{
  "schema": "ferrofinder.endpoint_parent_recovery.v4_variable_cell",
  "status": "complete",
  "input_atom_count": 40,
  "input_formula": "Na4O24Se8Y4",
  "input_spacegroup": "Pna2_1",
  "input_pointgroup": "mm2",
  "input_is_polar_point_group": true,
  "input_energy_eV": -241.63214831245645,
  "input_cartesian_polarization_e_A2": [
    1.4759986503476647e-18,
    3.898439183361008e-18,
    0.000527499566286317
  ],
  "input_reduced_polarization": [
    7.020467990562451e-17,
    2.760671002230171e-16,
    0.05939765213979416
  ],
  "input_formal_targets": [
    {
      "orbit_id": 0,
      "representative_formal_class": [
        0.0,
        0.0,
        0.0
      ],
      "target_reduced_polarization": [
        0.0,
        0.0,
        0.0
      ]
    },
    {
      "orbit_id": 1,
      "representative_formal_class": [
        0.0,
        0.0,
        0.5
      ],
      "target_reduced_polarization": [
        0.0,
        0.0,
        0.5
      ]
    },
    {
      "orbit_id": 2,
      "representative_formal_class": [
        0.0,
        0.5,
        0.0
      ],
      "target_reduced_polarization": [
        0.0,
        0.5,
        0.0
      ]
    },
    {
      "orbit_id": 3,
      "representative_formal_class": [
        0.5,
        0.0,
        0.0
      ],
      "target_reduced_polarization": [
        0.5,
        0.0,
        0.0
      ]
    },
    {
      "orbit_id": 4,
      "representative_formal_class": [
        0.0,
        0.5,
        0.5
      ],
      "target_reduced_polarization": [
        0.0,
        0.5,
        0.5
      ]
    },
    {
      "orbit_id": 5,
      "representative_formal_class": [
        0.5,
        0.0,
        0.5
      ],
      "target_reduced_polarization": [
        0.5,
        0.0,
        0.5
      ]
    },
    {
      "orbit_id": 6,
      "representative_formal_class": [
        0.5,
        0.5,
        0.0
      ],
      "target_reduced_polarization": [
        0.5,
        0.5,
        0.0
      ]
    },
    {
      "orbit_id": 7,
      "representative_formal_class": [
        0.5,
        0.5,
        0.5
      ],
      "target_reduced_polarization": [
        0.5,
        0.5,
        0.5
      ]
    }
  ],
  "parent_candidates": [
    {
      "candidate_id": "inversion_parent_endpoint_00",
      "source": "same_species_inversion_center_projection_from_endpoint",
      "spacegroup": "Pnma",
      "spacegroup_number": 62,
      "pointgroup": "mmm",
      "has_inversion": true,
      "is_polar_point_group": false,
      "nonpolar_parent_hypothesis": true,
      "symmetry_tolerance_A": null,
      "target_reduced_polarization": [
        0.0,
        0.0,
        0.0
      ],
      "formal_class": [
        0.0,
        0.0,
        0.0
      ],
      "target_residual": 2.9968150472343355e-15,
      "parent_symmetrization_rmsd_A": 0.3381836847006432,
      "parent_cell_rmsd_A": 0.0,
      "energy_eV": -239.91011594509442,
      "reduced_polarization": [
        7.149087251458253e-16,
        1.330866829976857e-15,
        -2.5881652619003786e-15
      ],
      "cartesian_polarization_e_A2": [
        1.5030398469952557e-17,
        1.879363167007561e-17,
        -2.2985017150452185e-17
      ],
      "ranking_score": 0.3381836847006492
    },
    {
      "candidate_id": "inversion_parent_endpoint_01",
      "source": "same_species_inversion_center_projection_from_endpoint",
      "spacegroup": "Pnma",
      "spacegroup_number": 62,
      "pointgroup": "mmm",
      "has_inversion": true,
      "is_polar_point_group": false,
      "nonpolar_parent_hypothesis": true,
      "symmetry_tolerance_A": null,
      "target_reduced_polarization": [
        0.0,
        0.0,
        0.0
      ],
      "formal_class": [
        0.0,
        0.0,
        0.0
      ],
      "target_residual": 2.397643868014798e-15,
      "parent_symmetrization_rmsd_A": 0.4509028795005294,
      "parent_cell_rmsd_A": 0.0,
      "energy_eV": -233.75564423164502,
      "reduced_polarization": [
        2.2899587575323173e-15,
        6.885719869724385e-16,
        -1.7508176771679032e-16
      ],
      "cartesian_polarization_e_A2": [
        4.814459719798146e-17,
        9.72356362786286e-18,
        -1.5548688072364714e-18
      ],
      "ranking_score": 0.45090287950053415
    },
    {
      "candidate_id": "bec_projection_00",
      "source": "MACEField_BEC_backprojection",
      "spacegroup": "Pna2_1",
      "spacegroup_number": 33,
      "pointgroup": "mm2",
      "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": 3.519125172760632e-05,
      "parent_symmetrization_rmsd_A": 0.0032895354718403703,
      "parent_cell_rmsd_A": 0.001577826234013651,
      "energy_eV": -241.6293341450452,
      "reduced_polarization": [
        -1.3763845344053808e-15,
        2.7531880863014576e-15,
        3.519125172760632e-05
      ],
      "cartesian_polarization_e_A2": [
        -2.89296531836138e-17,
        3.887703782579876e-17,
        3.1253081465718835e-07
      ],
      "ranking_score": 0.503754374533799
    },
    {
      "candidate_id": "inversion_parent_bec_00_00",
      "source": "same_species_inversion_center_projection_after_BEC",
      "spacegroup": "Pnma",
      "spacegroup_number": 62,
      "pointgroup": "mmm",
      "has_inversion": true,
      "is_polar_point_group": false,
      "nonpolar_parent_hypothesis": true,
      "symmetry_tolerance_A": null,
      "target_reduced_polarization": [
        0.0,
        0.0,
        0.0
      ],
      "formal_class": [
        0.0,
        0.0,
        0.0
      ],
      "target_residual": 3.903320912802575e-15,
      "parent_symmetrization_rmsd_A": 0.33818391239098694,
      "parent_cell_rmsd_A": 0.001577826234013651,
      "energy_eV": -239.9121468027385,
      "reduced_polarization": [
        4.716614067513732e-16,
        7.802428698828662e-16,
        -3.795348564980585e-15
      ],
      "cartesian_polarization_e_A2": [
        9.913588318372329e-18,
        1.1017601562918338e-17,
        -3.370620028246592e-17
      ],
      "ranking_score": 0.33857836894949817
    },
    {
      "candidate_id": "bec_projection_01",
      "source": "MACEField_BEC_backprojection",
      "spacegroup": "Pna2_1",
      "spacegroup_number": 33,
      "pointgroup": "mm2",
      "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": 1.1460501320170738e-07,
      "parent_symmetrization_rmsd_A": 0.024369424471041904,
      "parent_cell_rmsd_A": 0.011681462624373624,
      "energy_eV": -241.36139912314277,
      "reduced_polarization": [
        1.39846002467764e-15,
        1.4812914074791074e-15,
        0.4999998853949868
      ],
      "cartesian_polarization_e_A2": [
        4.986856556091831e-17,
        2.086786842065118e-17,
        0.00444000553936589
      ],
      "ranking_score": 0.5272900193371617
    },
    {
      "candidate_id": "bec_projection_02",
      "source": "MACEField_BEC_backprojection",
      "spacegroup": "Pc",
      "spacegroup_number": 7,
      "pointgroup": "m",
      "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": 3.1023825699528163e-06,
      "parent_symmetrization_rmsd_A": 0.053773712407858464,
      "parent_cell_rmsd_A": 0.04370587637088591,
      "energy_eV": -240.4466960632666,
      "reduced_polarization": [
        -2.2423856731770207e-16,
        0.5000018319848211,
        2.5037190788368866e-06
      ],
      "cartesian_polarization_e_A2": [
        5.981786971293014e-17,
        0.007060642423554114,
        -6.554433885107167e-05
      ],
      "ranking_score": 0.5647063862657198
    },
    {
      "candidate_id": "bec_projection_03",
      "source": "MACEField_BEC_backprojection",
      "spacegroup": "Pc",
      "spacegroup_number": 7,
      "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": 1.2953217112241142e-05,
      "parent_symmetrization_rmsd_A": 0.08838890286678269,
      "parent_cell_rmsd_A": 0.028323166912900925,
      "energy_eV": -238.69168013551212,
      "reduced_polarization": [
        0.5000006954161146,
        6.017502397122579e-16,
        -1.2934536326611639e-05
      ],
      "cartesian_polarization_e_A2": [
        0.010509616997629007,
        5.757800839974611e-16,
        4.2391210589503675e-05
      ],
      "ranking_score": 0.5954956010292324
    },
    {
      "candidate_id": "bec_projection_04",
      "source": "MACEField_BEC_backprojection",
      "spacegroup": "Pc",
      "spacegroup_number": 7,
      "pointgroup": "m",
      "has_inversion": false,
      "is_polar_point_group": true,
      "nonpolar_parent_hypothesis": false,
      "symmetry_tolerance_A": null,
      "target_reduced_polarization": [
        0.0,
        0.5,
        0.5
      ],
      "formal_class": [
        0.0,
        0.5,
        0.5
      ],
      "target_residual": 4.485342406279131e-06,
      "parent_symmetrization_rmsd_A": 0.05900383763176656,
      "parent_cell_rmsd_A": 0.04478341300666133,
      "energy_eV": -240.12379228096898,
      "reduced_polarization": [
        1.16329232915907e-15,
        0.49999712742251756,
        0.5000034447924624
      ],
      "cartesian_polarization_e_A2": [
        1.397789032583388e-16,
        0.00702215163654861,
        0.004375002448826292
      ],
      "ranking_score": 0.5702086615682445
    },
    {
      "candidate_id": "bec_projection_05",
      "source": "MACEField_BEC_backprojection",
      "spacegroup": "Pc",
      "spacegroup_number": 7,
      "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": 1.8871608954467417e-05,
      "parent_symmetrization_rmsd_A": 0.09158294534448921,
      "parent_cell_rmsd_A": 0.030781564292703918,
      "energy_eV": -238.53442153121262,
      "reduced_polarization": [
        0.49999772978647505,
        -1.2501464642439748e-16,
        0.4999812654395546
      ],
      "cartesian_polarization_e_A2": [
        0.010551971114352254,
        6.935398233735165e-16,
        0.004482459779092939
      ],
      "ranking_score": 0.5993160796355741
    },
    {
      "candidate_id": "bec_projection_06",
      "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": 4.9031646477931075e-05,
      "parent_symmetrization_rmsd_A": 0.10378721945331165,
      "parent_cell_rmsd_A": 0.05225748351230633,
      "energy_eV": -237.38624629043142,
      "reduced_polarization": [
        0.4999971124207137,
        0.5000004196364775,
        -4.894474586131767e-05
      ],
      "cartesian_polarization_e_A2": [
        0.010508824551898242,
        0.0070604578159975595,
        -2.3316465564889146e-05
      ],
      "ranking_score": 0.6169496536243441
    },
    {
      "candidate_id": "bec_projection_07",
      "source": "MACEField_BEC_backprojection",
      "spacegroup": "P1",
      "spacegroup_number": 1,
      "pointgroup": "1",
      "has_inversion": false,
      "is_polar_point_group": true,
      "nonpolar_parent_hypothesis": false,
      "symmetry_tolerance_A": null,
      "target_reduced_polarization": [
        0.5,
        0.5,
        0.5
      ],
      "formal_class": [
        0.5,
        0.5,
        0.5
      ],
      "target_residual": 5.4375874530682816e-05,
      "parent_symmetrization_rmsd_A": 0.10641388829565165,
      "parent_cell_rmsd_A": 0.05308678075231711,
      "energy_eV": -237.18433916759693,
      "reduced_polarization": [
        0.4999892575911218,
        0.4999975188694145,
        0.49994675358816326
      ],
      "cartesian_polarization_e_A2": [
        0.01055148711535656,
        0.007022095582869329,
        0.00441748489107372
      ],
      "ranking_score": 0.6197943352327923
    }
  ],
  "formal_branches": [
    {
      "orbit_id": 0,
      "formal_class": [
        0.0,
        0.0,
        0.0
      ],
      "formal_classes_in_orbit": [
        [
          0.0,
          0.0,
          0.0
        ]
      ],
      "target_reduced_polarization": [
        0.0,
        0.0,
        0.0
      ],
      "bec_backprojection": {
        "converged_to_target": true,
        "history": [
          {
            "iteration": 0,
            "reduced_polarization": [
              7.020467990562451e-17,
              2.760671002230171e-16,
              0.05939765213979416
            ],
            "branch_aligned_reduced_polarization": [
              7.020467990562451e-17,
              2.760671002230171e-16,
              0.05939765213979416
            ],
            "target_residual": 0.05939765213979416,
            "energy_eV": -241.63214831245645,
            "max_atomic_step_A": 0.005241291515320276,
            "max_log_strain_component": 0.00016522874044088518,
            "step_scale": 1.0,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 1.5115606407059583,
            "cell_principal_stretches": [
              1.0001652423914609,
              1.0001096110408214,
              0.9998781962386244
            ],
            "cell_volume_ratio": 1.0001530343029095,
            "cell_rmsd_from_input_A": 0.001577826234013651
          },
          {
            "iteration": 1,
            "reduced_polarization": [
              -1.3763845344053808e-15,
              2.7531880863014576e-15,
              3.519125172760632e-05
            ],
            "branch_aligned_reduced_polarization": [
              -1.3763845344053808e-15,
              2.7531880863014576e-15,
              3.519125172760632e-05
            ],
            "target_residual": 3.519125172760632e-05,
            "energy_eV": -241.6293341450452
          }
        ],
        "iterations": 1
      },
      "parent": {
        "candidate_id": "inversion_parent_endpoint_00",
        "source": "same_species_inversion_center_projection_from_endpoint",
        "spacegroup": "Pnma",
        "spacegroup_number": 62,
        "pointgroup": "mmm",
        "has_inversion": true,
        "is_polar_point_group": false,
        "nonpolar_parent_hypothesis": true,
        "symmetry_tolerance_A": null,
        "target_reduced_polarization": [
          0.0,
          0.0,
          0.0
        ],
        "formal_class": [
          0.0,
          0.0,
          0.0
        ],
        "target_residual": 2.9968150472343355e-15,
        "parent_symmetrization_rmsd_A": 0.3381836847006432,
        "parent_cell_rmsd_A": 0.0,
        "energy_eV": -239.91011594509442,
        "reduced_polarization": [
          7.149087251458253e-16,
          1.330866829976857e-15,
          -2.5881652619003786e-15
        ],
        "cartesian_polarization_e_A2": [
          1.5030398469952557e-17,
          1.879363167007561e-17,
          -2.2985017150452185e-17
        ],
        "ranking_score": 0.3381836847006492
      },
      "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": [
          -241.6321483124565,
          -241.5196821533819,
          -241.30052837691062,
          -241.01502177901585,
          -240.700865098026,
          -240.39661253167873,
          -240.14103426051716,
          -239.97022589807182,
          -239.9101159450944
        ],
        "cartesian_polarizations_e_A2": [
          [
            8.563045605070422e-18,
            1.3407926671097107e-18,
            0.0005274995662863013
          ],
          [
            -5.013888545074129e-18,
            4.191385480376575e-18,
            0.001186637114255235
          ],
          [
            -2.5903212955338027e-17,
            -4.5451744698492214e-17,
            0.0017195492230747383
          ],
          [
            -9.93763976798962e-18,
            -5.633582634914751e-18,
            0.002080020848671317
          ],
          [
            -4.2263136927130465e-17,
            1.1503775740495922e-17,
            0.002212291369359646
          ],
          [
            -3.710277523354855e-17,
            8.179961985896219e-18,
            0.00206381047741409
          ],
          [
            -4.367153258585915e-17,
            4.4617974468524826e-18,
            0.001610234781821604
          ],
          [
            -2.825805049673239e-17,
            1.58867030304596e-17,
            0.000885792799094238
          ],
          [
            1.7779586795790954e-17,
            3.267477928250556e-17,
            -2.4787763593624904e-18
          ]
        ],
        "raw_reduced_polarization": [
          [
            4.0729432617003546e-16,
            9.494793331369662e-17,
            0.059397652139792395
          ],
          [
            -2.3848154624429703e-16,
            2.96812026829371e-16,
            0.13361804072165723
          ],
          [
            -1.232065336664357e-15,
            -3.2186551511550606e-15,
            0.19362515747360529
          ],
          [
            -4.726757837920674e-16,
            -3.989408962760363e-16,
            0.23421508321362022
          ],
          [
            -2.010211865083951e-15,
            8.146373101956661e-16,
            0.24910904498785688
          ],
          [
            -1.7647634422077981e-15,
            5.792621813928047e-16,
            0.23238975850336055
          ],
          [
            -2.0772010634671807e-15,
            3.1596118985062075e-16,
            0.18131610250864758
          ],
          [
            -1.3440712763611165e-15,
            1.1250133274984224e-15,
            0.09974228589218634
          ],
          [
            8.456716403898893e-16,
            2.3138571984010103e-15,
            -2.791158615774918e-16
          ]
        ],
        "unwrapped_reduced_polarization": [
          [
            4.0729432617003546e-16,
            9.494793331369662e-17,
            0.059397652139792395
          ],
          [
            -2.38481546244297e-16,
            2.96812026829371e-16,
            0.13361804072165723
          ],
          [
            -1.232065336664357e-15,
            -3.2186551511550606e-15,
            0.19362515747360529
          ],
          [
            -4.726757837920674e-16,
            -3.989408962760361e-16,
            0.23421508321362022
          ],
          [
            -2.010211865083951e-15,
            8.146373101956662e-16,
            0.24910904498785688
          ],
          [
            -1.7647634422077981e-15,
            5.792621813928047e-16,
            0.23238975850336055
          ],
          [
            -2.0772010634671807e-15,
            3.1596118985062075e-16,
            0.18131610250864758
          ],
          [
            -1.3440712763611165e-15,
            1.1250133274984224e-15,
            0.09974228589218634
          ],
          [
            8.456716403898891e-16,
            2.3138571984010103e-15,
            -2.7755575615628914e-16
          ]
        ],
        "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": [
          [
            4.440892098500626e-16,
            1.1102230246251565e-16,
            0.05939765213979242
          ],
          [
            -2.220446049250313e-16,
            3.3306690738754696e-16,
            0.13361804072165717
          ],
          [
            -1.2212453270876722e-15,
            -3.219646771412954e-15,
            0.1936251574736053
          ],
          [
            -4.996003610813204e-16,
            -3.885780586188048e-16,
            0.23421508321362028
          ],
          [
            -1.9984014443252818e-15,
            7.771561172376096e-16,
            0.2491090449878569
          ],
          [
            -1.7763568394002505e-15,
            5.551115123125783e-16,
            0.23238975850336052
          ],
          [
            -2.0539125955565396e-15,
            3.3306690738754696e-16,
            0.1813161025086476
          ],
          [
            -1.3322676295501878e-15,
            1.1102230246251565e-15,
            0.09974228589218637
          ],
          [
            8.881784197001252e-16,
            2.3314683517128287e-15,
            -2.7755575615628914e-16
          ]
        ]
      },
      "reflected": {
        "reached": true,
        "construction": "reflect_displacements_about_reconstructed_parent",
        "energies_eV": [
          -239.9101159450944,
          -239.97022589807182,
          -240.14103426051716,
          -240.39661253167878,
          -240.70086509802587,
          -241.01502177901585,
          -241.30052837691073,
          -241.51968215338195,
          -241.63214831245656
        ],
        "cartesian_polarizations_e_A2": [
          [
            1.537968059331727e-17,
            2.922702670993773e-17,
            1.1717851880622683e-18
          ],
          [
            -4.796432255366419e-17,
            2.7266539952987395e-18,
            -0.0008857927990942708
          ],
          [
            -6.017792970615937e-17,
            1.5661359725063008e-17,
            -0.0016102347818216668
          ],
          [
            2.62750294092424e-17,
            4.806572704109266e-17,
            -0.002063810477414122
          ],
          [
            -3.3790228644218675e-17,
            -3.312546589329874e-18,
            -0.0022122913693596704
          ],
          [
            -7.323657425389177e-19,
            3.920973513900667e-18,
            -0.0020800208486713443
          ],
          [
            -1.0309456221893994e-17,
            -2.1227339368358784e-17,
            -0.001719549223074768
          ],
          [
            4.101248158217939e-18,
            1.8421815216171235e-17,
            -0.0011866371142552623
          ],
          [
            2.443848147026019e-17,
            -2.535112185711638e-18,
            -0.000527499566286329
          ]
        ],
        "raw_reduced_polarization": [
          [
            7.315220463448663e-16,
            2.069705369880076e-15,
            1.3194568001845069e-16
          ],
          [
            -2.2813841401392644e-15,
            1.9308739379760157e-16,
            -0.09974228589219004
          ],
          [
            -2.8623144685186302e-15,
            1.1090556916473809e-15,
            -0.18131610250865465
          ],
          [
            1.2497504850375298e-15,
            3.4037637270271414e-15,
            -0.23238975850336413
          ],
          [
            -1.6072048476104422e-15,
            -2.345772470103094e-16,
            -0.24910904498785963
          ],
          [
            -3.4834383159279344e-17,
            2.7766286380812124e-16,
            -0.2342150832136233
          ],
          [
            -4.903609321652399e-16,
            -1.5032092971681049e-15,
            -0.19362515747360862
          ],
          [
            1.9507254569196432e-16,
            1.3045367308226384e-15,
            -0.13361804072166028
          ],
          [
            1.1623965703457983e-15,
            -1.795234033242163e-16,
            -0.05939765213979551
          ]
        ],
        "unwrapped_reduced_polarization": [
          [
            7.315220463448663e-16,
            2.069705369880076e-15,
            1.3194568001845069e-16
          ],
          [
            -2.2813841401392644e-15,
            1.9308739379760147e-16,
            -0.09974228589219004
          ],
          [
            -2.8623144685186302e-15,
            1.1090556916473809e-15,
            -0.18131610250865465
          ],
          [
            1.2497504850375294e-15,
            3.4037637270271414e-15,
            -0.23238975850336413
          ],
          [
            -1.6072048476104422e-15,
            -2.3457724701030913e-16,
            -0.24910904498785963
          ],
          [
            -3.4834383159279276e-17,
            2.7766286380812124e-16,
            -0.2342150832136233
          ],
          [
            -4.903609321652399e-16,
            -1.5032092971681049e-15,
            -0.19362515747360862
          ],
          [
            1.950725456919643e-16,
            1.3045367308226386e-15,
            -0.13361804072166028
          ],
          [
            1.1623965703457983e-15,
            -1.7952340332421626e-16,
            -0.059397652139795504
          ]
        ],
        "gauge_integer_shift": [
          0,
          0,
          0
        ],
        "expected_opposite_endpoint_reduced_polarization": [
          1.284048954609743e-15,
          4.532766463488324e-15,
          -0.059397652139792964
        ],
        "actual_opposite_endpoint_branch_residual": 5.354458131521775e-15
      },
      "pnp_branch": {
        "construction": "incoming_path_concatenated_with_parent_reflection",
        "reduced_polarization": [
          [
            4.0729432617003546e-16,
            9.494793331369662e-17,
            0.059397652139792395
          ],
          [
            -2.3848154624429703e-16,
            2.96812026829371e-16,
            0.13361804072165723
          ],
          [
            -1.232065336664357e-15,
            -3.2186551511550606e-15,
            0.19362515747360529
          ],
          [
            -4.726757837920674e-16,
            -3.989408962760363e-16,
            0.23421508321362022
          ],
          [
            -2.010211865083951e-15,
            8.146373101956661e-16,
            0.24910904498785688
          ],
          [
            -1.7647634422077981e-15,
            5.792621813928047e-16,
            0.23238975850336055
          ],
          [
            -2.0772010634671807e-15,
            3.1596118985062075e-16,
            0.18131610250864758
          ],
          [
            -1.3440712763611165e-15,
            1.1250133274984224e-15,
            0.09974228589218634
          ],
          [
            8.456716403898893e-16,
            2.3138571984010103e-15,
            -2.791158615774918e-16
          ],
          [
            -2.2813841401392644e-15,
            1.9308739379760157e-16,
            -0.09974228589219004
          ],
          [
            -2.8623144685186302e-15,
            1.1090556916473809e-15,
            -0.18131610250865465
          ],
          [
            1.2497504850375298e-15,
            3.4037637270271414e-15,
            -0.23238975850336413
          ],
          [
            -1.6072048476104422e-15,
            -2.345772470103094e-16,
            -0.24910904498785963
          ],
          [
            -3.4834383159279344e-17,
            2.7766286380812124e-16,
            -0.2342150832136233
          ],
          [
            -4.903609321652399e-16,
            -1.5032092971681049e-15,
            -0.19362515747360862
          ],
          [
            1.9507254569196432e-16,
            1.3045367308226384e-15,
            -0.13361804072166028
          ],
          [
            1.1623965703457983e-15,
            -1.795234033242163e-16,
            -0.05939765213979551
          ]
        ],
        "unwrapped_reduced_polarization": [
          [
            4.0729432617003546e-16,
            9.494793331369662e-17,
            0.059397652139792395
          ],
          [
            -2.38481546244297e-16,
            2.96812026829371e-16,
            0.13361804072165723
          ],
          [
            -1.232065336664357e-15,
            -3.2186551511550606e-15,
            0.19362515747360529
          ],
          [
            -4.726757837920674e-16,
            -3.989408962760361e-16,
            0.23421508321362022
          ],
          [
            -2.010211865083951e-15,
            8.146373101956662e-16,
            0.24910904498785688
          ],
          [
            -1.7647634422077981e-15,
            5.792621813928047e-16,
            0.23238975850336055
          ],
          [
            -2.0772010634671807e-15,
            3.1596118985062075e-16,
            0.18131610250864758
          ],
          [
            -1.3440712763611165e-15,
            1.1250133274984224e-15,
            0.09974228589218634
          ],
          [
            8.456716403898891e-16,
            2.3138571984010103e-15,
            -2.7755575615628914e-16
          ],
          [
            -2.2813841401392648e-15,
            1.9308739379760147e-16,
            -0.09974228589219004
          ],
          [
            -2.8623144685186302e-15,
            1.1090556916473809e-15,
            -0.18131610250865465
          ],
          [
            1.2497504850375294e-15,
            3.4037637270271414e-15,
            -0.23238975850336413
          ],
          [
            -1.6072048476104422e-15,
            -2.3457724701030913e-16,
            -0.24910904498785963
          ],
          [
            -3.4834383159279276e-17,
            2.7766286380812124e-16,
            -0.2342150832136233
          ],
          [
            -4.903609321652399e-16,
            -1.5032092971681049e-15,
            -0.19362515747360862
          ],
          [
            1.950725456919643e-16,
            1.3045367308226386e-15,
            -0.13361804072166028
          ],
          [
            1.1623965703457983e-15,
            -1.7952340332421626e-16,
            -0.059397652139795504
          ]
        ],
        "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": [
          [
            4.440892098500626e-16,
            1.1102230246251565e-16,
            0.05939765213979242
          ],
          [
            -2.220446049250313e-16,
            3.3306690738754696e-16,
            0.13361804072165717
          ],
          [
            -1.2212453270876722e-15,
            -3.219646771412954e-15,
            0.1936251574736053
          ],
          [
            -4.996003610813204e-16,
            -3.885780586188048e-16,
            0.23421508321362028
          ],
          [
            -1.9984014443252818e-15,
            7.771561172376096e-16,
            0.2491090449878569
          ],
          [
            -1.7763568394002505e-15,
            5.551115123125783e-16,
            0.23238975850336052
          ],
          [
            -2.0539125955565396e-15,
            3.3306690738754696e-16,
            0.1813161025086476
          ],
          [
            -1.3322676295501878e-15,
            1.1102230246251565e-15,
            0.09974228589218637
          ],
          [
            8.881784197001252e-16,
            2.3314683517128287e-15,
            -2.7755575615628914e-16
          ],
          [
            -2.275957200481571e-15,
            2.220446049250313e-16,
            -0.09974228589219003
          ],
          [
            -2.886579864025407e-15,
            1.1102230246251565e-15,
            -0.18131610250865465
          ],
          [
            1.2212453270876722e-15,
            3.4416913763379853e-15,
            -0.23238975850336413
          ],
          [
            -1.609823385706477e-15,
            -2.220446049250313e-16,
            -0.24910904498785963
          ],
          [
            -5.551115123125783e-17,
            3.3306690738754696e-16,
            -0.23421508321362328
          ],
          [
            -4.996003610813204e-16,
            -1.4988010832439613e-15,
            -0.19362515747360864
          ],
          [
            2.220446049250313e-16,
            1.3322676295501878e-15,
            -0.13361804072166028
          ],
          [
            1.1102230246251565e-15,
            -1.6653345369377348e-16,
            -0.05939765213979553
          ]
        ]
      },
      "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,
        0.0,
        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": [
              7.020467990562451e-17,
              2.760671002230171e-16,
              0.05939765213979416
            ],
            "branch_aligned_reduced_polarization": [
              7.020467990562451e-17,
              2.760671002230171e-16,
              0.059397652139794144
            ],
            "target_residual": 0.44060234786020586,
            "energy_eV": -241.63214831245645,
            "max_atomic_step_A": 0.038879067846567805,
            "max_log_strain_component": 0.0012256405489042086,
            "step_scale": 1.0,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 1.5115606407059583,
            "cell_principal_stretches": [
              1.0009039843308996,
              0.9991872976910544,
              0.9987751102417088
            ],
            "cell_volume_ratio": 0.9988655466829862,
            "cell_rmsd_from_input_A": 0.01171165019986906
          },
          {
            "iteration": 1,
            "reduced_polarization": [
              -1.7933799574580878e-15,
              5.944393372011438e-16,
              0.5011410850357343
            ],
            "branch_aligned_reduced_polarization": [
              -1.7933799574580878e-15,
              5.944393372011438e-16,
              0.5011410850357343
            ],
            "target_residual": 0.0011410850357342905,
            "energy_eV": -241.36001785072477,
            "max_atomic_step_A": 0.00010012122007754619,
            "max_log_strain_component": 3.1573715722472725e-06,
            "step_scale": 1.0,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 1.5115606407059583,
            "cell_principal_stretches": [
              1.0009016545280864,
              0.9991893904440027,
              0.9987782637508272
            ],
            "cell_volume_ratio": 0.9988684674931517,
            "cell_rmsd_from_input_A": 0.011681462624373624
          },
          {
            "iteration": 2,
            "reduced_polarization": [
              1.39846002467764e-15,
              1.4812914074791074e-15,
              0.4999998853949868
            ],
            "branch_aligned_reduced_polarization": [
              1.39846002467764e-15,
              1.4812914074791074e-15,
              0.4999998853949868
            ],
            "target_residual": 1.1460501320170738e-07,
            "energy_eV": -241.36139912314277
          }
        ],
        "iterations": 2
      },
      "parent": {
        "candidate_id": "bec_projection_01",
        "source": "MACEField_BEC_backprojection",
        "spacegroup": "Pna2_1",
        "spacegroup_number": 33,
        "pointgroup": "mm2",
        "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": 1.1460501320170738e-07,
        "parent_symmetrization_rmsd_A": 0.024369424471041904,
        "parent_cell_rmsd_A": 0.011681462624373624,
        "energy_eV": -241.36139912314277,
        "reduced_polarization": [
          1.39846002467764e-15,
          1.4812914074791074e-15,
          0.4999998853949868
        ],
        "cartesian_polarization_e_A2": [
          4.986856556091831e-17,
          2.086786842065118e-17,
          0.00444000553936589
        ],
        "ranking_score": 0.5272900193371617
      },
      "branch_status": "awaiting_branch_sampling"
    },
    {
      "orbit_id": 2,
      "formal_class": [
        0.0,
        0.5,
        0.0
      ],
      "formal_classes_in_orbit": [
        [
          0.0,
          0.5,
          0.0
        ]
      ],
      "target_reduced_polarization": [
        0.0,
        0.5,
        0.0
      ],
      "bec_backprojection": {
        "converged_to_target": true,
        "history": [
          {
            "iteration": 0,
            "reduced_polarization": [
              7.020467990562451e-17,
              2.760671002230171e-16,
              0.05939765213979416
            ],
            "branch_aligned_reduced_polarization": [
              7.020467990562451e-17,
              2.7755575615628914e-16,
              0.05939765213979416
            ],
            "target_residual": 0.5035157207870671,
            "energy_eV": -241.63214831245645,
            "max_atomic_step_A": 0.07929633103066874,
            "max_log_strain_component": 0.009285410037145165,
            "step_scale": 1.0,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 1.5115606407059583,
            "cell_principal_stretches": [
              1.009467403574258,
              0.9998781962386366,
              0.9908936811659212
            ],
            "cell_volume_ratio": 1.0001530343029499,
            "cell_rmsd_from_input_A": 0.04368808016260021
          },
          {
            "iteration": 1,
            "reduced_polarization": [
              9.14185670158238e-15,
              0.5000957036834417,
              0.010339725151086146
            ],
            "branch_aligned_reduced_polarization": [
              9.14185670158238e-15,
              0.5000957036834417,
              0.010339725151086146
            ],
            "target_residual": 0.010340168054486723,
            "energy_eV": -240.4467704555167,
            "max_atomic_step_A": 0.0009253086769419981,
            "max_log_strain_component": 2.9304088343646335e-05,
            "step_scale": 1.0,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 1.5115606407059583,
            "cell_principal_stretches": [
              1.0094927412041186,
              0.9998565953220376,
              0.9909171095084844
            ],
            "cell_volume_ratio": 1.0001801780958806,
            "cell_rmsd_from_input_A": 0.04370587637088591
          },
          {
            "iteration": 2,
            "reduced_polarization": [
              -2.2423856731770207e-16,
              0.5000018319848211,
              2.5037190788368866e-06
            ],
            "branch_aligned_reduced_polarization": [
              -2.2423856731770207e-16,
              0.5000018319848211,
              2.5037190788368866e-06
            ],
            "target_residual": 3.1023825699528163e-06,
            "energy_eV": -240.4466960632666
          }
        ],
        "iterations": 2
      },
      "parent": {
        "candidate_id": "bec_projection_02",
        "source": "MACEField_BEC_backprojection",
        "spacegroup": "Pc",
        "spacegroup_number": 7,
        "pointgroup": "m",
        "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": 3.1023825699528163e-06,
        "parent_symmetrization_rmsd_A": 0.053773712407858464,
        "parent_cell_rmsd_A": 0.04370587637088591,
        "energy_eV": -240.4466960632666,
        "reduced_polarization": [
          -2.2423856731770207e-16,
          0.5000018319848211,
          2.5037190788368866e-06
        ],
        "cartesian_polarization_e_A2": [
          5.981786971293014e-17,
          0.007060642423554114,
          -6.554433885107167e-05
        ],
        "ranking_score": 0.5647063862657198
      },
      "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
        ]
      ],
      "target_reduced_polarization": [
        0.5,
        0.0,
        0.0
      ],
      "bec_backprojection": {
        "converged_to_target": true,
        "history": [
          {
            "iteration": 0,
            "reduced_polarization": [
              7.020467990562451e-17,
              2.760671002230171e-16,
              0.05939765213979416
            ],
            "branch_aligned_reduced_polarization": [
              5.551115123125783e-17,
              2.760671002230171e-16,
              0.05939765213979416
            ],
            "target_residual": 0.5035157207870673,
            "energy_eV": -241.63214831245645,
            "max_atomic_step_A": 0.12000000000000001,
            "max_log_strain_component": 0.003218284627171226,
            "step_scale": 0.8178668249585958,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 1.5115606407059583,
            "cell_principal_stretches": [
              1.0032434279727132,
              1.0000896463391244,
              0.9968024534519686
            ],
            "cell_volume_ratio": 1.000125159935267,
            "cell_rmsd_from_input_A": 0.02254872480874616
          },
          {
            "iteration": 1,
            "reduced_polarization": [
              0.40347455354830913,
              -4.971779846152907e-14,
              0.006348465334067633
            ],
            "branch_aligned_reduced_polarization": [
              0.40347455354830913,
              -4.971779846152907e-14,
              0.006348465334067633
            ],
            "target_residual": 0.09673399001796679,
            "energy_eV": -239.7679197057587,
            "max_atomic_step_A": 0.029869977171512317,
            "max_log_strain_component": 0.0008169962209663288,
            "step_scale": 1.0,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 1.5115606407059583,
            "cell_principal_stretches": [
              1.0040654533264082,
              1.0001000071807138,
              0.9959904616559054
            ],
            "cell_volume_ratio": 1.0001396255337525,
            "cell_rmsd_from_input_A": 0.028262907706766607
          },
          {
            "iteration": 2,
            "reduced_polarization": [
              0.4990069813759592,
              -8.185853714210418e-15,
              -0.0008717867328065656
            ],
            "branch_aligned_reduced_polarization": [
              0.4990069813759592,
              -8.185853714210418e-15,
              -0.0008717867328065656
            ],
            "target_residual": 0.001321400051153844,
            "energy_eV": -238.70372688145608,
            "max_atomic_step_A": 0.0003360894183515921,
            "max_log_strain_component": 8.775771498144365e-06,
            "step_scale": 1.0,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 1.5115606407059583,
            "cell_principal_stretches": [
              1.0040738721001312,
              1.0000983972163007,
              0.9959814755330303
            ],
            "cell_volume_ratio": 1.0001373777299498,
            "cell_rmsd_from_input_A": 0.028323166912900925
          },
          {
            "iteration": 3,
            "reduced_polarization": [
              0.5000006954161146,
              6.017502397122579e-16,
              -1.2934536326611639e-05
            ],
            "branch_aligned_reduced_polarization": [
              0.5000006954161146,
              6.017502397122579e-16,
              -1.2934536326611639e-05
            ],
            "target_residual": 1.2953217112241142e-05,
            "energy_eV": -238.69168013551212
          }
        ],
        "iterations": 3
      },
      "parent": {
        "candidate_id": "bec_projection_03",
        "source": "MACEField_BEC_backprojection",
        "spacegroup": "Pc",
        "spacegroup_number": 7,
        "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": 1.2953217112241142e-05,
        "parent_symmetrization_rmsd_A": 0.08838890286678269,
        "parent_cell_rmsd_A": 0.028323166912900925,
        "energy_eV": -238.69168013551212,
        "reduced_polarization": [
          0.5000006954161146,
          6.017502397122579e-16,
          -1.2934536326611639e-05
        ],
        "cartesian_polarization_e_A2": [
          0.010509616997629007,
          5.757800839974611e-16,
          4.2391210589503675e-05
        ],
        "ranking_score": 0.5954956010292324
      },
      "branch_status": "awaiting_branch_sampling"
    },
    {
      "orbit_id": 4,
      "formal_class": [
        0.0,
        0.5,
        0.5
      ],
      "formal_classes_in_orbit": [
        [
          0.0,
          0.5,
          0.5
        ]
      ],
      "target_reduced_polarization": [
        0.0,
        0.5,
        0.5
      ],
      "bec_backprojection": {
        "converged_to_target": true,
        "history": [
          {
            "iteration": 0,
            "reduced_polarization": [
              7.020467990562451e-17,
              2.760671002230171e-16,
              0.05939765213979416
            ],
            "branch_aligned_reduced_polarization": [
              7.020467990562451e-17,
              2.7755575615628914e-16,
              0.059397652139794144
            ],
            "target_residual": 0.6664311134242801,
            "energy_eV": -241.63214831245645,
            "max_atomic_step_A": 0.08833383849960934,
            "max_log_strain_component": 0.009285410037145198,
            "step_scale": 1.0,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 1.5115606407059583,
            "cell_principal_stretches": [
              1.0083026422891201,
              1.0009039843309118,
              0.9897458972614407
            ],
            "cell_volume_ratio": 0.9988655466830269,
            "cell_rmsd_from_input_A": 0.04504497283733133
          },
          {
            "iteration": 1,
            "reduced_polarization": [
              3.984736683939847e-15,
              0.5026573142227202,
              0.5065836646968169
            ],
            "branch_aligned_reduced_polarization": [
              3.984736683939847e-15,
              0.5026573142227202,
              0.5065836646968169
            ],
            "target_residual": 0.0070997154674243505,
            "energy_eV": -240.10129026752156,
            "max_atomic_step_A": 0.0007155324178904867,
            "max_log_strain_component": 4.8184219144107e-05,
            "step_scale": 1.0,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 1.5115606407059583,
            "cell_principal_stretches": [
              1.0082694452250773,
              1.0008903948738184,
              0.9898088052131278
            ],
            "cell_volume_ratio": 0.9988825836305,
            "cell_rmsd_from_input_A": 0.04478341300666133
          },
          {
            "iteration": 2,
            "reduced_polarization": [
              1.16329232915907e-15,
              0.49999712742251756,
              0.5000034447924624
            ],
            "branch_aligned_reduced_polarization": [
              1.16329232915907e-15,
              0.49999712742251756,
              0.5000034447924624
            ],
            "target_residual": 4.485342406279131e-06,
            "energy_eV": -240.12379228096898
          }
        ],
        "iterations": 2
      },
      "parent": {
        "candidate_id": "bec_projection_04",
        "source": "MACEField_BEC_backprojection",
        "spacegroup": "Pc",
        "spacegroup_number": 7,
        "pointgroup": "m",
        "has_inversion": false,
        "is_polar_point_group": true,
        "nonpolar_parent_hypothesis": false,
        "symmetry_tolerance_A": null,
        "target_reduced_polarization": [
          0.0,
          0.5,
          0.5
        ],
        "formal_class": [
          0.0,
          0.5,
          0.5
        ],
        "target_residual": 4.485342406279131e-06,
        "parent_symmetrization_rmsd_A": 0.05900383763176656,
        "parent_cell_rmsd_A": 0.04478341300666133,
        "energy_eV": -240.12379228096898,
        "reduced_polarization": [
          1.16329232915907e-15,
          0.49999712742251756,
          0.5000034447924624
        ],
        "cartesian_polarization_e_A2": [
          1.397789032583388e-16,
          0.00702215163654861,
          0.004375002448826292
        ],
        "ranking_score": 0.5702086615682445
      },
      "branch_status": "awaiting_branch_sampling"
    },
    {
      "orbit_id": 5,
      "formal_class": [
        0.5,
        0.0,
        0.5
      ],
      "formal_classes_in_orbit": [
        [
          0.5,
          0.0,
          0.5
        ]
      ],
      "target_reduced_polarization": [
        0.5,
        0.0,
        0.5
      ],
      "bec_backprojection": {
        "converged_to_target": true,
        "history": [
          {
            "iteration": 0,
            "reduced_polarization": [
              7.020467990562451e-17,
              2.760671002230171e-16,
              0.05939765213979416
            ],
            "branch_aligned_reduced_polarization": [
              5.551115123125783e-17,
              2.760671002230171e-16,
              0.059397652139794144
            ],
            "target_residual": 0.6664311134242802,
            "energy_eV": -241.63214831245645,
            "max_atomic_step_A": 0.12,
            "max_log_strain_component": 0.0030575630436387308,
            "step_scale": 0.7770224415502552,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 1.5115606407059583,
            "cell_principal_stretches": [
              1.0030469968728262,
              0.9993684548313381,
              0.996712799133001
            ],
            "cell_volume_ratio": 0.999118392771688,
            "cell_rmsd_from_input_A": 0.023279291022208996
          },
          {
            "iteration": 1,
            "reduced_polarization": [
              0.383201327323468,
              -4.961136214625668e-14,
              0.3972413797880365
            ],
            "branch_aligned_reduced_polarization": [
              0.383201327323468,
              -4.961136214625668e-14,
              0.3972413797880365
            ],
            "target_residual": 0.15556755435136924,
            "energy_eV": -239.8468625949622,
            "max_atomic_step_A": 0.038279875134533424,
            "max_log_strain_component": 0.0009776216586953582,
            "step_scale": 1.0,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 1.5115606407059583,
            "cell_principal_stretches": [
              1.0040220328471452,
              0.9991747522686578,
              0.9956684042195717
            ],
            "cell_volume_ratio": 0.9988480373582904,
            "cell_rmsd_from_input_A": 0.030690962883555887
          },
          {
            "iteration": 2,
            "reduced_polarization": [
              0.4985834170568635,
              -1.0948560075629456e-14,
              0.49903176652470593
            ],
            "branch_aligned_reduced_polarization": [
              0.4985834170568635,
              -1.0948560075629456e-14,
              0.49903176652470593
            ],
            "target_residual": 0.0017158622606332163,
            "energy_eV": -238.55227848112753,
            "max_atomic_step_A": 0.00046795127580846833,
            "max_log_strain_component": 1.2415981002518323e-05,
            "step_scale": 1.0,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 1.5115606407059583,
            "cell_principal_stretches": [
              1.0040343328725145,
              0.9991729245750554,
              0.9956554852314297
            ],
            "cell_volume_ratio": 0.9988454865004084,
            "cell_rmsd_from_input_A": 0.030781564292703918
          },
          {
            "iteration": 3,
            "reduced_polarization": [
              0.49999772978647505,
              -1.2501464642439748e-16,
              0.4999812654395546
            ],
            "branch_aligned_reduced_polarization": [
              0.49999772978647505,
              -1.2501464642439748e-16,
              0.4999812654395546
            ],
            "target_residual": 1.8871608954467417e-05,
            "energy_eV": -238.53442153121262
          }
        ],
        "iterations": 3
      },
      "parent": {
        "candidate_id": "bec_projection_05",
        "source": "MACEField_BEC_backprojection",
        "spacegroup": "Pc",
        "spacegroup_number": 7,
        "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": 1.8871608954467417e-05,
        "parent_symmetrization_rmsd_A": 0.09158294534448921,
        "parent_cell_rmsd_A": 0.030781564292703918,
        "energy_eV": -238.53442153121262,
        "reduced_polarization": [
          0.49999772978647505,
          -1.2501464642439748e-16,
          0.4999812654395546
        ],
        "cartesian_polarization_e_A2": [
          0.010551971114352254,
          6.935398233735165e-16,
          0.004482459779092939
        ],
        "ranking_score": 0.5993160796355741
      },
      "branch_status": "awaiting_branch_sampling"
    },
    {
      "orbit_id": 6,
      "formal_class": [
        0.5,
        0.5,
        0.0
      ],
      "formal_classes_in_orbit": [
        [
          0.5,
          0.5,
          0.0
        ]
      ],
      "target_reduced_polarization": [
        0.5,
        0.5,
        0.0
      ],
      "bec_backprojection": {
        "converged_to_target": true,
        "history": [
          {
            "iteration": 0,
            "reduced_polarization": [
              7.020467990562451e-17,
              2.760671002230171e-16,
              0.05939765213979416
            ],
            "branch_aligned_reduced_polarization": [
              5.551115123125783e-17,
              2.7755575615628914e-16,
              0.05939765213979416
            ],
            "target_residual": 0.7095971258958985,
            "energy_eV": -241.63214831245645,
            "max_atomic_step_A": 0.12,
            "max_log_strain_component": 0.006315217683984325,
            "step_scale": 0.680122650345001,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 1.5115606407059583,
            "cell_principal_stretches": [
              1.006964808019884,
              0.9999411293032948,
              0.9932451977198564
            ],
            "cell_volume_ratio": 1.0001040795483827,
            "cell_rmsd_from_input_A": 0.03511483000406428
          },
          {
            "iteration": 1,
            "reduced_polarization": [
              0.3361828705768804,
              0.33973660410922873,
              0.020524011715161748
            ],
            "branch_aligned_reduced_polarization": [
              0.3361828705768804,
              0.33973660410922873,
              0.020524011715161748
            ],
            "target_residual": 0.23009051047741472,
            "energy_eV": -239.77835881326538,
            "max_atomic_step_A": 0.058147704347958795,
            "max_log_strain_component": 0.0029925373409289886,
            "step_scale": 1.0,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 1.5115606407059583,
            "cell_principal_stretches": [
              1.010332452774282,
              0.9999061350307089,
              0.990033277185161
            ],
            "cell_volume_ratio": 1.0001688596344012,
            "cell_rmsd_from_input_A": 0.05213609157437075
          },
          {
            "iteration": 2,
            "reduced_polarization": [
              0.49634879911361657,
              0.500179483259112,
              -0.0002977579026626006
            ],
            "branch_aligned_reduced_polarization": [
              0.49634879911361657,
              0.500179483259112,
              -0.0002977579026626006
            ],
            "target_residual": 0.003667716172446643,
            "energy_eV": -237.42966990762824,
            "max_atomic_step_A": 0.0012401356929246316,
            "max_log_strain_component": 3.29367294143315e-05,
            "step_scale": 1.0,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 1.5115606407059583,
            "cell_principal_stretches": [
              1.010344028392545,
              0.9999071116091075,
              0.9900202264357543
            ],
            "cell_volume_ratio": 1.0001681111302287,
            "cell_rmsd_from_input_A": 0.05225748351230633
          },
          {
            "iteration": 3,
            "reduced_polarization": [
              0.4999971124207137,
              0.5000004196364775,
              -4.894474586131767e-05
            ],
            "branch_aligned_reduced_polarization": [
              0.4999971124207137,
              0.5000004196364775,
              -4.894474586131767e-05
            ],
            "target_residual": 4.9031646477931075e-05,
            "energy_eV": -237.38624629043142
          }
        ],
        "iterations": 3
      },
      "parent": {
        "candidate_id": "bec_projection_06",
        "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": 4.9031646477931075e-05,
        "parent_symmetrization_rmsd_A": 0.10378721945331165,
        "parent_cell_rmsd_A": 0.05225748351230633,
        "energy_eV": -237.38624629043142,
        "reduced_polarization": [
          0.4999971124207137,
          0.5000004196364775,
          -4.894474586131767e-05
        ],
        "cartesian_polarization_e_A2": [
          0.010508824551898242,
          0.0070604578159975595,
          -2.3316465564889146e-05
        ],
        "ranking_score": 0.6169496536243441
      },
      "branch_status": "awaiting_branch_sampling"
    },
    {
      "orbit_id": 7,
      "formal_class": [
        0.5,
        0.5,
        0.5
      ],
      "formal_classes_in_orbit": [
        [
          0.5,
          0.5,
          0.5
        ]
      ],
      "target_reduced_polarization": [
        0.5,
        0.5,
        0.5
      ],
      "bec_backprojection": {
        "converged_to_target": true,
        "history": [
          {
            "iteration": 0,
            "reduced_polarization": [
              7.020467990562451e-17,
              2.760671002230171e-16,
              0.05939765213979416
            ],
            "branch_aligned_reduced_polarization": [
              5.551115123125783e-17,
              2.7755575615628914e-16,
              0.059397652139794144
            ],
            "target_residual": 0.833144902726966,
            "energy_eV": -241.63214831245645,
            "max_atomic_step_A": 0.11999999999999998,
            "max_log_strain_component": 0.006094848817495677,
            "step_scale": 0.6563898409582566,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 1.5115606407059583,
            "cell_principal_stretches": [
              1.0060733493994762,
              1.000416968878503,
              0.9928090502465742
            ],
            "cell_volume_ratio": 0.9992552111592763,
            "cell_rmsd_from_input_A": 0.03469090733615656
          },
          {
            "iteration": 1,
            "reduced_polarization": [
              0.32438951289859136,
              0.32943767249511274,
              0.34848363745979133
            ],
            "branch_aligned_reduced_polarization": [
              0.32438951289859136,
              0.32943767249511274,
              0.34848363745979133
            ],
            "target_residual": 0.2879023425769481,
            "energy_eV": -239.80589345730078,
            "max_atomic_step_A": 0.06382092728080728,
            "max_log_strain_component": 0.0031429250428458913,
            "step_scale": 1.0,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 1.5115606407059583,
            "cell_principal_stretches": [
              1.009270330669809,
              1.0006217640884087,
              0.9890753068237976
            ],
            "cell_volume_ratio": 0.9988650344711297,
            "cell_rmsd_from_input_A": 0.053010292081954395
          },
          {
            "iteration": 2,
            "reduced_polarization": [
              0.4959464105892697,
              0.5011255581277138,
              0.49805134154314895
            ],
            "branch_aligned_reduced_polarization": [
              0.4959464105892697,
              0.5011255581277138,
              0.49805134154314895
            ],
            "target_residual": 0.004636349640730786,
            "energy_eV": -237.22829620970666,
            "max_atomic_step_A": 0.0014214022932973888,
            "max_log_strain_component": 3.6267812617336814e-05,
            "step_scale": 1.0,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 1.5115606407059583,
            "cell_principal_stretches": [
              1.0092668795248343,
              1.0006193885365855,
              0.9890757516136334
            ],
            "cell_volume_ratio": 0.9988596967230947,
            "cell_rmsd_from_input_A": 0.05308678075231711
          },
          {
            "iteration": 3,
            "reduced_polarization": [
              0.4999892575911218,
              0.4999975188694145,
              0.49994675358816326
            ],
            "branch_aligned_reduced_polarization": [
              0.4999892575911218,
              0.4999975188694145,
              0.49994675358816326
            ],
            "target_residual": 5.4375874530682816e-05,
            "energy_eV": -237.18433916759693
          }
        ],
        "iterations": 3
      },
      "parent": {
        "candidate_id": "bec_projection_07",
        "source": "MACEField_BEC_backprojection",
        "spacegroup": "P1",
        "spacegroup_number": 1,
        "pointgroup": "1",
        "has_inversion": false,
        "is_polar_point_group": true,
        "nonpolar_parent_hypothesis": false,
        "symmetry_tolerance_A": null,
        "target_reduced_polarization": [
          0.5,
          0.5,
          0.5
        ],
        "formal_class": [
          0.5,
          0.5,
          0.5
        ],
        "target_residual": 5.4375874530682816e-05,
        "parent_symmetrization_rmsd_A": 0.10641388829565165,
        "parent_cell_rmsd_A": 0.05308678075231711,
        "energy_eV": -237.18433916759693,
        "reduced_polarization": [
          0.4999892575911218,
          0.4999975188694145,
          0.49994675358816326
        ],
        "cartesian_polarization_e_A2": [
          0.01055148711535656,
          0.007022095582869329,
          0.00441748489107372
        ],
        "ranking_score": 0.6197943352327923
      },
      "branch_status": "awaiting_branch_sampling"
    }
  ],
  "sampled_polarization_branches": [
    {
      "orbit_id": 0,
      "candidate_id": "inversion_parent_endpoint_00",
      "formal_class": [
        0.0,
        0.0,
        0.0
      ],
      "construction": "MACEField-BEC-parent plus variable-cell P-N-P path and symmetric log-strain continuation beyond both polar endpoints",
      "geometry_diagnostics": {
        "collision_aware": false,
        "permutations_tested": 1,
        "selected_order": [
          0,
          1,
          2,
          3,
          4,
          5,
          6,
          7,
          8,
          9,
          10,
          11,
          12,
          13,
          14,
          15,
          16,
          17,
          18,
          19,
          20,
          21,
          22,
          23,
          24,
          25,
          26,
          27,
          28,
          29,
          30,
          31,
          32,
          33,
          34,
          35,
          36,
          37,
          38,
          39
        ],
        "endpoint_rmsd_A": 0.3381836847006432,
        "minimum_distance_A_by_image": [
          1.7178167219826461,
          1.7087147425024092,
          1.70081840406377,
          1.6941445650811708,
          1.6872156062368913,
          1.681518545102823,
          1.677640110609304,
          1.6755929313323006,
          1.6753837202090247
        ],
        "minimum_distance_A": 1.6753837202090247,
        "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": [
          615.8509028431272,
          615.8509028431272,
          615.8509028431272,
          615.8509028431272,
          615.8509028431272,
          615.8509028431272,
          615.8509028431272,
          615.8509028431272,
          615.8509028431272
        ],
        "cell_deformation_log_strain_norm": 0.0
      },
      "parent_reduced_polarization": [
        8.456716403898893e-16,
        2.3138571984010103e-15,
        -2.791158615774918e-16
      ],
      "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": [
          -241.6321483124565,
          -241.5196821533819,
          -241.30052837691062,
          -241.01502177901585,
          -240.700865098026,
          -240.39661253167873,
          -240.14103426051716,
          -239.97022589807182,
          -239.9101159450944
        ],
        "cartesian_polarizations_e_A2": [
          [
            8.563045605070422e-18,
            1.3407926671097107e-18,
            0.0005274995662863013
          ],
          [
            -5.013888545074129e-18,
            4.191385480376575e-18,
            0.001186637114255235
          ],
          [
            -2.5903212955338027e-17,
            -4.5451744698492214e-17,
            0.0017195492230747383
          ],
          [
            -9.93763976798962e-18,
            -5.633582634914751e-18,
            0.002080020848671317
          ],
          [
            -4.2263136927130465e-17,
            1.1503775740495922e-17,
            0.002212291369359646
          ],
          [
            -3.710277523354855e-17,
            8.179961985896219e-18,
            0.00206381047741409
          ],
          [
            -4.367153258585915e-17,
            4.4617974468524826e-18,
            0.001610234781821604
          ],
          [
            -2.825805049673239e-17,
            1.58867030304596e-17,
            0.000885792799094238
          ],
          [
            1.7779586795790954e-17,
            3.267477928250556e-17,
            -2.4787763593624904e-18
          ]
        ],
        "raw_reduced_polarization": [
          [
            4.0729432617003546e-16,
            9.494793331369662e-17,
            0.059397652139792395
          ],
          [
            -2.3848154624429703e-16,
            2.96812026829371e-16,
            0.13361804072165723
          ],
          [
            -1.232065336664357e-15,
            -3.2186551511550606e-15,
            0.19362515747360529
          ],
          [
            -4.726757837920674e-16,
            -3.989408962760363e-16,
            0.23421508321362022
          ],
          [
            -2.010211865083951e-15,
            8.146373101956661e-16,
            0.24910904498785688
          ],
          [
            -1.7647634422077981e-15,
            5.792621813928047e-16,
            0.23238975850336055
          ],
          [
            -2.0772010634671807e-15,
            3.1596118985062075e-16,
            0.18131610250864758
          ],
          [
            -1.3440712763611165e-15,
            1.1250133274984224e-15,
            0.09974228589218634
          ],
          [
            8.456716403898893e-16,
            2.3138571984010103e-15,
            -2.791158615774918e-16
          ]
        ],
        "unwrapped_reduced_polarization": [
          [
            4.0729432617003546e-16,
            9.494793331369662e-17,
            0.059397652139792395
          ],
          [
            -2.38481546244297e-16,
            2.96812026829371e-16,
            0.13361804072165723
          ],
          [
            -1.232065336664357e-15,
            -3.2186551511550606e-15,
            0.19362515747360529
          ],
          [
            -4.726757837920674e-16,
            -3.989408962760361e-16,
            0.23421508321362022
          ],
          [
            -2.010211865083951e-15,
            8.146373101956662e-16,
            0.24910904498785688
          ],
          [
            -1.7647634422077981e-15,
            5.792621813928047e-16,
            0.23238975850336055
          ],
          [
            -2.0772010634671807e-15,
            3.1596118985062075e-16,
            0.18131610250864758
          ],
          [
            -1.3440712763611165e-15,
            1.1250133274984224e-15,
            0.09974228589218634
          ],
          [
            8.456716403898891e-16,
            2.3138571984010103e-15,
            -2.7755575615628914e-16
          ]
        ],
        "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": [
          [
            4.440892098500626e-16,
            1.1102230246251565e-16,
            0.05939765213979242
          ],
          [
            -2.220446049250313e-16,
            3.3306690738754696e-16,
            0.13361804072165717
          ],
          [
            -1.2212453270876722e-15,
            -3.219646771412954e-15,
            0.1936251574736053
          ],
          [
            -4.996003610813204e-16,
            -3.885780586188048e-16,
            0.23421508321362028
          ],
          [
            -1.9984014443252818e-15,
            7.771561172376096e-16,
            0.2491090449878569
          ],
          [
            -1.7763568394002505e-15,
            5.551115123125783e-16,
            0.23238975850336052
          ],
          [
            -2.0539125955565396e-15,
            3.3306690738754696e-16,
            0.1813161025086476
          ],
          [
            -1.3322676295501878e-15,
            1.1102230246251565e-15,
            0.09974228589218637
          ],
          [
            8.881784197001252e-16,
            2.3314683517128287e-15,
            -2.7755575615628914e-16
          ]
        ]
      },
      "reflected": {
        "reached": true,
        "construction": "reflect_displacements_about_reconstructed_parent",
        "energies_eV": [
          -239.9101159450944,
          -239.97022589807182,
          -240.14103426051716,
          -240.39661253167878,
          -240.70086509802587,
          -241.01502177901585,
          -241.30052837691073,
          -241.51968215338195,
          -241.63214831245656
        ],
        "cartesian_polarizations_e_A2": [
          [
            1.537968059331727e-17,
            2.922702670993773e-17,
            1.1717851880622683e-18
          ],
          [
            -4.796432255366419e-17,
            2.7266539952987395e-18,
            -0.0008857927990942708
          ],
          [
            -6.017792970615937e-17,
            1.5661359725063008e-17,
            -0.0016102347818216668
          ],
          [
            2.62750294092424e-17,
            4.806572704109266e-17,
            -0.002063810477414122
          ],
          [
            -3.3790228644218675e-17,
            -3.312546589329874e-18,
            -0.0022122913693596704
          ],
          [
            -7.323657425389177e-19,
            3.920973513900667e-18,
            -0.0020800208486713443
          ],
          [
            -1.0309456221893994e-17,
            -2.1227339368358784e-17,
            -0.001719549223074768
          ],
          [
            4.101248158217939e-18,
            1.8421815216171235e-17,
            -0.0011866371142552623
          ],
          [
            2.443848147026019e-17,
            -2.535112185711638e-18,
            -0.000527499566286329
          ]
        ],
        "raw_reduced_polarization": [
          [
            7.315220463448663e-16,
            2.069705369880076e-15,
            1.3194568001845069e-16
          ],
          [
            -2.2813841401392644e-15,
            1.9308739379760157e-16,
            -0.09974228589219004
          ],
          [
            -2.8623144685186302e-15,
            1.1090556916473809e-15,
            -0.18131610250865465
          ],
          [
            1.2497504850375298e-15,
            3.4037637270271414e-15,
            -0.23238975850336413
          ],
          [
            -1.6072048476104422e-15,
            -2.345772470103094e-16,
            -0.24910904498785963
          ],
          [
            -3.4834383159279344e-17,
            2.7766286380812124e-16,
            -0.2342150832136233
          ],
          [
            -4.903609321652399e-16,
            -1.5032092971681049e-15,
            -0.19362515747360862
          ],
          [
            1.9507254569196432e-16,
            1.3045367308226384e-15,
            -0.13361804072166028
          ],
          [
            1.1623965703457983e-15,
            -1.795234033242163e-16,
            -0.05939765213979551
          ]
        ],
        "unwrapped_reduced_polarization": [
          [
            7.315220463448663e-16,
            2.069705369880076e-15,
            1.3194568001845069e-16
          ],
          [
            -2.2813841401392644e-15,
            1.9308739379760147e-16,
            -0.09974228589219004
          ],
          [
            -2.8623144685186302e-15,
            1.1090556916473809e-15,
            -0.18131610250865465
          ],
          [
            1.2497504850375294e-15,
            3.4037637270271414e-15,
            -0.23238975850336413
          ],
          [
            -1.6072048476104422e-15,
            -2.3457724701030913e-16,
            -0.24910904498785963
          ],
          [
            -3.4834383159279276e-17,
            2.7766286380812124e-16,
            -0.2342150832136233
          ],
          [
            -4.903609321652399e-16,
            -1.5032092971681049e-15,
            -0.19362515747360862
          ],
          [
            1.950725456919643e-16,
            1.3045367308226386e-15,
            -0.13361804072166028
          ],
          [
            1.1623965703457983e-15,
            -1.7952340332421626e-16,
            -0.059397652139795504
          ]
        ],
        "gauge_integer_shift": [
          0,
          0,
          0
        ],
        "expected_opposite_endpoint_reduced_polarization": [
          1.284048954609743e-15,
          4.532766463488324e-15,
          -0.059397652139792964
        ],
        "actual_opposite_endpoint_branch_residual": 5.354458131521775e-15
      },
      "pnp_branch": {
        "construction": "incoming_path_concatenated_with_parent_reflection",
        "reduced_polarization": [
          [
            4.0729432617003546e-16,
            9.494793331369662e-17,
            0.059397652139792395
          ],
          [
            -2.3848154624429703e-16,
            2.96812026829371e-16,
            0.13361804072165723
          ],
          [
            -1.232065336664357e-15,
            -3.2186551511550606e-15,
            0.19362515747360529
          ],
          [
            -4.726757837920674e-16,
            -3.989408962760363e-16,
            0.23421508321362022
          ],
          [
            -2.010211865083951e-15,
            8.146373101956661e-16,
            0.24910904498785688
          ],
          [
            -1.7647634422077981e-15,
            5.792621813928047e-16,
            0.23238975850336055
          ],
          [
            -2.0772010634671807e-15,
            3.1596118985062075e-16,
            0.18131610250864758
          ],
          [
            -1.3440712763611165e-15,
            1.1250133274984224e-15,
            0.09974228589218634
          ],
          [
            8.456716403898893e-16,
            2.3138571984010103e-15,
            -2.791158615774918e-16
          ],
          [
            -2.2813841401392644e-15,
            1.9308739379760157e-16,
            -0.09974228589219004
          ],
          [
            -2.8623144685186302e-15,
            1.1090556916473809e-15,
            -0.18131610250865465
          ],
          [
            1.2497504850375298e-15,
            3.4037637270271414e-15,
            -0.23238975850336413
          ],
          [
            -1.6072048476104422e-15,
            -2.345772470103094e-16,
            -0.24910904498785963
          ],
          [
            -3.4834383159279344e-17,
            2.7766286380812124e-16,
            -0.2342150832136233
          ],
          [
            -4.903609321652399e-16,
            -1.5032092971681049e-15,
            -0.19362515747360862
          ],
          [
            1.9507254569196432e-16,
            1.3045367308226384e-15,
            -0.13361804072166028
          ],
          [
            1.1623965703457983e-15,
            -1.795234033242163e-16,
            -0.05939765213979551
          ]
        ],
        "unwrapped_reduced_polarization": [
          [
            4.0729432617003546e-16,
            9.494793331369662e-17,
            0.059397652139792395
          ],
          [
            -2.38481546244297e-16,
            2.96812026829371e-16,
            0.13361804072165723
          ],
          [
            -1.232065336664357e-15,
            -3.2186551511550606e-15,
            0.19362515747360529
          ],
          [
            -4.726757837920674e-16,
            -3.989408962760361e-16,
            0.23421508321362022
          ],
          [
            -2.010211865083951e-15,
            8.146373101956662e-16,
            0.24910904498785688
          ],
          [
            -1.7647634422077981e-15,
            5.792621813928047e-16,
            0.23238975850336055
          ],
          [
            -2.0772010634671807e-15,
            3.1596118985062075e-16,
            0.18131610250864758
          ],
          [
            -1.3440712763611165e-15,
            1.1250133274984224e-15,
            0.09974228589218634
          ],
          [
            8.456716403898891e-16,
            2.3138571984010103e-15,
            -2.7755575615628914e-16
          ],
          [
            -2.2813841401392648e-15,
            1.9308739379760147e-16,
            -0.09974228589219004
          ],
          [
            -2.8623144685186302e-15,
            1.1090556916473809e-15,
            -0.18131610250865465
          ],
          [
            1.2497504850375294e-15,
            3.4037637270271414e-15,
            -0.23238975850336413
          ],
          [
            -1.6072048476104422e-15,
            -2.3457724701030913e-16,
            -0.24910904498785963
          ],
          [
            -3.4834383159279276e-17,
            2.7766286380812124e-16,
            -0.2342150832136233
          ],
          [
            -4.903609321652399e-16,
            -1.5032092971681049e-15,
            -0.19362515747360862
          ],
          [
            1.950725456919643e-16,
            1.3045367308226386e-15,
            -0.13361804072166028
          ],
          [
            1.1623965703457983e-15,
            -1.7952340332421626e-16,
            -0.059397652139795504
          ]
        ],
        "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": [
          [
            4.440892098500626e-16,
            1.1102230246251565e-16,
            0.05939765213979242
          ],
          [
            -2.220446049250313e-16,
            3.3306690738754696e-16,
            0.13361804072165717
          ],
          [
            -1.2212453270876722e-15,
            -3.219646771412954e-15,
            0.1936251574736053
          ],
          [
            -4.996003610813204e-16,
            -3.885780586188048e-16,
            0.23421508321362028
          ],
          [
            -1.9984014443252818e-15,
            7.771561172376096e-16,
            0.2491090449878569
          ],
          [
            -1.7763568394002505e-15,
            5.551115123125783e-16,
            0.23238975850336052
          ],
          [
            -2.0539125955565396e-15,
            3.3306690738754696e-16,
            0.1813161025086476
          ],
          [
            -1.3322676295501878e-15,
            1.1102230246251565e-15,
            0.09974228589218637
          ],
          [
            8.881784197001252e-16,
            2.3314683517128287e-15,
            -2.7755575615628914e-16
          ],
          [
            -2.275957200481571e-15,
            2.220446049250313e-16,
            -0.09974228589219003
          ],
          [
            -2.886579864025407e-15,
            1.1102230246251565e-15,
            -0.18131610250865465
          ],
          [
            1.2212453270876722e-15,
            3.4416913763379853e-15,
            -0.23238975850336413
          ],
          [
            -1.609823385706477e-15,
            -2.220446049250313e-16,
            -0.24910904498785963
          ],
          [
            -5.551115123125783e-17,
            3.3306690738754696e-16,
            -0.23421508321362328
          ],
          [
            -4.996003610813204e-16,
            -1.4988010832439613e-15,
            -0.19362515747360864
          ],
          [
            2.220446049250313e-16,
            1.3322676295501878e-15,
            -0.13361804072166028
          ],
          [
            1.1102230246251565e-15,
            -1.6653345369377348e-16,
            -0.05939765213979553
          ]
        ]
      },
      "incoming_structure_ids": [
        "incoming_00_000",
        "incoming_00_001",
        "incoming_00_002",
        "incoming_00_003",
        "incoming_00_004",
        "incoming_00_005",
        "incoming_00_006",
        "incoming_00_007",
        "incoming_00_008"
      ],
      "reflected_structure_ids": [
        "reflected_00_001",
        "reflected_00_002",
        "reflected_00_003",
        "reflected_00_004",
        "reflected_00_005",
        "reflected_00_006",
        "reflected_00_007",
        "reflected_00_008"
      ],
      "positive_extension_structure_ids": [
        "extension_plus_00_000",
        "extension_plus_00_001",
        "extension_plus_00_002",
        "extension_plus_00_003"
      ],
      "negative_extension_structure_ids": [
        "extension_minus_00_000",
        "extension_minus_00_001",
        "extension_minus_00_002",
        "extension_minus_00_003"
      ],
      "extension": {
        "enabled": true,
        "fraction_beyond_polar_endpoint": 0.35,
        "images_per_side": 4,
        "construction": "continue fractional atomic displacements and symmetric log strain beyond +P; reflect these structures about N for the -P side",
        "positive_path_coordinates": [
          1.35,
          1.2625,
          1.175,
          1.0875
        ],
        "negative_path_coordinates": [
          -1.0875,
          -1.175,
          -1.2625,
          -1.35
        ]
      },
      "branch_coordinates": [
        1.35,
        1.2625,
        1.175,
        1.0875,
        1.0,
        0.875,
        0.75,
        0.625,
        0.5,
        0.375,
        0.25,
        0.125,
        0.0,
        -0.125,
        -0.25,
        -0.375,
        -0.5,
        -0.625,
        -0.75,
        -0.875,
        -1.0,
        -1.0875,
        -1.175,
        -1.2625,
        -1.35
      ],
      "parent": {
        "candidate_id": "inversion_parent_endpoint_00",
        "source": "same_species_inversion_center_projection_from_endpoint",
        "spacegroup": "Pnma",
        "spacegroup_number": 62,
        "pointgroup": "mmm",
        "has_inversion": true,
        "is_polar_point_group": false,
        "nonpolar_parent_hypothesis": true,
        "symmetry_tolerance_A": null,
        "target_reduced_polarization": [
          0.0,
          0.0,
          0.0
        ],
        "formal_class": [
          0.0,
          0.0,
          0.0
        ],
        "target_residual": 2.9968150472343355e-15,
        "parent_symmetrization_rmsd_A": 0.3381836847006432,
        "parent_cell_rmsd_A": 0.0,
        "energy_eV": -239.91011594509442,
        "reduced_polarization": [
          7.149087251458253e-16,
          1.330866829976857e-15,
          -2.5881652619003786e-15
        ],
        "cartesian_polarization_e_A2": [
          1.5030398469952557e-17,
          1.879363167007561e-17,
          -2.2985017150452185e-17
        ],
        "ranking_score": 0.3381836847006492
      }
    }
  ],
  "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": 53,
      "full_response": 20,
      "energy_polarization": 33
    },
    "model_evaluations_for_recovery_and_path_properties": {
      "total": 78,
      "full_response": 45,
      "energy_polarization": 33
    },
    "elapsed_seconds": 720.5472556220484
  }
}