{
  "schema": "ferrofinder.endpoint_parent_recovery.v4_variable_cell",
  "status": "complete",
  "input_atom_count": 80,
  "input_formula": "Cs20N40Na4W16",
  "input_spacegroup": "I4_1",
  "input_pointgroup": "4",
  "input_is_polar_point_group": true,
  "input_energy_eV": -583.9498401770968,
  "input_cartesian_polarization_e_A2": [
    -0.0005215581414258504,
    -1.2543669894818928e-08,
    -1.0456814226161247e-08
  ],
  "input_reduced_polarization": [
    -0.1056944262051161,
    -1.6001675710785093e-06,
    -1.333952117825338e-06
  ],
  "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": [
        0.5,
        0.0,
        0.0
      ],
      "target_reduced_polarization": [
        -0.5,
        0.0,
        0.0
      ]
    },
    {
      "orbit_id": 2,
      "representative_formal_class": [
        0.0,
        0.5,
        0.0
      ],
      "target_reduced_polarization": [
        0.0,
        -0.5,
        0.0
      ]
    },
    {
      "orbit_id": 3,
      "representative_formal_class": [
        0.5,
        0.5,
        0.0
      ],
      "target_reduced_polarization": [
        -0.5,
        -0.5,
        0.0
      ]
    },
    {
      "orbit_id": 4,
      "representative_formal_class": [
        0.0,
        0.5,
        0.5
      ],
      "target_reduced_polarization": [
        0.0,
        -0.5,
        -0.5
      ]
    },
    {
      "orbit_id": 5,
      "representative_formal_class": [
        0.5,
        0.5,
        0.5
      ],
      "target_reduced_polarization": [
        -0.5,
        -0.5,
        -0.5
      ]
    }
  ],
  "parent_candidates": [
    {
      "candidate_id": "inversion_parent_endpoint_00",
      "source": "same_species_inversion_center_projection_from_endpoint",
      "spacegroup": "I4_1/a",
      "spacegroup_number": 88,
      "pointgroup": "4/m",
      "has_inversion": true,
      "is_polar_point_group": false,
      "nonpolar_parent_hypothesis": true,
      "symmetry_tolerance_A": null,
      "target_reduced_polarization": [
        0.0,
        0.0,
        0.0
      ],
      "formal_class": [
        0.0,
        0.0,
        0.0
      ],
      "target_residual": 3.889824798023194e-15,
      "parent_symmetrization_rmsd_A": 0.20080611766342815,
      "parent_cell_rmsd_A": 0.0,
      "energy_eV": -583.7531044960523,
      "reduced_polarization": [
        -1.0530839295310707e-16,
        2.0394226806853488e-15,
        -3.31064982008004e-15
      ],
      "cartesian_polarization_e_A2": [
        -5.196532274897486e-19,
        1.598697870453756e-17,
        -2.595209353757627e-17
      ],
      "ranking_score": 0.20080611766343592
    },
    {
      "candidate_id": "bec_projection_00",
      "source": "MACEField_BEC_backprojection",
      "spacegroup": "I4_1",
      "spacegroup_number": 80,
      "pointgroup": "4",
      "has_inversion": false,
      "is_polar_point_group": true,
      "nonpolar_parent_hypothesis": false,
      "symmetry_tolerance_A": null,
      "target_reduced_polarization": [
        0.0,
        0.0,
        0.0
      ],
      "formal_class": [
        0.0,
        0.0,
        0.0
      ],
      "target_residual": 7.5632851194438e-05,
      "parent_symmetrization_rmsd_A": 0.0030039967740152734,
      "parent_cell_rmsd_A": 0.00025014463722437005,
      "energy_eV": -583.9331908145834,
      "reduced_polarization": [
        7.563285118379384e-05,
        -1.1861915090488696e-09,
        -4.5060465327242396e-10
      ],
      "cartesian_polarization_e_A2": [
        3.73208236243941e-07,
        -9.297029335134691e-12,
        -3.5330887015946725e-12
      ],
      "ranking_score": 0.5032177986357103
    },
    {
      "candidate_id": "inversion_parent_bec_00_00",
      "source": "same_species_inversion_center_projection_after_BEC",
      "spacegroup": "I4_1/a",
      "spacegroup_number": 88,
      "pointgroup": "4/m",
      "has_inversion": true,
      "is_polar_point_group": false,
      "nonpolar_parent_hypothesis": true,
      "symmetry_tolerance_A": null,
      "target_reduced_polarization": [
        0.0,
        0.0,
        0.0
      ],
      "formal_class": [
        0.0,
        0.0,
        0.0
      ],
      "target_residual": 6.798018229045038e-15,
      "parent_symmetrization_rmsd_A": 0.2008061610665675,
      "parent_cell_rmsd_A": 0.00025014463722437005,
      "energy_eV": -583.7521795072346,
      "reduced_polarization": [
        -5.866551354617477e-15,
        2.06669543959508e-15,
        2.7432457064618485e-15
      ],
      "cartesian_polarization_e_A2": [
        -2.8948337221007907e-17,
        1.6201286934671796e-17,
        2.1504915770833222e-17
      ],
      "ranking_score": 0.2008686972258872
    },
    {
      "candidate_id": "bec_projection_01",
      "source": "MACEField_BEC_backprojection",
      "spacegroup": "I4_1",
      "spacegroup_number": 80,
      "pointgroup": "4",
      "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": 9.52093306561011e-08,
      "parent_symmetrization_rmsd_A": 0.01127729957797656,
      "parent_cell_rmsd_A": 0.0009393736951361244,
      "energy_eV": -583.7282694952075,
      "reduced_polarization": [
        -0.5000000952093304,
        -1.1680619682254246e-12,
        -6.608013190890271e-12
      ],
      "cartesian_polarization_e_A2": [
        -0.0024675041569014377,
        -8.124852547388128e-13,
        1.107562538974822e-11
      ],
      "ranking_score": 0.5115123334204219
    },
    {
      "candidate_id": "bec_projection_02",
      "source": "MACEField_BEC_backprojection",
      "spacegroup": "P1",
      "spacegroup_number": 1,
      "pointgroup": "1",
      "has_inversion": false,
      "is_polar_point_group": true,
      "nonpolar_parent_hypothesis": false,
      "symmetry_tolerance_A": null,
      "target_reduced_polarization": [
        0.0,
        -0.5,
        0.0
      ],
      "formal_class": [
        0.0,
        0.5,
        0.0
      ],
      "target_residual": 7.5467806191014225e-06,
      "parent_symmetrization_rmsd_A": 0.022298932077071527,
      "parent_cell_rmsd_A": 0.010502375003294533,
      "energy_eV": -583.0796008074033,
      "reduced_polarization": [
        -2.862974762726614e-06,
        -0.4999935243212123,
        -2.6120600030219443e-06
      ],
      "cartesian_polarization_e_A2": [
        1.3223724638035713e-06,
        -0.0039195627928415,
        -1.9763629912153335e-08
      ],
      "ranking_score": 0.5249396193891334
    },
    {
      "candidate_id": "bec_projection_03",
      "source": "MACEField_BEC_backprojection",
      "spacegroup": "P1",
      "spacegroup_number": 1,
      "pointgroup": "1",
      "has_inversion": false,
      "is_polar_point_group": true,
      "nonpolar_parent_hypothesis": false,
      "symmetry_tolerance_A": null,
      "target_reduced_polarization": [
        -0.5,
        -0.5,
        0.0
      ],
      "formal_class": [
        0.5,
        0.5,
        0.0
      ],
      "target_residual": 1.6443541384564432e-05,
      "parent_symmetrization_rmsd_A": 0.025016037139033425,
      "parent_cell_rmsd_A": 0.010593742881722905,
      "energy_eV": -582.8440434360498,
      "reduced_polarization": [
        -0.4999899290423793,
        -0.4999875799994685,
        3.835290427921476e-06
      ],
      "cartesian_polarization_e_A2": [
        -0.00246611301150692,
        -0.003918058130594876,
        -2.588270904318273e-06
      ],
      "ranking_score": 0.5276973599422333
    },
    {
      "candidate_id": "bec_projection_04",
      "source": "MACEField_BEC_backprojection",
      "spacegroup": "P1",
      "spacegroup_number": 1,
      "pointgroup": "1",
      "has_inversion": false,
      "is_polar_point_group": true,
      "nonpolar_parent_hypothesis": false,
      "symmetry_tolerance_A": null,
      "target_reduced_polarization": [
        0.0,
        -0.5,
        -0.5
      ],
      "formal_class": [
        0.0,
        0.5,
        0.5
      ],
      "target_residual": 6.864357705272066e-05,
      "parent_symmetrization_rmsd_A": 0.031901908826682826,
      "parent_cell_rmsd_A": 0.01512501613803386,
      "energy_eV": -582.1431407929381,
      "reduced_polarization": [
        -2.8937267481804485e-05,
        -0.4999617792750898,
        -0.4999508700558863
      ],
      "cartesian_polarization_e_A2": [
        2.6294905788786712e-06,
        -0.00391931744314982,
        -0.003919229321144302
      ],
      "ranking_score": 0.5358204500152968
    },
    {
      "candidate_id": "bec_projection_05",
      "source": "MACEField_BEC_backprojection",
      "spacegroup": "P1",
      "spacegroup_number": 1,
      "pointgroup": "1",
      "has_inversion": false,
      "is_polar_point_group": true,
      "nonpolar_parent_hypothesis": false,
      "symmetry_tolerance_A": null,
      "target_reduced_polarization": [
        -0.5,
        -0.5,
        -0.5
      ],
      "formal_class": [
        0.5,
        0.5,
        0.5
      ],
      "target_residual": 0.00010078600375951552,
      "parent_symmetrization_rmsd_A": 0.034019256711356395,
      "parent_cell_rmsd_A": 0.015235761712312966,
      "energy_eV": -581.8741717788834,
      "reduced_polarization": [
        -0.49995540848646763,
        -0.49996158237262545,
        -0.49991818617854167
      ],
      "cartesian_polarization_e_A2": [
        -0.0024644990683579714,
        -0.0039151470627493065,
        -0.003920130643880572
      ],
      "ranking_score": 0.5380297691469537
    }
  ],
  "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": [
              -0.1056944262051161,
              -1.6001675710785093e-06,
              -1.333952117825338e-06
            ],
            "branch_aligned_reduced_polarization": [
              -0.1056944262051161,
              -1.6001675710785093e-06,
              -1.333952117825338e-06
            ],
            "target_residual": 0.10569442622564681,
            "energy_eV": -583.9498401770968,
            "max_atomic_step_A": 0.004118967560838911,
            "max_log_strain_component": 4.336515517136741e-05,
            "step_scale": 1.0,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 0.5911270001239367,
            "cell_principal_stretches": [
              1.0000113945004163,
              1.0000113937045292,
              0.9999566357845989
            ],
            "cell_volume_ratio": 0.9999794231311716,
            "cell_rmsd_from_input_A": 0.00025014463722437005
          },
          {
            "iteration": 1,
            "reduced_polarization": [
              7.563285118379384e-05,
              -1.1861915090488696e-09,
              -4.5060465327242396e-10
            ],
            "branch_aligned_reduced_polarization": [
              7.563285118379384e-05,
              -1.1861915090488696e-09,
              -4.5060465327242396e-10
            ],
            "target_residual": 7.5632851194438e-05,
            "energy_eV": -583.9331908145834
          }
        ],
        "iterations": 1
      },
      "parent": {
        "candidate_id": "inversion_parent_endpoint_00",
        "source": "same_species_inversion_center_projection_from_endpoint",
        "spacegroup": "I4_1/a",
        "spacegroup_number": 88,
        "pointgroup": "4/m",
        "has_inversion": true,
        "is_polar_point_group": false,
        "nonpolar_parent_hypothesis": true,
        "symmetry_tolerance_A": null,
        "target_reduced_polarization": [
          0.0,
          0.0,
          0.0
        ],
        "formal_class": [
          0.0,
          0.0,
          0.0
        ],
        "target_residual": 3.889824798023194e-15,
        "parent_symmetrization_rmsd_A": 0.20080611766342815,
        "parent_cell_rmsd_A": 0.0,
        "energy_eV": -583.7531044960523,
        "reduced_polarization": [
          -1.0530839295310707e-16,
          2.0394226806853488e-15,
          -3.31064982008004e-15
        ],
        "cartesian_polarization_e_A2": [
          -5.196532274897486e-19,
          1.598697870453756e-17,
          -2.595209353757627e-17
        ],
        "ranking_score": 0.20080611766343592
      },
      "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": [
          -583.9498401770969,
          -583.9724976367177,
          -583.956803163574,
          -583.9181183687667,
          -583.8700838267323,
          -583.8234393272093,
          -583.7856534706136,
          -583.7614075222741,
          -583.7531044960524
        ],
        "cartesian_polarizations_e_A2": [
          [
            -0.000521558141425837,
            -1.2543669894910631e-08,
            -1.045681423112088e-08
          ],
          [
            -0.0004687160995546307,
            -1.0873507448218977e-08,
            -8.996019243383373e-09
          ],
          [
            -0.0004113513435083075,
            -9.242209294976137e-09,
            -7.59487877410101e-09
          ],
          [
            -0.0003497479638880465,
            -7.646958018470707e-09,
            -6.2478142757693564e-09
          ],
          [
            -0.0002844876930885417,
            -6.07979495898572e-09,
            -4.9472942610328216e-09
          ],
          [
            -0.0002162857999249396,
            -4.5350028229652674e-09,
            -3.6829369095752223e-09
          ],
          [
            -0.0001457530090616121,
            -3.0098708773745393e-09,
            -2.4433011624775964e-09
          ],
          [
            -7.340296508402139e-05,
            -1.5004444292826902e-09,
            -1.2183326490775026e-09
          ],
          [
            -4.997841334974935e-18,
            2.3628937932327982e-17,
            1.1279531820218662e-17
          ]
        ],
        "raw_reduced_polarization": [
          [
            -0.10569442620511338,
            -1.6001675710902077e-06,
            -1.3339521184580274e-06
          ],
          [
            -0.09498591865537954,
            -1.3871087288184578e-06,
            -1.1476018089415847e-06
          ],
          [
            -0.0833608772781382,
            -1.1790077164777519e-06,
            -9.688614912936031e-07
          ],
          [
            -0.07087687339803558,
            -9.755051225965191e-07,
            -7.970195228381211e-07
          ],
          [
            -0.05765179583086892,
            -7.755856789721412e-07,
            -6.31115128783594e-07
          ],
          [
            -0.043830594719287026,
            -5.785200434089762e-07,
            -4.6982392381551485e-07
          ],
          [
            -0.029537034199717,
            -3.8396241383055654e-07,
            -3.1168639794881265e-07
          ],
          [
            -0.014875205006099599,
            -1.9140829901265678e-07,
            -1.5541993788000075e-07
          ],
          [
            -1.0128189557548826e-15,
            3.0142901188714618e-15,
            1.438904338762703e-15
          ]
        ],
        "unwrapped_reduced_polarization": [
          [
            -0.10569442620511338,
            -1.6001675710902077e-06,
            -1.3339521184580274e-06
          ],
          [
            -0.09498591865537954,
            -1.3871087288184578e-06,
            -1.1476018089415847e-06
          ],
          [
            -0.0833608772781382,
            -1.1790077164777519e-06,
            -9.688614912936031e-07
          ],
          [
            -0.07087687339803558,
            -9.755051225965191e-07,
            -7.970195228381211e-07
          ],
          [
            -0.05765179583086892,
            -7.755856789721412e-07,
            -6.31115128783594e-07
          ],
          [
            -0.043830594719287026,
            -5.785200434089762e-07,
            -4.6982392381551485e-07
          ],
          [
            -0.029537034199717,
            -3.8396241383055654e-07,
            -3.1168639794881265e-07
          ],
          [
            -0.014875205006099599,
            -1.9140829901265678e-07,
            -1.5541993788000075e-07
          ],
          [
            -1.0130785099704553e-15,
            3.0142901184471513e-15,
            1.4389043395189556e-15
          ]
        ],
        "berry_integer_shifts": [
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ]
        ],
        "folded_reduced_polarization": [
          [
            -0.10569442620511338,
            -1.6001675711141417e-06,
            -1.3339521184319025e-06
          ],
          [
            -0.09498591865537953,
            -1.3871087288230832e-06,
            -1.1476018089151552e-06
          ],
          [
            -0.08336087727813823,
            -1.179007716456404e-06,
            -9.688614913128113e-07
          ],
          [
            -0.07087687339803561,
            -9.755051225690536e-07,
            -7.970195228246268e-07
          ],
          [
            -0.057651795830868935,
            -7.755856789581905e-07,
            -6.311151287685668e-07
          ],
          [
            -0.04383059471928702,
            -5.785200434260673e-07,
            -4.69823923821e-07
          ],
          [
            -0.029537034199716983,
            -3.8396241380800333e-07,
            -3.116863979690798e-07
          ],
          [
            -0.014875205006099623,
            -1.9140829898844913e-07,
            -1.5541993786394315e-07
          ],
          [
            -9.992007221626409e-16,
            2.9976021664879227e-15,
            1.4432899320127035e-15
          ]
        ]
      },
      "reflected": {
        "reached": true,
        "construction": "reflect_displacements_about_reconstructed_parent",
        "energies_eV": [
          -583.7531044960524,
          -583.761407522274,
          -583.7856534706139,
          -583.8234393272094,
          -583.8700838267324,
          -583.918118368767,
          -583.9568031635738,
          -583.9724976367175,
          -583.9498401770969
        ],
        "cartesian_polarizations_e_A2": [
          [
            1.543675764013665e-18,
            1.0117954017594517e-17,
            -5.502210644009103e-19
          ],
          [
            7.340296508401082e-05,
            1.500444436618971e-09,
            1.2183326596463322e-09
          ],
          [
            0.00014575300906162063,
            3.009870880461891e-09,
            2.4433011796643627e-09
          ],
          [
            0.00021628579992492606,
            4.535002825257856e-09,
            3.6829368948644508e-09
          ],
          [
            0.00028448769308854873,
            6.079794959046855e-09,
            4.947294244908288e-09
          ],
          [
            0.0003497479638880598,
            7.646958027488218e-09,
            6.247814274485507e-09
          ],
          [
            0.0004113513435083206,
            9.24220929564863e-09,
            7.594878757380405e-09
          ],
          [
            0.00046871609955463563,
            1.0873507464542202e-08,
            8.996019212922524e-09
          ],
          [
            0.0005215581414258531,
            1.2543669923277584e-08,
            1.0456814210930824e-08
          ]
        ],
        "raw_reduced_polarization": [
          [
            3.1282787318422983e-16,
            1.2907244881584137e-15,
            -7.019045554940014e-17
          ],
          [
            0.014875205006097458,
            1.9140829994852953e-07,
            1.554199392282424e-07
          ],
          [
            0.029537034199718728,
            3.83962414224403e-07,
            3.1168640014128957e-07
          ],
          [
            0.04383059471928428,
            5.785200437014366e-07,
            4.69823921938895e-07
          ],
          [
            0.05765179583087035,
            7.7558567897994e-07,
            6.311151267266238e-07
          ],
          [
            0.07087687339803828,
            9.755051237468623e-07,
            7.970195226743434e-07
          ],
          [
            0.08336087727814087,
            1.1790077165635402e-06,
            9.688614891605933e-07
          ],
          [
            0.09498591865538054,
            1.3871087309007746e-06,
            1.1476018050557633e-06
          ],
          [
            0.10569442620511665,
            1.6001675747089156e-06,
            1.3339521158824276e-06
          ]
        ],
        "unwrapped_reduced_polarization": [
          [
            3.1282787318422983e-16,
            1.2907244881584137e-15,
            -7.019045554940014e-17
          ],
          [
            0.014875205006097458,
            1.9140829994852953e-07,
            1.554199392282424e-07
          ],
          [
            0.029537034199718728,
            3.83962414224403e-07,
            3.1168640014128957e-07
          ],
          [
            0.04383059471928428,
            5.785200437014366e-07,
            4.69823921938895e-07
          ],
          [
            0.05765179583087035,
            7.7558567897994e-07,
            6.311151267266238e-07
          ],
          [
            0.07087687339803828,
            9.755051237468623e-07,
            7.970195226743434e-07
          ],
          [
            0.08336087727814087,
            1.1790077165635402e-06,
            9.688614891605933e-07
          ],
          [
            0.09498591865538054,
            1.3871087309007746e-06,
            1.1476018050557633e-06
          ],
          [
            0.10569442620511665,
            1.6001675747089156e-06,
            1.3339521158824276e-06
          ]
        ],
        "gauge_integer_shift": [
          0,
          0,
          0
        ],
        "expected_opposite_endpoint_reduced_polarization": [
          0.10569442620511135,
          1.6001675771187879e-06,
          1.333952121335836e-06
        ],
        "actual_opposite_endpoint_branch_residual": 7.978163166642585e-15
      },
      "pnp_branch": {
        "construction": "incoming_path_concatenated_with_parent_reflection",
        "reduced_polarization": [
          [
            -0.10569442620511338,
            -1.6001675710902077e-06,
            -1.3339521184580274e-06
          ],
          [
            -0.09498591865537954,
            -1.3871087288184578e-06,
            -1.1476018089415847e-06
          ],
          [
            -0.0833608772781382,
            -1.1790077164777519e-06,
            -9.688614912936031e-07
          ],
          [
            -0.07087687339803558,
            -9.755051225965191e-07,
            -7.970195228381211e-07
          ],
          [
            -0.05765179583086892,
            -7.755856789721412e-07,
            -6.31115128783594e-07
          ],
          [
            -0.043830594719287026,
            -5.785200434089762e-07,
            -4.6982392381551485e-07
          ],
          [
            -0.029537034199717,
            -3.8396241383055654e-07,
            -3.1168639794881265e-07
          ],
          [
            -0.014875205006099599,
            -1.9140829901265678e-07,
            -1.5541993788000075e-07
          ],
          [
            -1.0128189557548826e-15,
            3.0142901188714618e-15,
            1.438904338762703e-15
          ],
          [
            0.014875205006097458,
            1.9140829994852953e-07,
            1.554199392282424e-07
          ],
          [
            0.029537034199718728,
            3.83962414224403e-07,
            3.1168640014128957e-07
          ],
          [
            0.04383059471928428,
            5.785200437014366e-07,
            4.69823921938895e-07
          ],
          [
            0.05765179583087035,
            7.7558567897994e-07,
            6.311151267266238e-07
          ],
          [
            0.07087687339803828,
            9.755051237468623e-07,
            7.970195226743434e-07
          ],
          [
            0.08336087727814087,
            1.1790077165635402e-06,
            9.688614891605933e-07
          ],
          [
            0.09498591865538054,
            1.3871087309007746e-06,
            1.1476018050557633e-06
          ],
          [
            0.10569442620511665,
            1.6001675747089156e-06,
            1.3339521158824276e-06
          ]
        ],
        "unwrapped_reduced_polarization": [
          [
            -0.10569442620511338,
            -1.6001675710902077e-06,
            -1.3339521184580274e-06
          ],
          [
            -0.09498591865537954,
            -1.3871087288184578e-06,
            -1.1476018089415847e-06
          ],
          [
            -0.0833608772781382,
            -1.1790077164777519e-06,
            -9.688614912936031e-07
          ],
          [
            -0.07087687339803558,
            -9.755051225965191e-07,
            -7.970195228381211e-07
          ],
          [
            -0.05765179583086892,
            -7.755856789721412e-07,
            -6.31115128783594e-07
          ],
          [
            -0.043830594719287026,
            -5.785200434089762e-07,
            -4.6982392381551485e-07
          ],
          [
            -0.029537034199717,
            -3.8396241383055654e-07,
            -3.1168639794881265e-07
          ],
          [
            -0.014875205006099599,
            -1.9140829901265678e-07,
            -1.5541993788000075e-07
          ],
          [
            -1.0130785099704553e-15,
            3.0142901184471513e-15,
            1.4389043395189556e-15
          ],
          [
            0.014875205006097458,
            1.9140829994852953e-07,
            1.554199392282424e-07
          ],
          [
            0.029537034199718728,
            3.83962414224403e-07,
            3.1168640014128957e-07
          ],
          [
            0.04383059471928428,
            5.785200437014366e-07,
            4.69823921938895e-07
          ],
          [
            0.05765179583087035,
            7.7558567897994e-07,
            6.311151267266238e-07
          ],
          [
            0.07087687339803828,
            9.755051237468623e-07,
            7.970195226743434e-07
          ],
          [
            0.08336087727814087,
            1.1790077165635402e-06,
            9.688614891605933e-07
          ],
          [
            0.09498591865538054,
            1.3871087309007746e-06,
            1.1476018050557633e-06
          ],
          [
            0.10569442620511665,
            1.6001675747089156e-06,
            1.3339521158824276e-06
          ]
        ],
        "berry_integer_shifts": [
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ]
        ],
        "folded_reduced_polarization": [
          [
            -0.10569442620511338,
            -1.6001675711141417e-06,
            -1.3339521184319025e-06
          ],
          [
            -0.09498591865537953,
            -1.3871087288230832e-06,
            -1.1476018089151552e-06
          ],
          [
            -0.08336087727813823,
            -1.179007716456404e-06,
            -9.688614913128113e-07
          ],
          [
            -0.07087687339803561,
            -9.755051225690536e-07,
            -7.970195228246268e-07
          ],
          [
            -0.057651795830868935,
            -7.755856789581905e-07,
            -6.311151287685668e-07
          ],
          [
            -0.04383059471928702,
            -5.785200434260673e-07,
            -4.69823923821e-07
          ],
          [
            -0.029537034199716983,
            -3.8396241380800333e-07,
            -3.116863979690798e-07
          ],
          [
            -0.014875205006099623,
            -1.9140829898844913e-07,
            -1.5541993786394315e-07
          ],
          [
            -9.992007221626409e-16,
            2.9976021664879227e-15,
            1.4432899320127035e-15
          ],
          [
            0.014875205006097403,
            1.9140829998764985e-07,
            1.5541993925172193e-07
          ],
          [
            0.02953703419971876,
            3.839624141965814e-07,
            3.116864001340147e-07
          ],
          [
            0.0438305947192843,
            5.785200436481119e-07,
            4.6982392198913203e-07
          ],
          [
            0.05765179583087032,
            7.755856790137017e-07,
            6.311151267146542e-07
          ],
          [
            0.07087687339803828,
            9.75505123790299e-07,
            7.970195227136045e-07
          ],
          [
            0.0833608772781409,
            1.1790077165674262e-06,
            9.688614891478764e-07
          ],
          [
            0.09498591865538053,
            1.3871087308769958e-06,
            1.1476018050293746e-06
          ],
          [
            0.10569442620511671,
            1.6001675746668553e-06,
            1.3339521158783896e-06
          ]
        ]
      },
      "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": [
        0.5,
        0.0,
        0.0
      ],
      "formal_classes_in_orbit": [
        [
          0.5,
          0.0,
          0.0
        ]
      ],
      "target_reduced_polarization": [
        -0.5,
        0.0,
        0.0
      ],
      "bec_backprojection": {
        "converged_to_target": true,
        "history": [
          {
            "iteration": 0,
            "reduced_polarization": [
              -0.1056944262051161,
              -1.6001675710785093e-06,
              -1.333952117825338e-06
            ],
            "branch_aligned_reduced_polarization": [
              -0.1056944262051161,
              -1.6001675710785093e-06,
              -1.333952117825338e-06
            ],
            "target_residual": 0.3943055738003872,
            "energy_eV": -583.9498401770968,
            "max_atomic_step_A": 0.015366250048991366,
            "max_log_strain_component": 0.00016177884703193174,
            "step_scale": 1.0,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 0.5911270001239367,
            "cell_principal_stretches": [
              1.0001617919340344,
              0.999957495583309,
              0.999957492613017
            ],
            "cell_volume_ratio": 1.0000767681831804,
            "cell_rmsd_from_input_A": 0.0009332725194916739
          },
          {
            "iteration": 1,
            "reduced_polarization": [
              -0.497498736316903,
              -6.738850931950592e-09,
              -8.817075125125945e-09
            ],
            "branch_aligned_reduced_polarization": [
              -0.497498736316903,
              -6.738850931950592e-09,
              -8.817075125125945e-09
            ],
            "target_residual": 0.002501263683121617,
            "energy_eV": -583.7310951200892,
            "max_atomic_step_A": 0.00010190601015529401,
            "max_log_strain_component": 1.0575425230390294e-06,
            "step_scale": 1.0,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 0.5911270001239367,
            "cell_principal_stretches": [
              1.0001628496482187,
              0.9999572177394038,
              0.999957214749697
            ],
            "cell_volume_ratio": 1.0000772700334288,
            "cell_rmsd_from_input_A": 0.0009393736951361244
          },
          {
            "iteration": 2,
            "reduced_polarization": [
              -0.5000000952093304,
              -1.1680619682254246e-12,
              -6.608013190890271e-12
            ],
            "branch_aligned_reduced_polarization": [
              -0.5000000952093304,
              -1.1680619682254246e-12,
              -6.608013190890271e-12
            ],
            "target_residual": 9.52093306561011e-08,
            "energy_eV": -583.7282694952075
          }
        ],
        "iterations": 2
      },
      "parent": {
        "candidate_id": "bec_projection_01",
        "source": "MACEField_BEC_backprojection",
        "spacegroup": "I4_1",
        "spacegroup_number": 80,
        "pointgroup": "4",
        "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": 9.52093306561011e-08,
        "parent_symmetrization_rmsd_A": 0.01127729957797656,
        "parent_cell_rmsd_A": 0.0009393736951361244,
        "energy_eV": -583.7282694952075,
        "reduced_polarization": [
          -0.5000000952093304,
          -1.1680619682254246e-12,
          -6.608013190890271e-12
        ],
        "cartesian_polarization_e_A2": [
          -0.0024675041569014377,
          -8.124852547388128e-13,
          1.107562538974822e-11
        ],
        "ranking_score": 0.5115123334204219
      },
      "branch_status": "awaiting_branch_sampling"
    },
    {
      "orbit_id": 2,
      "formal_class": [
        0.0,
        0.5,
        0.0
      ],
      "formal_classes_in_orbit": [
        [
          0.0,
          0.5,
          0.0
        ],
        [
          0.0,
          0.0,
          0.5
        ]
      ],
      "target_reduced_polarization": [
        0.0,
        -0.5,
        0.0
      ],
      "bec_backprojection": {
        "converged_to_target": true,
        "history": [
          {
            "iteration": 0,
            "reduced_polarization": [
              -0.1056944262051161,
              -1.6001675710785093e-06,
              -1.333952117825338e-06
            ],
            "branch_aligned_reduced_polarization": [
              -0.1056944262051161,
              -1.6001675710586305e-06,
              -1.333952117825338e-06
            ],
            "target_residual": 0.511047660759344,
            "energy_eV": -583.9498401770968,
            "max_atomic_step_A": 0.0402508000755411,
            "max_log_strain_component": 0.0010389656175695302,
            "step_scale": 1.0,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 0.5911270001239367,
            "cell_principal_stretches": [
              1.0010773997252331,
              1.0000113698697783,
              0.9988918128144538
            ],
            "cell_volume_ratio": 0.9999793880852714,
            "cell_rmsd_from_input_A": 0.010330194608725746
          },
          {
            "iteration": 1,
            "reduced_polarization": [
              -0.0012125230650372422,
              -0.49237279765116465,
              -0.0010046544375839437
            ],
            "branch_aligned_reduced_polarization": [
              -0.0012125230650372422,
              -0.49237279765116465,
              -0.0010046544375839437
            ],
            "target_residual": 0.007788052284896647,
            "energy_eV": -583.106705925291,
            "max_atomic_step_A": 0.0006513122721872153,
            "max_log_strain_component": 1.8072469545906245e-05,
            "step_scale": 1.0,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 0.5911270001239367,
            "cell_principal_stretches": [
              1.0010954261503002,
              1.0000115176273614,
              0.9988734107217251
            ],
            "cell_volume_ratio": 0.9999791200308913,
            "cell_rmsd_from_input_A": 0.010502375003294533
          },
          {
            "iteration": 2,
            "reduced_polarization": [
              -2.862974762726614e-06,
              -0.4999935243212123,
              -2.6120600030219443e-06
            ],
            "branch_aligned_reduced_polarization": [
              -2.862974762726614e-06,
              -0.4999935243212123,
              -2.6120600030219443e-06
            ],
            "target_residual": 7.5467806191014225e-06,
            "energy_eV": -583.0796008074033
          }
        ],
        "iterations": 2
      },
      "parent": {
        "candidate_id": "bec_projection_02",
        "source": "MACEField_BEC_backprojection",
        "spacegroup": "P1",
        "spacegroup_number": 1,
        "pointgroup": "1",
        "has_inversion": false,
        "is_polar_point_group": true,
        "nonpolar_parent_hypothesis": false,
        "symmetry_tolerance_A": null,
        "target_reduced_polarization": [
          0.0,
          -0.5,
          0.0
        ],
        "formal_class": [
          0.0,
          0.5,
          0.0
        ],
        "target_residual": 7.5467806191014225e-06,
        "parent_symmetrization_rmsd_A": 0.022298932077071527,
        "parent_cell_rmsd_A": 0.010502375003294533,
        "energy_eV": -583.0796008074033,
        "reduced_polarization": [
          -2.862974762726614e-06,
          -0.4999935243212123,
          -2.6120600030219443e-06
        ],
        "cartesian_polarization_e_A2": [
          1.3223724638035713e-06,
          -0.0039195627928415,
          -1.9763629912153335e-08
        ],
        "ranking_score": 0.5249396193891334
      },
      "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
        ],
        [
          0.5,
          0.0,
          0.5
        ]
      ],
      "target_reduced_polarization": [
        -0.5,
        -0.5,
        0.0
      ],
      "bec_backprojection": {
        "converged_to_target": true,
        "history": [
          {
            "iteration": 0,
            "reduced_polarization": [
              -0.1056944262051161,
              -1.6001675710785093e-06,
              -1.333952117825338e-06
            ],
            "branch_aligned_reduced_polarization": [
              -0.1056944262051161,
              -1.6001675710586305e-06,
              -1.333952117825338e-06
            ],
            "target_residual": 0.6367694130236482,
            "energy_eV": -583.9498401770968,
            "max_atomic_step_A": 0.047955069709937174,
            "max_log_strain_component": 0.0010389630001430828,
            "step_scale": 1.0,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 0.5911270001239367,
            "cell_principal_stretches": [
              1.001157530403626,
              0.9999574716111281,
              0.9989629366237195
            ],
            "cell_volume_ratio": 1.0000767331338682,
            "cell_rmsd_from_input_A": 0.01037052894494601
          },
          {
            "iteration": 1,
            "reduced_polarization": [
              -0.4886390351628881,
              -0.49053273279443566,
              -0.00039716073599311733
            ],
            "branch_aligned_reduced_polarization": [
              -0.4886390351628881,
              -0.49053273279443566,
              -0.00039716073599311733
            ],
            "target_residual": 0.01479386383004325,
            "energy_eV": -582.892666080748,
            "max_atomic_step_A": 0.0010658523891944592,
            "max_log_strain_component": 2.2591461576771553e-05,
            "step_scale": 1.0,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 0.5911270001239367,
            "cell_principal_stretches": [
              1.0011831128637316,
              0.9999560935787632,
              0.9989412721012919
            ],
            "cell_volume_ratio": 1.0000792205428888,
            "cell_rmsd_from_input_A": 0.010593742881722905
          },
          {
            "iteration": 2,
            "reduced_polarization": [
              -0.4999899290423793,
              -0.4999875799994685,
              3.835290427921476e-06
            ],
            "branch_aligned_reduced_polarization": [
              -0.4999899290423793,
              -0.4999875799994685,
              3.835290427921476e-06
            ],
            "target_residual": 1.6443541384564432e-05,
            "energy_eV": -582.8440434360498
          }
        ],
        "iterations": 2
      },
      "parent": {
        "candidate_id": "bec_projection_03",
        "source": "MACEField_BEC_backprojection",
        "spacegroup": "P1",
        "spacegroup_number": 1,
        "pointgroup": "1",
        "has_inversion": false,
        "is_polar_point_group": true,
        "nonpolar_parent_hypothesis": false,
        "symmetry_tolerance_A": null,
        "target_reduced_polarization": [
          -0.5,
          -0.5,
          0.0
        ],
        "formal_class": [
          0.5,
          0.5,
          0.0
        ],
        "target_residual": 1.6443541384564432e-05,
        "parent_symmetrization_rmsd_A": 0.025016037139033425,
        "parent_cell_rmsd_A": 0.010593742881722905,
        "energy_eV": -582.8440434360498,
        "reduced_polarization": [
          -0.4999899290423793,
          -0.4999875799994685,
          3.835290427921476e-06
        ],
        "cartesian_polarization_e_A2": [
          -0.00246611301150692,
          -0.003918058130594876,
          -2.588270904318273e-06
        ],
        "ranking_score": 0.5276973599422333
      },
      "branch_status": "awaiting_branch_sampling"
    },
    {
      "orbit_id": 4,
      "formal_class": [
        0.0,
        0.5,
        0.5
      ],
      "formal_classes_in_orbit": [
        [
          0.0,
          0.5,
          0.5
        ]
      ],
      "target_reduced_polarization": [
        0.0,
        -0.5,
        -0.5
      ],
      "bec_backprojection": {
        "converged_to_target": true,
        "history": [
          {
            "iteration": 0,
            "reduced_polarization": [
              -0.1056944262051161,
              -1.6001675710785093e-06,
              -1.333952117825338e-06
            ],
            "branch_aligned_reduced_polarization": [
              -0.1056944262051161,
              -1.6001675710586305e-06,
              -1.3339521178212799e-06
            ],
            "target_residual": 0.7149604028304504,
            "energy_eV": -583.9498401770968,
            "max_atomic_step_A": 0.05417823496756846,
            "max_log_strain_component": 0.0013766788799374928,
            "step_scale": 1.0,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 0.5911270001239367,
            "cell_principal_stretches": [
              1.0015303996192726,
              1.0000113624491214,
              0.9984399859461377
            ],
            "cell_volume_ratio": 0.9999793602059978,
            "cell_rmsd_from_input_A": 0.014607039299351162
          },
          {
            "iteration": 1,
            "reduced_polarization": [
              -0.0024172611959868665,
              -0.4866208755783932,
              -0.48358320585777975
            ],
            "branch_aligned_reduced_polarization": [
              -0.0024172611959868665,
              -0.4866208755783932,
              -0.48358320585777975
            ],
            "target_residual": 0.021315610521082832,
            "energy_eV": -582.2568821985421,
            "max_atomic_step_A": 0.001691182230084177,
            "max_log_strain_component": 5.149794598200573e-05,
            "step_scale": 1.0,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 0.5911270001239367,
            "cell_principal_stretches": [
              1.0015848257936284,
              1.0000116846616336,
              0.9983848238815477
            ],
            "cell_volume_ratio": 0.999978774179493,
            "cell_rmsd_from_input_A": 0.01512501613803386
          },
          {
            "iteration": 2,
            "reduced_polarization": [
              -2.8937267481804485e-05,
              -0.4999617792750898,
              -0.4999508700558863
            ],
            "branch_aligned_reduced_polarization": [
              -2.8937267481804485e-05,
              -0.4999617792750898,
              -0.4999508700558863
            ],
            "target_residual": 6.864357705272066e-05,
            "energy_eV": -582.1431407929381
          }
        ],
        "iterations": 2
      },
      "parent": {
        "candidate_id": "bec_projection_04",
        "source": "MACEField_BEC_backprojection",
        "spacegroup": "P1",
        "spacegroup_number": 1,
        "pointgroup": "1",
        "has_inversion": false,
        "is_polar_point_group": true,
        "nonpolar_parent_hypothesis": false,
        "symmetry_tolerance_A": null,
        "target_reduced_polarization": [
          0.0,
          -0.5,
          -0.5
        ],
        "formal_class": [
          0.0,
          0.5,
          0.5
        ],
        "target_residual": 6.864357705272066e-05,
        "parent_symmetrization_rmsd_A": 0.031901908826682826,
        "parent_cell_rmsd_A": 0.01512501613803386,
        "energy_eV": -582.1431407929381,
        "reduced_polarization": [
          -2.8937267481804485e-05,
          -0.4999617792750898,
          -0.4999508700558863
        ],
        "cartesian_polarization_e_A2": [
          2.6294905788786712e-06,
          -0.00391931744314982,
          -0.003919229321144302
        ],
        "ranking_score": 0.5358204500152968
      },
      "branch_status": "awaiting_branch_sampling"
    },
    {
      "orbit_id": 5,
      "formal_class": [
        0.5,
        0.5,
        0.5
      ],
      "formal_classes_in_orbit": [
        [
          0.5,
          0.5,
          0.5
        ]
      ],
      "target_reduced_polarization": [
        -0.5,
        -0.5,
        -0.5
      ],
      "bec_backprojection": {
        "converged_to_target": true,
        "history": [
          {
            "iteration": 0,
            "reduced_polarization": [
              -0.1056944262051161,
              -1.6001675710785093e-06,
              -1.333952117825338e-06
            ],
            "branch_aligned_reduced_polarization": [
              -0.1056944262051161,
              -1.6001675710586305e-06,
              -1.3339521178212799e-06
            ],
            "target_residual": 0.8096134580220141,
            "energy_eV": -583.9498401770968,
            "max_atomic_step_A": 0.06404520943396816,
            "max_log_strain_component": 0.001376683353200773,
            "step_scale": 1.0,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 0.5911270001239367,
            "cell_principal_stretches": [
              1.001609278505544,
              0.9999574617364619,
              0.998512364102976
            ],
            "cell_volume_ratio": 1.0000767052518809,
            "cell_rmsd_from_input_A": 0.014636536606363788
          },
          {
            "iteration": 1,
            "reduced_polarization": [
              -0.48035446091297135,
              -0.4855519090820388,
              -0.4812904712084823
            ],
            "branch_aligned_reduced_polarization": [
              -0.48035446091297135,
              -0.4855519090820388,
              -0.4812904712084823
            ],
            "target_residual": 0.030736639451870353,
            "energy_eV": -582.0314702827732,
            "max_atomic_step_A": 0.002614851538341899,
            "max_log_strain_component": 5.999288864823072e-05,
            "step_scale": 1.0,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 0.5911270001239367,
            "cell_principal_stretches": [
              1.0016764112945415,
              0.9999548705112296,
              0.9984526984214496
            ],
            "cell_volume_ratio": 1.0000813806037847,
            "cell_rmsd_from_input_A": 0.015235761712312966
          },
          {
            "iteration": 2,
            "reduced_polarization": [
              -0.49995540848646763,
              -0.49996158237262545,
              -0.49991818617854167
            ],
            "branch_aligned_reduced_polarization": [
              -0.49995540848646763,
              -0.49996158237262545,
              -0.49991818617854167
            ],
            "target_residual": 0.00010078600375951552,
            "energy_eV": -581.8741717788834
          }
        ],
        "iterations": 2
      },
      "parent": {
        "candidate_id": "bec_projection_05",
        "source": "MACEField_BEC_backprojection",
        "spacegroup": "P1",
        "spacegroup_number": 1,
        "pointgroup": "1",
        "has_inversion": false,
        "is_polar_point_group": true,
        "nonpolar_parent_hypothesis": false,
        "symmetry_tolerance_A": null,
        "target_reduced_polarization": [
          -0.5,
          -0.5,
          -0.5
        ],
        "formal_class": [
          0.5,
          0.5,
          0.5
        ],
        "target_residual": 0.00010078600375951552,
        "parent_symmetrization_rmsd_A": 0.034019256711356395,
        "parent_cell_rmsd_A": 0.015235761712312966,
        "energy_eV": -581.8741717788834,
        "reduced_polarization": [
          -0.49995540848646763,
          -0.49996158237262545,
          -0.49991818617854167
        ],
        "cartesian_polarization_e_A2": [
          -0.0024644990683579714,
          -0.0039151470627493065,
          -0.003920130643880572
        ],
        "ranking_score": 0.5380297691469537
      },
      "branch_status": "awaiting_branch_sampling"
    }
  ],
  "sampled_polarization_branches": [
    {
      "orbit_id": 0,
      "candidate_id": "inversion_parent_endpoint_00",
      "formal_class": [
        0.0,
        0.0,
        0.0
      ],
      "construction": "MACEField-BEC-parent plus variable-cell P-N-P path and symmetric log-strain continuation beyond both polar endpoints",
      "geometry_diagnostics": {
        "collision_aware": false,
        "permutations_tested": 1,
        "selected_order": [
          0,
          1,
          2,
          3,
          4,
          5,
          6,
          7,
          8,
          9,
          10,
          11,
          12,
          13,
          14,
          15,
          16,
          17,
          18,
          19,
          20,
          21,
          22,
          23,
          24,
          25,
          26,
          27,
          28,
          29,
          30,
          31,
          32,
          33,
          34,
          35,
          36,
          37,
          38,
          39,
          40,
          41,
          42,
          43,
          44,
          45,
          46,
          47,
          48,
          49,
          50,
          51,
          52,
          53,
          54,
          55,
          56,
          57,
          58,
          59,
          60,
          61,
          62,
          63,
          64,
          65,
          66,
          67,
          68,
          69,
          70,
          71,
          72,
          73,
          74,
          75,
          76,
          77,
          78,
          79
        ],
        "endpoint_rmsd_A": 0.20080611766342815,
        "minimum_distance_A_by_image": [
          1.7829144150131375,
          1.7787797295942824,
          1.7752145024732193,
          1.7722221704371128,
          1.7698056393876374,
          1.767967270412433,
          1.7667088683517616,
          1.766031672988284,
          1.7659363529597223
        ],
        "minimum_distance_A": 1.7659363529597223,
        "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": [
          1815.9986718258178,
          1815.9986718258178,
          1815.9986718258178,
          1815.9986718258178,
          1815.9986718258178,
          1815.9986718258178,
          1815.9986718258178,
          1815.9986718258178,
          1815.9986718258178
        ],
        "cell_deformation_log_strain_norm": 0.0
      },
      "parent_reduced_polarization": [
        -1.0128189557548826e-15,
        3.0142901188714618e-15,
        1.438904338762703e-15
      ],
      "incoming": {
        "reached": true,
        "construction": "variable_cell_linear_interpolation",
        "continuation_fractions": [
          0.0,
          0.125,
          0.25,
          0.375,
          0.5,
          0.625,
          0.75,
          0.875,
          1.0
        ],
        "energies_eV": [
          -583.9498401770969,
          -583.9724976367177,
          -583.956803163574,
          -583.9181183687667,
          -583.8700838267323,
          -583.8234393272093,
          -583.7856534706136,
          -583.7614075222741,
          -583.7531044960524
        ],
        "cartesian_polarizations_e_A2": [
          [
            -0.000521558141425837,
            -1.2543669894910631e-08,
            -1.045681423112088e-08
          ],
          [
            -0.0004687160995546307,
            -1.0873507448218977e-08,
            -8.996019243383373e-09
          ],
          [
            -0.0004113513435083075,
            -9.242209294976137e-09,
            -7.59487877410101e-09
          ],
          [
            -0.0003497479638880465,
            -7.646958018470707e-09,
            -6.2478142757693564e-09
          ],
          [
            -0.0002844876930885417,
            -6.07979495898572e-09,
            -4.9472942610328216e-09
          ],
          [
            -0.0002162857999249396,
            -4.5350028229652674e-09,
            -3.6829369095752223e-09
          ],
          [
            -0.0001457530090616121,
            -3.0098708773745393e-09,
            -2.4433011624775964e-09
          ],
          [
            -7.340296508402139e-05,
            -1.5004444292826902e-09,
            -1.2183326490775026e-09
          ],
          [
            -4.997841334974935e-18,
            2.3628937932327982e-17,
            1.1279531820218662e-17
          ]
        ],
        "raw_reduced_polarization": [
          [
            -0.10569442620511338,
            -1.6001675710902077e-06,
            -1.3339521184580274e-06
          ],
          [
            -0.09498591865537954,
            -1.3871087288184578e-06,
            -1.1476018089415847e-06
          ],
          [
            -0.0833608772781382,
            -1.1790077164777519e-06,
            -9.688614912936031e-07
          ],
          [
            -0.07087687339803558,
            -9.755051225965191e-07,
            -7.970195228381211e-07
          ],
          [
            -0.05765179583086892,
            -7.755856789721412e-07,
            -6.31115128783594e-07
          ],
          [
            -0.043830594719287026,
            -5.785200434089762e-07,
            -4.6982392381551485e-07
          ],
          [
            -0.029537034199717,
            -3.8396241383055654e-07,
            -3.1168639794881265e-07
          ],
          [
            -0.014875205006099599,
            -1.9140829901265678e-07,
            -1.5541993788000075e-07
          ],
          [
            -1.0128189557548826e-15,
            3.0142901188714618e-15,
            1.438904338762703e-15
          ]
        ],
        "unwrapped_reduced_polarization": [
          [
            -0.10569442620511338,
            -1.6001675710902077e-06,
            -1.3339521184580274e-06
          ],
          [
            -0.09498591865537954,
            -1.3871087288184578e-06,
            -1.1476018089415847e-06
          ],
          [
            -0.0833608772781382,
            -1.1790077164777519e-06,
            -9.688614912936031e-07
          ],
          [
            -0.07087687339803558,
            -9.755051225965191e-07,
            -7.970195228381211e-07
          ],
          [
            -0.05765179583086892,
            -7.755856789721412e-07,
            -6.31115128783594e-07
          ],
          [
            -0.043830594719287026,
            -5.785200434089762e-07,
            -4.6982392381551485e-07
          ],
          [
            -0.029537034199717,
            -3.8396241383055654e-07,
            -3.1168639794881265e-07
          ],
          [
            -0.014875205006099599,
            -1.9140829901265678e-07,
            -1.5541993788000075e-07
          ],
          [
            -1.0130785099704553e-15,
            3.0142901184471513e-15,
            1.4389043395189556e-15
          ]
        ],
        "berry_integer_shifts": [
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ]
        ],
        "folded_reduced_polarization": [
          [
            -0.10569442620511338,
            -1.6001675711141417e-06,
            -1.3339521184319025e-06
          ],
          [
            -0.09498591865537953,
            -1.3871087288230832e-06,
            -1.1476018089151552e-06
          ],
          [
            -0.08336087727813823,
            -1.179007716456404e-06,
            -9.688614913128113e-07
          ],
          [
            -0.07087687339803561,
            -9.755051225690536e-07,
            -7.970195228246268e-07
          ],
          [
            -0.057651795830868935,
            -7.755856789581905e-07,
            -6.311151287685668e-07
          ],
          [
            -0.04383059471928702,
            -5.785200434260673e-07,
            -4.69823923821e-07
          ],
          [
            -0.029537034199716983,
            -3.8396241380800333e-07,
            -3.116863979690798e-07
          ],
          [
            -0.014875205006099623,
            -1.9140829898844913e-07,
            -1.5541993786394315e-07
          ],
          [
            -9.992007221626409e-16,
            2.9976021664879227e-15,
            1.4432899320127035e-15
          ]
        ]
      },
      "reflected": {
        "reached": true,
        "construction": "reflect_displacements_about_reconstructed_parent",
        "energies_eV": [
          -583.7531044960524,
          -583.761407522274,
          -583.7856534706139,
          -583.8234393272094,
          -583.8700838267324,
          -583.918118368767,
          -583.9568031635738,
          -583.9724976367175,
          -583.9498401770969
        ],
        "cartesian_polarizations_e_A2": [
          [
            1.543675764013665e-18,
            1.0117954017594517e-17,
            -5.502210644009103e-19
          ],
          [
            7.340296508401082e-05,
            1.500444436618971e-09,
            1.2183326596463322e-09
          ],
          [
            0.00014575300906162063,
            3.009870880461891e-09,
            2.4433011796643627e-09
          ],
          [
            0.00021628579992492606,
            4.535002825257856e-09,
            3.6829368948644508e-09
          ],
          [
            0.00028448769308854873,
            6.079794959046855e-09,
            4.947294244908288e-09
          ],
          [
            0.0003497479638880598,
            7.646958027488218e-09,
            6.247814274485507e-09
          ],
          [
            0.0004113513435083206,
            9.24220929564863e-09,
            7.594878757380405e-09
          ],
          [
            0.00046871609955463563,
            1.0873507464542202e-08,
            8.996019212922524e-09
          ],
          [
            0.0005215581414258531,
            1.2543669923277584e-08,
            1.0456814210930824e-08
          ]
        ],
        "raw_reduced_polarization": [
          [
            3.1282787318422983e-16,
            1.2907244881584137e-15,
            -7.019045554940014e-17
          ],
          [
            0.014875205006097458,
            1.9140829994852953e-07,
            1.554199392282424e-07
          ],
          [
            0.029537034199718728,
            3.83962414224403e-07,
            3.1168640014128957e-07
          ],
          [
            0.04383059471928428,
            5.785200437014366e-07,
            4.69823921938895e-07
          ],
          [
            0.05765179583087035,
            7.7558567897994e-07,
            6.311151267266238e-07
          ],
          [
            0.07087687339803828,
            9.755051237468623e-07,
            7.970195226743434e-07
          ],
          [
            0.08336087727814087,
            1.1790077165635402e-06,
            9.688614891605933e-07
          ],
          [
            0.09498591865538054,
            1.3871087309007746e-06,
            1.1476018050557633e-06
          ],
          [
            0.10569442620511665,
            1.6001675747089156e-06,
            1.3339521158824276e-06
          ]
        ],
        "unwrapped_reduced_polarization": [
          [
            3.1282787318422983e-16,
            1.2907244881584137e-15,
            -7.019045554940014e-17
          ],
          [
            0.014875205006097458,
            1.9140829994852953e-07,
            1.554199392282424e-07
          ],
          [
            0.029537034199718728,
            3.83962414224403e-07,
            3.1168640014128957e-07
          ],
          [
            0.04383059471928428,
            5.785200437014366e-07,
            4.69823921938895e-07
          ],
          [
            0.05765179583087035,
            7.7558567897994e-07,
            6.311151267266238e-07
          ],
          [
            0.07087687339803828,
            9.755051237468623e-07,
            7.970195226743434e-07
          ],
          [
            0.08336087727814087,
            1.1790077165635402e-06,
            9.688614891605933e-07
          ],
          [
            0.09498591865538054,
            1.3871087309007746e-06,
            1.1476018050557633e-06
          ],
          [
            0.10569442620511665,
            1.6001675747089156e-06,
            1.3339521158824276e-06
          ]
        ],
        "gauge_integer_shift": [
          0,
          0,
          0
        ],
        "expected_opposite_endpoint_reduced_polarization": [
          0.10569442620511135,
          1.6001675771187879e-06,
          1.333952121335836e-06
        ],
        "actual_opposite_endpoint_branch_residual": 7.978163166642585e-15
      },
      "pnp_branch": {
        "construction": "incoming_path_concatenated_with_parent_reflection",
        "reduced_polarization": [
          [
            -0.10569442620511338,
            -1.6001675710902077e-06,
            -1.3339521184580274e-06
          ],
          [
            -0.09498591865537954,
            -1.3871087288184578e-06,
            -1.1476018089415847e-06
          ],
          [
            -0.0833608772781382,
            -1.1790077164777519e-06,
            -9.688614912936031e-07
          ],
          [
            -0.07087687339803558,
            -9.755051225965191e-07,
            -7.970195228381211e-07
          ],
          [
            -0.05765179583086892,
            -7.755856789721412e-07,
            -6.31115128783594e-07
          ],
          [
            -0.043830594719287026,
            -5.785200434089762e-07,
            -4.6982392381551485e-07
          ],
          [
            -0.029537034199717,
            -3.8396241383055654e-07,
            -3.1168639794881265e-07
          ],
          [
            -0.014875205006099599,
            -1.9140829901265678e-07,
            -1.5541993788000075e-07
          ],
          [
            -1.0128189557548826e-15,
            3.0142901188714618e-15,
            1.438904338762703e-15
          ],
          [
            0.014875205006097458,
            1.9140829994852953e-07,
            1.554199392282424e-07
          ],
          [
            0.029537034199718728,
            3.83962414224403e-07,
            3.1168640014128957e-07
          ],
          [
            0.04383059471928428,
            5.785200437014366e-07,
            4.69823921938895e-07
          ],
          [
            0.05765179583087035,
            7.7558567897994e-07,
            6.311151267266238e-07
          ],
          [
            0.07087687339803828,
            9.755051237468623e-07,
            7.970195226743434e-07
          ],
          [
            0.08336087727814087,
            1.1790077165635402e-06,
            9.688614891605933e-07
          ],
          [
            0.09498591865538054,
            1.3871087309007746e-06,
            1.1476018050557633e-06
          ],
          [
            0.10569442620511665,
            1.6001675747089156e-06,
            1.3339521158824276e-06
          ]
        ],
        "unwrapped_reduced_polarization": [
          [
            -0.10569442620511338,
            -1.6001675710902077e-06,
            -1.3339521184580274e-06
          ],
          [
            -0.09498591865537954,
            -1.3871087288184578e-06,
            -1.1476018089415847e-06
          ],
          [
            -0.0833608772781382,
            -1.1790077164777519e-06,
            -9.688614912936031e-07
          ],
          [
            -0.07087687339803558,
            -9.755051225965191e-07,
            -7.970195228381211e-07
          ],
          [
            -0.05765179583086892,
            -7.755856789721412e-07,
            -6.31115128783594e-07
          ],
          [
            -0.043830594719287026,
            -5.785200434089762e-07,
            -4.6982392381551485e-07
          ],
          [
            -0.029537034199717,
            -3.8396241383055654e-07,
            -3.1168639794881265e-07
          ],
          [
            -0.014875205006099599,
            -1.9140829901265678e-07,
            -1.5541993788000075e-07
          ],
          [
            -1.0130785099704553e-15,
            3.0142901184471513e-15,
            1.4389043395189556e-15
          ],
          [
            0.014875205006097458,
            1.9140829994852953e-07,
            1.554199392282424e-07
          ],
          [
            0.029537034199718728,
            3.83962414224403e-07,
            3.1168640014128957e-07
          ],
          [
            0.04383059471928428,
            5.785200437014366e-07,
            4.69823921938895e-07
          ],
          [
            0.05765179583087035,
            7.7558567897994e-07,
            6.311151267266238e-07
          ],
          [
            0.07087687339803828,
            9.755051237468623e-07,
            7.970195226743434e-07
          ],
          [
            0.08336087727814087,
            1.1790077165635402e-06,
            9.688614891605933e-07
          ],
          [
            0.09498591865538054,
            1.3871087309007746e-06,
            1.1476018050557633e-06
          ],
          [
            0.10569442620511665,
            1.6001675747089156e-06,
            1.3339521158824276e-06
          ]
        ],
        "berry_integer_shifts": [
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ]
        ],
        "folded_reduced_polarization": [
          [
            -0.10569442620511338,
            -1.6001675711141417e-06,
            -1.3339521184319025e-06
          ],
          [
            -0.09498591865537953,
            -1.3871087288230832e-06,
            -1.1476018089151552e-06
          ],
          [
            -0.08336087727813823,
            -1.179007716456404e-06,
            -9.688614913128113e-07
          ],
          [
            -0.07087687339803561,
            -9.755051225690536e-07,
            -7.970195228246268e-07
          ],
          [
            -0.057651795830868935,
            -7.755856789581905e-07,
            -6.311151287685668e-07
          ],
          [
            -0.04383059471928702,
            -5.785200434260673e-07,
            -4.69823923821e-07
          ],
          [
            -0.029537034199716983,
            -3.8396241380800333e-07,
            -3.116863979690798e-07
          ],
          [
            -0.014875205006099623,
            -1.9140829898844913e-07,
            -1.5541993786394315e-07
          ],
          [
            -9.992007221626409e-16,
            2.9976021664879227e-15,
            1.4432899320127035e-15
          ],
          [
            0.014875205006097403,
            1.9140829998764985e-07,
            1.5541993925172193e-07
          ],
          [
            0.02953703419971876,
            3.839624141965814e-07,
            3.116864001340147e-07
          ],
          [
            0.0438305947192843,
            5.785200436481119e-07,
            4.6982392198913203e-07
          ],
          [
            0.05765179583087032,
            7.755856790137017e-07,
            6.311151267146542e-07
          ],
          [
            0.07087687339803828,
            9.75505123790299e-07,
            7.970195227136045e-07
          ],
          [
            0.0833608772781409,
            1.1790077165674262e-06,
            9.688614891478764e-07
          ],
          [
            0.09498591865538053,
            1.3871087308769958e-06,
            1.1476018050293746e-06
          ],
          [
            0.10569442620511671,
            1.6001675746668553e-06,
            1.3339521158783896e-06
          ]
        ]
      },
      "incoming_structure_ids": [
        "incoming_00_000",
        "incoming_00_001",
        "incoming_00_002",
        "incoming_00_003",
        "incoming_00_004",
        "incoming_00_005",
        "incoming_00_006",
        "incoming_00_007",
        "incoming_00_008"
      ],
      "reflected_structure_ids": [
        "reflected_00_001",
        "reflected_00_002",
        "reflected_00_003",
        "reflected_00_004",
        "reflected_00_005",
        "reflected_00_006",
        "reflected_00_007",
        "reflected_00_008"
      ],
      "positive_extension_structure_ids": [
        "extension_plus_00_000",
        "extension_plus_00_001",
        "extension_plus_00_002",
        "extension_plus_00_003"
      ],
      "negative_extension_structure_ids": [
        "extension_minus_00_000",
        "extension_minus_00_001",
        "extension_minus_00_002",
        "extension_minus_00_003"
      ],
      "extension": {
        "enabled": true,
        "fraction_beyond_polar_endpoint": 0.35,
        "images_per_side": 4,
        "construction": "continue fractional atomic displacements and symmetric log strain beyond +P; reflect these structures about N for the -P side",
        "positive_path_coordinates": [
          1.35,
          1.2625,
          1.175,
          1.0875
        ],
        "negative_path_coordinates": [
          -1.0875,
          -1.175,
          -1.2625,
          -1.35
        ]
      },
      "branch_coordinates": [
        1.35,
        1.2625,
        1.175,
        1.0875,
        1.0,
        0.875,
        0.75,
        0.625,
        0.5,
        0.375,
        0.25,
        0.125,
        0.0,
        -0.125,
        -0.25,
        -0.375,
        -0.5,
        -0.625,
        -0.75,
        -0.875,
        -1.0,
        -1.0875,
        -1.175,
        -1.2625,
        -1.35
      ],
      "parent": {
        "candidate_id": "inversion_parent_endpoint_00",
        "source": "same_species_inversion_center_projection_from_endpoint",
        "spacegroup": "I4_1/a",
        "spacegroup_number": 88,
        "pointgroup": "4/m",
        "has_inversion": true,
        "is_polar_point_group": false,
        "nonpolar_parent_hypothesis": true,
        "symmetry_tolerance_A": null,
        "target_reduced_polarization": [
          0.0,
          0.0,
          0.0
        ],
        "formal_class": [
          0.0,
          0.0,
          0.0
        ],
        "target_residual": 3.889824798023194e-15,
        "parent_symmetrization_rmsd_A": 0.20080611766342815,
        "parent_cell_rmsd_A": 0.0,
        "energy_eV": -583.7531044960523,
        "reduced_polarization": [
          -1.0530839295310707e-16,
          2.0394226806853488e-15,
          -3.31064982008004e-15
        ],
        "cartesian_polarization_e_A2": [
          -5.196532274897486e-19,
          1.598697870453756e-17,
          -2.595209353757627e-17
        ],
        "ranking_score": 0.20080611766343592
      }
    }
  ],
  "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": 44,
      "full_response": 12,
      "energy_polarization": 32
    },
    "model_evaluations_for_recovery_and_path_properties": {
      "total": 69,
      "full_response": 37,
      "energy_polarization": 32
    },
    "elapsed_seconds": 924.4501239610254
  }
}
