{
  "schema": "ferrofinder.endpoint_parent_recovery.v4_variable_cell",
  "status": "complete",
  "input_atom_count": 26,
  "input_formula": "Ga2I6O18",
  "input_spacegroup": "P6_3",
  "input_pointgroup": "6",
  "input_is_polar_point_group": true,
  "input_energy_eV": -116.91961156262805,
  "input_cartesian_polarization_e_A2": [
    -3.204673633419969e-11,
    0.01199725551701859,
    1.0043743553568382e-11
  ],
  "input_reduced_polarization": [
    -1.1372969382962451e-09,
    0.8879111979331813,
    5.025079803358887e-10
  ],
  "input_formal_targets": [
    {
      "orbit_id": 0,
      "representative_formal_class": [
        0.0,
        0.0,
        0.0
      ],
      "target_reduced_polarization": [
        0.0,
        1.0,
        0.0
      ]
    },
    {
      "orbit_id": 1,
      "representative_formal_class": [
        0.0,
        0.5,
        0.0
      ],
      "target_reduced_polarization": [
        0.0,
        0.5,
        0.0
      ]
    },
    {
      "orbit_id": 2,
      "representative_formal_class": [
        0.5,
        0.0,
        0.0
      ],
      "target_reduced_polarization": [
        -0.5,
        1.0,
        0.0
      ]
    },
    {
      "orbit_id": 3,
      "representative_formal_class": [
        0.5,
        0.5,
        0.0
      ],
      "target_reduced_polarization": [
        -0.5,
        0.5,
        0.0
      ]
    }
  ],
  "parent_candidates": [
    {
      "candidate_id": "inversion_parent_endpoint_00",
      "source": "same_species_inversion_center_projection_from_endpoint",
      "spacegroup": "P6_3/m",
      "spacegroup_number": 176,
      "pointgroup": "6/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": 5.514102239379626e-15,
      "parent_symmetrization_rmsd_A": 0.6550340150439594,
      "parent_cell_rmsd_A": 0.0,
      "energy_eV": -99.23692990425167,
      "reduced_polarization": [
        4.507862604394056e-15,
        7.615664971811311e-16,
        3.0829392982360684e-15
      ],
      "cartesian_polarization_e_A2": [
        6.846217568777262e-17,
        1.0290114463192544e-17,
        6.16194228039998e-17
      ],
      "ranking_score": 0.6550340150439704
    },
    {
      "candidate_id": "inversion_parent_endpoint_01",
      "source": "same_species_inversion_center_projection_from_endpoint",
      "spacegroup": "P2_1/m",
      "spacegroup_number": 11,
      "pointgroup": "2/m",
      "has_inversion": true,
      "is_polar_point_group": false,
      "nonpolar_parent_hypothesis": true,
      "symmetry_tolerance_A": null,
      "target_reduced_polarization": [
        0.0,
        0.0,
        0.0
      ],
      "formal_class": [
        0.0,
        0.0,
        0.0
      ],
      "target_residual": 9.491948921680312e-15,
      "parent_symmetrization_rmsd_A": 1.2693989583822671,
      "parent_cell_rmsd_A": 0.0,
      "energy_eV": -65.5203426442456,
      "reduced_polarization": [
        1.68095316588471e-15,
        9.182294380178207e-15,
        1.719581548411684e-15
      ],
      "cartesian_polarization_e_A2": [
        1.895182697429738e-17,
        1.2406908727799593e-16,
        3.436967524406399e-17
      ],
      "ranking_score": 1.269398958382286
    },
    {
      "candidate_id": "inversion_parent_endpoint_02",
      "source": "same_species_inversion_center_projection_from_endpoint",
      "spacegroup": "P6_3/m",
      "spacegroup_number": 176,
      "pointgroup": "6/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": 8.04456985275569e-15,
      "parent_symmetrization_rmsd_A": 1.3217768026407557,
      "parent_cell_rmsd_A": 0.0,
      "energy_eV": -6.520065760044865,
      "reduced_polarization": [
        7.261727008897036e-15,
        -2.633521913472441e-15,
        2.246550087441071e-15
      ],
      "cartesian_polarization_e_A2": [
        1.416709698316307e-16,
        -3.5583553151645513e-17,
        4.490231765756747e-17
      ],
      "ranking_score": 1.3217768026407717
    },
    {
      "candidate_id": "bec_projection_00",
      "source": "MACEField_BEC_backprojection",
      "spacegroup": "P6_3",
      "spacegroup_number": 173,
      "pointgroup": "6",
      "has_inversion": false,
      "is_polar_point_group": true,
      "nonpolar_parent_hypothesis": false,
      "symmetry_tolerance_A": null,
      "target_reduced_polarization": [
        0.0,
        1.0,
        0.0
      ],
      "formal_class": [
        0.0,
        0.0,
        0.0
      ],
      "target_residual": 0.0009117362845363353,
      "parent_symmetrization_rmsd_A": 0.012746783836532133,
      "parent_cell_rmsd_A": 0.01348268852500823,
      "energy_eV": -116.8486235870064,
      "reduced_polarization": [
        1.173395561995738e-11,
        1.0009117362845363,
        -4.9950817034579566e-12
      ],
      "cartesian_polarization_e_A2": [
        -6.9716058846313e-13,
        0.013548996655975275,
        2.1070001908990076e-13
      ],
      "ranking_score": 0.5179409285368568
    },
    {
      "candidate_id": "inversion_parent_bec_00_00",
      "source": "same_species_inversion_center_projection_after_BEC",
      "spacegroup": "P6_3/m",
      "spacegroup_number": 176,
      "pointgroup": "6/m",
      "has_inversion": true,
      "is_polar_point_group": false,
      "nonpolar_parent_hypothesis": true,
      "symmetry_tolerance_A": null,
      "target_reduced_polarization": [
        0.0,
        1.0,
        0.0
      ],
      "formal_class": [
        0.0,
        0.0,
        0.0
      ],
      "target_residual": 1.2581561859405989e-14,
      "parent_symmetrization_rmsd_A": 0.6550362963774207,
      "parent_cell_rmsd_A": 0.01348268852500823,
      "energy_eV": -99.26186531728216,
      "reduced_polarization": [
        -4.1858127863322914e-17,
        4.735774260123842e-15,
        1.1594434196469255e-14
      ],
      "cartesian_polarization_e_A2": [
        -1.3539022813168155e-16,
        6.410654136960733e-17,
        2.328217188600005e-16
      ],
      "ranking_score": 0.658406968508698
    },
    {
      "candidate_id": "inversion_parent_bec_00_01",
      "source": "same_species_inversion_center_projection_after_BEC",
      "spacegroup": "P2_1/m",
      "spacegroup_number": 11,
      "pointgroup": "2/m",
      "has_inversion": true,
      "is_polar_point_group": false,
      "nonpolar_parent_hypothesis": true,
      "symmetry_tolerance_A": null,
      "target_reduced_polarization": [
        0.0,
        1.0,
        0.0
      ],
      "formal_class": [
        0.0,
        0.0,
        0.0
      ],
      "target_residual": 2.7329552088190916e-15,
      "parent_symmetrization_rmsd_A": 1.2694002838251688,
      "parent_cell_rmsd_A": 0.01348268852500823,
      "energy_eV": -64.90326202023356,
      "reduced_polarization": [
        1.6002190118221703e-15,
        -1.1599658122628437e-15,
        1.9172240670319287e-15
      ],
      "cartesian_polarization_e_A2": [
        1.487689845914257e-17,
        -1.5702056776733366e-17,
        3.849876533337831e-17
      ],
      "ranking_score": 1.2727709559564264
    },
    {
      "candidate_id": "bec_projection_01",
      "source": "MACEField_BEC_backprojection",
      "spacegroup": "P6_3",
      "spacegroup_number": 173,
      "pointgroup": "6",
      "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": 0.0002861567826184519,
      "parent_symmetrization_rmsd_A": 0.04503230368556878,
      "parent_cell_rmsd_A": 0.04896342492811077,
      "energy_eV": -116.48306184804876,
      "reduced_polarization": [
        6.767130465089834e-13,
        0.5002861567826185,
        1.2387720851563453e-12
      ],
      "cartesian_polarization_e_A2": [
        -5.701350327855979e-13,
        0.006715184028774714,
        2.5887322598471427e-13
      ],
      "ranking_score": 0.5578454734828334
    },
    {
      "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": [
        -0.5,
        1.0,
        0.0
      ],
      "formal_class": [
        0.5,
        0.0,
        0.0
      ],
      "target_residual": 0.00018294928924648772,
      "parent_symmetrization_rmsd_A": 0.08271769686248041,
      "parent_cell_rmsd_A": 0.18950125669965154,
      "energy_eV": -114.1251775444464,
      "reduced_polarization": [
        -0.4998569580448977,
        1.0001104414214796,
        -2.8497963749468866e-05
      ],
      "cartesian_polarization_e_A2": [
        -0.011183499407730795,
        0.013198316895438633,
        -5.352835489715811e-06
      ],
      "ranking_score": 0.6304589096158862
    },
    {
      "candidate_id": "bec_projection_03",
      "source": "MACEField_BEC_backprojection",
      "spacegroup": "P1",
      "spacegroup_number": 1,
      "pointgroup": "1",
      "has_inversion": false,
      "is_polar_point_group": true,
      "nonpolar_parent_hypothesis": false,
      "symmetry_tolerance_A": null,
      "target_reduced_polarization": [
        -0.5,
        0.5,
        0.0
      ],
      "formal_class": [
        0.5,
        0.5,
        0.0
      ],
      "target_residual": 0.00029045562764925376,
      "parent_symmetrization_rmsd_A": 0.10003373808959201,
      "parent_cell_rmsd_A": 0.22439758103146124,
      "energy_eV": -114.03878781130784,
      "reduced_polarization": [
        -0.4998748466507593,
        0.5002568116186639,
        -5.24299849914843e-05
      ],
      "cartesian_polarization_e_A2": [
        -0.011088688918874117,
        0.006341501406264595,
        -4.892428133988008e-06
      ],
      "ranking_score": 0.6567140446027558
    }
  ],
  "formal_branches": [
    {
      "orbit_id": 0,
      "formal_class": [
        0.0,
        0.0,
        0.0
      ],
      "formal_classes_in_orbit": [
        [
          0.0,
          0.0,
          0.0
        ]
      ],
      "target_reduced_polarization": [
        0.0,
        1.0,
        0.0
      ],
      "bec_backprojection": {
        "converged_to_target": true,
        "history": [
          {
            "iteration": 0,
            "reduced_polarization": [
              -1.1372969382962451e-09,
              0.8879111979331813,
              5.025079803358887e-10
            ],
            "branch_aligned_reduced_polarization": [
              -1.1372969382962451e-09,
              0.8879111979331813,
              5.025079803358887e-10
            ],
            "target_residual": 0.11208880206681872,
            "energy_eV": -116.91961156262805,
            "max_atomic_step_A": 0.01217677683304542,
            "max_log_strain_component": 0.003734306736721241,
            "step_scale": 1.0,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 8.348618817905193,
            "cell_principal_stretches": [
              0.9990805681562384,
              0.9990805616076357,
              0.9962726571155964
            ],
            "cell_volume_ratio": 0.9944414831893478,
            "cell_rmsd_from_input_A": 0.01348268852500823
          },
          {
            "iteration": 1,
            "reduced_polarization": [
              1.173395561995738e-11,
              1.0009117362845363,
              -4.9950817034579566e-12
            ],
            "branch_aligned_reduced_polarization": [
              1.173395561995738e-11,
              1.0009117362845363,
              -4.9950817034579566e-12
            ],
            "target_residual": 0.0009117362845363353,
            "energy_eV": -116.8486235870064
          }
        ],
        "iterations": 1
      },
      "parent": {
        "candidate_id": "bec_projection_00",
        "source": "MACEField_BEC_backprojection",
        "spacegroup": "P6_3",
        "spacegroup_number": 173,
        "pointgroup": "6",
        "has_inversion": false,
        "is_polar_point_group": true,
        "nonpolar_parent_hypothesis": false,
        "symmetry_tolerance_A": null,
        "target_reduced_polarization": [
          0.0,
          1.0,
          0.0
        ],
        "formal_class": [
          0.0,
          0.0,
          0.0
        ],
        "target_residual": 0.0009117362845363353,
        "parent_symmetrization_rmsd_A": 0.012746783836532133,
        "parent_cell_rmsd_A": 0.01348268852500823,
        "energy_eV": -116.8486235870064,
        "reduced_polarization": [
          1.173395561995738e-11,
          1.0009117362845363,
          -4.9950817034579566e-12
        ],
        "cartesian_polarization_e_A2": [
          -6.9716058846313e-13,
          0.013548996655975275,
          2.1070001908990076e-13
        ],
        "ranking_score": 0.5179409285368568
      },
      "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": [
          -116.91961156262808,
          -116.91581140210724,
          -116.910584717938,
          -116.90392001442777,
          -116.89580579549164,
          -116.88623055974101,
          -116.87518279707515,
          -116.8626509853284,
          -116.84862358700646
        ],
        "cartesian_polarizations_e_A2": [
          [
            -3.204674177375515e-11,
            0.01199725551701859,
            1.0043746576506049e-11
          ],
          [
            -2.815335801207796e-11,
            0.012190054214695047,
            8.822861572633622e-12
          ],
          [
            -2.4252072839604705e-11,
            0.01238320389298438,
            7.599303998814048e-12
          ],
          [
            -2.0343470717609316e-11,
            0.012576696051976782,
            6.373465172992533e-12
          ],
          [
            -1.6427562644668755e-11,
            0.012770522194547874,
            5.145151725366337e-12
          ],
          [
            -1.250471850413234e-11,
            0.01296467382232309,
            3.914581697839218e-12
          ],
          [
            -8.575190516286834e-12,
            0.013159142437629747,
            2.682000174632144e-12
          ],
          [
            -4.639299163028583e-12,
            0.013353919545535798,
            1.447310070845872e-12
          ],
          [
            -6.972130931141322e-13,
            0.01354899665597538,
            2.1066926798333752e-13
          ]
        ],
        "raw_reduced_polarization": [
          [
            -1.1372970983646692e-09,
            0.8879111979331813,
            5.025081315793264e-10
          ],
          [
            -9.944387177304257e-10,
            0.9019726926590267,
            4.394214265061993e-10
          ],
          [
            -8.513388982029297e-10,
            0.9160536378581905,
            3.762184308538802e-10
          ],
          [
            -7.080132969826744e-10,
            0.9301533892318526,
            3.129187791948937e-10
          ],
          [
            -5.644673494124573e-10,
            0.9442713032728905,
            2.4951288038897285e-10
          ],
          [
            -4.20711732929878e-10,
            0.9584067369669784,
            1.8601169454198517e-10
          ],
          [
            -2.7675135732125004e-10,
            0.9725590479366268,
            1.2242750954272883e-10
          ],
          [
            -1.3260260328477636e-10,
            0.9867275945914334,
            5.875553987565375e-11
          ],
          [
            1.1730925516170217e-11,
            1.000911736284544,
            -4.996613097032262e-12
          ]
        ],
        "unwrapped_reduced_polarization": [
          [
            -1.1372970983646692e-09,
            0.8879111979331813,
            5.025081315793264e-10
          ],
          [
            -9.944387177304257e-10,
            0.9019726926590267,
            4.394214265061993e-10
          ],
          [
            -8.513388982029297e-10,
            0.9160536378581905,
            3.762184308538802e-10
          ],
          [
            -7.080132969826744e-10,
            0.9301533892318526,
            3.129187791948937e-10
          ],
          [
            -5.644673494124573e-10,
            0.9442713032728905,
            2.4951288038897285e-10
          ],
          [
            -4.20711732929878e-10,
            0.9584067369669784,
            1.8601169454198517e-10
          ],
          [
            -2.7675135732125004e-10,
            0.9725590479366268,
            1.2242750954272883e-10
          ],
          [
            -1.3260260328477636e-10,
            0.9867275945914334,
            5.875553987565375e-11
          ],
          [
            1.173092551617022e-11,
            1.000911736284544,
            -4.996613097032265e-12
          ]
        ],
        "berry_integer_shifts": [
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ]
        ],
        "folded_reduced_polarization": [
          [
            -1.1372970898371193e-09,
            -0.1120888020668187,
            5.025081462051162e-10
          ],
          [
            -9.944386980542674e-10,
            -0.0980273073409732,
            4.394213881653286e-10
          ],
          [
            -8.513388882747108e-10,
            -0.0839463621418095,
            3.7621838977486277e-10
          ],
          [
            -7.080133146430967e-10,
            -0.06984661076814724,
            3.1291880198125455e-10
          ],
          [
            -5.644673617410945e-10,
            -0.05572869672710956,
            2.4951285482188723e-10
          ],
          [
            -4.207117432208918e-10,
            -0.04159326303302158,
            1.8601165052700708e-10
          ],
          [
            -2.76751344063797e-10,
            -0.02744095206337316,
            1.2242751257218742e-10
          ],
          [
            -1.3260259557057452e-10,
            -0.013272405408566446,
            5.875555597611992e-11
          ],
          [
            1.1730949545096792e-11,
            0.0009117362845441068,
            -4.996614233476748e-12
          ]
        ]
      },
      "reflected": {
        "reached": true,
        "construction": "reflect_displacements_about_reconstructed_parent",
        "energies_eV": [
          -116.84862358700644,
          -116.8460680514379,
          -116.84303011415228,
          -116.83950534571315,
          -116.83548938625071,
          -116.83097794373286,
          -116.82596679127775,
          -116.82045176353948,
          -116.81442875221501
        ],
        "cartesian_polarizations_e_A2": [
          [
            -6.972186675959904e-13,
            0.013548996655975315,
            2.10698734346035e-13
          ],
          [
            1.7527125738962527e-12,
            0.01366216832189218,
            -6.045201821271636e-13
          ],
          [
            4.194170540727695e-12,
            0.013775019536586332,
            -1.4157901643847828e-12
          ],
          [
            6.627073761375428e-12,
            0.0138875425853593,
            -2.222811212935965e-12
          ],
          [
            9.051619655890138e-12,
            0.013999730270773959,
            -3.0258893462615453e-12
          ],
          [
            1.1467588414304133e-11,
            0.014111575928058452,
            -3.8248047199130896e-12
          ],
          [
            1.3875118081497618e-11,
            0.01422307343709218,
            -4.619371684231879e-12
          ],
          [
            1.6274189626525224e-11,
            0.014334217230642307,
            -5.409922066742747e-12
          ],
          [
            1.8664894373682914e-11,
            0.014445002298572315,
            -6.196182354770596e-12
          ]
        ],
        "raw_reduced_polarization": [
          [
            1.173141880820722e-11,
            1.0009117362845392,
            -4.9951456832298175e-12
          ],
          [
            9.283892331539635e-11,
            1.0095042462398676,
            -4.3792731589773597e-11
          ],
          [
            1.7369773324952134e-10,
            1.0180769719082043,
            -8.240691461269342e-11
          ],
          [
            2.543117933657589e-10,
            1.0266293279825232,
            -1.2082219119156992e-10
          ],
          [
            3.3468185363437616e-10,
            1.0351607668711067,
            -1.5905360368307616e-10
          ],
          [
            4.148037617789281e-10,
            1.0436707798804667,
            -1.970899700761766e-10
          ],
          [
            4.946879985613682e-10,
            1.0521588981470325,
            -2.3492179544399486e-10
          ],
          [
            5.743253382806258e-10,
            1.0606246932926622,
            -2.7256544199091116e-10
          ],
          [
            6.537264663213641e-10,
            1.0690677777829167,
            -3.1000702718882343e-10
          ]
        ],
        "unwrapped_reduced_polarization": [
          [
            1.173141880820722e-11,
            1.0009117362845392,
            -4.9951456832298175e-12
          ],
          [
            9.283892331539635e-11,
            1.0095042462398676,
            -4.3792731589773597e-11
          ],
          [
            1.7369773324952134e-10,
            1.0180769719082043,
            -8.240691461269342e-11
          ],
          [
            2.543117933657589e-10,
            1.0266293279825232,
            -1.2082219119156992e-10
          ],
          [
            3.3468185363437616e-10,
            1.0351607668711067,
            -1.5905360368307616e-10
          ],
          [
            4.148037617789281e-10,
            1.0436707798804667,
            -1.970899700761766e-10
          ],
          [
            4.946879985613682e-10,
            1.0521588981470325,
            -2.3492179544399486e-10
          ],
          [
            5.743253382806258e-10,
            1.0606246932926622,
            -2.7256544199091116e-10
          ],
          [
            6.537264663213641e-10,
            1.0690677777829167,
            -3.1000702718882343e-10
          ]
        ],
        "gauge_integer_shift": [
          0,
          0,
          0
        ],
        "expected_opposite_endpoint_reduced_polarization": [
          1.0874182902779337e-09,
          1.1175984512585517,
          -4.814277469979149e-10
        ],
        "actual_opposite_endpoint_branch_residual": 0.048530673475635
      },
      "pnp_branch": {
        "construction": "incoming_path_concatenated_with_parent_reflection",
        "reduced_polarization": [
          [
            -1.1372970983646692e-09,
            0.8879111979331813,
            5.025081315793264e-10
          ],
          [
            -9.944387177304257e-10,
            0.9019726926590267,
            4.394214265061993e-10
          ],
          [
            -8.513388982029297e-10,
            0.9160536378581905,
            3.762184308538802e-10
          ],
          [
            -7.080132969826744e-10,
            0.9301533892318526,
            3.129187791948937e-10
          ],
          [
            -5.644673494124573e-10,
            0.9442713032728905,
            2.4951288038897285e-10
          ],
          [
            -4.20711732929878e-10,
            0.9584067369669784,
            1.8601169454198517e-10
          ],
          [
            -2.7675135732125004e-10,
            0.9725590479366268,
            1.2242750954272883e-10
          ],
          [
            -1.3260260328477636e-10,
            0.9867275945914334,
            5.875553987565375e-11
          ],
          [
            1.1730925516170217e-11,
            1.000911736284544,
            -4.996613097032262e-12
          ],
          [
            9.283892331539635e-11,
            1.0095042462398676,
            -4.3792731589773597e-11
          ],
          [
            1.7369773324952134e-10,
            1.0180769719082043,
            -8.240691461269342e-11
          ],
          [
            2.543117933657589e-10,
            1.0266293279825232,
            -1.2082219119156992e-10
          ],
          [
            3.3468185363437616e-10,
            1.0351607668711067,
            -1.5905360368307616e-10
          ],
          [
            4.148037617789281e-10,
            1.0436707798804667,
            -1.970899700761766e-10
          ],
          [
            4.946879985613682e-10,
            1.0521588981470325,
            -2.3492179544399486e-10
          ],
          [
            5.743253382806258e-10,
            1.0606246932926622,
            -2.7256544199091116e-10
          ],
          [
            6.537264663213641e-10,
            1.0690677777829167,
            -3.1000702718882343e-10
          ]
        ],
        "unwrapped_reduced_polarization": [
          [
            -1.1372970983646692e-09,
            0.8879111979331813,
            5.025081315793264e-10
          ],
          [
            -9.944387177304257e-10,
            0.9019726926590267,
            4.394214265061993e-10
          ],
          [
            -8.513388982029297e-10,
            0.9160536378581905,
            3.762184308538802e-10
          ],
          [
            -7.080132969826744e-10,
            0.9301533892318526,
            3.129187791948937e-10
          ],
          [
            -5.644673494124573e-10,
            0.9442713032728905,
            2.4951288038897285e-10
          ],
          [
            -4.20711732929878e-10,
            0.9584067369669784,
            1.8601169454198517e-10
          ],
          [
            -2.7675135732125004e-10,
            0.9725590479366268,
            1.2242750954272883e-10
          ],
          [
            -1.3260260328477636e-10,
            0.9867275945914334,
            5.875553987565375e-11
          ],
          [
            1.173092551617022e-11,
            1.000911736284544,
            -4.996613097032265e-12
          ],
          [
            9.283892331539635e-11,
            1.0095042462398676,
            -4.3792731589773597e-11
          ],
          [
            1.7369773324952134e-10,
            1.0180769719082043,
            -8.240691461269342e-11
          ],
          [
            2.543117933657589e-10,
            1.0266293279825232,
            -1.2082219119156992e-10
          ],
          [
            3.3468185363437616e-10,
            1.0351607668711067,
            -1.5905360368307616e-10
          ],
          [
            4.148037617789281e-10,
            1.0436707798804667,
            -1.970899700761766e-10
          ],
          [
            4.946879985613682e-10,
            1.0521588981470325,
            -2.3492179544399486e-10
          ],
          [
            5.743253382806258e-10,
            1.0606246932926622,
            -2.7256544199091116e-10
          ],
          [
            6.537264663213641e-10,
            1.0690677777829167,
            -3.1000702718882343e-10
          ]
        ],
        "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": [
          [
            -1.1372970898371193e-09,
            -0.1120888020668187,
            5.025081462051162e-10
          ],
          [
            -9.944386980542674e-10,
            -0.0980273073409732,
            4.394213881653286e-10
          ],
          [
            -8.513388882747108e-10,
            -0.0839463621418095,
            3.7621838977486277e-10
          ],
          [
            -7.080133146430967e-10,
            -0.06984661076814724,
            3.1291880198125455e-10
          ],
          [
            -5.644673617410945e-10,
            -0.05572869672710956,
            2.4951285482188723e-10
          ],
          [
            -4.207117432208918e-10,
            -0.04159326303302158,
            1.8601165052700708e-10
          ],
          [
            -2.76751344063797e-10,
            -0.02744095206337316,
            1.2242751257218742e-10
          ],
          [
            -1.3260259557057452e-10,
            -0.013272405408566446,
            5.875555597611992e-11
          ],
          [
            1.1730949545096792e-11,
            0.0009117362845441068,
            -4.996614233476748e-12
          ],
          [
            9.283895874290238e-11,
            0.009504246239867564,
            -4.37927472063393e-11
          ],
          [
            1.7369772287167962e-10,
            0.018076971908204342,
            -8.240691462546579e-11
          ],
          [
            2.5431179384582947e-10,
            0.026629327982523154,
            -1.2082218558973068e-10
          ],
          [
            3.346818377991667e-10,
            0.0351607668711067,
            -1.5905360362111765e-10
          ],
          [
            4.1480374690650024e-10,
            0.04367077988046675,
            -1.9708995546707797e-10
          ],
          [
            4.946879572642615e-10,
            0.05215889814703245,
            -2.3492180423190234e-10
          ],
          [
            5.743253650436486e-10,
            0.06062469329266218,
            -2.725654146829015e-10
          ],
          [
            6.537265173633955e-10,
            0.06906777778291673,
            -3.1000702005457015e-10
          ]
        ]
      },
      "incoming_structure_ids": [
        "incoming_00_000",
        "incoming_00_001",
        "incoming_00_002",
        "incoming_00_003",
        "incoming_00_004",
        "incoming_00_005",
        "incoming_00_006",
        "incoming_00_007",
        "incoming_00_008"
      ],
      "reflected_structure_ids": [
        "reflected_00_001",
        "reflected_00_002",
        "reflected_00_003",
        "reflected_00_004",
        "reflected_00_005",
        "reflected_00_006",
        "reflected_00_007",
        "reflected_00_008"
      ]
    },
    {
      "orbit_id": 1,
      "formal_class": [
        0.0,
        0.5,
        0.0
      ],
      "formal_classes_in_orbit": [
        [
          0.0,
          0.5,
          0.0
        ]
      ],
      "target_reduced_polarization": [
        0.0,
        0.5,
        0.0
      ],
      "bec_backprojection": {
        "converged_to_target": true,
        "history": [
          {
            "iteration": 0,
            "reduced_polarization": [
              -1.1372969382962451e-09,
              0.8879111979331813,
              5.025079803358887e-10
            ],
            "branch_aligned_reduced_polarization": [
              -1.1372969382962451e-09,
              0.8879111979331813,
              5.025079803358887e-10
            ],
            "target_residual": 0.3879111979331813,
            "energy_eV": -116.91961156262805,
            "max_atomic_step_A": 0.042140766814691866,
            "max_log_strain_component": 0.0129234979139839,
            "step_scale": 1.0,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 8.348618817905193,
            "cell_principal_stretches": [
              1.0130073672186442,
              1.003188481527205,
              1.0031884587709516
            ],
            "cell_volume_ratio": 1.0194775533002236,
            "cell_rmsd_from_input_A": 0.04711105863283461
          },
          {
            "iteration": 1,
            "reduced_polarization": [
              -1.8523551222467472e-11,
              0.5137203470718283,
              2.9296168421399935e-11
            ],
            "branch_aligned_reduced_polarization": [
              -1.8523551222467472e-11,
              0.5137203470718283,
              2.9296168421399935e-11
            ],
            "target_residual": 0.013720347071828343,
            "energy_eV": -116.51506288080132,
            "max_atomic_step_A": 0.0015324325729770692,
            "max_log_strain_component": 0.0005042063392685784,
            "step_scale": 1.0,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 8.348618817905193,
            "cell_principal_stretches": [
              1.0135182607419742,
              1.0033130850109642,
              1.0033130613639456
            ],
            "cell_volume_ratio": 1.0202451059278062,
            "cell_rmsd_from_input_A": 0.04896342492811077
          },
          {
            "iteration": 2,
            "reduced_polarization": [
              6.767130465089834e-13,
              0.5002861567826185,
              1.2387720851563453e-12
            ],
            "branch_aligned_reduced_polarization": [
              6.767130465089834e-13,
              0.5002861567826185,
              1.2387720851563453e-12
            ],
            "target_residual": 0.0002861567826184519,
            "energy_eV": -116.48306184804876
          }
        ],
        "iterations": 2
      },
      "parent": {
        "candidate_id": "bec_projection_01",
        "source": "MACEField_BEC_backprojection",
        "spacegroup": "P6_3",
        "spacegroup_number": 173,
        "pointgroup": "6",
        "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": 0.0002861567826184519,
        "parent_symmetrization_rmsd_A": 0.04503230368556878,
        "parent_cell_rmsd_A": 0.04896342492811077,
        "energy_eV": -116.48306184804876,
        "reduced_polarization": [
          6.767130465089834e-13,
          0.5002861567826185,
          1.2387720851563453e-12
        ],
        "cartesian_polarization_e_A2": [
          -5.701350327855979e-13,
          0.006715184028774714,
          2.5887322598471427e-13
        ],
        "ranking_score": 0.5578454734828334
      },
      "branch_status": "awaiting_branch_sampling"
    },
    {
      "orbit_id": 2,
      "formal_class": [
        0.5,
        0.0,
        0.0
      ],
      "formal_classes_in_orbit": [
        [
          0.5,
          0.0,
          0.0
        ],
        [
          0.0,
          0.0,
          0.5
        ],
        [
          0.5,
          0.0,
          0.5
        ]
      ],
      "target_reduced_polarization": [
        -0.5,
        1.0,
        0.0
      ],
      "bec_backprojection": {
        "converged_to_target": true,
        "history": [
          {
            "iteration": 0,
            "reduced_polarization": [
              -1.1372969382962451e-09,
              0.8879111979331813,
              5.025079803358887e-10
            ],
            "branch_aligned_reduced_polarization": [
              -1.1372969233036656e-09,
              0.8879111979331813,
              5.025079803358887e-10
            ],
            "target_residual": 0.5124098929680003,
            "energy_eV": -116.91961156262805,
            "max_atomic_step_A": 0.06439770768508941,
            "max_log_strain_component": 0.02,
            "step_scale": 0.7147642550092458,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 8.348618817905193,
            "cell_principal_stretches": [
              1.0185329201230395,
              0.9993427343658217,
              0.978543625702233
            ],
            "cell_volume_ratio": 0.9960238137672655,
            "cell_rmsd_from_input_A": 0.12942536522602988
          },
          {
            "iteration": 1,
            "reduced_polarization": [
              -0.352579881504356,
              0.9789979424133426,
              -0.00018030499621435168
            ],
            "branch_aligned_reduced_polarization": [
              -0.352579881504356,
              0.9789979424133426,
              -0.00018030499621435168
            ],
            "target_residual": 0.1489087313425061,
            "energy_eV": -115.60089107589906,
            "max_atomic_step_A": 0.027310113029251917,
            "max_log_strain_component": 0.008939527435018501,
            "step_scale": 1.0,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 8.348618817905193,
            "cell_principal_stretches": [
              1.0275342821022564,
              0.9992886971038509,
              0.969706084523888
            ],
            "cell_volume_ratio": 0.995697498763341,
            "cell_rmsd_from_input_A": 0.1871507294014898
          },
          {
            "iteration": 2,
            "reduced_polarization": [
              -0.4947978335479702,
              1.003526345579255,
              -2.3749112150566948e-08
            ],
            "branch_aligned_reduced_polarization": [
              -0.4947978335479702,
              1.003526345579255,
              -2.3749112150566948e-08
            ],
            "target_residual": 0.006284715501875887,
            "energy_eV": -114.17941011366162,
            "max_atomic_step_A": 0.001215543844501669,
            "max_log_strain_component": 0.0003594209415450722,
            "step_scale": 1.0,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 8.348618817905193,
            "cell_principal_stretches": [
              1.0280025003123334,
              0.999327612341745,
              0.9694554150832535
            ],
            "cell_volume_ratio": 0.9959324873647796,
            "cell_rmsd_from_input_A": 0.18950125669965154
          },
          {
            "iteration": 3,
            "reduced_polarization": [
              -0.4998569580448977,
              1.0001104414214796,
              -2.8497963749468866e-05
            ],
            "branch_aligned_reduced_polarization": [
              -0.4998569580448977,
              1.0001104414214796,
              -2.8497963749468866e-05
            ],
            "target_residual": 0.00018294928924648772,
            "energy_eV": -114.1251775444464
          }
        ],
        "iterations": 3
      },
      "parent": {
        "candidate_id": "bec_projection_02",
        "source": "MACEField_BEC_backprojection",
        "spacegroup": "P1",
        "spacegroup_number": 1,
        "pointgroup": "1",
        "has_inversion": false,
        "is_polar_point_group": true,
        "nonpolar_parent_hypothesis": false,
        "symmetry_tolerance_A": null,
        "target_reduced_polarization": [
          -0.5,
          1.0,
          0.0
        ],
        "formal_class": [
          0.5,
          0.0,
          0.0
        ],
        "target_residual": 0.00018294928924648772,
        "parent_symmetrization_rmsd_A": 0.08271769686248041,
        "parent_cell_rmsd_A": 0.18950125669965154,
        "energy_eV": -114.1251775444464,
        "reduced_polarization": [
          -0.4998569580448977,
          1.0001104414214796,
          -2.8497963749468866e-05
        ],
        "cartesian_polarization_e_A2": [
          -0.011183499407730795,
          0.013198316895438633,
          -5.352835489715811e-06
        ],
        "ranking_score": 0.6304589096158862
      },
      "branch_status": "awaiting_branch_sampling"
    },
    {
      "orbit_id": 3,
      "formal_class": [
        0.5,
        0.5,
        0.0
      ],
      "formal_classes_in_orbit": [
        [
          0.5,
          0.5,
          0.0
        ],
        [
          0.0,
          0.5,
          0.5
        ],
        [
          0.5,
          0.5,
          0.5
        ]
      ],
      "target_reduced_polarization": [
        -0.5,
        0.5,
        0.0
      ],
      "bec_backprojection": {
        "converged_to_target": true,
        "history": [
          {
            "iteration": 0,
            "reduced_polarization": [
              -1.1372969382962451e-09,
              0.8879111979331813,
              5.025079803358887e-10
            ],
            "branch_aligned_reduced_polarization": [
              -1.1372969233036656e-09,
              0.8879111979331813,
              5.025079803358887e-10
            ],
            "target_residual": 0.6328310172112764,
            "energy_eV": -116.91961156262805,
            "max_atomic_step_A": 0.07682086656477659,
            "max_log_strain_component": 0.02,
            "step_scale": 0.7147642552057033,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 8.348618817905193,
            "cell_principal_stretches": [
              1.0264007642830053,
              1.0022779698142088,
              0.9855596309589847
            ],
            "cell_volume_ratio": 1.0138835052504387,
            "cell_rmsd_from_input_A": 0.13619732600073242
          },
          {
            "iteration": 1,
            "reduced_polarization": [
              -0.3402305060980293,
              0.6394353027458896,
              -0.0011647560370586214
            ],
            "branch_aligned_reduced_polarization": [
              -0.3402305060980293,
              0.6394353027458896,
              -0.0011647560370586214
            ],
            "target_residual": 0.2120609617307146,
            "energy_eV": -115.71029617621198,
            "max_atomic_step_A": 0.039302217826426254,
            "max_log_strain_component": 0.01073605347764164,
            "step_scale": 1.0,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 8.348618817905193,
            "cell_principal_stretches": [
              1.0418320638474463,
              1.003836975667871,
              0.9786275564273978
            ],
            "cell_volume_ratio": 1.023477615122544,
            "cell_rmsd_from_input_A": 0.21330089695382717
          },
          {
            "iteration": 2,
            "reduced_polarization": [
              -0.4863796627423081,
              0.5221957358129412,
              -0.002132473648180746
            ],
            "branch_aligned_reduced_polarization": [
              -0.4863796627423081,
              0.5221957358129412,
              -0.002132473648180746
            ],
            "target_residual": 0.02612875272858114,
            "energy_eV": -114.25496315711345,
            "max_atomic_step_A": 0.004863232735246705,
            "max_log_strain_component": 0.0012603426620218024,
            "step_scale": 1.0,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 8.348618817905193,
            "cell_principal_stretches": [
              1.0439563859778807,
              1.0041208479644685,
              0.9780343493916093
            ],
            "cell_volume_ratio": 1.02523269438977,
            "cell_rmsd_from_input_A": 0.2233076221671968
          },
          {
            "iteration": 3,
            "reduced_polarization": [
              -0.49873981222837016,
              0.5024536900168344,
              -0.0004283550546692101
            ],
            "branch_aligned_reduced_polarization": [
              -0.49873981222837016,
              0.5024536900168344,
              -0.0004283550546692101
            ],
            "target_residual": 0.0027914433491186457,
            "energy_eV": -114.0595536185716,
            "max_atomic_step_A": 0.0005251329973732187,
            "max_log_strain_component": 0.00013209145208861332,
            "step_scale": 1.0,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 8.348618817905193,
            "cell_principal_stretches": [
              1.0441855784154603,
              1.0041526425525649,
              0.9779763428376678
            ],
            "cell_volume_ratio": 1.0254294252595255,
            "cell_rmsd_from_input_A": 0.22439758103146124
          },
          {
            "iteration": 4,
            "reduced_polarization": [
              -0.4998748466507593,
              0.5002568116186639,
              -5.24299849914843e-05
            ],
            "branch_aligned_reduced_polarization": [
              -0.4998748466507593,
              0.5002568116186639,
              -5.24299849914843e-05
            ],
            "target_residual": 0.00029045562764925376,
            "energy_eV": -114.03878781130784
          }
        ],
        "iterations": 4
      },
      "parent": {
        "candidate_id": "bec_projection_03",
        "source": "MACEField_BEC_backprojection",
        "spacegroup": "P1",
        "spacegroup_number": 1,
        "pointgroup": "1",
        "has_inversion": false,
        "is_polar_point_group": true,
        "nonpolar_parent_hypothesis": false,
        "symmetry_tolerance_A": null,
        "target_reduced_polarization": [
          -0.5,
          0.5,
          0.0
        ],
        "formal_class": [
          0.5,
          0.5,
          0.0
        ],
        "target_residual": 0.00029045562764925376,
        "parent_symmetrization_rmsd_A": 0.10003373808959201,
        "parent_cell_rmsd_A": 0.22439758103146124,
        "energy_eV": -114.03878781130784,
        "reduced_polarization": [
          -0.4998748466507593,
          0.5002568116186639,
          -5.24299849914843e-05
        ],
        "cartesian_polarization_e_A2": [
          -0.011088688918874117,
          0.006341501406264595,
          -4.892428133988008e-06
        ],
        "ranking_score": 0.6567140446027558
      },
      "branch_status": "awaiting_branch_sampling"
    }
  ],
  "sampled_polarization_branches": [
    {
      "orbit_id": 0,
      "candidate_id": "bec_projection_00",
      "formal_class": [
        0.0,
        0.0,
        0.0
      ],
      "construction": "MACEField-BEC-parent plus variable-cell P-N-P path and symmetric log-strain continuation beyond both polar endpoints",
      "geometry_diagnostics": {
        "collision_aware": false,
        "permutations_tested": 1,
        "selected_order": [
          0,
          1,
          2,
          3,
          4,
          5,
          6,
          7,
          8,
          9,
          10,
          11,
          12,
          13,
          14,
          15,
          16,
          17,
          18,
          19,
          20,
          21,
          22,
          23,
          24,
          25
        ],
        "endpoint_rmsd_A": 0.012746783836532133,
        "minimum_distance_A_by_image": [
          1.802284805274488,
          1.7999933479005523,
          1.797705433998582,
          1.7954210644617057,
          1.7931402401870677,
          1.7908629620757976,
          1.788589231032989,
          1.7863190479676847,
          1.7840524137928413
        ],
        "minimum_distance_A": 1.7840524137928413,
        "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": [
          400.54976974883124,
          400.2707827563511,
          399.99199008115176,
          399.713391587889,
          399.43498714131283,
          399.1567766062683,
          398.8787598476938,
          398.60093673062136,
          398.3233071201798
        ],
        "cell_deformation_log_strain_norm": 0.003954405707173662
      },
      "parent_reduced_polarization": [
        1.1730925516170217e-11,
        1.000911736284544,
        -4.996613097032262e-12
      ],
      "incoming": {
        "reached": true,
        "construction": "variable_cell_linear_interpolation",
        "continuation_fractions": [
          0.0,
          0.125,
          0.25,
          0.375,
          0.5,
          0.625,
          0.75,
          0.875,
          1.0
        ],
        "energies_eV": [
          -116.91961156262808,
          -116.91581140210724,
          -116.910584717938,
          -116.90392001442777,
          -116.89580579549164,
          -116.88623055974101,
          -116.87518279707515,
          -116.8626509853284,
          -116.84862358700646
        ],
        "cartesian_polarizations_e_A2": [
          [
            -3.204674177375515e-11,
            0.01199725551701859,
            1.0043746576506049e-11
          ],
          [
            -2.815335801207796e-11,
            0.012190054214695047,
            8.822861572633622e-12
          ],
          [
            -2.4252072839604705e-11,
            0.01238320389298438,
            7.599303998814048e-12
          ],
          [
            -2.0343470717609316e-11,
            0.012576696051976782,
            6.373465172992533e-12
          ],
          [
            -1.6427562644668755e-11,
            0.012770522194547874,
            5.145151725366337e-12
          ],
          [
            -1.250471850413234e-11,
            0.01296467382232309,
            3.914581697839218e-12
          ],
          [
            -8.575190516286834e-12,
            0.013159142437629747,
            2.682000174632144e-12
          ],
          [
            -4.639299163028583e-12,
            0.013353919545535798,
            1.447310070845872e-12
          ],
          [
            -6.972130931141322e-13,
            0.01354899665597538,
            2.1066926798333752e-13
          ]
        ],
        "raw_reduced_polarization": [
          [
            -1.1372970983646692e-09,
            0.8879111979331813,
            5.025081315793264e-10
          ],
          [
            -9.944387177304257e-10,
            0.9019726926590267,
            4.394214265061993e-10
          ],
          [
            -8.513388982029297e-10,
            0.9160536378581905,
            3.762184308538802e-10
          ],
          [
            -7.080132969826744e-10,
            0.9301533892318526,
            3.129187791948937e-10
          ],
          [
            -5.644673494124573e-10,
            0.9442713032728905,
            2.4951288038897285e-10
          ],
          [
            -4.20711732929878e-10,
            0.9584067369669784,
            1.8601169454198517e-10
          ],
          [
            -2.7675135732125004e-10,
            0.9725590479366268,
            1.2242750954272883e-10
          ],
          [
            -1.3260260328477636e-10,
            0.9867275945914334,
            5.875553987565375e-11
          ],
          [
            1.1730925516170217e-11,
            1.000911736284544,
            -4.996613097032262e-12
          ]
        ],
        "unwrapped_reduced_polarization": [
          [
            -1.1372970983646692e-09,
            0.8879111979331813,
            5.025081315793264e-10
          ],
          [
            -9.944387177304257e-10,
            0.9019726926590267,
            4.394214265061993e-10
          ],
          [
            -8.513388982029297e-10,
            0.9160536378581905,
            3.762184308538802e-10
          ],
          [
            -7.080132969826744e-10,
            0.9301533892318526,
            3.129187791948937e-10
          ],
          [
            -5.644673494124573e-10,
            0.9442713032728905,
            2.4951288038897285e-10
          ],
          [
            -4.20711732929878e-10,
            0.9584067369669784,
            1.8601169454198517e-10
          ],
          [
            -2.7675135732125004e-10,
            0.9725590479366268,
            1.2242750954272883e-10
          ],
          [
            -1.3260260328477636e-10,
            0.9867275945914334,
            5.875553987565375e-11
          ],
          [
            1.173092551617022e-11,
            1.000911736284544,
            -4.996613097032265e-12
          ]
        ],
        "berry_integer_shifts": [
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ]
        ],
        "folded_reduced_polarization": [
          [
            -1.1372970898371193e-09,
            -0.1120888020668187,
            5.025081462051162e-10
          ],
          [
            -9.944386980542674e-10,
            -0.0980273073409732,
            4.394213881653286e-10
          ],
          [
            -8.513388882747108e-10,
            -0.0839463621418095,
            3.7621838977486277e-10
          ],
          [
            -7.080133146430967e-10,
            -0.06984661076814724,
            3.1291880198125455e-10
          ],
          [
            -5.644673617410945e-10,
            -0.05572869672710956,
            2.4951285482188723e-10
          ],
          [
            -4.207117432208918e-10,
            -0.04159326303302158,
            1.8601165052700708e-10
          ],
          [
            -2.76751344063797e-10,
            -0.02744095206337316,
            1.2242751257218742e-10
          ],
          [
            -1.3260259557057452e-10,
            -0.013272405408566446,
            5.875555597611992e-11
          ],
          [
            1.1730949545096792e-11,
            0.0009117362845441068,
            -4.996614233476748e-12
          ]
        ]
      },
      "reflected": {
        "reached": true,
        "construction": "reflect_displacements_about_reconstructed_parent",
        "energies_eV": [
          -116.84862358700644,
          -116.8460680514379,
          -116.84303011415228,
          -116.83950534571315,
          -116.83548938625071,
          -116.83097794373286,
          -116.82596679127775,
          -116.82045176353948,
          -116.81442875221501
        ],
        "cartesian_polarizations_e_A2": [
          [
            -6.972186675959904e-13,
            0.013548996655975315,
            2.10698734346035e-13
          ],
          [
            1.7527125738962527e-12,
            0.01366216832189218,
            -6.045201821271636e-13
          ],
          [
            4.194170540727695e-12,
            0.013775019536586332,
            -1.4157901643847828e-12
          ],
          [
            6.627073761375428e-12,
            0.0138875425853593,
            -2.222811212935965e-12
          ],
          [
            9.051619655890138e-12,
            0.013999730270773959,
            -3.0258893462615453e-12
          ],
          [
            1.1467588414304133e-11,
            0.014111575928058452,
            -3.8248047199130896e-12
          ],
          [
            1.3875118081497618e-11,
            0.01422307343709218,
            -4.619371684231879e-12
          ],
          [
            1.6274189626525224e-11,
            0.014334217230642307,
            -5.409922066742747e-12
          ],
          [
            1.8664894373682914e-11,
            0.014445002298572315,
            -6.196182354770596e-12
          ]
        ],
        "raw_reduced_polarization": [
          [
            1.173141880820722e-11,
            1.0009117362845392,
            -4.9951456832298175e-12
          ],
          [
            9.283892331539635e-11,
            1.0095042462398676,
            -4.3792731589773597e-11
          ],
          [
            1.7369773324952134e-10,
            1.0180769719082043,
            -8.240691461269342e-11
          ],
          [
            2.543117933657589e-10,
            1.0266293279825232,
            -1.2082219119156992e-10
          ],
          [
            3.3468185363437616e-10,
            1.0351607668711067,
            -1.5905360368307616e-10
          ],
          [
            4.148037617789281e-10,
            1.0436707798804667,
            -1.970899700761766e-10
          ],
          [
            4.946879985613682e-10,
            1.0521588981470325,
            -2.3492179544399486e-10
          ],
          [
            5.743253382806258e-10,
            1.0606246932926622,
            -2.7256544199091116e-10
          ],
          [
            6.537264663213641e-10,
            1.0690677777829167,
            -3.1000702718882343e-10
          ]
        ],
        "unwrapped_reduced_polarization": [
          [
            1.173141880820722e-11,
            1.0009117362845392,
            -4.9951456832298175e-12
          ],
          [
            9.283892331539635e-11,
            1.0095042462398676,
            -4.3792731589773597e-11
          ],
          [
            1.7369773324952134e-10,
            1.0180769719082043,
            -8.240691461269342e-11
          ],
          [
            2.543117933657589e-10,
            1.0266293279825232,
            -1.2082219119156992e-10
          ],
          [
            3.3468185363437616e-10,
            1.0351607668711067,
            -1.5905360368307616e-10
          ],
          [
            4.148037617789281e-10,
            1.0436707798804667,
            -1.970899700761766e-10
          ],
          [
            4.946879985613682e-10,
            1.0521588981470325,
            -2.3492179544399486e-10
          ],
          [
            5.743253382806258e-10,
            1.0606246932926622,
            -2.7256544199091116e-10
          ],
          [
            6.537264663213641e-10,
            1.0690677777829167,
            -3.1000702718882343e-10
          ]
        ],
        "gauge_integer_shift": [
          0,
          0,
          0
        ],
        "expected_opposite_endpoint_reduced_polarization": [
          1.0874182902779337e-09,
          1.1175984512585517,
          -4.814277469979149e-10
        ],
        "actual_opposite_endpoint_branch_residual": 0.048530673475635
      },
      "pnp_branch": {
        "construction": "incoming_path_concatenated_with_parent_reflection",
        "reduced_polarization": [
          [
            -1.1372970983646692e-09,
            0.8879111979331813,
            5.025081315793264e-10
          ],
          [
            -9.944387177304257e-10,
            0.9019726926590267,
            4.394214265061993e-10
          ],
          [
            -8.513388982029297e-10,
            0.9160536378581905,
            3.762184308538802e-10
          ],
          [
            -7.080132969826744e-10,
            0.9301533892318526,
            3.129187791948937e-10
          ],
          [
            -5.644673494124573e-10,
            0.9442713032728905,
            2.4951288038897285e-10
          ],
          [
            -4.20711732929878e-10,
            0.9584067369669784,
            1.8601169454198517e-10
          ],
          [
            -2.7675135732125004e-10,
            0.9725590479366268,
            1.2242750954272883e-10
          ],
          [
            -1.3260260328477636e-10,
            0.9867275945914334,
            5.875553987565375e-11
          ],
          [
            1.1730925516170217e-11,
            1.000911736284544,
            -4.996613097032262e-12
          ],
          [
            9.283892331539635e-11,
            1.0095042462398676,
            -4.3792731589773597e-11
          ],
          [
            1.7369773324952134e-10,
            1.0180769719082043,
            -8.240691461269342e-11
          ],
          [
            2.543117933657589e-10,
            1.0266293279825232,
            -1.2082219119156992e-10
          ],
          [
            3.3468185363437616e-10,
            1.0351607668711067,
            -1.5905360368307616e-10
          ],
          [
            4.148037617789281e-10,
            1.0436707798804667,
            -1.970899700761766e-10
          ],
          [
            4.946879985613682e-10,
            1.0521588981470325,
            -2.3492179544399486e-10
          ],
          [
            5.743253382806258e-10,
            1.0606246932926622,
            -2.7256544199091116e-10
          ],
          [
            6.537264663213641e-10,
            1.0690677777829167,
            -3.1000702718882343e-10
          ]
        ],
        "unwrapped_reduced_polarization": [
          [
            -1.1372970983646692e-09,
            0.8879111979331813,
            5.025081315793264e-10
          ],
          [
            -9.944387177304257e-10,
            0.9019726926590267,
            4.394214265061993e-10
          ],
          [
            -8.513388982029297e-10,
            0.9160536378581905,
            3.762184308538802e-10
          ],
          [
            -7.080132969826744e-10,
            0.9301533892318526,
            3.129187791948937e-10
          ],
          [
            -5.644673494124573e-10,
            0.9442713032728905,
            2.4951288038897285e-10
          ],
          [
            -4.20711732929878e-10,
            0.9584067369669784,
            1.8601169454198517e-10
          ],
          [
            -2.7675135732125004e-10,
            0.9725590479366268,
            1.2242750954272883e-10
          ],
          [
            -1.3260260328477636e-10,
            0.9867275945914334,
            5.875553987565375e-11
          ],
          [
            1.173092551617022e-11,
            1.000911736284544,
            -4.996613097032265e-12
          ],
          [
            9.283892331539635e-11,
            1.0095042462398676,
            -4.3792731589773597e-11
          ],
          [
            1.7369773324952134e-10,
            1.0180769719082043,
            -8.240691461269342e-11
          ],
          [
            2.543117933657589e-10,
            1.0266293279825232,
            -1.2082219119156992e-10
          ],
          [
            3.3468185363437616e-10,
            1.0351607668711067,
            -1.5905360368307616e-10
          ],
          [
            4.148037617789281e-10,
            1.0436707798804667,
            -1.970899700761766e-10
          ],
          [
            4.946879985613682e-10,
            1.0521588981470325,
            -2.3492179544399486e-10
          ],
          [
            5.743253382806258e-10,
            1.0606246932926622,
            -2.7256544199091116e-10
          ],
          [
            6.537264663213641e-10,
            1.0690677777829167,
            -3.1000702718882343e-10
          ]
        ],
        "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": [
          [
            -1.1372970898371193e-09,
            -0.1120888020668187,
            5.025081462051162e-10
          ],
          [
            -9.944386980542674e-10,
            -0.0980273073409732,
            4.394213881653286e-10
          ],
          [
            -8.513388882747108e-10,
            -0.0839463621418095,
            3.7621838977486277e-10
          ],
          [
            -7.080133146430967e-10,
            -0.06984661076814724,
            3.1291880198125455e-10
          ],
          [
            -5.644673617410945e-10,
            -0.05572869672710956,
            2.4951285482188723e-10
          ],
          [
            -4.207117432208918e-10,
            -0.04159326303302158,
            1.8601165052700708e-10
          ],
          [
            -2.76751344063797e-10,
            -0.02744095206337316,
            1.2242751257218742e-10
          ],
          [
            -1.3260259557057452e-10,
            -0.013272405408566446,
            5.875555597611992e-11
          ],
          [
            1.1730949545096792e-11,
            0.0009117362845441068,
            -4.996614233476748e-12
          ],
          [
            9.283895874290238e-11,
            0.009504246239867564,
            -4.37927472063393e-11
          ],
          [
            1.7369772287167962e-10,
            0.018076971908204342,
            -8.240691462546579e-11
          ],
          [
            2.5431179384582947e-10,
            0.026629327982523154,
            -1.2082218558973068e-10
          ],
          [
            3.346818377991667e-10,
            0.0351607668711067,
            -1.5905360362111765e-10
          ],
          [
            4.1480374690650024e-10,
            0.04367077988046675,
            -1.9708995546707797e-10
          ],
          [
            4.946879572642615e-10,
            0.05215889814703245,
            -2.3492180423190234e-10
          ],
          [
            5.743253650436486e-10,
            0.06062469329266218,
            -2.725654146829015e-10
          ],
          [
            6.537265173633955e-10,
            0.06906777778291673,
            -3.1000702005457015e-10
          ]
        ]
      },
      "incoming_structure_ids": [
        "incoming_00_000",
        "incoming_00_001",
        "incoming_00_002",
        "incoming_00_003",
        "incoming_00_004",
        "incoming_00_005",
        "incoming_00_006",
        "incoming_00_007",
        "incoming_00_008"
      ],
      "reflected_structure_ids": [
        "reflected_00_001",
        "reflected_00_002",
        "reflected_00_003",
        "reflected_00_004",
        "reflected_00_005",
        "reflected_00_006",
        "reflected_00_007",
        "reflected_00_008"
      ],
      "positive_extension_structure_ids": [
        "extension_plus_00_000",
        "extension_plus_00_001",
        "extension_plus_00_002",
        "extension_plus_00_003"
      ],
      "negative_extension_structure_ids": [
        "extension_minus_00_000",
        "extension_minus_00_001",
        "extension_minus_00_002",
        "extension_minus_00_003"
      ],
      "extension": {
        "enabled": true,
        "fraction_beyond_polar_endpoint": 0.35,
        "images_per_side": 4,
        "construction": "continue fractional atomic displacements and symmetric log strain beyond +P; reflect these structures about N for the -P side",
        "positive_path_coordinates": [
          1.35,
          1.2625,
          1.175,
          1.0875
        ],
        "negative_path_coordinates": [
          -1.0875,
          -1.175,
          -1.2625,
          -1.35
        ]
      },
      "branch_coordinates": [
        1.35,
        1.2625,
        1.175,
        1.0875,
        1.0,
        0.875,
        0.75,
        0.625,
        0.5,
        0.375,
        0.25,
        0.125,
        0.0,
        -0.125,
        -0.25,
        -0.375,
        -0.5,
        -0.625,
        -0.75,
        -0.875,
        -1.0,
        -1.0875,
        -1.175,
        -1.2625,
        -1.35
      ],
      "parent": {
        "candidate_id": "bec_projection_00",
        "source": "MACEField_BEC_backprojection",
        "spacegroup": "P6_3",
        "spacegroup_number": 173,
        "pointgroup": "6",
        "has_inversion": false,
        "is_polar_point_group": true,
        "nonpolar_parent_hypothesis": false,
        "symmetry_tolerance_A": null,
        "target_reduced_polarization": [
          0.0,
          1.0,
          0.0
        ],
        "formal_class": [
          0.0,
          0.0,
          0.0
        ],
        "target_residual": 0.0009117362845363353,
        "parent_symmetrization_rmsd_A": 0.012746783836532133,
        "parent_cell_rmsd_A": 0.01348268852500823,
        "energy_eV": -116.8486235870064,
        "reduced_polarization": [
          1.173395561995738e-11,
          1.0009117362845363,
          -4.9950817034579566e-12
        ],
        "cartesian_polarization_e_A2": [
          -6.9716058846313e-13,
          0.013548996655975275,
          2.1070001908990076e-13
        ],
        "ranking_score": 0.5179409285368568
      }
    }
  ],
  "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": 46,
      "full_response": 11,
      "energy_polarization": 35
    },
    "model_evaluations_for_recovery_and_path_properties": {
      "total": 71,
      "full_response": 36,
      "energy_polarization": 35
    },
    "elapsed_seconds": 321.52248510101344
  }
}
