{
  "schema": "ferrofinder.endpoint_parent_recovery.v4_variable_cell",
  "status": "complete",
  "input_atom_count": 24,
  "input_formula": "O12Rb8Sn4",
  "input_spacegroup": "Cmc2_1",
  "input_pointgroup": "mm2",
  "input_is_polar_point_group": true,
  "input_energy_eV": -117.64889124927558,
  "input_cartesian_polarization_e_A2": [
    1.2038989439271776e-17,
    7.315482620118455e-18,
    0.002313235055601511
  ],
  "input_reduced_polarization": [
    5.337136725241911e-16,
    4.697256997876045e-16,
    0.19035342094590907
  ],
  "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": [
        0.5,
        0.0,
        0.0
      ],
      "target_reduced_polarization": [
        0.5,
        0.0,
        0.0
      ]
    },
    {
      "orbit_id": 3,
      "representative_formal_class": [
        0.0,
        0.5,
        0.0
      ],
      "target_reduced_polarization": [
        0.0,
        0.5,
        0.0
      ]
    },
    {
      "orbit_id": 4,
      "representative_formal_class": [
        0.5,
        0.0,
        0.5
      ],
      "target_reduced_polarization": [
        0.5,
        0.0,
        0.5
      ]
    },
    {
      "orbit_id": 5,
      "representative_formal_class": [
        0.0,
        0.5,
        0.5
      ],
      "target_reduced_polarization": [
        0.0,
        0.5,
        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": "Cmcm",
      "spacegroup_number": 63,
      "pointgroup": "mmm",
      "has_inversion": true,
      "is_polar_point_group": false,
      "nonpolar_parent_hypothesis": true,
      "symmetry_tolerance_A": null,
      "target_reduced_polarization": [
        0.0,
        0.0,
        0.0
      ],
      "formal_class": [
        0.0,
        0.0,
        0.0
      ],
      "target_residual": 2.171532051863965e-15,
      "parent_symmetrization_rmsd_A": 0.14532126740066198,
      "parent_cell_rmsd_A": 0.0,
      "energy_eV": -117.63564424237045,
      "reduced_polarization": [
        1.820943466023795e-15,
        -1.1544067173614032e-15,
        2.589623075442429e-16
      ],
      "cartesian_polarization_e_A2": [
        4.1075056318662635e-17,
        -1.7978667722936878e-17,
        3.146991973740393e-18
      ],
      "ranking_score": 0.1453212674006663
    },
    {
      "candidate_id": "bec_projection_00",
      "source": "MACEField_BEC_backprojection",
      "spacegroup": "Cmc2_1",
      "spacegroup_number": 36,
      "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": 0.0005608744447280642,
      "parent_symmetrization_rmsd_A": 0.021060928144286215,
      "parent_cell_rmsd_A": 0.01503932451674683,
      "energy_eV": -117.55905377957603,
      "reduced_polarization": [
        2.1789056001459794e-16,
        -3.338531956069718e-15,
        0.0005608744447280642
      ],
      "cartesian_polarization_e_A2": [
        4.919813947002881e-18,
        -5.178017514911178e-17,
        6.816415334909597e-06
      ],
      "ranking_score": 0.5259425081629291
    },
    {
      "candidate_id": "inversion_parent_bec_00_00",
      "source": "same_species_inversion_center_projection_after_BEC",
      "spacegroup": "Cmcm",
      "spacegroup_number": 63,
      "pointgroup": "mmm",
      "has_inversion": true,
      "is_polar_point_group": false,
      "nonpolar_parent_hypothesis": true,
      "symmetry_tolerance_A": null,
      "target_reduced_polarization": [
        0.0,
        0.0,
        0.0
      ],
      "formal_class": [
        0.0,
        0.0,
        0.0
      ],
      "target_residual": 1.773447387384068e-15,
      "parent_symmetrization_rmsd_A": 0.1453218006123821,
      "parent_cell_rmsd_A": 0.01503932451674683,
      "energy_eV": -117.62416024037091,
      "reduced_polarization": [
        1.1191000615233497e-15,
        1.6732019965626756e-16,
        -1.3655528693187963e-15
      ],
      "cartesian_polarization_e_A2": [
        2.5232758460337494e-17,
        2.5975958511784932e-18,
        -1.6595827473593344e-17
      ],
      "ranking_score": 0.14908163174157235
    },
    {
      "candidate_id": "symmetry_parent_00_00",
      "source": "spglib_refine_cell_after_MACEField_BEC_backprojection",
      "spacegroup": "Cmcm",
      "spacegroup_number": 63,
      "pointgroup": "mmm",
      "has_inversion": true,
      "is_polar_point_group": false,
      "nonpolar_parent_hypothesis": true,
      "symmetry_tolerance_A": null,
      "target_reduced_polarization": [
        0.0,
        0.0,
        0.0
      ],
      "formal_class": [
        0.0,
        0.0,
        0.0
      ],
      "target_residual": 5.036453079235516e-15,
      "parent_symmetrization_rmsd_A": 1.652860183737477,
      "parent_cell_rmsd_A": 0.01503932451674588,
      "energy_eV": -117.6241602403709,
      "reduced_polarization": [
        -5.02093084162436e-15,
        -3.9502317108930556e-16,
        8.3544759712146e-18
      ],
      "cartesian_polarization_e_A2": [
        -1.1320876437117698e-16,
        -6.132616100440686e-18,
        1.0153355828670631e-19
      ],
      "ranking_score": 1.6566200148666734
    },
    {
      "candidate_id": "bec_projection_01",
      "source": "MACEField_BEC_backprojection",
      "spacegroup": "Cmc2_1",
      "spacegroup_number": 36,
      "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": 2.4878206659750823e-06,
      "parent_symmetrization_rmsd_A": 0.03419891929364545,
      "parent_cell_rmsd_A": 0.02424939867454528,
      "energy_eV": -117.45350966445437,
      "reduced_polarization": [
        -8.558155369612409e-16,
        2.584103586157002e-15,
        0.499997512179334
      ],
      "cartesian_polarization_e_A2": [
        -2.9813166510312556e-17,
        -3.155955797838733e-17,
        0.006075420104901404
      ],
      "ranking_score": 0.5402662446036137
    },
    {
      "candidate_id": "bec_projection_02",
      "source": "MACEField_BEC_backprojection",
      "spacegroup": "Cc",
      "spacegroup_number": 9,
      "pointgroup": "m",
      "has_inversion": false,
      "is_polar_point_group": true,
      "nonpolar_parent_hypothesis": false,
      "symmetry_tolerance_A": null,
      "target_reduced_polarization": [
        0.5,
        0.0,
        0.0
      ],
      "formal_class": [
        0.5,
        0.0,
        0.0
      ],
      "target_residual": 0.0005112328798618844,
      "parent_symmetrization_rmsd_A": 0.16111889079135797,
      "parent_cell_rmsd_A": 0.16543055773912088,
      "energy_eV": -113.73499399828987,
      "reduced_polarization": [
        0.4998060325734508,
        -5.827313507952982e-16,
        0.0004730070769975391
      ],
      "cartesian_polarization_e_A2": [
        0.01126853743772121,
        7.339827758736906e-18,
        -0.00024648475674961983
      ],
      "ranking_score": 0.703498995985862
    },
    {
      "candidate_id": "bec_projection_03",
      "source": "MACEField_BEC_backprojection",
      "spacegroup": "Cm",
      "spacegroup_number": 8,
      "pointgroup": "m",
      "has_inversion": false,
      "is_polar_point_group": true,
      "nonpolar_parent_hypothesis": false,
      "symmetry_tolerance_A": null,
      "target_reduced_polarization": [
        0.0,
        0.5,
        0.0
      ],
      "formal_class": [
        0.0,
        0.5,
        0.0
      ],
      "target_residual": 2.285223697437653e-05,
      "parent_symmetrization_rmsd_A": 0.09338136329835935,
      "parent_cell_rmsd_A": 0.03336643619411875,
      "energy_eV": -115.6849864892499,
      "reduced_polarization": [
        -2.496618929838325e-16,
        0.5000224151154163,
        4.448295809090676e-06
      ],
      "cartesian_polarization_e_A2": [
        1.3602875798391506e-18,
        0.007763372924862533,
        4.673577715452821e-05
      ],
      "ranking_score": 0.6017686768208378
    },
    {
      "candidate_id": "bec_projection_04",
      "source": "MACEField_BEC_backprojection",
      "spacegroup": "Cc",
      "spacegroup_number": 9,
      "pointgroup": "m",
      "has_inversion": false,
      "is_polar_point_group": true,
      "nonpolar_parent_hypothesis": false,
      "symmetry_tolerance_A": null,
      "target_reduced_polarization": [
        0.5,
        0.0,
        0.5
      ],
      "formal_class": [
        0.5,
        0.0,
        0.5
      ],
      "target_residual": 0.00036741328503827074,
      "parent_symmetrization_rmsd_A": 0.15463828248523717,
      "parent_cell_rmsd_A": 0.14936026363429766,
      "energy_eV": -113.37382428209692,
      "reduced_polarization": [
        0.4999324496299088,
        2.9316252611935404e-16,
        0.5003611502035485
      ],
      "cartesian_polarization_e_A2": [
        0.011160904874867369,
        -2.0592400954851813e-16,
        0.005848683208081034
      ],
      "ranking_score": 0.6927131749638882
    },
    {
      "candidate_id": "bec_projection_05",
      "source": "MACEField_BEC_backprojection",
      "spacegroup": "Cm",
      "spacegroup_number": 8,
      "pointgroup": "m",
      "has_inversion": false,
      "is_polar_point_group": true,
      "nonpolar_parent_hypothesis": false,
      "symmetry_tolerance_A": null,
      "target_reduced_polarization": [
        0.0,
        0.5,
        0.5
      ],
      "formal_class": [
        0.0,
        0.5,
        0.5
      ],
      "target_residual": 1.5152602443184389e-05,
      "parent_symmetrization_rmsd_A": 0.09757071063851327,
      "parent_cell_rmsd_A": 0.039427424098642,
      "energy_eV": -115.76985679933512,
      "reduced_polarization": [
        -1.7085850614950452e-15,
        0.5000147040834027,
        0.49999634058855974
      ],
      "cartesian_polarization_e_A2": [
        -1.306584236376185e-16,
        0.007865934493740838,
        0.006122856287634039
      ],
      "ranking_score": 0.6074578718680601
    },
    {
      "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": 0.0005888488499491867,
      "parent_symmetrization_rmsd_A": 0.18778183984603117,
      "parent_cell_rmsd_A": 0.16986887667987724,
      "energy_eV": -111.71751742187962,
      "reduced_polarization": [
        0.4997888588730893,
        0.49993198859438903,
        0.0005454693770691354
      ],
      "cartesian_polarization_e_A2": [
        0.011267879941360602,
        0.007744511371462578,
        -0.00019952645096895684
      ],
      "ranking_score": 0.7314267567158989
    },
    {
      "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": 0.0007440305003708601,
      "parent_symmetrization_rmsd_A": 0.18287198585627065,
      "parent_cell_rmsd_A": 0.1554207564473681,
      "energy_eV": -111.48344693265408,
      "reduced_polarization": [
        0.49994927376566284,
        0.4998769722718186,
        0.5007320330680581
      ],
      "cartesian_polarization_e_A2": [
        0.01115881270224233,
        0.007860091804000428,
        0.005897958316315333
      ],
      "ranking_score": 0.7232152359688544
    }
  ],
  "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": [
              5.337136725241911e-16,
              4.697256997876045e-16,
              0.19035342094590907
            ],
            "branch_aligned_reduced_polarization": [
              5.337136725241911e-16,
              4.697256997876045e-16,
              0.19035342094590907
            ],
            "target_residual": 0.19035342094590907,
            "energy_eV": -117.64889124927558,
            "max_atomic_step_A": 0.03563382165070623,
            "max_log_strain_component": 0.0018336178882706496,
            "step_scale": 1.0,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 1.6029440898777152,
            "cell_principal_stretches": [
              1.0018352999935065,
              1.0013343690058747,
              0.9985954064078698
            ],
            "cell_volume_ratio": 1.0017630688381085,
            "cell_rmsd_from_input_A": 0.01503932451674683
          },
          {
            "iteration": 1,
            "reduced_polarization": [
              2.1789056001459794e-16,
              -3.338531956069718e-15,
              0.0005608744447280642
            ],
            "branch_aligned_reduced_polarization": [
              2.1789056001459794e-16,
              -3.338531956069718e-15,
              0.0005608744447280642
            ],
            "target_residual": 0.0005608744447280642,
            "energy_eV": -117.55905377957603
          }
        ],
        "iterations": 1
      },
      "parent": {
        "candidate_id": "inversion_parent_endpoint_00",
        "source": "same_species_inversion_center_projection_from_endpoint",
        "spacegroup": "Cmcm",
        "spacegroup_number": 63,
        "pointgroup": "mmm",
        "has_inversion": true,
        "is_polar_point_group": false,
        "nonpolar_parent_hypothesis": true,
        "symmetry_tolerance_A": null,
        "target_reduced_polarization": [
          0.0,
          0.0,
          0.0
        ],
        "formal_class": [
          0.0,
          0.0,
          0.0
        ],
        "target_residual": 2.171532051863965e-15,
        "parent_symmetrization_rmsd_A": 0.14532126740066198,
        "parent_cell_rmsd_A": 0.0,
        "energy_eV": -117.63564424237045,
        "reduced_polarization": [
          1.820943466023795e-15,
          -1.1544067173614032e-15,
          2.589623075442429e-16
        ],
        "cartesian_polarization_e_A2": [
          4.1075056318662635e-17,
          -1.7978667722936878e-17,
          3.146991973740393e-18
        ],
        "ranking_score": 0.1453212674006663
      },
      "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": [
          -117.64889124927556,
          -117.64749192737636,
          -117.64541392496591,
          -117.64302821637068,
          -117.6406645405608,
          -117.6385881838909,
          -117.63698840792736,
          -117.63598535273397,
          -117.63564424237043
        ],
        "cartesian_polarizations_e_A2": [
          [
            1.2158960098595932e-17,
            1.4333471336528027e-17,
            0.0023132350556015176
          ],
          [
            1.0937926705808001e-17,
            -4.910441543146636e-18,
            0.001994546950543451
          ],
          [
            -1.69874337135742e-17,
            9.59149019668642e-18,
            0.0016861717148483502
          ],
          [
            1.8643562561975096e-17,
            7.240213078216207e-19,
            0.0013876261058843608
          ],
          [
            -5.802450921946319e-17,
            -9.634501363487706e-18,
            0.0010980555465584412
          ],
          [
            2.6747608282036077e-18,
            -1.2394384566570121e-17,
            0.0008162301800611207
          ],
          [
            -1.6877206184519883e-17,
            5.555609045165902e-17,
            0.0005405717130029117
          ],
          [
            -1.4547333104885507e-17,
            1.9491227088782046e-17,
            0.0002691964788508744
          ],
          [
            4.5175992216991585e-17,
            -3.498241566504464e-18,
            -2.596173203454806e-17
          ]
        ],
        "raw_reduced_polarization": [
          [
            5.390322236788399e-16,
            9.203493745470995e-16,
            0.19035342094590962
          ],
          [
            4.849012503420165e-16,
            -3.1529848540373254e-16,
            0.16412894761983082
          ],
          [
            -7.530885943348215e-16,
            6.158676984966337e-16,
            0.13875310831313328
          ],
          [
            8.265082625147754e-16,
            4.648926573106129e-17,
            0.11418613755196362
          ],
          [
            -2.572348291203977e-15,
            -6.186294370549146e-16,
            0.09035771318175795
          ],
          [
            1.1857776202441337e-16,
            -7.958409945446038e-16,
            0.06716663171677907
          ],
          [
            -7.482019765965469e-16,
            3.567245637779456e-15,
            0.044483017230575975
          ],
          [
            -6.449138124097257e-16,
            1.251527856660947e-15,
            0.022151864996068207
          ],
          [
            2.0027465625481354e-15,
            -2.246214027401773e-16,
            -2.1363607189379098e-15
          ]
        ],
        "unwrapped_reduced_polarization": [
          [
            5.390322236788399e-16,
            9.203493745470995e-16,
            0.19035342094590962
          ],
          [
            4.849012503420165e-16,
            -3.152984854037326e-16,
            0.16412894761983082
          ],
          [
            -7.530885943348214e-16,
            6.158676984966336e-16,
            0.13875310831313328
          ],
          [
            8.265082625147755e-16,
            4.648926573106129e-17,
            0.11418613755196362
          ],
          [
            -2.572348291203977e-15,
            -6.186294370549146e-16,
            0.09035771318175795
          ],
          [
            1.1857776202441317e-16,
            -7.958409945446038e-16,
            0.06716663171677907
          ],
          [
            -7.482019765965469e-16,
            3.567245637779456e-15,
            0.044483017230575975
          ],
          [
            -6.449138124097257e-16,
            1.251527856660947e-15,
            0.022151864996068207
          ],
          [
            2.0027465625481354e-15,
            -2.246214027401772e-16,
            -2.1371793224034263e-15
          ]
        ],
        "berry_integer_shifts": [
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ]
        ],
        "folded_reduced_polarization": [
          [
            5.551115123125783e-16,
            8.881784197001252e-16,
            0.19035342094590968
          ],
          [
            4.440892098500626e-16,
            -3.3306690738754696e-16,
            0.16412894761983088
          ],
          [
            -7.771561172376096e-16,
            6.661338147750939e-16,
            0.13875310831313326
          ],
          [
            7.771561172376096e-16,
            0.0,
            0.1141861375519636
          ],
          [
            -2.55351295663786e-15,
            -6.106226635438361e-16,
            0.09035771318175789
          ],
          [
            1.1102230246251565e-16,
            -7.771561172376096e-16,
            0.06716663171677906
          ],
          [
            -7.216449660063518e-16,
            3.552713678800501e-15,
            0.044483017230576016
          ],
          [
            -6.661338147750939e-16,
            1.2212453270876722e-15,
            0.02215186499606825
          ],
          [
            1.9984014443252818e-15,
            -2.220446049250313e-16,
            -2.1094237467877974e-15
          ]
        ]
      },
      "reflected": {
        "reached": true,
        "construction": "reflect_displacements_about_reconstructed_parent",
        "energies_eV": [
          -117.63564424237043,
          -117.63598535273394,
          -117.63698840792739,
          -117.63858818389092,
          -117.64066454056079,
          -117.64302821637068,
          -117.64541392496594,
          -117.64749192737638,
          -117.64889124927556
        ],
        "cartesian_polarizations_e_A2": [
          [
            2.3674776125605905e-17,
            1.3261776430396023e-17,
            3.443210104128844e-17
          ],
          [
            5.295891047703365e-18,
            3.048774873431043e-17,
            -0.00026919647885088627
          ],
          [
            -2.6058494400127656e-17,
            -1.8286914418346084e-17,
            -0.0005405717130029426
          ],
          [
            -9.072540570014767e-18,
            5.1785444828746414e-17,
            -0.0008162301800611025
          ],
          [
            -2.6528975802840102e-17,
            2.8652605617455624e-17,
            -0.0010980555465584024
          ],
          [
            -2.2003939890403696e-17,
            -6.509023242594372e-18,
            -0.0013876261058843658
          ],
          [
            -6.015791379424516e-17,
            4.9986144350892686e-17,
            -0.001686171714848318
          ],
          [
            -3.2293909902997634e-17,
            5.574964070226479e-17,
            -0.0019945469505434806
          ],
          [
            -2.1163118739894865e-17,
            6.654544356938718e-17,
            -0.0023132350556014872
          ]
        ],
        "raw_reduced_polarization": [
          [
            1.0495525206598634e-15,
            8.515360554699344e-16,
            2.8333775280178544e-15
          ],
          [
            2.3477796659058454e-16,
            1.9576123480614227e-15,
            -0.022151864996069186
          ],
          [
            -1.1552277553608737e-15,
            -1.1741991770290828e-15,
            -0.04448301723057852
          ],
          [
            -4.022047673662711e-16,
            3.3251332241701655e-15,
            -0.06716663171677759
          ],
          [
            -1.1760851835165031e-15,
            1.839778169574772e-15,
            -0.09035771318175476
          ],
          [
            -9.754808431511734e-16,
            -4.1794310181983814e-16,
            -0.11418613755196402
          ],
          [
            -2.6669265941695515e-15,
            3.2096004944820827e-15,
            -0.13875310831313065
          ],
          [
            -1.4316568131765698e-15,
            3.57967346129172e-15,
            -0.16412894761983324
          ],
          [
            -9.382054766066846e-16,
            4.2728698394202176e-15,
            -0.1903534209459071
          ]
        ],
        "unwrapped_reduced_polarization": [
          [
            1.0495525206598634e-15,
            8.515360554699344e-16,
            2.8333775280178544e-15
          ],
          [
            2.347779665905846e-16,
            1.9576123480614227e-15,
            -0.022151864996069186
          ],
          [
            -1.1552277553608737e-15,
            -1.174199177029083e-15,
            -0.04448301723057852
          ],
          [
            -4.0220476736627115e-16,
            3.3251332241701655e-15,
            -0.06716663171677759
          ],
          [
            -1.1760851835165031e-15,
            1.839778169574772e-15,
            -0.09035771318175476
          ],
          [
            -9.754808431511734e-16,
            -4.179431018198383e-16,
            -0.11418613755196402
          ],
          [
            -2.6669265941695515e-15,
            3.2096004944820827e-15,
            -0.13875310831313065
          ],
          [
            -1.4316568131765698e-15,
            3.57967346129172e-15,
            -0.16412894761983324
          ],
          [
            -9.382054766066846e-16,
            4.2728698394202176e-15,
            -0.1903534209459071
          ]
        ],
        "gauge_integer_shift": [
          0,
          0,
          0
        ],
        "expected_opposite_endpoint_reduced_polarization": [
          3.466460901417431e-15,
          -1.3695921800274544e-15,
          -0.1903534209459139
        ],
        "actual_opposite_endpoint_branch_residual": 9.873198139779386e-15
      },
      "pnp_branch": {
        "construction": "incoming_path_concatenated_with_parent_reflection",
        "reduced_polarization": [
          [
            5.390322236788399e-16,
            9.203493745470995e-16,
            0.19035342094590962
          ],
          [
            4.849012503420165e-16,
            -3.1529848540373254e-16,
            0.16412894761983082
          ],
          [
            -7.530885943348215e-16,
            6.158676984966337e-16,
            0.13875310831313328
          ],
          [
            8.265082625147754e-16,
            4.648926573106129e-17,
            0.11418613755196362
          ],
          [
            -2.572348291203977e-15,
            -6.186294370549146e-16,
            0.09035771318175795
          ],
          [
            1.1857776202441337e-16,
            -7.958409945446038e-16,
            0.06716663171677907
          ],
          [
            -7.482019765965469e-16,
            3.567245637779456e-15,
            0.044483017230575975
          ],
          [
            -6.449138124097257e-16,
            1.251527856660947e-15,
            0.022151864996068207
          ],
          [
            2.0027465625481354e-15,
            -2.246214027401773e-16,
            -2.1363607189379098e-15
          ],
          [
            2.3477796659058454e-16,
            1.9576123480614227e-15,
            -0.022151864996069186
          ],
          [
            -1.1552277553608737e-15,
            -1.1741991770290828e-15,
            -0.04448301723057852
          ],
          [
            -4.022047673662711e-16,
            3.3251332241701655e-15,
            -0.06716663171677759
          ],
          [
            -1.1760851835165031e-15,
            1.839778169574772e-15,
            -0.09035771318175476
          ],
          [
            -9.754808431511734e-16,
            -4.1794310181983814e-16,
            -0.11418613755196402
          ],
          [
            -2.6669265941695515e-15,
            3.2096004944820827e-15,
            -0.13875310831313065
          ],
          [
            -1.4316568131765698e-15,
            3.57967346129172e-15,
            -0.16412894761983324
          ],
          [
            -9.382054766066846e-16,
            4.2728698394202176e-15,
            -0.1903534209459071
          ]
        ],
        "unwrapped_reduced_polarization": [
          [
            5.390322236788399e-16,
            9.203493745470995e-16,
            0.19035342094590962
          ],
          [
            4.849012503420165e-16,
            -3.152984854037326e-16,
            0.16412894761983082
          ],
          [
            -7.530885943348214e-16,
            6.158676984966336e-16,
            0.13875310831313328
          ],
          [
            8.265082625147755e-16,
            4.648926573106129e-17,
            0.11418613755196362
          ],
          [
            -2.572348291203977e-15,
            -6.186294370549146e-16,
            0.09035771318175795
          ],
          [
            1.1857776202441317e-16,
            -7.958409945446038e-16,
            0.06716663171677907
          ],
          [
            -7.482019765965469e-16,
            3.567245637779456e-15,
            0.044483017230575975
          ],
          [
            -6.449138124097257e-16,
            1.251527856660947e-15,
            0.022151864996068207
          ],
          [
            2.0027465625481354e-15,
            -2.246214027401772e-16,
            -2.1371793224034263e-15
          ],
          [
            2.347779665905846e-16,
            1.9576123480614227e-15,
            -0.022151864996069186
          ],
          [
            -1.1552277553608737e-15,
            -1.174199177029083e-15,
            -0.04448301723057852
          ],
          [
            -4.0220476736627115e-16,
            3.3251332241701655e-15,
            -0.06716663171677759
          ],
          [
            -1.1760851835165031e-15,
            1.839778169574772e-15,
            -0.09035771318175476
          ],
          [
            -9.754808431511734e-16,
            -4.179431018198383e-16,
            -0.11418613755196402
          ],
          [
            -2.6669265941695515e-15,
            3.2096004944820827e-15,
            -0.13875310831313065
          ],
          [
            -1.4316568131765698e-15,
            3.57967346129172e-15,
            -0.16412894761983324
          ],
          [
            -9.382054766066846e-16,
            4.2728698394202176e-15,
            -0.1903534209459071
          ]
        ],
        "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": [
          [
            5.551115123125783e-16,
            8.881784197001252e-16,
            0.19035342094590968
          ],
          [
            4.440892098500626e-16,
            -3.3306690738754696e-16,
            0.16412894761983088
          ],
          [
            -7.771561172376096e-16,
            6.661338147750939e-16,
            0.13875310831313326
          ],
          [
            7.771561172376096e-16,
            0.0,
            0.1141861375519636
          ],
          [
            -2.55351295663786e-15,
            -6.106226635438361e-16,
            0.09035771318175789
          ],
          [
            1.1102230246251565e-16,
            -7.771561172376096e-16,
            0.06716663171677906
          ],
          [
            -7.216449660063518e-16,
            3.552713678800501e-15,
            0.044483017230576016
          ],
          [
            -6.661338147750939e-16,
            1.2212453270876722e-15,
            0.02215186499606825
          ],
          [
            1.9984014443252818e-15,
            -2.220446049250313e-16,
            -2.1094237467877974e-15
          ],
          [
            2.220446049250313e-16,
            1.9984014443252818e-15,
            -0.022151864996069193
          ],
          [
            -1.1657341758564144e-15,
            -1.1657341758564144e-15,
            -0.044483017230578514
          ],
          [
            -3.885780586188048e-16,
            3.3306690738754696e-15,
            -0.06716663171677761
          ],
          [
            -1.1657341758564144e-15,
            1.887379141862766e-15,
            -0.09035771318175478
          ],
          [
            -9.992007221626409e-16,
            -4.440892098500626e-16,
            -0.11418613755196405
          ],
          [
            -2.6645352591003757e-15,
            3.219646771412954e-15,
            -0.13875310831313065
          ],
          [
            -1.4432899320127035e-15,
            3.552713678800501e-15,
            -0.1641289476198332
          ],
          [
            -9.43689570931383e-16,
            4.218847493575595e-15,
            -0.19035342094590713
          ]
        ]
      },
      "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": [
              5.337136725241911e-16,
              4.697256997876045e-16,
              0.19035342094590907
            ],
            "branch_aligned_reduced_polarization": [
              5.337136725241911e-16,
              4.697256997876045e-16,
              0.19035342094590907
            ],
            "target_residual": 0.30964657905409093,
            "energy_eV": -117.64889124927558,
            "max_atomic_step_A": 0.05796528855607056,
            "max_log_strain_component": 0.002982733399662577,
            "step_scale": 1.0,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 1.6029440898777152,
            "cell_principal_stretches": [
              1.0022890646355185,
              0.9978331891078446,
              0.9970217105301535
            ],
            "cell_volume_ratio": 0.9971386549685216,
            "cell_rmsd_from_input_A": 0.024406654583285576
          },
          {
            "iteration": 1,
            "reduced_polarization": [
              -3.241753483909346e-15,
              3.7139408785383334e-15,
              0.5020394061128098
            ],
            "branch_aligned_reduced_polarization": [
              -3.241753483909346e-15,
              3.7139408785383334e-15,
              0.5020394061128098
            ],
            "target_residual": 0.0020394061128098384,
            "energy_eV": -117.45078001610572,
            "max_atomic_step_A": 0.0003772800124918903,
            "max_log_strain_component": 1.9246063867656933e-05,
            "step_scale": 1.0,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 1.6029440898777152,
            "cell_principal_stretches": [
              1.0022742776809346,
              0.9978471553774692,
              0.9970408994583269
            ],
            "cell_volume_ratio": 0.9971570915058752,
            "cell_rmsd_from_input_A": 0.02424939867454528
          },
          {
            "iteration": 2,
            "reduced_polarization": [
              -8.558155369612409e-16,
              2.584103586157002e-15,
              0.499997512179334
            ],
            "branch_aligned_reduced_polarization": [
              -8.558155369612409e-16,
              2.584103586157002e-15,
              0.499997512179334
            ],
            "target_residual": 2.4878206659750823e-06,
            "energy_eV": -117.45350966445437
          }
        ],
        "iterations": 2
      },
      "parent": {
        "candidate_id": "bec_projection_01",
        "source": "MACEField_BEC_backprojection",
        "spacegroup": "Cmc2_1",
        "spacegroup_number": 36,
        "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": 2.4878206659750823e-06,
        "parent_symmetrization_rmsd_A": 0.03419891929364545,
        "parent_cell_rmsd_A": 0.02424939867454528,
        "energy_eV": -117.45350966445437,
        "reduced_polarization": [
          -8.558155369612409e-16,
          2.584103586157002e-15,
          0.499997512179334
        ],
        "cartesian_polarization_e_A2": [
          -2.9813166510312556e-17,
          -3.155955797838733e-17,
          0.006075420104901404
        ],
        "ranking_score": 0.5402662446036137
      },
      "branch_status": "awaiting_branch_sampling"
    },
    {
      "orbit_id": 2,
      "formal_class": [
        0.5,
        0.0,
        0.0
      ],
      "formal_classes_in_orbit": [
        [
          0.5,
          0.0,
          0.0
        ]
      ],
      "target_reduced_polarization": [
        0.5,
        0.0,
        0.0
      ],
      "bec_backprojection": {
        "converged_to_target": true,
        "history": [
          {
            "iteration": 0,
            "reduced_polarization": [
              5.337136725241911e-16,
              4.697256997876045e-16,
              0.19035342094590907
            ],
            "branch_aligned_reduced_polarization": [
              5.551115123125783e-16,
              4.697256997876045e-16,
              0.19035342094590907
            ],
            "target_residual": 0.5350088082132947,
            "energy_eV": -117.64889124927558,
            "max_atomic_step_A": 0.12,
            "max_log_strain_component": 0.012655838906442904,
            "step_scale": 0.6362641046769278,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 1.6029440898777152,
            "cell_principal_stretches": [
              1.013758178756129,
              0.9991060790755557,
              0.9884183063559174
            ],
            "cell_volume_ratio": 1.0011214180106167,
            "cell_rmsd_from_input_A": 0.09229815155795736
          },
          {
            "iteration": 1,
            "reduced_polarization": [
              0.31127563136749353,
              -1.0374345367162584e-14,
              0.08748076423244945
            ],
            "branch_aligned_reduced_polarization": [
              0.31127563136749353,
              -1.0374345367162584e-14,
              0.08748076423244945
            ],
            "target_residual": 0.20801387315857467,
            "energy_eV": -116.22909303835995,
            "max_atomic_step_A": 0.07349796848867109,
            "max_log_strain_component": 0.008414444258978608,
            "step_scale": 1.0,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 1.6029440898777152,
            "cell_principal_stretches": [
              1.0235028819356653,
              0.9980864467572601,
              0.9812626331601167
            ],
            "cell_volume_ratio": 1.0024033033601891,
            "cell_rmsd_from_input_A": 0.15490333816074486
          },
          {
            "iteration": 2,
            "reduced_polarization": [
              0.48359450906005835,
              -7.026350638860058e-15,
              0.03343538527199872
            ],
            "branch_aligned_reduced_polarization": [
              0.48359450906005835,
              -7.026350638860058e-15,
              0.03343538527199872
            ],
            "target_residual": 0.03724332317701384,
            "energy_eV": -114.06354681398997,
            "max_atomic_step_A": 0.009884448215625653,
            "max_log_strain_component": 0.0011635875305928951,
            "step_scale": 1.0,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 1.6029440898777152,
            "cell_principal_stretches": [
              1.0252065893179105,
              0.9976449931328026,
              0.9806089603131724
            ],
            "cell_volume_ratio": 1.00295921621564,
            "cell_rmsd_from_input_A": 0.16427452976570805
          },
          {
            "iteration": 3,
            "reduced_polarization": [
              0.49819692540482574,
              -2.7806979435249457e-15,
              0.004096330642644131
            ],
            "branch_aligned_reduced_polarization": [
              0.49819692540482574,
              -2.7806979435249457e-15,
              0.004096330642644131
            ],
            "target_residual": 0.00447560082331167,
            "energy_eV": -113.7702137411517,
            "max_atomic_step_A": 0.0011551884312510732,
            "max_log_strain_component": 0.00014161093174289467,
            "step_scale": 1.0,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 1.6029440898777152,
            "cell_principal_stretches": [
              1.0254183351756267,
              0.997587667270738,
              0.9805334157577105
            ],
            "cell_volume_ratio": 1.0030314460794334,
            "cell_rmsd_from_input_A": 0.16543055773912088
          },
          {
            "iteration": 4,
            "reduced_polarization": [
              0.4998060325734508,
              -5.827313507952982e-16,
              0.0004730070769975391
            ],
            "branch_aligned_reduced_polarization": [
              0.4998060325734508,
              -5.827313507952982e-16,
              0.0004730070769975391
            ],
            "target_residual": 0.0005112328798618844,
            "energy_eV": -113.73499399828987
          }
        ],
        "iterations": 4
      },
      "parent": {
        "candidate_id": "bec_projection_02",
        "source": "MACEField_BEC_backprojection",
        "spacegroup": "Cc",
        "spacegroup_number": 9,
        "pointgroup": "m",
        "has_inversion": false,
        "is_polar_point_group": true,
        "nonpolar_parent_hypothesis": false,
        "symmetry_tolerance_A": null,
        "target_reduced_polarization": [
          0.5,
          0.0,
          0.0
        ],
        "formal_class": [
          0.5,
          0.0,
          0.0
        ],
        "target_residual": 0.0005112328798618844,
        "parent_symmetrization_rmsd_A": 0.16111889079135797,
        "parent_cell_rmsd_A": 0.16543055773912088,
        "energy_eV": -113.73499399828987,
        "reduced_polarization": [
          0.4998060325734508,
          -5.827313507952982e-16,
          0.0004730070769975391
        ],
        "cartesian_polarization_e_A2": [
          0.01126853743772121,
          7.339827758736906e-18,
          -0.00024648475674961983
        ],
        "ranking_score": 0.703498995985862
      },
      "branch_status": "awaiting_branch_sampling"
    },
    {
      "orbit_id": 3,
      "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": [
              5.337136725241911e-16,
              4.697256997876045e-16,
              0.19035342094590907
            ],
            "branch_aligned_reduced_polarization": [
              5.337136725241911e-16,
              4.440892098500626e-16,
              0.19035342094590907
            ],
            "target_residual": 0.5350088082132948,
            "energy_eV": -117.64889124927558,
            "max_atomic_step_A": 0.11722138683276317,
            "max_log_strain_component": 0.005951985615422712,
            "step_scale": 1.0,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 1.6029440898777152,
            "cell_principal_stretches": [
              1.0064028357390153,
              1.0013343690058796,
              0.9940633044979019
            ],
            "cell_volume_ratio": 1.0017630688381334,
            "cell_rmsd_from_input_A": 0.03328067788154852
          },
          {
            "iteration": 1,
            "reduced_polarization": [
              5.457605695494173e-15,
              0.49584916536311213,
              -0.004011694924479605
            ],
            "branch_aligned_reduced_polarization": [
              5.457605695494173e-15,
              0.49584916536311213,
              -0.004011694924479605
            ],
            "target_residual": 0.005772618500289402,
            "energy_eV": -115.71085928638936,
            "max_atomic_step_A": 0.0012464622282050378,
            "max_log_strain_component": 5.192988626245937e-05,
            "step_scale": 1.0,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 1.6029440898777152,
            "cell_principal_stretches": [
              1.0064394572029445,
              1.0013053303104953,
              0.9940178800937722
            ],
            "cell_volume_ratio": 1.0017246926949097,
            "cell_rmsd_from_input_A": 0.03336643619411875
          },
          {
            "iteration": 2,
            "reduced_polarization": [
              -2.496618929838325e-16,
              0.5000224151154163,
              4.448295809090676e-06
            ],
            "branch_aligned_reduced_polarization": [
              -2.496618929838325e-16,
              0.5000224151154163,
              4.448295809090676e-06
            ],
            "target_residual": 2.285223697437653e-05,
            "energy_eV": -115.6849864892499
          }
        ],
        "iterations": 2
      },
      "parent": {
        "candidate_id": "bec_projection_03",
        "source": "MACEField_BEC_backprojection",
        "spacegroup": "Cm",
        "spacegroup_number": 8,
        "pointgroup": "m",
        "has_inversion": false,
        "is_polar_point_group": true,
        "nonpolar_parent_hypothesis": false,
        "symmetry_tolerance_A": null,
        "target_reduced_polarization": [
          0.0,
          0.5,
          0.0
        ],
        "formal_class": [
          0.0,
          0.5,
          0.0
        ],
        "target_residual": 2.285223697437653e-05,
        "parent_symmetrization_rmsd_A": 0.09338136329835935,
        "parent_cell_rmsd_A": 0.03336643619411875,
        "energy_eV": -115.6849864892499,
        "reduced_polarization": [
          -2.496618929838325e-16,
          0.5000224151154163,
          4.448295809090676e-06
        ],
        "cartesian_polarization_e_A2": [
          1.3602875798391506e-18,
          0.007763372924862533,
          4.673577715452821e-05
        ],
        "ranking_score": 0.6017686768208378
      },
      "branch_status": "awaiting_branch_sampling"
    },
    {
      "orbit_id": 4,
      "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": [
              5.337136725241911e-16,
              4.697256997876045e-16,
              0.19035342094590907
            ],
            "branch_aligned_reduced_polarization": [
              5.551115123125783e-16,
              4.697256997876045e-16,
              0.19035342094590907
            ],
            "target_residual": 0.5881164883931591,
            "energy_eV": -117.64889124927558,
            "max_atomic_step_A": 0.12,
            "max_log_strain_component": 0.012299618281114068,
            "step_scale": 0.618355343438828,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 1.6029440898777152,
            "cell_principal_stretches": [
              1.0107668893626103,
              1.0014148377223109,
              0.9862010494355937
            ],
            "cell_volume_ratio": 0.9982297046669528,
            "cell_rmsd_from_input_A": 0.08966062270684558
          },
          {
            "iteration": 1,
            "reduced_polarization": [
              0.30618100712694335,
              -2.2711265074365903e-15,
              0.39568965265813266
            ],
            "branch_aligned_reduced_polarization": [
              0.30618100712694335,
              -2.2711265074365903e-15,
              0.39568965265813266
            ],
            "target_residual": 0.2201055441394128,
            "energy_eV": -116.07499529820653,
            "max_atomic_step_A": 0.07143322295285791,
            "max_log_strain_component": 0.008104047566517305,
            "step_scale": 1.0,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 1.6029440898777152,
            "cell_principal_stretches": [
              1.0181701185137613,
              1.0021326981187009,
              0.9774507642918508
            ],
            "cell_volume_ratio": 0.9973336454901526,
            "cell_rmsd_from_input_A": 0.14800275790128842
          },
          {
            "iteration": 2,
            "reduced_polarization": [
              0.495951883984517,
              -4.7177254814639565e-15,
              0.5156349898153724
            ],
            "branch_aligned_reduced_polarization": [
              0.495951883984517,
              -4.7177254814639565e-15,
              0.5156349898153724
            ],
            "target_residual": 0.016150546424242355,
            "energy_eV": -113.37566887771304,
            "max_atomic_step_A": 0.0034809110109017367,
            "max_log_strain_component": 0.0002085313820886309,
            "step_scale": 1.0,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 1.6029440898777152,
            "cell_principal_stretches": [
              1.0185249002999333,
              1.0020079174680043,
              0.9773844845628352
            ],
            "cell_volume_ratio": 0.9974892973271171,
            "cell_rmsd_from_input_A": 0.14936026363429766
          },
          {
            "iteration": 3,
            "reduced_polarization": [
              0.4999324496299088,
              2.9316252611935404e-16,
              0.5003611502035485
            ],
            "branch_aligned_reduced_polarization": [
              0.4999324496299088,
              2.9316252611935404e-16,
              0.5003611502035485
            ],
            "target_residual": 0.00036741328503827074,
            "energy_eV": -113.37382428209692
          }
        ],
        "iterations": 3
      },
      "parent": {
        "candidate_id": "bec_projection_04",
        "source": "MACEField_BEC_backprojection",
        "spacegroup": "Cc",
        "spacegroup_number": 9,
        "pointgroup": "m",
        "has_inversion": false,
        "is_polar_point_group": true,
        "nonpolar_parent_hypothesis": false,
        "symmetry_tolerance_A": null,
        "target_reduced_polarization": [
          0.5,
          0.0,
          0.5
        ],
        "formal_class": [
          0.5,
          0.0,
          0.5
        ],
        "target_residual": 0.00036741328503827074,
        "parent_symmetrization_rmsd_A": 0.15463828248523717,
        "parent_cell_rmsd_A": 0.14936026363429766,
        "energy_eV": -113.37382428209692,
        "reduced_polarization": [
          0.4999324496299088,
          2.9316252611935404e-16,
          0.5003611502035485
        ],
        "cartesian_polarization_e_A2": [
          0.011160904874867369,
          -2.0592400954851813e-16,
          0.005848683208081034
        ],
        "ranking_score": 0.6927131749638882
      },
      "branch_status": "awaiting_branch_sampling"
    },
    {
      "orbit_id": 5,
      "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": [
              5.337136725241911e-16,
              4.697256997876045e-16,
              0.19035342094590907
            ],
            "branch_aligned_reduced_polarization": [
              5.337136725241911e-16,
              4.440892098500626e-16,
              0.19035342094590907
            ],
            "target_residual": 0.5881164883931592,
            "energy_eV": -117.64889124927558,
            "max_atomic_step_A": 0.12,
            "max_log_strain_component": 0.0056609428294076,
            "step_scale": 0.9511015642842334,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 1.6029440898777152,
            "cell_principal_stretches": [
              1.0058768113539225,
              0.9979390335104773,
              0.9934993733836018
            ],
            "cell_volume_ratio": 0.9972783796890594,
            "cell_rmsd_from_input_A": 0.03656431081223016
          },
          {
            "iteration": 1,
            "reduced_polarization": [
              2.4595667179285618e-15,
              0.4686093270118829,
              0.47709953296352037
            ],
            "branch_aligned_reduced_polarization": [
              2.4595667179285618e-15,
              0.4686093270118829,
              0.47709953296352037
            ],
            "target_residual": 0.03885621882190539,
            "energy_eV": -116.00010999163544,
            "max_atomic_step_A": 0.009083136928219167,
            "max_log_strain_component": 0.0004061942773204821,
            "step_scale": 1.0,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 1.6029440898777152,
            "cell_principal_stretches": [
              1.006311102518999,
              0.9977578452150674,
              0.9930127314247902
            ],
            "cell_volume_ratio": 0.9970391967326342,
            "cell_rmsd_from_input_A": 0.039427424098642
          },
          {
            "iteration": 2,
            "reduced_polarization": [
              -1.7085850614950452e-15,
              0.5000147040834027,
              0.49999634058855974
            ],
            "branch_aligned_reduced_polarization": [
              -1.7085850614950452e-15,
              0.5000147040834027,
              0.49999634058855974
            ],
            "target_residual": 1.5152602443184389e-05,
            "energy_eV": -115.76985679933512
          }
        ],
        "iterations": 2
      },
      "parent": {
        "candidate_id": "bec_projection_05",
        "source": "MACEField_BEC_backprojection",
        "spacegroup": "Cm",
        "spacegroup_number": 8,
        "pointgroup": "m",
        "has_inversion": false,
        "is_polar_point_group": true,
        "nonpolar_parent_hypothesis": false,
        "symmetry_tolerance_A": null,
        "target_reduced_polarization": [
          0.0,
          0.5,
          0.5
        ],
        "formal_class": [
          0.0,
          0.5,
          0.5
        ],
        "target_residual": 1.5152602443184389e-05,
        "parent_symmetrization_rmsd_A": 0.09757071063851327,
        "parent_cell_rmsd_A": 0.039427424098642,
        "energy_eV": -115.76985679933512,
        "reduced_polarization": [
          -1.7085850614950452e-15,
          0.5000147040834027,
          0.49999634058855974
        ],
        "cartesian_polarization_e_A2": [
          -1.306584236376185e-16,
          0.007865934493740838,
          0.006122856287634039
        ],
        "ranking_score": 0.6074578718680601
      },
      "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": [
              5.337136725241911e-16,
              4.697256997876045e-16,
              0.19035342094590907
            ],
            "branch_aligned_reduced_polarization": [
              5.551115123125783e-16,
              4.440892098500626e-16,
              0.19035342094590907
            ],
            "target_residual": 0.7322802911903402,
            "energy_eV": -117.64889124927558,
            "max_atomic_step_A": 0.12,
            "max_log_strain_component": 0.01088997696431742,
            "step_scale": 0.5474865391676303,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 1.6029440898777152,
            "cell_principal_stretches": [
              1.0122551402678677,
              0.9993561083350617,
              0.9894835403598992
            ],
            "cell_volume_ratio": 1.0009648717380535,
            "cell_rmsd_from_input_A": 0.0810235884331235
          },
          {
            "iteration": 1,
            "reduced_polarization": [
              0.26858647621268916,
              0.27075422786091646,
              0.09686203365217831
            ],
            "branch_aligned_reduced_polarization": [
              0.26858647621268916,
              0.27075422786091646,
              0.09686203365217831
            ],
            "target_residual": 0.3398353963296652,
            "energy_eV": -116.07449870692093,
            "max_atomic_step_A": 0.10363119825079008,
            "max_log_strain_component": 0.010152999530935352,
            "step_scale": 1.0,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 1.6029440898777152,
            "cell_principal_stretches": [
              1.0241164058843637,
              0.9984923834055196,
              0.9801245655827505
            ],
            "cell_volume_ratio": 1.0022483597070213,
            "cell_rmsd_from_input_A": 0.15750182384962425
          },
          {
            "iteration": 2,
            "reduced_polarization": [
              0.4789393473881478,
              0.4937338008501152,
              0.03634150915007052
            ],
            "branch_aligned_reduced_polarization": [
              0.4789393473881478,
              0.4937338008501152,
              0.03634150915007052
            ],
            "target_residual": 0.04246788936982615,
            "energy_eV": -112.1871666673184,
            "max_atomic_step_A": 0.013334462715032807,
            "max_log_strain_component": 0.0014103110772943977,
            "step_scale": 1.0,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 1.6029440898777152,
            "cell_principal_stretches": [
              1.0260711265895206,
              0.998064255324717,
              0.9792622290350184
            ],
            "cell_volume_ratio": 1.0028476764565013,
            "cell_rmsd_from_input_A": 0.16859119049775018
          },
          {
            "iteration": 3,
            "reduced_polarization": [
              0.49795340390145704,
              0.49955588127213174,
              0.004966312872394972
            ],
            "branch_aligned_reduced_polarization": [
              0.49795340390145704,
              0.49955588127213174,
              0.004966312872394972
            ],
            "target_residual": 0.005389810811292971,
            "energy_eV": -111.76291409110205,
            "max_atomic_step_A": 0.0015678769821135406,
            "max_log_strain_component": 0.00015854638045231155,
            "step_scale": 1.0,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 1.6029440898777152,
            "cell_principal_stretches": [
              1.026303829681375,
              0.9980052375278198,
              0.9791785302146713
            ],
            "cell_volume_ratio": 1.0029300695234156,
            "cell_rmsd_from_input_A": 0.16986887667987724
          },
          {
            "iteration": 4,
            "reduced_polarization": [
              0.4997888588730893,
              0.49993198859438903,
              0.0005454693770691354
            ],
            "branch_aligned_reduced_polarization": [
              0.4997888588730893,
              0.49993198859438903,
              0.0005454693770691354
            ],
            "target_residual": 0.0005888488499491867,
            "energy_eV": -111.71751742187962
          }
        ],
        "iterations": 4
      },
      "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": 0.0005888488499491867,
        "parent_symmetrization_rmsd_A": 0.18778183984603117,
        "parent_cell_rmsd_A": 0.16986887667987724,
        "energy_eV": -111.71751742187962,
        "reduced_polarization": [
          0.4997888588730893,
          0.49993198859438903,
          0.0005454693770691354
        ],
        "cartesian_polarization_e_A2": [
          0.011267879941360602,
          0.007744511371462578,
          -0.00019952645096895684
        ],
        "ranking_score": 0.7314267567158989
      },
      "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": [
              5.337136725241911e-16,
              4.697256997876045e-16,
              0.19035342094590907
            ],
            "branch_aligned_reduced_polarization": [
              5.551115123125783e-16,
              4.440892098500626e-16,
              0.19035342094590907
            ],
            "target_residual": 0.7719332898119503,
            "energy_eV": -117.64889124927558,
            "max_atomic_step_A": 0.11999999999999998,
            "max_log_strain_component": 0.010651223964982498,
            "step_scale": 0.5354833867504267,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 1.6029440898777152,
            "cell_principal_stretches": [
              1.00991484271957,
              1.0010193118040938,
              0.9876575952464444
            ],
            "cell_volume_ratio": 0.998466777589314,
            "cell_rmsd_from_input_A": 0.07931061731497611
          },
          {
            "iteration": 1,
            "reduced_polarization": [
              0.2648249337334104,
              0.2645727537119756,
              0.36356617308090505
            ],
            "branch_aligned_reduced_polarization": [
              0.2648249337334104,
              0.2645727537119756,
              0.36356617308090505
            ],
            "target_residual": 0.35964911958191487,
            "energy_eV": -116.02679282507528,
            "max_atomic_step_A": 0.10339268421905821,
            "max_log_strain_component": 0.009932860281948026,
            "step_scale": 1.0,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 1.6029440898777152,
            "cell_principal_stretches": [
              1.0193779299397192,
              1.0018725502089751,
              0.9763995111892323
            ],
            "cell_volume_ratio": 0.9971838993949113,
            "cell_rmsd_from_input_A": 0.15258111248507603
          },
          {
            "iteration": 2,
            "reduced_polarization": [
              0.49190386718590823,
              0.4934657804594531,
              0.5156228828341446
            ],
            "branch_aligned_reduced_polarization": [
              0.49190386718590823,
              0.4934657804594531,
              0.5156228828341446
            ],
            "target_residual": 0.018770132114529405,
            "energy_eV": -111.60183757723848,
            "max_atomic_step_A": 0.0048249728933552755,
            "max_log_strain_component": 0.0004147709867505792,
            "step_scale": 1.0,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 1.6029440898777152,
            "cell_principal_stretches": [
              1.0199347130793952,
              1.001772767943197,
              0.9761189244155105
            ],
            "cell_volume_ratio": 0.9973425031152132,
            "cell_rmsd_from_input_A": 0.1554207564473681
          },
          {
            "iteration": 3,
            "reduced_polarization": [
              0.49994927376566284,
              0.4998769722718186,
              0.5007320330680581
            ],
            "branch_aligned_reduced_polarization": [
              0.49994927376566284,
              0.4998769722718186,
              0.5007320330680581
            ],
            "target_residual": 0.0007440305003708601,
            "energy_eV": -111.48344693265408
          }
        ],
        "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": 0.0007440305003708601,
        "parent_symmetrization_rmsd_A": 0.18287198585627065,
        "parent_cell_rmsd_A": 0.1554207564473681,
        "energy_eV": -111.48344693265408,
        "reduced_polarization": [
          0.49994927376566284,
          0.4998769722718186,
          0.5007320330680581
        ],
        "cartesian_polarization_e_A2": [
          0.01115881270224233,
          0.007860091804000428,
          0.005897958316315333
        ],
        "ranking_score": 0.7232152359688544
      },
      "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
        ],
        "endpoint_rmsd_A": 0.14532126740066198,
        "minimum_distance_A_by_image": [
          1.9637984154120938,
          1.9615235763306904,
          1.9595499129673684,
          1.9578783361340122,
          1.9565096201088665,
          1.9554444008555663,
          1.9546831745526982,
          1.9542262964417996,
          1.9540739799999995
        ],
        "minimum_distance_A": 1.9540739799999995,
        "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": [
          483.9831899445251,
          483.9831899445251,
          483.9831899445251,
          483.9831899445251,
          483.9831899445251,
          483.9831899445251,
          483.9831899445251,
          483.9831899445251,
          483.9831899445251
        ],
        "cell_deformation_log_strain_norm": 0.0
      },
      "parent_reduced_polarization": [
        2.0027465625481354e-15,
        -2.246214027401773e-16,
        -2.1363607189379098e-15
      ],
      "incoming": {
        "reached": true,
        "construction": "variable_cell_linear_interpolation",
        "continuation_fractions": [
          0.0,
          0.125,
          0.25,
          0.375,
          0.5,
          0.625,
          0.75,
          0.875,
          1.0
        ],
        "energies_eV": [
          -117.64889124927556,
          -117.64749192737636,
          -117.64541392496591,
          -117.64302821637068,
          -117.6406645405608,
          -117.6385881838909,
          -117.63698840792736,
          -117.63598535273397,
          -117.63564424237043
        ],
        "cartesian_polarizations_e_A2": [
          [
            1.2158960098595932e-17,
            1.4333471336528027e-17,
            0.0023132350556015176
          ],
          [
            1.0937926705808001e-17,
            -4.910441543146636e-18,
            0.001994546950543451
          ],
          [
            -1.69874337135742e-17,
            9.59149019668642e-18,
            0.0016861717148483502
          ],
          [
            1.8643562561975096e-17,
            7.240213078216207e-19,
            0.0013876261058843608
          ],
          [
            -5.802450921946319e-17,
            -9.634501363487706e-18,
            0.0010980555465584412
          ],
          [
            2.6747608282036077e-18,
            -1.2394384566570121e-17,
            0.0008162301800611207
          ],
          [
            -1.6877206184519883e-17,
            5.555609045165902e-17,
            0.0005405717130029117
          ],
          [
            -1.4547333104885507e-17,
            1.9491227088782046e-17,
            0.0002691964788508744
          ],
          [
            4.5175992216991585e-17,
            -3.498241566504464e-18,
            -2.596173203454806e-17
          ]
        ],
        "raw_reduced_polarization": [
          [
            5.390322236788399e-16,
            9.203493745470995e-16,
            0.19035342094590962
          ],
          [
            4.849012503420165e-16,
            -3.1529848540373254e-16,
            0.16412894761983082
          ],
          [
            -7.530885943348215e-16,
            6.158676984966337e-16,
            0.13875310831313328
          ],
          [
            8.265082625147754e-16,
            4.648926573106129e-17,
            0.11418613755196362
          ],
          [
            -2.572348291203977e-15,
            -6.186294370549146e-16,
            0.09035771318175795
          ],
          [
            1.1857776202441337e-16,
            -7.958409945446038e-16,
            0.06716663171677907
          ],
          [
            -7.482019765965469e-16,
            3.567245637779456e-15,
            0.044483017230575975
          ],
          [
            -6.449138124097257e-16,
            1.251527856660947e-15,
            0.022151864996068207
          ],
          [
            2.0027465625481354e-15,
            -2.246214027401773e-16,
            -2.1363607189379098e-15
          ]
        ],
        "unwrapped_reduced_polarization": [
          [
            5.390322236788399e-16,
            9.203493745470995e-16,
            0.19035342094590962
          ],
          [
            4.849012503420165e-16,
            -3.152984854037326e-16,
            0.16412894761983082
          ],
          [
            -7.530885943348214e-16,
            6.158676984966336e-16,
            0.13875310831313328
          ],
          [
            8.265082625147755e-16,
            4.648926573106129e-17,
            0.11418613755196362
          ],
          [
            -2.572348291203977e-15,
            -6.186294370549146e-16,
            0.09035771318175795
          ],
          [
            1.1857776202441317e-16,
            -7.958409945446038e-16,
            0.06716663171677907
          ],
          [
            -7.482019765965469e-16,
            3.567245637779456e-15,
            0.044483017230575975
          ],
          [
            -6.449138124097257e-16,
            1.251527856660947e-15,
            0.022151864996068207
          ],
          [
            2.0027465625481354e-15,
            -2.246214027401772e-16,
            -2.1371793224034263e-15
          ]
        ],
        "berry_integer_shifts": [
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ]
        ],
        "folded_reduced_polarization": [
          [
            5.551115123125783e-16,
            8.881784197001252e-16,
            0.19035342094590968
          ],
          [
            4.440892098500626e-16,
            -3.3306690738754696e-16,
            0.16412894761983088
          ],
          [
            -7.771561172376096e-16,
            6.661338147750939e-16,
            0.13875310831313326
          ],
          [
            7.771561172376096e-16,
            0.0,
            0.1141861375519636
          ],
          [
            -2.55351295663786e-15,
            -6.106226635438361e-16,
            0.09035771318175789
          ],
          [
            1.1102230246251565e-16,
            -7.771561172376096e-16,
            0.06716663171677906
          ],
          [
            -7.216449660063518e-16,
            3.552713678800501e-15,
            0.044483017230576016
          ],
          [
            -6.661338147750939e-16,
            1.2212453270876722e-15,
            0.02215186499606825
          ],
          [
            1.9984014443252818e-15,
            -2.220446049250313e-16,
            -2.1094237467877974e-15
          ]
        ]
      },
      "reflected": {
        "reached": true,
        "construction": "reflect_displacements_about_reconstructed_parent",
        "energies_eV": [
          -117.63564424237043,
          -117.63598535273394,
          -117.63698840792739,
          -117.63858818389092,
          -117.64066454056079,
          -117.64302821637068,
          -117.64541392496594,
          -117.64749192737638,
          -117.64889124927556
        ],
        "cartesian_polarizations_e_A2": [
          [
            2.3674776125605905e-17,
            1.3261776430396023e-17,
            3.443210104128844e-17
          ],
          [
            5.295891047703365e-18,
            3.048774873431043e-17,
            -0.00026919647885088627
          ],
          [
            -2.6058494400127656e-17,
            -1.8286914418346084e-17,
            -0.0005405717130029426
          ],
          [
            -9.072540570014767e-18,
            5.1785444828746414e-17,
            -0.0008162301800611025
          ],
          [
            -2.6528975802840102e-17,
            2.8652605617455624e-17,
            -0.0010980555465584024
          ],
          [
            -2.2003939890403696e-17,
            -6.509023242594372e-18,
            -0.0013876261058843658
          ],
          [
            -6.015791379424516e-17,
            4.9986144350892686e-17,
            -0.001686171714848318
          ],
          [
            -3.2293909902997634e-17,
            5.574964070226479e-17,
            -0.0019945469505434806
          ],
          [
            -2.1163118739894865e-17,
            6.654544356938718e-17,
            -0.0023132350556014872
          ]
        ],
        "raw_reduced_polarization": [
          [
            1.0495525206598634e-15,
            8.515360554699344e-16,
            2.8333775280178544e-15
          ],
          [
            2.3477796659058454e-16,
            1.9576123480614227e-15,
            -0.022151864996069186
          ],
          [
            -1.1552277553608737e-15,
            -1.1741991770290828e-15,
            -0.04448301723057852
          ],
          [
            -4.022047673662711e-16,
            3.3251332241701655e-15,
            -0.06716663171677759
          ],
          [
            -1.1760851835165031e-15,
            1.839778169574772e-15,
            -0.09035771318175476
          ],
          [
            -9.754808431511734e-16,
            -4.1794310181983814e-16,
            -0.11418613755196402
          ],
          [
            -2.6669265941695515e-15,
            3.2096004944820827e-15,
            -0.13875310831313065
          ],
          [
            -1.4316568131765698e-15,
            3.57967346129172e-15,
            -0.16412894761983324
          ],
          [
            -9.382054766066846e-16,
            4.2728698394202176e-15,
            -0.1903534209459071
          ]
        ],
        "unwrapped_reduced_polarization": [
          [
            1.0495525206598634e-15,
            8.515360554699344e-16,
            2.8333775280178544e-15
          ],
          [
            2.347779665905846e-16,
            1.9576123480614227e-15,
            -0.022151864996069186
          ],
          [
            -1.1552277553608737e-15,
            -1.174199177029083e-15,
            -0.04448301723057852
          ],
          [
            -4.0220476736627115e-16,
            3.3251332241701655e-15,
            -0.06716663171677759
          ],
          [
            -1.1760851835165031e-15,
            1.839778169574772e-15,
            -0.09035771318175476
          ],
          [
            -9.754808431511734e-16,
            -4.179431018198383e-16,
            -0.11418613755196402
          ],
          [
            -2.6669265941695515e-15,
            3.2096004944820827e-15,
            -0.13875310831313065
          ],
          [
            -1.4316568131765698e-15,
            3.57967346129172e-15,
            -0.16412894761983324
          ],
          [
            -9.382054766066846e-16,
            4.2728698394202176e-15,
            -0.1903534209459071
          ]
        ],
        "gauge_integer_shift": [
          0,
          0,
          0
        ],
        "expected_opposite_endpoint_reduced_polarization": [
          3.466460901417431e-15,
          -1.3695921800274544e-15,
          -0.1903534209459139
        ],
        "actual_opposite_endpoint_branch_residual": 9.873198139779386e-15
      },
      "pnp_branch": {
        "construction": "incoming_path_concatenated_with_parent_reflection",
        "reduced_polarization": [
          [
            5.390322236788399e-16,
            9.203493745470995e-16,
            0.19035342094590962
          ],
          [
            4.849012503420165e-16,
            -3.1529848540373254e-16,
            0.16412894761983082
          ],
          [
            -7.530885943348215e-16,
            6.158676984966337e-16,
            0.13875310831313328
          ],
          [
            8.265082625147754e-16,
            4.648926573106129e-17,
            0.11418613755196362
          ],
          [
            -2.572348291203977e-15,
            -6.186294370549146e-16,
            0.09035771318175795
          ],
          [
            1.1857776202441337e-16,
            -7.958409945446038e-16,
            0.06716663171677907
          ],
          [
            -7.482019765965469e-16,
            3.567245637779456e-15,
            0.044483017230575975
          ],
          [
            -6.449138124097257e-16,
            1.251527856660947e-15,
            0.022151864996068207
          ],
          [
            2.0027465625481354e-15,
            -2.246214027401773e-16,
            -2.1363607189379098e-15
          ],
          [
            2.3477796659058454e-16,
            1.9576123480614227e-15,
            -0.022151864996069186
          ],
          [
            -1.1552277553608737e-15,
            -1.1741991770290828e-15,
            -0.04448301723057852
          ],
          [
            -4.022047673662711e-16,
            3.3251332241701655e-15,
            -0.06716663171677759
          ],
          [
            -1.1760851835165031e-15,
            1.839778169574772e-15,
            -0.09035771318175476
          ],
          [
            -9.754808431511734e-16,
            -4.1794310181983814e-16,
            -0.11418613755196402
          ],
          [
            -2.6669265941695515e-15,
            3.2096004944820827e-15,
            -0.13875310831313065
          ],
          [
            -1.4316568131765698e-15,
            3.57967346129172e-15,
            -0.16412894761983324
          ],
          [
            -9.382054766066846e-16,
            4.2728698394202176e-15,
            -0.1903534209459071
          ]
        ],
        "unwrapped_reduced_polarization": [
          [
            5.390322236788399e-16,
            9.203493745470995e-16,
            0.19035342094590962
          ],
          [
            4.849012503420165e-16,
            -3.152984854037326e-16,
            0.16412894761983082
          ],
          [
            -7.530885943348214e-16,
            6.158676984966336e-16,
            0.13875310831313328
          ],
          [
            8.265082625147755e-16,
            4.648926573106129e-17,
            0.11418613755196362
          ],
          [
            -2.572348291203977e-15,
            -6.186294370549146e-16,
            0.09035771318175795
          ],
          [
            1.1857776202441317e-16,
            -7.958409945446038e-16,
            0.06716663171677907
          ],
          [
            -7.482019765965469e-16,
            3.567245637779456e-15,
            0.044483017230575975
          ],
          [
            -6.449138124097257e-16,
            1.251527856660947e-15,
            0.022151864996068207
          ],
          [
            2.0027465625481354e-15,
            -2.246214027401772e-16,
            -2.1371793224034263e-15
          ],
          [
            2.347779665905846e-16,
            1.9576123480614227e-15,
            -0.022151864996069186
          ],
          [
            -1.1552277553608737e-15,
            -1.174199177029083e-15,
            -0.04448301723057852
          ],
          [
            -4.0220476736627115e-16,
            3.3251332241701655e-15,
            -0.06716663171677759
          ],
          [
            -1.1760851835165031e-15,
            1.839778169574772e-15,
            -0.09035771318175476
          ],
          [
            -9.754808431511734e-16,
            -4.179431018198383e-16,
            -0.11418613755196402
          ],
          [
            -2.6669265941695515e-15,
            3.2096004944820827e-15,
            -0.13875310831313065
          ],
          [
            -1.4316568131765698e-15,
            3.57967346129172e-15,
            -0.16412894761983324
          ],
          [
            -9.382054766066846e-16,
            4.2728698394202176e-15,
            -0.1903534209459071
          ]
        ],
        "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": [
          [
            5.551115123125783e-16,
            8.881784197001252e-16,
            0.19035342094590968
          ],
          [
            4.440892098500626e-16,
            -3.3306690738754696e-16,
            0.16412894761983088
          ],
          [
            -7.771561172376096e-16,
            6.661338147750939e-16,
            0.13875310831313326
          ],
          [
            7.771561172376096e-16,
            0.0,
            0.1141861375519636
          ],
          [
            -2.55351295663786e-15,
            -6.106226635438361e-16,
            0.09035771318175789
          ],
          [
            1.1102230246251565e-16,
            -7.771561172376096e-16,
            0.06716663171677906
          ],
          [
            -7.216449660063518e-16,
            3.552713678800501e-15,
            0.044483017230576016
          ],
          [
            -6.661338147750939e-16,
            1.2212453270876722e-15,
            0.02215186499606825
          ],
          [
            1.9984014443252818e-15,
            -2.220446049250313e-16,
            -2.1094237467877974e-15
          ],
          [
            2.220446049250313e-16,
            1.9984014443252818e-15,
            -0.022151864996069193
          ],
          [
            -1.1657341758564144e-15,
            -1.1657341758564144e-15,
            -0.044483017230578514
          ],
          [
            -3.885780586188048e-16,
            3.3306690738754696e-15,
            -0.06716663171677761
          ],
          [
            -1.1657341758564144e-15,
            1.887379141862766e-15,
            -0.09035771318175478
          ],
          [
            -9.992007221626409e-16,
            -4.440892098500626e-16,
            -0.11418613755196405
          ],
          [
            -2.6645352591003757e-15,
            3.219646771412954e-15,
            -0.13875310831313065
          ],
          [
            -1.4432899320127035e-15,
            3.552713678800501e-15,
            -0.1641289476198332
          ],
          [
            -9.43689570931383e-16,
            4.218847493575595e-15,
            -0.19035342094590713
          ]
        ]
      },
      "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": "Cmcm",
        "spacegroup_number": 63,
        "pointgroup": "mmm",
        "has_inversion": true,
        "is_polar_point_group": false,
        "nonpolar_parent_hypothesis": true,
        "symmetry_tolerance_A": null,
        "target_reduced_polarization": [
          0.0,
          0.0,
          0.0
        ],
        "formal_class": [
          0.0,
          0.0,
          0.0
        ],
        "target_residual": 2.171532051863965e-15,
        "parent_symmetrization_rmsd_A": 0.14532126740066198,
        "parent_cell_rmsd_A": 0.0,
        "energy_eV": -117.63564424237045,
        "reduced_polarization": [
          1.820943466023795e-15,
          -1.1544067173614032e-15,
          2.589623075442429e-16
        ],
        "cartesian_polarization_e_A2": [
          4.1075056318662635e-17,
          -1.7978667722936878e-17,
          3.146991973740393e-18
        ],
        "ranking_score": 0.1453212674006663
      }
    }
  ],
  "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": 55,
      "full_response": 22,
      "energy_polarization": 33
    },
    "model_evaluations_for_recovery_and_path_properties": {
      "total": 80,
      "full_response": 47,
      "energy_polarization": 33
    },
    "elapsed_seconds": 243.23592030099826
  }
}
