.689114073992877e-10
          ],
          [
            1.0212790874533072e-09,
            0.022655628339636493,
            -8.504588495192444e-10
          ],
          [
            1.3487050713324165e-09,
            0.030454289422242167,
            -1.1322813552383561e-09
          ],
          [
            1.6755356616433271e-09,
            0.03827615085622823,
            -1.414431275817282e-09
          ],
          [
            2.0016082339774288e-09,
            0.046127801773307366,
            -1.696943439322209e-09
          ],
          [
            2.3267456646624976e-09,
            0.054016458496407564,
            -1.979861066962789e-09
          ],
          [
            2.650769960937107e-09,
            0.061949746175696284,
            -2.2631937610193447e-09
          ]
        ],
        "unwrapped_reduced_polarization": [
          [
            -2.5866534620593444e-09,
            -0.06952051018295896,
            2.1936728766411396e-09
          ],
          [
            -2.263307816880919e-09,
            -0.06087594381967386,
            1.919743971713906e-09
          ],
          [
            -1.9384758291028225e-09,
            -0.05223994466215635,
            1.645539015592332e-09
          ],
          [
            -1.612228376437387e-09,
            -0.04361378541510243,
            1.3710317640780796e-09
          ],
          [
            -1.2846451671395734e-09,
            -0.03499855003096158,
            1.0962093413432733e-09
          ],
          [
            -9.55812164387127e-10,
            -0.026395003646973864,
            8.210625123253572e-10
          ],
          [
            -6.258302140657502e-10,
            -0.017803470992371447,
            5.455867852582532e-10
          ],
          [
            -2.94813834010488e-10,
            -0.009223724644861172,
            2.697736021564068e-10
          ],
          [
            3.7123969129894996e-11,
            -0.000654884670965205,
            -6.376669097510472e-12
          ],
          [
            3.653290203078758e-10,
            0.007105529688817493,
            -2.875670113946163e-10
          ],
          [
            6.934306011606176e-10,
            0.014874356083284059,
            -5.689114073992877e-10
          ],
          [
            1.0212790874533072e-09,
            0.022655628339636493,
            -8.504588495192444e-10
          ],
          [
            1.3487050713324165e-09,
            0.030454289422242167,
            -1.1322813552383561e-09
          ],
          [
            1.6755356616433271e-09,
            0.03827615085622823,
            -1.414431275817282e-09
          ],
          [
            2.0016082339774288e-09,
            0.046127801773307366,
            -1.696943439322209e-09
          ],
          [
            2.3267456646624976e-09,
            0.054016458496407564,
            -1.979861066962789e-09
          ],
          [
            2.650769960937107e-09,
            0.061949746175696284,
            -2.2631937610193447e-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": [
          [
            -2.5866534469898284e-09,
            -0.06952051018295896,
            2.193672909989175e-09
          ],
          [
            -2.263307818939353e-09,
            -0.06087594381967387,
            1.919743919387429e-09
          ],
          [
            -1.9384758243035094e-09,
            -0.05223994466215637,
            1.6455390383640633e-09
          ],
          [
            -1.61222835082242e-09,
            -0.04361378541510241,
            1.37103173258879e-09
          ],
          [
            -1.284645168020404e-09,
            -0.034998550030961584,
            1.096209345519128e-09
          ],
          [
            -9.558121516484164e-10,
            -0.02639500364697389,
            8.210625512816705e-10
          ],
          [
            -6.258302209793953e-10,
            -0.01780347099237145,
            5.455867979620166e-10
          ],
          [
            -2.948138400071798e-10,
            -0.009223724644861153,
            2.697736478651791e-10
          ],
          [
            3.712397056432337e-11,
            -0.0006548846709651945,
            -6.376676964237049e-12
          ],
          [
            3.6532898928243185e-10,
            0.007105529688817502,
            -2.875670257473928e-10
          ],
          [
            6.934306462369477e-10,
            0.014874356083284024,
            -5.689114179752153e-10
          ],
          [
            1.0212790613195466e-09,
            0.022655628339636524,
            -8.504588699942417e-10
          ],
          [
            1.3487050365412756e-09,
            0.030454289422242153,
            -1.132281379767619e-09
          ],
          [
            1.6755357101772006e-09,
            0.038276150856228264,
            -1.4144312943109583e-09
          ],
          [
            2.001608212509609e-09,
            0.04612780177330733,
            -1.6969434191160815e-09
          ],
          [
            2.3267456850106782e-09,
            0.05401645849640757,
            -1.979861052880949e-09
          ],
          [
            2.6507699368849558e-09,
            0.06194974617569626,
            -2.2631937435235727e-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_3mc",
        "spacegroup_number": 186,
        "pointgroup": "6mm",
        "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": 0.000654884670964318,
        "parent_symmetrization_rmsd_A": 0.032720020661631544,
        "parent_cell_rmsd_A": 0.061298904763691126,
        "energy_eV": -109.02148238198552,
        "reduced_polarization": [
          3.712705661942782e-11,
          -0.0006548846709643169,
          -6.375327953778243e-12
        ],
        "cartesian_polarization_e_A2": [
          5.890948504701358e-13,
          -1.8231740731196692e-05,
          -8.067116884652355e-14
        ],
        "ranking_score": 0.549354516194483
      }
    }
  ],
  "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": 74,
      "full_response": 15,
      "energy_polarization": 59
    },
    "model_evaluations_for_recovery_and_path_properties": {
      "total": 99,
      "full_response": 40,
      "energy_polarization": 59
    },
    "elapsed_seconds": 237.985873470956
  }
}