{
  "schema": "ferrofinder.endpoint_parent_recovery.v4_variable_cell",
  "status": "complete",
  "input_atom_count": 30,
  "input_formula": "O18Sb6Y6",
  "input_spacegroup": "P6_3cm",
  "input_pointgroup": "6mm",
  "input_is_polar_point_group": true,
  "input_energy_eV": -218.8411916166313,
  "input_cartesian_polarization_e_A2": [
    2.1501272347165343e-17,
    -8.613701428551503e-20,
    -0.00880201850703103
  ],
  "input_reduced_polarization": [
    1.539233656883536e-15,
    -7.136828098731235e-18,
    -0.3241120818847303
  ],
  "input_formal_targets": [
    {
      "orbit_id": 0,
      "representative_formal_class": [
        0.0,
        0.0,
        0.5
      ],
      "target_reduced_polarization": [
        0.0,
        0.0,
        -0.5
      ]
    },
    {
      "orbit_id": 1,
      "representative_formal_class": [
        0.0,
        0.0,
        0.0
      ],
      "target_reduced_polarization": [
        0.0,
        0.0,
        0.0
      ]
    },
    {
      "orbit_id": 2,
      "representative_formal_class": [
        0.5,
        0.0,
        0.5
      ],
      "target_reduced_polarization": [
        0.5,
        0.0,
        -0.5
      ]
    },
    {
      "orbit_id": 3,
      "representative_formal_class": [
        0.5,
        0.0,
        0.0
      ],
      "target_reduced_polarization": [
        0.5,
        0.0,
        0.0
      ]
    }
  ],
  "parent_candidates": [
    {
      "candidate_id": "inversion_parent_endpoint_00",
      "source": "same_species_inversion_center_projection_from_endpoint",
      "spacegroup": "P-3c1",
      "spacegroup_number": 165,
      "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": 1.5125111375639118e-14,
      "parent_symmetrization_rmsd_A": 0.1379397957226171,
      "parent_cell_rmsd_A": 0.0,
      "energy_eV": -216.5274938220213,
      "reduced_polarization": [
        -7.759632153224029e-15,
        -4.300704825763451e-15,
        1.224994044776523e-14
      ],
      "cartesian_polarization_e_A2": [
        -7.817376813320475e-17,
        -5.19067949920816e-17,
        3.3267566548045244e-16
      ],
      "ranking_score": 0.13793979572264736
    },
    {
      "candidate_id": "inversion_parent_endpoint_01",
      "source": "same_species_inversion_center_projection_from_endpoint",
      "spacegroup": "P-3c1",
      "spacegroup_number": 165,
      "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": 2.0583020856773235e-14,
      "parent_symmetrization_rmsd_A": 0.13793979572261716,
      "parent_cell_rmsd_A": 0.0,
      "energy_eV": -216.52749382202134,
      "reduced_polarization": [
        -1.733916104257656e-14,
        -2.7145211658883175e-16,
        1.1087856225544991e-14
      ],
      "cartesian_polarization_e_A2": [
        -2.397557975017067e-16,
        -3.2762558549788087e-18,
        3.011165616937904e-16
      ],
      "ranking_score": 0.13793979572265833
    },
    {
      "candidate_id": "bec_projection_00",
      "source": "MACEField_BEC_backprojection",
      "spacegroup": "P6_3cm",
      "spacegroup_number": 185,
      "pointgroup": "6mm",
      "has_inversion": false,
      "is_polar_point_group": true,
      "nonpolar_parent_hypothesis": false,
      "symmetry_tolerance_A": null,
      "target_reduced_polarization": [
        0.0,
        0.0,
        -0.5
      ],
      "formal_class": [
        0.0,
        0.0,
        0.5
      ],
      "target_residual": 3.1513972994501316e-06,
      "parent_symmetrization_rmsd_A": 0.0289848613665277,
      "parent_cell_rmsd_A": 0.02345543739660081,
      "energy_eV": -218.94698467544814,
      "reduced_polarization": [
        2.1747219430375002e-15,
        1.0325591906418892e-14,
        -0.49999684860270055
      ],
      "cartesian_polarization_e_A2": [
        6.647147961541347e-17,
        1.475212603255425e-16,
        -0.013620916317742501
      ],
      "ranking_score": 0.5348550235102768
    },
    {
      "candidate_id": "inversion_parent_bec_00_00",
      "source": "same_species_inversion_center_projection_after_BEC",
      "spacegroup": "P-3c1",
      "spacegroup_number": 165,
      "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,
        -0.5
      ],
      "formal_class": [
        0.0,
        0.0,
        0.5
      ],
      "target_residual": 0.4999999999999937,
      "parent_symmetrization_rmsd_A": 0.1379602644385773,
      "parent_cell_rmsd_A": 0.02345543739660081,
      "energy_eV": -216.4493462557759,
      "reduced_polarization": [
        -1.948749892256395e-14,
        -1.0616044958154558e-14,
        -6.270553220715291e-15
      ],
      "cartesian_polarization_e_A2": [
        -1.9755187258920701e-16,
        -1.2808974179002405e-16,
        -1.708224380293654e-16
      ],
      "ranking_score": 1.143824123787715
    },
    {
      "candidate_id": "inversion_parent_bec_00_01",
      "source": "same_species_inversion_center_projection_after_BEC",
      "spacegroup": "P-3c1",
      "spacegroup_number": 165,
      "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,
        -0.5
      ],
      "formal_class": [
        0.0,
        0.0,
        0.5
      ],
      "target_residual": 0.49999999999999767,
      "parent_symmetrization_rmsd_A": 0.13796026443857826,
      "parent_cell_rmsd_A": 0.02345543739660081,
      "energy_eV": -216.44934625577582,
      "reduced_polarization": [
        6.775541688688152e-15,
        6.7634069250115305e-15,
        2.3678097349432507e-15
      ],
      "cartesian_polarization_e_A2": [
        4.7283770783058895e-17,
        8.160506387075907e-17,
        6.450388306672143e-17
      ],
      "ranking_score": 1.1438241237877238
    },
    {
      "candidate_id": "bec_projection_01",
      "source": "MACEField_BEC_backprojection",
      "spacegroup": "P6_3cm",
      "spacegroup_number": 185,
      "pointgroup": "6mm",
      "has_inversion": false,
      "is_polar_point_group": true,
      "nonpolar_parent_hypothesis": false,
      "symmetry_tolerance_A": null,
      "target_reduced_polarization": [
        0.0,
        0.0,
        0.0
      ],
      "formal_class": [
        0.0,
        0.0,
        0.0
      ],
      "target_residual": 8.90934912430175e-06,
      "parent_symmetrization_rmsd_A": 0.053015868349048874,
      "parent_cell_rmsd_A": 0.04249886855193981,
      "energy_eV": -218.68682342561294,
      "reduced_polarization": [
        -1.4965727633996383e-15,
        4.499319884723431e-15,
        -8.90934912430175e-06
      ],
      "cartesian_polarization_e_A2": [
        -5.2242020878784293e-17,
        5.433344673893934e-17,
        -2.4058747744036975e-07
      ],
      "ranking_score": 0.5636584041852825
    },
    {
      "candidate_id": "bec_projection_02",
      "source": "MACEField_BEC_backprojection",
      "spacegroup": "Cm",
      "spacegroup_number": 8,
      "pointgroup": "m",
      "has_inversion": false,
      "is_polar_point_group": true,
      "nonpolar_parent_hypothesis": false,
      "symmetry_tolerance_A": null,
      "target_reduced_polarization": [
        0.5,
        0.0,
        -0.5
      ],
      "formal_class": [
        0.5,
        0.0,
        0.5
      ],
      "target_residual": 2.2859187196960945e-06,
      "parent_symmetrization_rmsd_A": 0.05988796368669918,
      "parent_cell_rmsd_A": 0.04513693942478758,
      "energy_eV": -218.78977349911187,
      "reduced_polarization": [
        0.5000021755520795,
        3.734910683364748e-11,
        -0.5000007017104396
      ],
      "cartesian_polarization_e_A2": [
        0.00691196764379686,
        1.5227057800595784e-10,
        -0.013593362790972702
      ],
      "ranking_score": 0.5711767703803354
    },
    {
      "candidate_id": "bec_projection_03",
      "source": "MACEField_BEC_backprojection",
      "spacegroup": "Cm",
      "spacegroup_number": 8,
      "pointgroup": "m",
      "has_inversion": false,
      "is_polar_point_group": true,
      "nonpolar_parent_hypothesis": false,
      "symmetry_tolerance_A": null,
      "target_reduced_polarization": [
        0.5,
        0.0,
        0.0
      ],
      "formal_class": [
        0.5,
        0.0,
        0.0
      ],
      "target_residual": 1.3826182843231615e-05,
      "parent_symmetrization_rmsd_A": 0.07498493354366173,
      "parent_cell_rmsd_A": 0.05790195321911445,
      "energy_eV": -218.53509575438005,
      "reduced_polarization": [
        0.49998690073800034,
        9.76005796415705e-11,
        -4.424100707397384e-06
      ],
      "cartesian_polarization_e_A2": [
        0.006972010996270113,
        -2.994770817117746e-10,
        2.8414037336239717e-05
      ],
      "ranking_score": 0.5894880742141269
    }
  ],
  "formal_branches": [
    {
      "orbit_id": 0,
      "formal_class": [
        0.0,
        0.0,
        0.5
      ],
      "formal_classes_in_orbit": [
        [
          0.0,
          0.0,
          0.5
        ]
      ],
      "target_reduced_polarization": [
        0.0,
        0.0,
        -0.5
      ],
      "bec_backprojection": {
        "converged_to_target": true,
        "history": [
          {
            "iteration": 0,
            "reduced_polarization": [
              1.539233656883536e-15,
              -7.136828098731235e-18,
              -0.3241120818847303
            ],
            "branch_aligned_reduced_polarization": [
              1.539233656883536e-15,
              -7.136828098731235e-18,
              -0.3241120818847303
            ],
            "target_residual": 0.17588791811526971,
            "energy_eV": -218.8411916166313,
            "max_atomic_step_A": 0.033657110768402526,
            "max_log_strain_component": 0.0018506042643051221,
            "step_scale": 1.0,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 2.6344065528419858,
            "cell_principal_stretches": [
              1.0018523176891707,
              0.9984548467843055,
              0.998454797796329
            ],
            "cell_volume_ratio": 0.9987586299464959,
            "cell_rmsd_from_input_A": 0.023301872275481205
          },
          {
            "iteration": 1,
            "reduced_polarization": [
              2.455868606448604e-15,
              -8.308063376618546e-15,
              -0.4988644065702881
            ],
            "branch_aligned_reduced_polarization": [
              2.455868606448604e-15,
              -8.308063376618546e-15,
              -0.4988644065702881
            ],
            "target_residual": 0.001135593429711923,
            "energy_eV": -218.94622542138111,
            "max_atomic_step_A": 0.00021540510058186275,
            "max_log_strain_component": 1.2177712739783478e-05,
            "step_scale": 1.0,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 2.6344065528419858,
            "cell_principal_stretches": [
              1.0018645180331893,
              0.9984446869721435,
              0.9984446376623083
            ],
            "cell_volume_ratio": 0.9987504663430429,
            "cell_rmsd_from_input_A": 0.02345543739660081
          },
          {
            "iteration": 2,
            "reduced_polarization": [
              2.1747219430375002e-15,
              1.0325591906418892e-14,
              -0.49999684860270055
            ],
            "branch_aligned_reduced_polarization": [
              2.1747219430375002e-15,
              1.0325591906418892e-14,
              -0.49999684860270055
            ],
            "target_residual": 3.1513972994501316e-06,
            "energy_eV": -218.94698467544814
          }
        ],
        "iterations": 2
      },
      "parent": {
        "candidate_id": "bec_projection_00",
        "source": "MACEField_BEC_backprojection",
        "spacegroup": "P6_3cm",
        "spacegroup_number": 185,
        "pointgroup": "6mm",
        "has_inversion": false,
        "is_polar_point_group": true,
        "nonpolar_parent_hypothesis": false,
        "symmetry_tolerance_A": null,
        "target_reduced_polarization": [
          0.0,
          0.0,
          -0.5
        ],
        "formal_class": [
          0.0,
          0.0,
          0.5
        ],
        "target_residual": 3.1513972994501316e-06,
        "parent_symmetrization_rmsd_A": 0.0289848613665277,
        "parent_cell_rmsd_A": 0.02345543739660081,
        "energy_eV": -218.94698467544814,
        "reduced_polarization": [
          2.1747219430375002e-15,
          1.0325591906418892e-14,
          -0.49999684860270055
        ],
        "cartesian_polarization_e_A2": [
          6.647147961541347e-17,
          1.475212603255425e-16,
          -0.013620916317742501
        ],
        "ranking_score": 0.5348550235102768
      },
      "branch_status": "awaiting_branch_sampling"
    },
    {
      "orbit_id": 1,
      "formal_class": [
        0.0,
        0.0,
        0.0
      ],
      "formal_classes_in_orbit": [
        [
          0.0,
          0.0,
          0.0
        ]
      ],
      "target_reduced_polarization": [
        0.0,
        0.0,
        0.0
      ],
      "bec_backprojection": {
        "converged_to_target": true,
        "history": [
          {
            "iteration": 0,
            "reduced_polarization": [
              1.539233656883536e-15,
              -7.136828098731235e-18,
              -0.3241120818847303
            ],
            "branch_aligned_reduced_polarization": [
              1.539233656883536e-15,
              -7.136828098731235e-18,
              -0.3241120818847303
            ],
            "target_residual": 0.3241120818847303,
            "energy_eV": -218.8411916166313,
            "max_atomic_step_A": 0.06202061152502145,
            "max_log_strain_component": 0.003410144410576322,
            "step_scale": 1.0,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 2.6344065528419858,
            "cell_principal_stretches": [
              1.0028536401583408,
              1.0028535494895483,
              0.9965956635280286
            ],
            "cell_volume_ratio": 1.0022915392639404,
            "cell_rmsd_from_input_A": 0.04275825292145588
          },
          {
            "iteration": 1,
            "reduced_polarization": [
              -3.2764302526154174e-14,
              -5.348628260395798e-15,
              0.0019798164833655374
            ],
            "branch_aligned_reduced_polarization": [
              -3.2764302526154174e-14,
              -5.348628260395798e-15,
              0.0019798164833655374
            ],
            "target_residual": 0.0019798164833655374,
            "energy_eV": -218.68554921636735,
            "max_atomic_step_A": 0.00038623441649404385,
            "max_log_strain_component": 2.0743094687973528e-05,
            "step_scale": 1.0,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 2.6344065528419858,
            "cell_principal_stretches": [
              1.0028362575536345,
              1.002836167437921,
              0.9966163362206499
            ],
            "cell_volume_ratio": 1.0022775845160055,
            "cell_rmsd_from_input_A": 0.04249886855193981
          },
          {
            "iteration": 2,
            "reduced_polarization": [
              -1.4965727633996383e-15,
              4.499319884723431e-15,
              -8.90934912430175e-06
            ],
            "branch_aligned_reduced_polarization": [
              -1.4965727633996383e-15,
              4.499319884723431e-15,
              -8.90934912430175e-06
            ],
            "target_residual": 8.90934912430175e-06,
            "energy_eV": -218.68682342561294
          }
        ],
        "iterations": 2
      },
      "parent": {
        "candidate_id": "inversion_parent_endpoint_00",
        "source": "same_species_inversion_center_projection_from_endpoint",
        "spacegroup": "P-3c1",
        "spacegroup_number": 165,
        "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": 1.5125111375639118e-14,
        "parent_symmetrization_rmsd_A": 0.1379397957226171,
        "parent_cell_rmsd_A": 0.0,
        "energy_eV": -216.5274938220213,
        "reduced_polarization": [
          -7.759632153224029e-15,
          -4.300704825763451e-15,
          1.224994044776523e-14
        ],
        "cartesian_polarization_e_A2": [
          -7.817376813320475e-17,
          -5.19067949920816e-17,
          3.3267566548045244e-16
        ],
        "ranking_score": 0.13793979572264736
      },
      "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": [
          -218.84119161663136,
          -218.93232954582692,
          -219.02615005044814,
          -219.09479485667316,
          -219.07851831465098,
          -218.87682796331072,
          -218.34869416126938,
          -217.40799137355216,
          -216.52749382202134
        ],
        "cartesian_polarizations_e_A2": [
          [
            -8.594256887251548e-18,
            -1.9099144187590692e-17,
            -0.008802018507031028
          ],
          [
            -2.491060233280194e-10,
            1.435152687198465e-10,
            -0.009256335146142632
          ],
          [
            -9.122705338005474e-11,
            5.171145748013176e-11,
            -0.009713680160730575
          ],
          [
            2.1810769655177972e-10,
            -1.2762404495760379e-10,
            -0.01012531951521572
          ],
          [
            4.055352109387204e-10,
            -2.363446238495423e-10,
            -0.010415095512981549
          ],
          [
            3.8702095467341026e-10,
            -2.2582114112432815e-10,
            -0.010775323867133339
          ],
          [
            2.8906929392081026e-10,
            -1.690536245375921e-10,
            -0.01088731968879722
          ],
          [
            6.9548372960755e-10,
            -4.0498636806689015e-10,
            -0.010638933908054432
          ],
          [
            -7.501456965694298e-17,
            -2.805214229389494e-17,
            4.2213267395843434e-16
          ]
        ],
        "raw_reduced_polarization": [
          [
            -1.4078960034748254e-15,
            -1.5824475694955488e-15,
            -0.32411208188473023
          ],
          [
            -1.1928917364093592e-08,
            1.1890867252511718e-08,
            -0.3408411437038701
          ],
          [
            -4.403644903724787e-09,
            4.284520259168201e-09,
            -0.3576817177948351
          ],
          [
            1.0362992420024905e-08,
            -1.057420991059743e-08,
            -0.3728392964867332
          ],
          [
            1.9307676761077813e-08,
            -1.9582185039319685e-08,
            -0.3835095651121723
          ],
          [
            1.841516327935321e-08,
            -1.871026850224451e-08,
            -0.396774063672904
          ],
          [
            1.3738459265951682e-08,
            -1.4006831648390862e-08,
            -0.4008980267039833
          ],
          [
            3.3126286952731165e-08,
            -3.3554890603039326e-08,
            -0.39175184819472403
          ],
          [
            -6.544715941960596e-15,
            -2.324242592029834e-15,
            1.5543968656615084e-14
          ]
        ],
        "unwrapped_reduced_polarization": [
          [
            -1.4078960034748254e-15,
            -1.5824475694955488e-15,
            -0.32411208188473023
          ],
          [
            -1.1928917364093592e-08,
            1.1890867252511718e-08,
            -0.3408411437038701
          ],
          [
            -4.403644903724786e-09,
            4.284520259168202e-09,
            -0.3576817177948351
          ],
          [
            1.0362992420024905e-08,
            -1.057420991059743e-08,
            -0.3728392964867332
          ],
          [
            1.9307676761077813e-08,
            -1.9582185039319685e-08,
            -0.3835095651121723
          ],
          [
            1.841516327935321e-08,
            -1.871026850224451e-08,
            -0.396774063672904
          ],
          [
            1.3738459265951682e-08,
            -1.4006831648390862e-08,
            -0.4008980267039833
          ],
          [
            3.3126286952731165e-08,
            -3.3554890603039326e-08,
            -0.39175184819472403
          ],
          [
            -6.544715945038003e-15,
            -2.324242591572488e-15,
            1.554312234475219e-14
          ]
        ],
        "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": [
          [
            -1.3877787807814457e-15,
            -1.609823385706477e-15,
            -0.32411208188473023
          ],
          [
            -1.192891735390944e-08,
            1.1890867290809126e-08,
            -0.3408411437038701
          ],
          [
            -4.403644893180569e-09,
            4.284520294106642e-09,
            -0.3576817177948351
          ],
          [
            1.0362992464152398e-08,
            -1.0574209896585529e-08,
            -0.3728392964867332
          ],
          [
            1.9307676790703e-08,
            -1.9582185040167843e-08,
            -0.3835095651121723
          ],
          [
            1.841516328315862e-08,
            -1.8710268501198613e-08,
            -0.396774063672904
          ],
          [
            1.3738459259116098e-08,
            -1.4006831638990747e-08,
            -0.4008980267039833
          ],
          [
            3.312628693574737e-08,
            -3.355489058831651e-08,
            -0.39175184819472403
          ],
          [
            -6.5503158452884236e-15,
            -2.3314683517128287e-15,
            1.554312234475219e-14
          ]
        ]
      },
      "reflected": {
        "reached": true,
        "construction": "reflect_displacements_about_reconstructed_parent",
        "energies_eV": [
          -216.52749382202134,
          -217.40799137355222,
          -218.34869416126938,
          -218.87682796331077,
          -219.07851831465098,
          -219.09479485667313,
          -219.0261500504481,
          -218.93232954582692,
          -218.8411916166313
        ],
        "cartesian_polarizations_e_A2": [
          [
            -1.1503841184477712e-16,
            -9.17081928584838e-17,
            3.696923586437553e-16
          ],
          [
            -6.954836705586412e-10,
            4.0498640364505047e-10,
            0.010638933908054243
          ],
          [
            -2.890692790985411e-10,
            1.69053682226857e-10,
            0.01088731968879711
          ],
          [
            -3.8702094875654857e-10,
            2.2582117820243027e-10,
            0.010775323867133256
          ],
          [
            -4.0553525511758164e-10,
            2.3634465338289927e-10,
            0.010415095512981329
          ],
          [
            -2.1810769710247578e-10,
            1.2762399913171038e-10,
            0.010125319515215475
          ],
          [
            9.122703499460822e-11,
            -5.171150019520881e-11,
            0.009713680160730324
          ],
          [
            2.4910601579682806e-10,
            -1.4351527927606996e-10,
            0.009256335146142412
          ],
          [
            7.41860551451115e-18,
            -8.342398550265244e-17,
            0.008802018507030688
          ]
        ],
        "raw_reduced_polarization": [
          [
            -1.2053677295617376e-14,
            -7.598424592554672e-15,
            1.3612986603151376e-14
          ],
          [
            -3.3126281241833335e-08,
            3.3554893550845405e-08,
            0.3917518481947171
          ],
          [
            -1.373845581249087e-08,
            1.4006836428198594e-08,
            0.4008980267039793
          ],
          [
            -1.841516131875337e-08,
            1.871027157432732e-08,
            0.39677406367290097
          ],
          [
            -1.9307678707603512e-08,
            1.9582187486287385e-08,
            0.3835095651121642
          ],
          [
            -1.0362994357977322e-08,
            1.0574206113721875e-08,
            0.3728392964867242
          ],
          [
            4.40364181493024e-09,
            -4.2845237982990226e-09,
            0.3576817177948258
          ],
          [
            1.1928916386385942e-08,
            -1.1890868127140967e-08,
            0.340841143703862
          ],
          [
            -2.9237063609029217e-15,
            -6.912041806673091e-15,
            0.3241120818847177
          ]
        ],
        "unwrapped_reduced_polarization": [
          [
            -1.2053677295617376e-14,
            -7.598424592554672e-15,
            1.3612986603151376e-14
          ],
          [
            -3.3126281241833335e-08,
            3.3554893550845405e-08,
            0.3917518481947171
          ],
          [
            -1.373845581249087e-08,
            1.4006836428198595e-08,
            0.4008980267039793
          ],
          [
            -1.841516131875337e-08,
            1.871027157432732e-08,
            0.39677406367290097
          ],
          [
            -1.9307678707603512e-08,
            1.9582187486287385e-08,
            0.3835095651121642
          ],
          [
            -1.0362994357977322e-08,
            1.0574206113721875e-08,
            0.3728392964867242
          ],
          [
            4.40364181493024e-09,
            -4.2845237982990226e-09,
            0.3576817177948258
          ],
          [
            1.1928916386385942e-08,
            -1.1890868127140967e-08,
            0.340841143703862
          ],
          [
            -2.923706360351135e-15,
            -6.912041806389493e-15,
            0.3241120818847177
          ]
        ],
        "gauge_integer_shift": [
          0,
          0,
          0
        ],
        "expected_opposite_endpoint_reduced_polarization": [
          -1.1681535880446364e-14,
          -3.0660376145641193e-15,
          0.3241120818847613
        ],
        "actual_opposite_endpoint_branch_residual": 4.466791053567248e-14
      },
      "pnp_branch": {
        "construction": "incoming_path_concatenated_with_parent_reflection",
        "reduced_polarization": [
          [
            -1.4078960034748254e-15,
            -1.5824475694955488e-15,
            -0.32411208188473023
          ],
          [
            -1.1928917364093592e-08,
            1.1890867252511718e-08,
            -0.3408411437038701
          ],
          [
            -4.403644903724787e-09,
            4.284520259168201e-09,
            -0.3576817177948351
          ],
          [
            1.0362992420024905e-08,
            -1.057420991059743e-08,
            -0.3728392964867332
          ],
          [
            1.9307676761077813e-08,
            -1.9582185039319685e-08,
            -0.3835095651121723
          ],
          [
            1.841516327935321e-08,
            -1.871026850224451e-08,
            -0.396774063672904
          ],
          [
            1.3738459265951682e-08,
            -1.4006831648390862e-08,
            -0.4008980267039833
          ],
          [
            3.3126286952731165e-08,
            -3.3554890603039326e-08,
            -0.39175184819472403
          ],
          [
            -6.544715941960596e-15,
            -2.324242592029834e-15,
            1.5543968656615084e-14
          ],
          [
            -3.3126281241833335e-08,
            3.3554893550845405e-08,
            0.3917518481947171
          ],
          [
            -1.373845581249087e-08,
            1.4006836428198594e-08,
            0.4008980267039793
          ],
          [
            -1.841516131875337e-08,
            1.871027157432732e-08,
            0.39677406367290097
          ],
          [
            -1.9307678707603512e-08,
            1.9582187486287385e-08,
            0.3835095651121642
          ],
          [
            -1.0362994357977322e-08,
            1.0574206113721875e-08,
            0.3728392964867242
          ],
          [
            4.40364181493024e-09,
            -4.2845237982990226e-09,
            0.3576817177948258
          ],
          [
            1.1928916386385942e-08,
            -1.1890868127140967e-08,
            0.340841143703862
          ],
          [
            -2.9237063609029217e-15,
            -6.912041806673091e-15,
            0.3241120818847177
          ]
        ],
        "unwrapped_reduced_polarization": [
          [
            -1.4078960034748254e-15,
            -1.5824475694955488e-15,
            -0.32411208188473023
          ],
          [
            -1.1928917364093592e-08,
            1.1890867252511718e-08,
            -0.3408411437038701
          ],
          [
            -4.403644903724786e-09,
            4.284520259168202e-09,
            -0.3576817177948351
          ],
          [
            1.0362992420024905e-08,
            -1.057420991059743e-08,
            -0.3728392964867332
          ],
          [
            1.9307676761077813e-08,
            -1.9582185039319685e-08,
            -0.3835095651121723
          ],
          [
            1.841516327935321e-08,
            -1.871026850224451e-08,
            -0.396774063672904
          ],
          [
            1.3738459265951682e-08,
            -1.4006831648390862e-08,
            -0.4008980267039833
          ],
          [
            3.3126286952731165e-08,
            -3.3554890603039326e-08,
            -0.39175184819472403
          ],
          [
            -6.544715945038003e-15,
            -2.324242591572488e-15,
            1.554312234475219e-14
          ],
          [
            -3.3126281241833335e-08,
            3.3554893550845405e-08,
            0.3917518481947171
          ],
          [
            -1.373845581249087e-08,
            1.4006836428198595e-08,
            0.4008980267039793
          ],
          [
            -1.841516131875337e-08,
            1.871027157432732e-08,
            0.39677406367290097
          ],
          [
            -1.9307678707603512e-08,
            1.9582187486287385e-08,
            0.3835095651121642
          ],
          [
            -1.0362994357977322e-08,
            1.0574206113721875e-08,
            0.3728392964867242
          ],
          [
            4.40364181493024e-09,
            -4.2845237982990226e-09,
            0.3576817177948258
          ],
          [
            1.1928916386385942e-08,
            -1.1890868127140967e-08,
            0.340841143703862
          ],
          [
            -2.923706360351135e-15,
            -6.912041806389493e-15,
            0.3241120818847177
          ]
        ],
        "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": [
          [
            -1.3877787807814457e-15,
            -1.609823385706477e-15,
            -0.32411208188473023
          ],
          [
            -1.192891735390944e-08,
            1.1890867290809126e-08,
            -0.3408411437038701
          ],
          [
            -4.403644893180569e-09,
            4.284520294106642e-09,
            -0.3576817177948351
          ],
          [
            1.0362992464152398e-08,
            -1.0574209896585529e-08,
            -0.3728392964867332
          ],
          [
            1.9307676790703e-08,
            -1.9582185040167843e-08,
            -0.3835095651121723
          ],
          [
            1.841516328315862e-08,
            -1.8710268501198613e-08,
            -0.396774063672904
          ],
          [
            1.3738459259116098e-08,
            -1.4006831638990747e-08,
            -0.4008980267039833
          ],
          [
            3.312628693574737e-08,
            -3.355489058831651e-08,
            -0.39175184819472403
          ],
          [
            -6.5503158452884236e-15,
            -2.3314683517128287e-15,
            1.554312234475219e-14
          ],
          [
            -3.3126281218098796e-08,
            3.3554893530407526e-08,
            0.3917518481947171
          ],
          [
            -1.3738455817424722e-08,
            1.4006836468460904e-08,
            0.4008980267039792
          ],
          [
            -1.8415161340268327e-08,
            1.871027155431193e-08,
            0.3967740636729009
          ],
          [
            -1.9307678733593292e-08,
            1.958218753816965e-08,
            0.3835095651121643
          ],
          [
            -1.036299435153154e-08,
            1.0574206066316094e-08,
            0.3728392964867242
          ],
          [
            4.4036417845561004e-09,
            -4.284523791309169e-09,
            0.3576817177948258
          ],
          [
            1.192891641021987e-08,
            -1.1890868123476395e-08,
            0.340841143703862
          ],
          [
            -2.942091015256665e-15,
            -6.938893903907228e-15,
            0.32411208188471763
          ]
        ]
      },
      "incoming_structure_ids": [
        "incoming_01_000",
        "incoming_01_001",
        "incoming_01_002",
        "incoming_01_003",
        "incoming_01_004",
        "incoming_01_005",
        "incoming_01_006",
        "incoming_01_007",
        "incoming_01_008"
      ],
      "reflected_structure_ids": [
        "reflected_01_001",
        "reflected_01_002",
        "reflected_01_003",
        "reflected_01_004",
        "reflected_01_005",
        "reflected_01_006",
        "reflected_01_007",
        "reflected_01_008"
      ]
    },
    {
      "orbit_id": 2,
      "formal_class": [
        0.5,
        0.0,
        0.5
      ],
      "formal_classes_in_orbit": [
        [
          0.5,
          0.0,
          0.5
        ],
        [
          0.0,
          0.5,
          0.5
        ],
        [
          0.5,
          0.5,
          0.5
        ]
      ],
      "target_reduced_polarization": [
        0.5,
        0.0,
        -0.5
      ],
      "bec_backprojection": {
        "converged_to_target": true,
        "history": [
          {
            "iteration": 0,
            "reduced_polarization": [
              1.539233656883536e-15,
              -7.136828098731235e-18,
              -0.3241120818847303
            ],
            "branch_aligned_reduced_polarization": [
              1.5543122344752192e-15,
              -7.136828098731235e-18,
              -0.3241120818847303
            ],
            "target_residual": 0.5300344891975637,
            "energy_eV": -218.8411916166313,
            "max_atomic_step_A": 0.05833693186219088,
            "max_log_strain_component": 0.004031933010261237,
            "step_scale": 1.0,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 2.6344065528419858,
            "cell_principal_stretches": [
              1.0045374594198824,
              0.9984548291228023,
              0.995785932713778
            ],
            "cell_volume_ratio": 0.9987586299465112,
            "cell_rmsd_from_input_A": 0.04539585893934334
          },
          {
            "iteration": 1,
            "reduced_polarization": [
              0.5054582118769154,
              -2.018303639973617e-08,
              -0.4986013990597676
            ],
            "branch_aligned_reduced_polarization": [
              0.5054582118769154,
              -2.018303639973617e-08,
              -0.4986013990597676
            ],
            "target_residual": 0.00563455069049227,
            "energy_eV": -218.78537236393248,
            "max_atomic_step_A": 0.000579591276219782,
            "max_log_strain_component": 4.331425108753293e-05,
            "step_scale": 1.0,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 2.6344065528419858,
            "cell_principal_stretches": [
              1.004504127806062,
              0.9984422065150216,
              0.9958214518140496
            ],
            "cell_volume_ratio": 0.9987484875530364,
            "cell_rmsd_from_input_A": 0.04513693942478758
          },
          {
            "iteration": 2,
            "reduced_polarization": [
              0.5000021755520795,
              3.734910683364748e-11,
              -0.5000007017104396
            ],
            "branch_aligned_reduced_polarization": [
              0.5000021755520795,
              3.734910683364748e-11,
              -0.5000007017104396
            ],
            "target_residual": 2.2859187196960945e-06,
            "energy_eV": -218.78977349911187
          }
        ],
        "iterations": 2
      },
      "parent": {
        "candidate_id": "bec_projection_02",
        "source": "MACEField_BEC_backprojection",
        "spacegroup": "Cm",
        "spacegroup_number": 8,
        "pointgroup": "m",
        "has_inversion": false,
        "is_polar_point_group": true,
        "nonpolar_parent_hypothesis": false,
        "symmetry_tolerance_A": null,
        "target_reduced_polarization": [
          0.5,
          0.0,
          -0.5
        ],
        "formal_class": [
          0.5,
          0.0,
          0.5
        ],
        "target_residual": 2.2859187196960945e-06,
        "parent_symmetrization_rmsd_A": 0.05988796368669918,
        "parent_cell_rmsd_A": 0.04513693942478758,
        "energy_eV": -218.78977349911187,
        "reduced_polarization": [
          0.5000021755520795,
          3.734910683364748e-11,
          -0.5000007017104396
        ],
        "cartesian_polarization_e_A2": [
          0.00691196764379686,
          1.5227057800595784e-10,
          -0.013593362790972702
        ],
        "ranking_score": 0.5711767703803354
      },
      "branch_status": "awaiting_branch_sampling"
    },
    {
      "orbit_id": 3,
      "formal_class": [
        0.5,
        0.0,
        0.0
      ],
      "formal_classes_in_orbit": [
        [
          0.5,
          0.0,
          0.0
        ],
        [
          0.0,
          0.5,
          0.0
        ],
        [
          0.5,
          0.5,
          0.0
        ]
      ],
      "target_reduced_polarization": [
        0.5,
        0.0,
        0.0
      ],
      "bec_backprojection": {
        "converged_to_target": true,
        "history": [
          {
            "iteration": 0,
            "reduced_polarization": [
              1.539233656883536e-15,
              -7.136828098731235e-18,
              -0.3241120818847303
            ],
            "branch_aligned_reduced_polarization": [
              1.5543122344752192e-15,
              -7.136828098731235e-18,
              -0.3241120818847303
            ],
            "target_residual": 0.5958595821363055,
            "energy_eV": -218.8411916166313,
            "max_atomic_step_A": 0.0824406841639224,
            "max_log_strain_component": 0.0040319330102835055,
            "step_scale": 1.0,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 2.6344065528419858,
            "cell_principal_stretches": [
              1.0048355090513374,
              1.0028535821776137,
              0.9946300139232719
            ],
            "cell_volume_ratio": 1.002291539263956,
            "cell_rmsd_from_input_A": 0.057635737649693854
          },
          {
            "iteration": 1,
            "reduced_polarization": [
              0.4910523902976834,
              2.3494334463993643e-08,
              0.002168842119354716
            ],
            "branch_aligned_reduced_polarization": [
              0.4910523902976834,
              2.3494334463993643e-08,
              0.002168842119354716
            ],
            "target_residual": 0.009206714697666563,
            "energy_eV": -218.53918917334852,
            "max_atomic_step_A": 0.0008792603781622637,
            "max_log_strain_component": 7.30941690525998e-05,
            "step_scale": 1.0,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 2.6344065528419858,
            "cell_principal_stretches": [
              1.004883020647613,
              1.0028347152539572,
              0.9945866683157508
            ],
            "cell_volume_ratio": 1.0022763925949576,
            "cell_rmsd_from_input_A": 0.05790195321911445
          },
          {
            "iteration": 2,
            "reduced_polarization": [
              0.49998690073800034,
              9.76005796415705e-11,
              -4.424100707397384e-06
            ],
            "branch_aligned_reduced_polarization": [
              0.49998690073800034,
              9.76005796415705e-11,
              -4.424100707397384e-06
            ],
            "target_residual": 1.3826182843231615e-05,
            "energy_eV": -218.53509575438005
          }
        ],
        "iterations": 2
      },
      "parent": {
        "candidate_id": "bec_projection_03",
        "source": "MACEField_BEC_backprojection",
        "spacegroup": "Cm",
        "spacegroup_number": 8,
        "pointgroup": "m",
        "has_inversion": false,
        "is_polar_point_group": true,
        "nonpolar_parent_hypothesis": false,
        "symmetry_tolerance_A": null,
        "target_reduced_polarization": [
          0.5,
          0.0,
          0.0
        ],
        "formal_class": [
          0.5,
          0.0,
          0.0
        ],
        "target_residual": 1.3826182843231615e-05,
        "parent_symmetrization_rmsd_A": 0.07498493354366173,
        "parent_cell_rmsd_A": 0.05790195321911445,
        "energy_eV": -218.53509575438005,
        "reduced_polarization": [
          0.49998690073800034,
          9.76005796415705e-11,
          -4.424100707397384e-06
        ],
        "cartesian_polarization_e_A2": [
          0.006972010996270113,
          -2.994770817117746e-10,
          2.8414037336239717e-05
        ],
        "ranking_score": 0.5894880742141269
      },
      "branch_status": "awaiting_branch_sampling"
    }
  ],
  "sampled_polarization_branches": [
    {
      "orbit_id": 1,
      "candidate_id": "inversion_parent_endpoint_00",
      "formal_class": [
        0.0,
        0.0,
        0.0
      ],
      "construction": "MACEField-BEC-parent plus variable-cell P-N-P path and symmetric log-strain continuation beyond both polar endpoints",
      "geometry_diagnostics": {
        "collision_aware": false,
        "permutations_tested": 1,
        "selected_order": [
          0,
          1,
          2,
          3,
          4,
          5,
          6,
          7,
          8,
          9,
          10,
          11,
          12,
          13,
          14,
          15,
          16,
          17,
          18,
          19,
          20,
          21,
          22,
          23,
          24,
          25,
          26,
          27,
          28,
          29
        ],
        "endpoint_rmsd_A": 0.1379397957226171,
        "minimum_distance_A_by_image": [
          2.205199845978928,
          2.1977746504786935,
          2.1913191834285732,
          2.1858420365688507,
          2.181350579295986,
          2.1778509100837184,
          2.1753478156616928,
          2.1738447385795023,
          2.1733437536638203
        ],
        "minimum_distance_A": 2.1733437536638203,
        "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": [
          467.8829388607413,
          467.8829388607413,
          467.8829388607413,
          467.8829388607413,
          467.8829388607413,
          467.8829388607413,
          467.8829388607413,
          467.8829388607413,
          467.8829388607413
        ],
        "cell_deformation_log_strain_norm": 0.0
      },
      "parent_reduced_polarization": [
        -6.544715941960596e-15,
        -2.324242592029834e-15,
        1.5543968656615084e-14
      ],
      "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": [
          -218.84119161663136,
          -218.93232954582692,
          -219.02615005044814,
          -219.09479485667316,
          -219.07851831465098,
          -218.87682796331072,
          -218.34869416126938,
          -217.40799137355216,
          -216.52749382202134
        ],
        "cartesian_polarizations_e_A2": [
          [
            -8.594256887251548e-18,
            -1.9099144187590692e-17,
            -0.008802018507031028
          ],
          [
            -2.491060233280194e-10,
            1.435152687198465e-10,
            -0.009256335146142632
          ],
          [
            -9.122705338005474e-11,
            5.171145748013176e-11,
            -0.009713680160730575
          ],
          [
            2.1810769655177972e-10,
            -1.2762404495760379e-10,
            -0.01012531951521572
          ],
          [
            4.055352109387204e-10,
            -2.363446238495423e-10,
            -0.010415095512981549
          ],
          [
            3.8702095467341026e-10,
            -2.2582114112432815e-10,
            -0.010775323867133339
          ],
          [
            2.8906929392081026e-10,
            -1.690536245375921e-10,
            -0.01088731968879722
          ],
          [
            6.9548372960755e-10,
            -4.0498636806689015e-10,
            -0.010638933908054432
          ],
          [
            -7.501456965694298e-17,
            -2.805214229389494e-17,
            4.2213267395843434e-16
          ]
        ],
        "raw_reduced_polarization": [
          [
            -1.4078960034748254e-15,
            -1.5824475694955488e-15,
            -0.32411208188473023
          ],
          [
            -1.1928917364093592e-08,
            1.1890867252511718e-08,
            -0.3408411437038701
          ],
          [
            -4.403644903724787e-09,
            4.284520259168201e-09,
            -0.3576817177948351
          ],
          [
            1.0362992420024905e-08,
            -1.057420991059743e-08,
            -0.3728392964867332
          ],
          [
            1.9307676761077813e-08,
            -1.9582185039319685e-08,
            -0.3835095651121723
          ],
          [
            1.841516327935321e-08,
            -1.871026850224451e-08,
            -0.396774063672904
          ],
          [
            1.3738459265951682e-08,
            -1.4006831648390862e-08,
            -0.4008980267039833
          ],
          [
            3.3126286952731165e-08,
            -3.3554890603039326e-08,
            -0.39175184819472403
          ],
          [
            -6.544715941960596e-15,
            -2.324242592029834e-15,
            1.5543968656615084e-14
          ]
        ],
        "unwrapped_reduced_polarization": [
          [
            -1.4078960034748254e-15,
            -1.5824475694955488e-15,
            -0.32411208188473023
          ],
          [
            -1.1928917364093592e-08,
            1.1890867252511718e-08,
            -0.3408411437038701
          ],
          [
            -4.403644903724786e-09,
            4.284520259168202e-09,
            -0.3576817177948351
          ],
          [
            1.0362992420024905e-08,
            -1.057420991059743e-08,
            -0.3728392964867332
          ],
          [
            1.9307676761077813e-08,
            -1.9582185039319685e-08,
            -0.3835095651121723
          ],
          [
            1.841516327935321e-08,
            -1.871026850224451e-08,
            -0.396774063672904
          ],
          [
            1.3738459265951682e-08,
            -1.4006831648390862e-08,
            -0.4008980267039833
          ],
          [
            3.3126286952731165e-08,
            -3.3554890603039326e-08,
            -0.39175184819472403
          ],
          [
            -6.544715945038003e-15,
            -2.324242591572488e-15,
            1.554312234475219e-14
          ]
        ],
        "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": [
          [
            -1.3877787807814457e-15,
            -1.609823385706477e-15,
            -0.32411208188473023
          ],
          [
            -1.192891735390944e-08,
            1.1890867290809126e-08,
            -0.3408411437038701
          ],
          [
            -4.403644893180569e-09,
            4.284520294106642e-09,
            -0.3576817177948351
          ],
          [
            1.0362992464152398e-08,
            -1.0574209896585529e-08,
            -0.3728392964867332
          ],
          [
            1.9307676790703e-08,
            -1.9582185040167843e-08,
            -0.3835095651121723
          ],
          [
            1.841516328315862e-08,
            -1.8710268501198613e-08,
            -0.396774063672904
          ],
          [
            1.3738459259116098e-08,
            -1.4006831638990747e-08,
            -0.4008980267039833
          ],
          [
            3.312628693574737e-08,
            -3.355489058831651e-08,
            -0.39175184819472403
          ],
          [
            -6.5503158452884236e-15,
            -2.3314683517128287e-15,
            1.554312234475219e-14
          ]
        ]
      },
      "reflected": {
        "reached": true,
        "construction": "reflect_displacements_about_reconstructed_parent",
        "energies_eV": [
          -216.52749382202134,
          -217.40799137355222,
          -218.34869416126938,
          -218.87682796331077,
          -219.07851831465098,
          -219.09479485667313,
          -219.0261500504481,
          -218.93232954582692,
          -218.8411916166313
        ],
        "cartesian_polarizations_e_A2": [
          [
            -1.1503841184477712e-16,
            -9.17081928584838e-17,
            3.696923586437553e-16
          ],
          [
            -6.954836705586412e-10,
            4.0498640364505047e-10,
            0.010638933908054243
          ],
          [
            -2.890692790985411e-10,
            1.69053682226857e-10,
            0.01088731968879711
          ],
          [
            -3.8702094875654857e-10,
            2.2582117820243027e-10,
            0.010775323867133256
          ],
          [
            -4.0553525511758164e-10,
            2.3634465338289927e-10,
            0.010415095512981329
          ],
          [
            -2.1810769710247578e-10,
            1.2762399913171038e-10,
            0.010125319515215475
          ],
          [
            9.122703499460822e-11,
            -5.171150019520881e-11,
            0.009713680160730324
          ],
          [
            2.4910601579682806e-10,
            -1.4351527927606996e-10,
            0.009256335146142412
          ],
          [
            7.41860551451115e-18,
            -8.342398550265244e-17,
            0.008802018507030688
          ]
        ],
        "raw_reduced_polarization": [
          [
            -1.2053677295617376e-14,
            -7.598424592554672e-15,
            1.3612986603151376e-14
          ],
          [
            -3.3126281241833335e-08,
            3.3554893550845405e-08,
            0.3917518481947171
          ],
          [
            -1.373845581249087e-08,
            1.4006836428198594e-08,
            0.4008980267039793
          ],
          [
            -1.841516131875337e-08,
            1.871027157432732e-08,
            0.39677406367290097
          ],
          [
            -1.9307678707603512e-08,
            1.9582187486287385e-08,
            0.3835095651121642
          ],
          [
            -1.0362994357977322e-08,
            1.0574206113721875e-08,
            0.3728392964867242
          ],
          [
            4.40364181493024e-09,
            -4.2845237982990226e-09,
            0.3576817177948258
          ],
          [
            1.1928916386385942e-08,
            -1.1890868127140967e-08,
            0.340841143703862
          ],
          [
            -2.9237063609029217e-15,
            -6.912041806673091e-15,
            0.3241120818847177
          ]
        ],
        "unwrapped_reduced_polarization": [
          [
            -1.2053677295617376e-14,
            -7.598424592554672e-15,
            1.3612986603151376e-14
          ],
          [
            -3.3126281241833335e-08,
            3.3554893550845405e-08,
            0.3917518481947171
          ],
          [
            -1.373845581249087e-08,
            1.4006836428198595e-08,
            0.4008980267039793
          ],
          [
            -1.841516131875337e-08,
            1.871027157432732e-08,
            0.39677406367290097
          ],
          [
            -1.9307678707603512e-08,
            1.9582187486287385e-08,
            0.3835095651121642
          ],
          [
            -1.0362994357977322e-08,
            1.0574206113721875e-08,
            0.3728392964867242
          ],
          [
            4.40364181493024e-09,
            -4.2845237982990226e-09,
            0.3576817177948258
          ],
          [
            1.1928916386385942e-08,
            -1.1890868127140967e-08,
            0.340841143703862
          ],
          [
            -2.923706360351135e-15,
            -6.912041806389493e-15,
            0.3241120818847177
          ]
        ],
        "gauge_integer_shift": [
          0,
          0,
          0
        ],
        "expected_opposite_endpoint_reduced_polarization": [
          -1.1681535880446364e-14,
          -3.0660376145641193e-15,
          0.3241120818847613
        ],
        "actual_opposite_endpoint_branch_residual": 4.466791053567248e-14
      },
      "pnp_branch": {
        "construction": "incoming_path_concatenated_with_parent_reflection",
        "reduced_polarization": [
          [
            -1.4078960034748254e-15,
            -1.5824475694955488e-15,
            -0.32411208188473023
          ],
          [
            -1.1928917364093592e-08,
            1.1890867252511718e-08,
            -0.3408411437038701
          ],
          [
            -4.403644903724787e-09,
            4.284520259168201e-09,
            -0.3576817177948351
          ],
          [
            1.0362992420024905e-08,
            -1.057420991059743e-08,
            -0.3728392964867332
          ],
          [
            1.9307676761077813e-08,
            -1.9582185039319685e-08,
            -0.3835095651121723
          ],
          [
            1.841516327935321e-08,
            -1.871026850224451e-08,
            -0.396774063672904
          ],
          [
            1.3738459265951682e-08,
            -1.4006831648390862e-08,
            -0.4008980267039833
          ],
          [
            3.3126286952731165e-08,
            -3.3554890603039326e-08,
            -0.39175184819472403
          ],
          [
            -6.544715941960596e-15,
            -2.324242592029834e-15,
            1.5543968656615084e-14
          ],
          [
            -3.3126281241833335e-08,
            3.3554893550845405e-08,
            0.3917518481947171
          ],
          [
            -1.373845581249087e-08,
            1.4006836428198594e-08,
            0.4008980267039793
          ],
          [
            -1.841516131875337e-08,
            1.871027157432732e-08,
            0.39677406367290097
          ],
          [
            -1.9307678707603512e-08,
            1.9582187486287385e-08,
            0.3835095651121642
          ],
          [
            -1.0362994357977322e-08,
            1.0574206113721875e-08,
            0.3728392964867242
          ],
          [
            4.40364181493024e-09,
            -4.2845237982990226e-09,
            0.3576817177948258
          ],
          [
            1.1928916386385942e-08,
            -1.1890868127140967e-08,
            0.340841143703862
          ],
          [
            -2.9237063609029217e-15,
            -6.912041806673091e-15,
            0.3241120818847177
          ]
        ],
        "unwrapped_reduced_polarization": [
          [
            -1.4078960034748254e-15,
            -1.5824475694955488e-15,
            -0.32411208188473023
          ],
          [
            -1.1928917364093592e-08,
            1.1890867252511718e-08,
            -0.3408411437038701
          ],
          [
            -4.403644903724786e-09,
            4.284520259168202e-09,
            -0.3576817177948351
          ],
          [
            1.0362992420024905e-08,
            -1.057420991059743e-08,
            -0.3728392964867332
          ],
          [
            1.9307676761077813e-08,
            -1.9582185039319685e-08,
            -0.3835095651121723
          ],
          [
            1.841516327935321e-08,
            -1.871026850224451e-08,
            -0.396774063672904
          ],
          [
            1.3738459265951682e-08,
            -1.4006831648390862e-08,
            -0.4008980267039833
          ],
          [
            3.3126286952731165e-08,
            -3.3554890603039326e-08,
            -0.39175184819472403
          ],
          [
            -6.544715945038003e-15,
            -2.324242591572488e-15,
            1.554312234475219e-14
          ],
          [
            -3.3126281241833335e-08,
            3.3554893550845405e-08,
            0.3917518481947171
          ],
          [
            -1.373845581249087e-08,
            1.4006836428198595e-08,
            0.4008980267039793
          ],
          [
            -1.841516131875337e-08,
            1.871027157432732e-08,
            0.39677406367290097
          ],
          [
            -1.9307678707603512e-08,
            1.9582187486287385e-08,
            0.3835095651121642
          ],
          [
            -1.0362994357977322e-08,
            1.0574206113721875e-08,
            0.3728392964867242
          ],
          [
            4.40364181493024e-09,
            -4.2845237982990226e-09,
            0.3576817177948258
          ],
          [
            1.1928916386385942e-08,
            -1.1890868127140967e-08,
            0.340841143703862
          ],
          [
            -2.923706360351135e-15,
            -6.912041806389493e-15,
            0.3241120818847177
          ]
        ],
        "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": [
          [
            -1.3877787807814457e-15,
            -1.609823385706477e-15,
            -0.32411208188473023
          ],
          [
            -1.192891735390944e-08,
            1.1890867290809126e-08,
            -0.3408411437038701
          ],
          [
            -4.403644893180569e-09,
            4.284520294106642e-09,
            -0.3576817177948351
          ],
          [
            1.0362992464152398e-08,
            -1.0574209896585529e-08,
            -0.3728392964867332
          ],
          [
            1.9307676790703e-08,
            -1.9582185040167843e-08,
            -0.3835095651121723
          ],
          [
            1.841516328315862e-08,
            -1.8710268501198613e-08,
            -0.396774063672904
          ],
          [
            1.3738459259116098e-08,
            -1.4006831638990747e-08,
            -0.4008980267039833
          ],
          [
            3.312628693574737e-08,
            -3.355489058831651e-08,
            -0.39175184819472403
          ],
          [
            -6.5503158452884236e-15,
            -2.3314683517128287e-15,
            1.554312234475219e-14
          ],
          [
            -3.3126281218098796e-08,
            3.3554893530407526e-08,
            0.3917518481947171
          ],
          [
            -1.3738455817424722e-08,
            1.4006836468460904e-08,
            0.4008980267039792
          ],
          [
            -1.8415161340268327e-08,
            1.871027155431193e-08,
            0.3967740636729009
          ],
          [
            -1.9307678733593292e-08,
            1.958218753816965e-08,
            0.3835095651121643
          ],
          [
            -1.036299435153154e-08,
            1.0574206066316094e-08,
            0.3728392964867242
          ],
          [
            4.4036417845561004e-09,
            -4.284523791309169e-09,
            0.3576817177948258
          ],
          [
            1.192891641021987e-08,
            -1.1890868123476395e-08,
            0.340841143703862
          ],
          [
            -2.942091015256665e-15,
            -6.938893903907228e-15,
            0.32411208188471763
          ]
        ]
      },
      "incoming_structure_ids": [
        "incoming_01_000",
        "incoming_01_001",
        "incoming_01_002",
        "incoming_01_003",
        "incoming_01_004",
        "incoming_01_005",
        "incoming_01_006",
        "incoming_01_007",
        "incoming_01_008"
      ],
      "reflected_structure_ids": [
        "reflected_01_001",
        "reflected_01_002",
        "reflected_01_003",
        "reflected_01_004",
        "reflected_01_005",
        "reflected_01_006",
        "reflected_01_007",
        "reflected_01_008"
      ],
      "positive_extension_structure_ids": [
        "extension_plus_01_000",
        "extension_plus_01_001",
        "extension_plus_01_002",
        "extension_plus_01_003"
      ],
      "negative_extension_structure_ids": [
        "extension_minus_01_000",
        "extension_minus_01_001",
        "extension_minus_01_002",
        "extension_minus_01_003"
      ],
      "extension": {
        "enabled": true,
        "fraction_beyond_polar_endpoint": 0.35,
        "images_per_side": 4,
        "construction": "continue fractional atomic displacements and symmetric log strain beyond +P; reflect these structures about N for the -P side",
        "positive_path_coordinates": [
          1.35,
          1.2625,
          1.175,
          1.0875
        ],
        "negative_path_coordinates": [
          -1.0875,
          -1.175,
          -1.2625,
          -1.35
        ]
      },
      "branch_coordinates": [
        1.35,
        1.2625,
        1.175,
        1.0875,
        1.0,
        0.875,
        0.75,
        0.625,
        0.5,
        0.375,
        0.25,
        0.125,
        0.0,
        -0.125,
        -0.25,
        -0.375,
        -0.5,
        -0.625,
        -0.75,
        -0.875,
        -1.0,
        -1.0875,
        -1.175,
        -1.2625,
        -1.35
      ],
      "parent": {
        "candidate_id": "inversion_parent_endpoint_00",
        "source": "same_species_inversion_center_projection_from_endpoint",
        "spacegroup": "P-3c1",
        "spacegroup_number": 165,
        "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": 1.5125111375639118e-14,
        "parent_symmetrization_rmsd_A": 0.1379397957226171,
        "parent_cell_rmsd_A": 0.0,
        "energy_eV": -216.5274938220213,
        "reduced_polarization": [
          -7.759632153224029e-15,
          -4.300704825763451e-15,
          1.224994044776523e-14
        ],
        "cartesian_polarization_e_A2": [
          -7.817376813320475e-17,
          -5.19067949920816e-17,
          3.3267566548045244e-16
        ],
        "ranking_score": 0.13793979572264736
      }
    }
  ],
  "path_sampling": {
    "num_images": 17,
    "images_per_leg_including_parent": 9,
    "extension_fraction_beyond_polar_endpoint": 0.35,
    "extension_images_per_side": 4,
    "total_images_per_sampled_branch": 25,
    "construction": "linear polar-to-parent interpolation plus parent-reflected second leg and symmetric log-strain continuation beyond both polar endpoints"
  },
  "branch_folding": "componentwise integer unwrap with per-image shifts, then reduced-coordinate fold [-0.5, 0.5)",
  "bec_backprojection_settings": {
    "variable_cell": true,
    "max_strain_step_log_component": 0.02,
    "strain_response_refresh_iterations": 4,
    "cell_principal_stretch_bounds": [
      0.85,
      1.15
    ],
    "cell_volume_ratio_bounds": [
      0.7,
      1.3
    ],
    "strain_jacobian": "branch-matched finite differences of reduced polarization in six symmetric log-strain coordinates at fixed fractional positions"
  },
  "model_input_contract": "one polar endpoint structure; no reference parent or path frame",
  "run": {
    "model_file": "MACEField-MH-0-omat-dielectric.model",
    "model_sha256": "f92e043aaf2cd8879919db8452503553fe7b608cb749d8d169dd96d4aa094aa2",
    "model_head": "mp-ferroelectric",
    "device": "cpu",
    "dtype": "float64",
    "num_images": 17,
    "compute_becs_for_every_image": true,
    "compute_polarizability_for_every_image": true,
    "initial_structure_relaxation": {
      "enabled": false
    },
    "model_evaluations_for_recovery": {
      "total": 43,
      "full_response": 9,
      "energy_polarization": 34
    },
    "model_evaluations_for_recovery_and_path_properties": {
      "total": 68,
      "full_response": 34,
      "energy_polarization": 34
    },
    "elapsed_seconds": 323.8752912490163
  }
}
