{
  "schema": "ferrofinder.endpoint_parent_recovery.v4_variable_cell",
  "status": "complete",
  "input_atom_count": 40,
  "input_formula": "C4H8Al4Na4O20",
  "input_spacegroup": "Ima2",
  "input_pointgroup": "mm2",
  "input_is_polar_point_group": true,
  "input_energy_eV": -246.2005182693247,
  "input_cartesian_polarization_e_A2": [
    2.050730541680937e-17,
    -1.7515493353741738e-17,
    -0.0004502191267995486
  ],
  "input_reduced_polarization": [
    1.4636376871550856e-15,
    -6.7009724475262425e-16,
    -0.02671201566078685
  ],
  "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": "Imma",
      "spacegroup_number": 74,
      "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": 1.1159375881937921e-15,
      "parent_symmetrization_rmsd_A": 0.0477586508086499,
      "parent_cell_rmsd_A": 0.0,
      "energy_eV": -246.2066709499466,
      "reduced_polarization": [
        -9.316683919422624e-16,
        5.902923563519672e-16,
        -1.6989891768913237e-16
      ],
      "cartesian_polarization_e_A2": [
        -1.3053782659754087e-17,
        1.542949463740045e-17,
        -2.8635705870178556e-18
      ],
      "ranking_score": 0.04775865080865213
    },
    {
      "candidate_id": "symmetry_projection_00",
      "source": "spglib_refine_cell_from_polar_endpoint",
      "spacegroup": "Imma",
      "spacegroup_number": 74,
      "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": 9.145391961592055e-16,
      "parent_symmetrization_rmsd_A": 2.296125077938766,
      "parent_cell_rmsd_A": 3.845510462763666,
      "energy_eV": -237.95963628791753,
      "reduced_polarization": [
        -8.751329677754657e-16,
        -1.2531353601602483e-16,
        2.3413830894407635e-16
      ],
      "cartesian_polarization_e_A2": [
        -1.2261654101961274e-17,
        -2.1121038366311205e-18,
        6.1200788785219654e-18
      ],
      "ranking_score": 3.2575026936296845
    },
    {
      "candidate_id": "bec_projection_00",
      "source": "MACEField_BEC_backprojection",
      "spacegroup": "Ima2",
      "spacegroup_number": 46,
      "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": 6.804515106370545e-06,
      "parent_symmetrization_rmsd_A": 0.005796398795289642,
      "parent_cell_rmsd_A": 0.00022751374982523284,
      "energy_eV": -246.19044920568982,
      "reduced_polarization": [
        -2.5708007468413967e-15,
        3.060371020862247e-16,
        -6.804515106370545e-06
      ],
      "cartesian_polarization_e_A2": [
        -3.6022103325636425e-17,
        7.999651273737028e-18,
        -1.1468679563134058e-07
      ],
      "ranking_score": 0.5058668862629587
    },
    {
      "candidate_id": "inversion_parent_bec_00_00",
      "source": "same_species_inversion_center_projection_after_BEC",
      "spacegroup": "Imma",
      "spacegroup_number": 74,
      "pointgroup": "mmm",
      "has_inversion": true,
      "is_polar_point_group": false,
      "nonpolar_parent_hypothesis": true,
      "symmetry_tolerance_A": null,
      "target_reduced_polarization": [
        0.0,
        0.0,
        0.0
      ],
      "formal_class": [
        0.0,
        0.0,
        0.0
      ],
      "target_residual": 3.9760453858421205e-15,
      "parent_symmetrization_rmsd_A": 0.047758664212109045,
      "parent_cell_rmsd_A": 0.00022751374982523284,
      "energy_eV": -246.2063536941983,
      "reduced_polarization": [
        -3.2653206387535685e-15,
        1.381083628823872e-15,
        1.799785000104482e-15
      ],
      "cartesian_polarization_e_A2": [
        -4.5753621762735576e-17,
        3.6101874498287366e-17,
        3.033450161556523e-17
      ],
      "ranking_score": 0.04781554264957331
    },
    {
      "candidate_id": "symmetry_parent_00_00",
      "source": "spglib_refine_cell_after_MACEField_BEC_backprojection",
      "spacegroup": "Imma",
      "spacegroup_number": 74,
      "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": 7.851240254033804e-15,
      "parent_symmetrization_rmsd_A": 2.294965640704552,
      "parent_cell_rmsd_A": 3.8456833483643273,
      "energy_eV": -238.11212029981573,
      "reduced_polarization": [
        6.6708870179338e-17,
        7.850893020499787e-15,
        3.16580774515501e-17
      ],
      "cartesian_polarization_e_A2": [
        9.347236464869594e-19,
        1.3232298691241158e-16,
        8.275501317658994e-19
      ],
      "ranking_score": 3.2563864777956493
    },
    {
      "candidate_id": "bec_projection_01",
      "source": "MACEField_BEC_backprojection",
      "spacegroup": "Ima2",
      "spacegroup_number": 46,
      "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": 0.00011441375161236333,
      "parent_symmetrization_rmsd_A": 0.10216967740190698,
      "parent_cell_rmsd_A": 0.004025330578858951,
      "energy_eV": -243.1141269577929,
      "reduced_polarization": [
        -7.265813096365766e-16,
        2.1022107699238723e-15,
        -0.5001144137516124
      ],
      "cartesian_polarization_e_A2": [
        9.824407610624181e-17,
        3.613289607571138e-16,
        -0.008429564023451068
      ],
      "ranking_score": 0.6034048375498464
    },
    {
      "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": 2.325037392011885e-06,
      "parent_symmetrization_rmsd_A": 0.05569551400256592,
      "parent_cell_rmsd_A": 0.001764861955438428,
      "energy_eV": -245.04787229946817,
      "reduced_polarization": [
        0.4999976763394026,
        1.0832436682872693e-15,
        -8.000189018389285e-08
      ],
      "cartesian_polarization_e_A2": [
        0.007005961670660128,
        2.4481696681393854e-17,
        2.693349004807756e-06
      ],
      "ranking_score": 0.5561413795662096
    },
    {
      "candidate_id": "symmetry_parent_02_00",
      "source": "spglib_refine_cell_after_MACEField_BEC_backprojection",
      "spacegroup": "Imma",
      "spacegroup_number": 74,
      "pointgroup": "mmm",
      "has_inversion": true,
      "is_polar_point_group": false,
      "nonpolar_parent_hypothesis": true,
      "symmetry_tolerance_A": null,
      "target_reduced_polarization": [
        0.5,
        0.0,
        0.0
      ],
      "formal_class": [
        0.5,
        0.0,
        0.0
      ],
      "target_residual": 0.49999999999999917,
      "parent_symmetrization_rmsd_A": 2.382422927920772,
      "parent_cell_rmsd_A": 3.8456836073016607,
      "energy_eV": -238.3061541541383,
      "reduced_polarization": [
        8.303762534839698e-16,
        -1.8255194849318638e-16,
        2.1369202124034664e-16
      ],
      "cartesian_polarization_e_A2": [
        1.1635219899579634e-17,
        -3.076823901619425e-18,
        5.585962942041647e-18
      ],
      "ranking_score": 4.343843829746185
    },
    {
      "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": 5.186781896694824e-06,
      "parent_symmetrization_rmsd_A": 0.08227488377026891,
      "parent_cell_rmsd_A": 0.010943274975788668,
      "energy_eV": -240.09947087641328,
      "reduced_polarization": [
        -9.055483367221084e-16,
        -0.5000029871241941,
        -4.240258894554443e-06
      ],
      "cartesian_polarization_e_A2": [
        8.442315488791578e-17,
        -0.013070225946544441,
        -1.6917866937541223e-05
      ],
      "ranking_score": 0.5850210760780095
    },
    {
      "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": 1.378900359744401e-06,
      "parent_symmetrization_rmsd_A": 0.11491857994393156,
      "parent_cell_rmsd_A": 0.0043623224496816765,
      "energy_eV": -241.92022212444945,
      "reduced_polarization": [
        0.5000003822237207,
        1.227944790930918e-16,
        -0.49999867513350504
      ],
      "cartesian_polarization_e_A2": [
        0.006995383948613977,
        3.268695560004536e-16,
        -0.008424899200210107
      ],
      "ranking_score": 0.6160119183570715
    },
    {
      "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": 1.7595184059415241e-06,
      "parent_symmetrization_rmsd_A": 0.12337378125565751,
      "parent_cell_rmsd_A": 0.011352382120221377,
      "energy_eV": -237.8759254741254,
      "reduced_polarization": [
        -5.546703054504272e-15,
        -0.5000012989394568,
        -0.49999881312961597
      ],
      "cartesian_polarization_e_A2": [
        4.902210327230416e-16,
        -0.013067738177377868,
        -0.008444093686828167
      ],
      "ranking_score": 0.6262153958225247
    },
    {
      "candidate_id": "bec_projection_06",
      "source": "MACEField_BEC_backprojection",
      "spacegroup": "P1",
      "spacegroup_number": 1,
      "pointgroup": "1",
      "has_inversion": false,
      "is_polar_point_group": true,
      "nonpolar_parent_hypothesis": false,
      "symmetry_tolerance_A": null,
      "target_reduced_polarization": [
        0.5,
        -0.5,
        0.0
      ],
      "formal_class": [
        0.5,
        0.5,
        0.0
      ],
      "target_residual": 4.409490899465222e-06,
      "parent_symmetrization_rmsd_A": 0.1006680479447973,
      "parent_cell_rmsd_A": 0.011201254520728725,
      "energy_eV": -238.72102537296058,
      "reduced_polarization": [
        0.49999691389301526,
        -0.4999991409124903,
        -3.0301026916439734e-06
      ],
      "cartesian_polarization_e_A2": [
        0.0070059447286611185,
        -0.013070110721227832,
        -1.4186757957238304e-05
      ],
      "ranking_score": 0.6034771805567785
    },
    {
      "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": 1.5175317735931813e-05,
      "parent_symmetrization_rmsd_A": 0.1362054110129262,
      "parent_cell_rmsd_A": 0.011615354722151751,
      "energy_eV": -236.31272196534428,
      "reduced_polarization": [
        0.4999877408443399,
        -0.5000026020314859,
        -0.5000085576166678
      ],
      "cartesian_polarization_e_A2": [
        0.006995560170051361,
        -0.013067983655282686,
        -0.008441571622520265
      ],
      "ranking_score": 0.639139600328936
    }
  ],
  "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": [
              1.4636376871550856e-15,
              -6.7009724475262425e-16,
              -0.02671201566078685
            ],
            "branch_aligned_reduced_polarization": [
              1.4636376871550856e-15,
              -6.7009724475262425e-16,
              -0.02671201566078685
            ],
            "target_residual": 0.02671201566078685,
            "energy_eV": -246.2005182693247,
            "max_atomic_step_A": 0.007117101100841586,
            "max_log_strain_component": 5.8607346097496944e-05,
            "step_scale": 1.0,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 0.11819268475247496,
            "cell_principal_stretches": [
              1.0000018982775587,
              1.0000005069630067,
              0.9999413943712794
            ],
            "cell_volume_ratio": 0.9999437994718465,
            "cell_rmsd_from_input_A": 0.00022751374982523284
          },
          {
            "iteration": 1,
            "reduced_polarization": [
              -2.5708007468413967e-15,
              3.060371020862247e-16,
              -6.804515106370545e-06
            ],
            "branch_aligned_reduced_polarization": [
              -2.5708007468413967e-15,
              3.060371020862247e-16,
              -6.804515106370545e-06
            ],
            "target_residual": 6.804515106370545e-06,
            "energy_eV": -246.19044920568982
          }
        ],
        "iterations": 1
      },
      "parent": {
        "candidate_id": "inversion_parent_endpoint_00",
        "source": "same_species_inversion_center_projection_from_endpoint",
        "spacegroup": "Imma",
        "spacegroup_number": 74,
        "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": 1.1159375881937921e-15,
        "parent_symmetrization_rmsd_A": 0.0477586508086499,
        "parent_cell_rmsd_A": 0.0,
        "energy_eV": -246.2066709499466,
        "reduced_polarization": [
          -9.316683919422624e-16,
          5.902923563519672e-16,
          -1.6989891768913237e-16
        ],
        "cartesian_polarization_e_A2": [
          -1.3053782659754087e-17,
          1.542949463740045e-17,
          -2.8635705870178556e-18
        ],
        "ranking_score": 0.04775865080865213
      },
      "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": [
          -246.20051826932468,
          -246.2019507675797,
          -246.203196873077,
          -246.2042548500275,
          -246.20512297267092,
          -246.205799579371,
          -246.2062834731964,
          -246.20657405021734,
          -246.20667094994658
        ],
        "cartesian_polarizations_e_A2": [
          [
            4.779579109308331e-18,
            -2.1946085668615386e-17,
            -0.0004502191267995526
          ],
          [
            2.475247758360898e-17,
            -2.1842647715738958e-17,
            -0.00039452078423788084
          ],
          [
            -4.345371137131426e-17,
            9.119779511938365e-18,
            -0.00033859558370507475
          ],
          [
            -9.297127967479235e-18,
            -2.858335431151949e-17,
            -0.00028247260502094716
          ],
          [
            -3.917028014392035e-17,
            -1.792924516524745e-18,
            -0.00022618240831002556
          ],
          [
            -7.368550745035293e-18,
            3.482411080173062e-18,
            -0.00016975677823639622
          ],
          [
            -5.913827549917342e-17,
            -3.568609374236752e-18,
            -0.0001132285792750543
          ],
          [
            -4.877027221346307e-17,
            7.447532607102786e-18,
            -5.663156021069768e-05
          ],
          [
            -2.376516875023686e-17,
            -2.2308118503682884e-17,
            -4.4334727700335963e-17
          ]
        ],
        "raw_reduced_polarization": [
          [
            3.4112585592979464e-16,
            -8.396001895374908e-16,
            -0.026712015660787087
          ],
          [
            1.766622103952075e-15,
            -8.356429223440698e-16,
            -0.02340736930032789
          ],
          [
            -3.1013577023962975e-15,
            3.488990575532856e-16,
            -0.020089263197007937
          ],
          [
            -6.635502129086306e-16,
            -1.0935248344486722e-15,
            -0.016759422689792226
          ],
          [
            -2.795642678051275e-15,
            -6.859263135263083e-17,
            -0.013419660945817343
          ],
          [
            -5.259047130252525e-16,
            1.3322799551184063e-16,
            -0.010071863785552264
          ],
          [
            -4.220788982983676e-15,
            -1.3652571817302482e-16,
            -0.006717981095882061
          ],
          [
            -3.4808087641746843e-15,
            2.849232379263126e-16,
            -0.003360015230797757
          ],
          [
            -1.6961563656205985e-15,
            -8.534506247144644e-16,
            -2.6304300953774632e-15
          ]
        ],
        "unwrapped_reduced_polarization": [
          [
            3.4112585592979464e-16,
            -8.396001895374908e-16,
            -0.026712015660787087
          ],
          [
            1.766622103952075e-15,
            -8.356429223440698e-16,
            -0.02340736930032789
          ],
          [
            -3.1013577023962975e-15,
            3.4889905755328556e-16,
            -0.020089263197007937
          ],
          [
            -6.635502129086306e-16,
            -1.0935248344486722e-15,
            -0.016759422689792226
          ],
          [
            -2.795642678051275e-15,
            -6.859263135263092e-17,
            -0.013419660945817343
          ],
          [
            -5.259047130252524e-16,
            1.3322799551184063e-16,
            -0.010071863785552264
          ],
          [
            -4.220788982983676e-15,
            -1.3652571817302482e-16,
            -0.006717981095882061
          ],
          [
            -3.4808087641746843e-15,
            2.849232379263126e-16,
            -0.003360015230797757
          ],
          [
            -1.6961563656205986e-15,
            -8.534506247144645e-16,
            -2.6302744704498338e-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": [
          [
            3.3306690738754696e-16,
            -8.326672684688674e-16,
            -0.02671201566078707
          ],
          [
            1.7763568394002505e-15,
            -8.326672684688674e-16,
            -0.023407369300327885
          ],
          [
            -3.1086244689504383e-15,
            3.3306690738754696e-16,
            -0.020089263197007934
          ],
          [
            -6.661338147750939e-16,
            -1.1102230246251565e-15,
            -0.016759422689792247
          ],
          [
            -2.7755575615628914e-15,
            -5.551115123125783e-17,
            -0.013419660945817369
          ],
          [
            -4.996003610813204e-16,
            1.1102230246251565e-16,
            -0.010071863785552249
          ],
          [
            -4.218847493575595e-15,
            -1.1102230246251565e-16,
            -0.006717981095882064
          ],
          [
            -3.497202527569243e-15,
            3.3306690738754696e-16,
            -0.0033600152307977638
          ],
          [
            -1.7208456881689926e-15,
            -8.326672684688674e-16,
            -2.609024107869118e-15
          ]
        ]
      },
      "reflected": {
        "reached": true,
        "construction": "reflect_displacements_about_reconstructed_parent",
        "energies_eV": [
          -246.20667094994658,
          -246.20657405021737,
          -246.20628347319635,
          -246.20579957937096,
          -246.20512297267086,
          -246.20425485002744,
          -246.203196873077,
          -246.20195076757975,
          -246.20051826932462
        ],
        "cartesian_polarizations_e_A2": [
          [
            -1.9935073987505378e-17,
            3.4996507389858e-18,
            -1.982111911312779e-17
          ],
          [
            -6.045012849900675e-17,
            -2.241155645655931e-18,
            5.663156021074125e-05
          ],
          [
            -1.8005260643595943e-17,
            -3.306566560283135e-17,
            0.00011322857927504217
          ],
          [
            -8.561322600946715e-19,
            -6.102839219709227e-18,
            0.00016975677823631918
          ],
          [
            4.48822754330953e-18,
            1.4136520226445103e-17,
            0.00022618240830998433
          ],
          [
            3.588812086964643e-17,
            2.348041530294906e-17,
            0.0002824726050209707
          ],
          [
            6.38028522232192e-18,
            -5.396013208386972e-18,
            0.00033859558370509497
          ],
          [
            3.4276046343392977e-18,
            -2.017040081090338e-18,
            0.0003945207842378834
          ],
          [
            -4.1473408772325794e-17,
            5.533930478888876e-18,
            0.0004502191267995651
          ]
        ],
        "raw_reduced_polarization": [
          [
            -1.4227966566695578e-15,
            1.3388754004407747e-16,
            -1.1760096642893714e-15
          ],
          [
            -4.314417933815494e-15,
            -8.574078919078854e-17,
            0.003360015230800342
          ],
          [
            -1.2850629329105403e-15,
            -1.265006412830249e-15,
            0.006717981095881341
          ],
          [
            -6.110346608661275e-17,
            -2.3347876441183953e-16,
            0.010071863785547693
          ],
          [
            3.2033164998511895e-16,
            5.408265164342046e-16,
            0.013419660945814897
          ],
          [
            2.5613899612055376e-15,
            8.98299652906569e-16,
            0.016759422689793625
          ],
          [
            4.553706943153308e-16,
            -2.0643743859012928e-16,
            0.020089263197009138
          ],
          [
            2.446333741815875e-16,
            -7.716671027170968e-17,
            0.02340736930032804
          ],
          [
            -2.9600204834423683e-15,
            2.1171379484802397e-16,
            0.026712015660787833
          ]
        ],
        "unwrapped_reduced_polarization": [
          [
            -1.4227966566695578e-15,
            1.3388754004407747e-16,
            -1.1760096642893714e-15
          ],
          [
            -4.314417933815494e-15,
            -8.574078919078852e-17,
            0.003360015230800342
          ],
          [
            -1.28506293291054e-15,
            -1.265006412830249e-15,
            0.006717981095881341
          ],
          [
            -6.110346608661282e-17,
            -2.3347876441183953e-16,
            0.010071863785547693
          ],
          [
            3.2033164998511895e-16,
            5.408265164342046e-16,
            0.013419660945814897
          ],
          [
            2.5613899612055376e-15,
            8.98299652906569e-16,
            0.016759422689793625
          ],
          [
            4.553706943153307e-16,
            -2.0643743859012938e-16,
            0.020089263197009138
          ],
          [
            2.446333741815875e-16,
            -7.716671027170968e-17,
            0.02340736930032804
          ],
          [
            -2.9600204834423683e-15,
            2.11713794848024e-16,
            0.026712015660787833
          ]
        ],
        "gauge_integer_shift": [
          0,
          0,
          0
        ],
        "expected_opposite_endpoint_reduced_polarization": [
          -3.733438587170992e-15,
          -8.67301059891438e-16,
          0.026712015660781827
        ],
        "actual_opposite_endpoint_branch_residual": 6.150596085584845e-15
      },
      "pnp_branch": {
        "construction": "incoming_path_concatenated_with_parent_reflection",
        "reduced_polarization": [
          [
            3.4112585592979464e-16,
            -8.396001895374908e-16,
            -0.026712015660787087
          ],
          [
            1.766622103952075e-15,
            -8.356429223440698e-16,
            -0.02340736930032789
          ],
          [
            -3.1013577023962975e-15,
            3.488990575532856e-16,
            -0.020089263197007937
          ],
          [
            -6.635502129086306e-16,
            -1.0935248344486722e-15,
            -0.016759422689792226
          ],
          [
            -2.795642678051275e-15,
            -6.859263135263083e-17,
            -0.013419660945817343
          ],
          [
            -5.259047130252525e-16,
            1.3322799551184063e-16,
            -0.010071863785552264
          ],
          [
            -4.220788982983676e-15,
            -1.3652571817302482e-16,
            -0.006717981095882061
          ],
          [
            -3.4808087641746843e-15,
            2.849232379263126e-16,
            -0.003360015230797757
          ],
          [
            -1.6961563656205985e-15,
            -8.534506247144644e-16,
            -2.6304300953774632e-15
          ],
          [
            -4.314417933815494e-15,
            -8.574078919078854e-17,
            0.003360015230800342
          ],
          [
            -1.2850629329105403e-15,
            -1.265006412830249e-15,
            0.006717981095881341
          ],
          [
            -6.110346608661275e-17,
            -2.3347876441183953e-16,
            0.010071863785547693
          ],
          [
            3.2033164998511895e-16,
            5.408265164342046e-16,
            0.013419660945814897
          ],
          [
            2.5613899612055376e-15,
            8.98299652906569e-16,
            0.016759422689793625
          ],
          [
            4.553706943153308e-16,
            -2.0643743859012928e-16,
            0.020089263197009138
          ],
          [
            2.446333741815875e-16,
            -7.716671027170968e-17,
            0.02340736930032804
          ],
          [
            -2.9600204834423683e-15,
            2.1171379484802397e-16,
            0.026712015660787833
          ]
        ],
        "unwrapped_reduced_polarization": [
          [
            3.4112585592979464e-16,
            -8.396001895374908e-16,
            -0.026712015660787087
          ],
          [
            1.766622103952075e-15,
            -8.356429223440698e-16,
            -0.02340736930032789
          ],
          [
            -3.1013577023962975e-15,
            3.4889905755328556e-16,
            -0.020089263197007937
          ],
          [
            -6.635502129086306e-16,
            -1.0935248344486722e-15,
            -0.016759422689792226
          ],
          [
            -2.795642678051275e-15,
            -6.859263135263092e-17,
            -0.013419660945817343
          ],
          [
            -5.259047130252524e-16,
            1.3322799551184063e-16,
            -0.010071863785552264
          ],
          [
            -4.220788982983676e-15,
            -1.3652571817302482e-16,
            -0.006717981095882061
          ],
          [
            -3.4808087641746843e-15,
            2.849232379263126e-16,
            -0.003360015230797757
          ],
          [
            -1.6961563656205986e-15,
            -8.534506247144645e-16,
            -2.6302744704498338e-15
          ],
          [
            -4.314417933815494e-15,
            -8.57407891907885e-17,
            0.003360015230800342
          ],
          [
            -1.28506293291054e-15,
            -1.265006412830249e-15,
            0.006717981095881341
          ],
          [
            -6.110346608661282e-17,
            -2.3347876441183953e-16,
            0.010071863785547693
          ],
          [
            3.2033164998511895e-16,
            5.408265164342046e-16,
            0.013419660945814897
          ],
          [
            2.5613899612055376e-15,
            8.98299652906569e-16,
            0.016759422689793625
          ],
          [
            4.553706943153307e-16,
            -2.0643743859012938e-16,
            0.020089263197009138
          ],
          [
            2.446333741815875e-16,
            -7.716671027170968e-17,
            0.02340736930032804
          ],
          [
            -2.9600204834423683e-15,
            2.11713794848024e-16,
            0.026712015660787833
          ]
        ],
        "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": [
          [
            3.3306690738754696e-16,
            -8.326672684688674e-16,
            -0.02671201566078707
          ],
          [
            1.7763568394002505e-15,
            -8.326672684688674e-16,
            -0.023407369300327885
          ],
          [
            -3.1086244689504383e-15,
            3.3306690738754696e-16,
            -0.020089263197007934
          ],
          [
            -6.661338147750939e-16,
            -1.1102230246251565e-15,
            -0.016759422689792247
          ],
          [
            -2.7755575615628914e-15,
            -5.551115123125783e-17,
            -0.013419660945817369
          ],
          [
            -4.996003610813204e-16,
            1.1102230246251565e-16,
            -0.010071863785552249
          ],
          [
            -4.218847493575595e-15,
            -1.1102230246251565e-16,
            -0.006717981095882064
          ],
          [
            -3.497202527569243e-15,
            3.3306690738754696e-16,
            -0.0033600152307977638
          ],
          [
            -1.7208456881689926e-15,
            -8.326672684688674e-16,
            -2.609024107869118e-15
          ],
          [
            -4.3298697960381105e-15,
            -1.1102230246251565e-16,
            0.0033600152308003173
          ],
          [
            -1.27675647831893e-15,
            -1.27675647831893e-15,
            0.006717981095881287
          ],
          [
            -5.551115123125783e-17,
            -2.220446049250313e-16,
            0.010071863785547697
          ],
          [
            3.3306690738754696e-16,
            5.551115123125783e-16,
            0.013419660945814926
          ],
          [
            2.55351295663786e-15,
            8.881784197001252e-16,
            0.01675942268979358
          ],
          [
            4.440892098500626e-16,
            -2.220446049250313e-16,
            0.0200892631970091
          ],
          [
            2.220446049250313e-16,
            -5.551115123125783e-17,
            0.02340736930032805
          ],
          [
            -2.942091015256665e-15,
            2.220446049250313e-16,
            0.026712015660787847
          ]
        ]
      },
      "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": [
              1.4636376871550856e-15,
              -6.7009724475262425e-16,
              -0.02671201566078685
            ],
            "branch_aligned_reduced_polarization": [
              1.4636376871550856e-15,
              -6.7009724475262425e-16,
              -0.026712015660786848
            ],
            "target_residual": 0.47328798433921315,
            "energy_eV": -246.2005182693247,
            "max_atomic_step_A": 0.12,
            "max_log_strain_component": 0.0009881665908705447,
            "step_scale": 0.9516106474148861,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 0.11819268475247496,
            "cell_principal_stretches": [
              1.0009886549883356,
              0.9999914522381345,
              0.9999679940691837
            ],
            "cell_volume_ratio": 1.0009480614758928,
            "cell_rmsd_from_input_A": 0.0038400563114608425
          },
          {
            "iteration": 1,
            "reduced_polarization": [
              -1.1818847623712474e-14,
              -2.053974554301479e-15,
              -0.47588932190466715
            ],
            "branch_aligned_reduced_polarization": [
              -1.1818847623712474e-14,
              -2.053974554301479e-15,
              -0.47588932190466715
            ],
            "target_residual": 0.02411067809533285,
            "energy_eV": -243.3512518713425,
            "max_atomic_step_A": 0.005683438006791767,
            "max_log_strain_component": 4.7627821646706195e-05,
            "step_scale": 1.0,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 0.11819268475247496,
            "cell_principal_stretches": [
              1.0010363310328099,
              0.9999910402534979,
              0.9999664514677559
            ],
            "cell_volume_ratio": 1.0009937790023131,
            "cell_rmsd_from_input_A": 0.004025330578858951
          },
          {
            "iteration": 2,
            "reduced_polarization": [
              -7.265813096365766e-16,
              2.1022107699238723e-15,
              -0.5001144137516124
            ],
            "branch_aligned_reduced_polarization": [
              -7.265813096365766e-16,
              2.1022107699238723e-15,
              -0.5001144137516124
            ],
            "target_residual": 0.00011441375161236333,
            "energy_eV": -243.1141269577929
          }
        ],
        "iterations": 2
      },
      "parent": {
        "candidate_id": "bec_projection_01",
        "source": "MACEField_BEC_backprojection",
        "spacegroup": "Ima2",
        "spacegroup_number": 46,
        "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": 0.00011441375161236333,
        "parent_symmetrization_rmsd_A": 0.10216967740190698,
        "parent_cell_rmsd_A": 0.004025330578858951,
        "energy_eV": -243.1141269577929,
        "reduced_polarization": [
          -7.265813096365766e-16,
          2.1022107699238723e-15,
          -0.5001144137516124
        ],
        "cartesian_polarization_e_A2": [
          9.824407610624181e-17,
          3.613289607571138e-16,
          -0.008429564023451068
        ],
        "ranking_score": 0.6034048375498464
      },
      "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": [
              1.4636376871550856e-15,
              -6.7009724475262425e-16,
              -0.02671201566078685
            ],
            "branch_aligned_reduced_polarization": [
              1.4432899320127035e-15,
              -6.7009724475262425e-16,
              -0.02671201566078685
            ],
            "target_residual": 0.5007130233783227,
            "energy_eV": -246.2005182693247,
            "max_atomic_step_A": 0.08019311926728105,
            "max_log_strain_component": 0.00037990860269647734,
            "step_scale": 1.0,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 0.11819268475247496,
            "cell_principal_stretches": [
              1.0003520684216045,
              1.0000018982775607,
              0.9995899772390324
            ],
            "cell_volume_ratio": 0.9999437994718426,
            "cell_rmsd_from_input_A": 0.0017434025180202858
          },
          {
            "iteration": 1,
            "reduced_polarization": [
              0.4941776596424964,
              1.8319619286356118e-15,
              -0.00010132205003689512
            ],
            "branch_aligned_reduced_polarization": [
              0.4941776596424964,
              1.8319619286356118e-15,
              -0.00010132205003689512
            ],
            "target_residual": 0.0058232219085690914,
            "energy_eV": -245.07536958505668,
            "max_atomic_step_A": 0.0009638356530602617,
            "max_log_strain_component": 4.73192685029751e-06,
            "step_scale": 1.0,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 0.11819268475247496,
            "cell_principal_stretches": [
              1.0003566850664412,
              1.0000019055666445,
              0.9995851411290805
            ],
            "cell_volume_ratio": 0.9999435836770642,
            "cell_rmsd_from_input_A": 0.001764861955438428
          },
          {
            "iteration": 2,
            "reduced_polarization": [
              0.4999976763394026,
              1.0832436682872693e-15,
              -8.000189018389285e-08
            ],
            "branch_aligned_reduced_polarization": [
              0.4999976763394026,
              1.0832436682872693e-15,
              -8.000189018389285e-08
            ],
            "target_residual": 2.325037392011885e-06,
            "energy_eV": -245.04787229946817
          }
        ],
        "iterations": 2
      },
      "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": 2.325037392011885e-06,
        "parent_symmetrization_rmsd_A": 0.05569551400256592,
        "parent_cell_rmsd_A": 0.001764861955438428,
        "energy_eV": -245.04787229946817,
        "reduced_polarization": [
          0.4999976763394026,
          1.0832436682872693e-15,
          -8.000189018389285e-08
        ],
        "cartesian_polarization_e_A2": [
          0.007005961670660128,
          2.4481696681393854e-17,
          2.693349004807756e-06
        ],
        "ranking_score": 0.5561413795662096
      },
      "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": [
              1.4636376871550856e-15,
              -6.7009724475262425e-16,
              -0.02671201566078685
            ],
            "branch_aligned_reduced_polarization": [
              1.4636376871550856e-15,
              -6.661338147750939e-16,
              -0.02671201566078685
            ],
            "target_residual": 0.5007130233783235,
            "energy_eV": -246.2005182693247,
            "max_atomic_step_A": 0.12,
            "max_log_strain_component": 0.0012067528237017743,
            "step_scale": 0.9582963939777017,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 0.11819268475247496,
            "cell_principal_stretches": [
              1.001180625358099,
              1.0000004858208154,
              0.9987664883360788
            ],
            "cell_volume_ratio": 0.9999461431734423,
            "cell_rmsd_from_input_A": 0.010245460362263974
          },
          {
            "iteration": 1,
            "reduced_polarization": [
              -1.2915392183176456e-14,
              -0.46886888674217003,
              -0.0017930324612124321
            ],
            "branch_aligned_reduced_polarization": [
              -1.2915392183176456e-14,
              -0.46886888674217003,
              -0.0017930324612124321
            ],
            "target_residual": 0.03118270639439108,
            "energy_eV": -240.89363412073382,
            "max_atomic_step_A": 0.008289594979246164,
            "max_log_strain_component": 8.220126874987313e-05,
            "step_scale": 1.0,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 0.11819268475247496,
            "cell_principal_stretches": [
              1.0012613575477018,
              1.000000514149961,
              0.9986827925700903
            ],
            "cell_volume_ratio": 0.9999430027686498,
            "cell_rmsd_from_input_A": 0.010943274975788668
          },
          {
            "iteration": 2,
            "reduced_polarization": [
              -9.055483367221084e-16,
              -0.5000029871241941,
              -4.240258894554443e-06
            ],
            "branch_aligned_reduced_polarization": [
              -9.055483367221084e-16,
              -0.5000029871241941,
              -4.240258894554443e-06
            ],
            "target_residual": 5.186781896694824e-06,
            "energy_eV": -240.09947087641328
          }
        ],
        "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": 5.186781896694824e-06,
        "parent_symmetrization_rmsd_A": 0.08227488377026891,
        "parent_cell_rmsd_A": 0.010943274975788668,
        "energy_eV": -240.09947087641328,
        "reduced_polarization": [
          -9.055483367221084e-16,
          -0.5000029871241941,
          -4.240258894554443e-06
        ],
        "cartesian_polarization_e_A2": [
          8.442315488791578e-17,
          -0.013070225946544441,
          -1.6917866937541223e-05
        ],
        "ranking_score": 0.5850210760780095
      },
      "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": [
              1.4636376871550856e-15,
              -6.7009724475262425e-16,
              -0.02671201566078685
            ],
            "branch_aligned_reduced_polarization": [
              1.4432899320127035e-15,
              -6.7009724475262425e-16,
              -0.026712015660786848
            ],
            "target_residual": 0.6884776801900507,
            "energy_eV": -246.2005182693247,
            "max_atomic_step_A": 0.11999999999999998,
            "max_log_strain_component": 0.0008347858387394431,
            "step_scale": 0.8039040175984159,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 0.11819268475247496,
            "cell_principal_stretches": [
              1.000934333216615,
              0.9999729618827298,
              0.9998936734623115
            ],
            "cell_volume_ratio": 1.0008008468321847,
            "cell_rmsd_from_input_A": 0.0035294690183432205
          },
          {
            "iteration": 1,
            "reduced_polarization": [
              0.39910395882042504,
              4.610968040477018e-15,
              -0.40478306991655916
            ],
            "branch_aligned_reduced_polarization": [
              0.39910395882042504,
              4.610968040477018e-15,
              -0.40478306991655916
            ],
            "target_residual": 0.13873094427785512,
            "energy_eV": -243.38662797588043,
            "max_atomic_step_A": 0.02686742972457016,
            "max_log_strain_component": 0.00019385431218683368,
            "step_scale": 1.0,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 0.11819268475247496,
            "cell_principal_stretches": [
              1.001157725669252,
              0.9999666831845683,
              0.9998626956552029
            ],
            "cell_volume_ratio": 1.0009869115563663,
            "cell_rmsd_from_input_A": 0.004369319766057738
          },
          {
            "iteration": 2,
            "reduced_polarization": [
              0.49961736564129394,
              -9.541702532306742e-16,
              -0.5011011264595308
            ],
            "branch_aligned_reduced_polarization": [
              0.49961736564129394,
              -9.541702532306742e-16,
              -0.5011011264595308
            ],
            "target_residual": 0.0011657137437386294,
            "energy_eV": -241.9106809068415,
            "max_atomic_step_A": 0.0002559043380828379,
            "max_log_strain_component": 2.1122115617550276e-06,
            "step_scale": 1.0,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 0.11819268475247496,
            "cell_principal_stretches": [
              1.001155992545108,
              0.9999667515962404,
              0.9998623328859709
            ],
            "cell_volume_ratio": 1.0009848840327582,
            "cell_rmsd_from_input_A": 0.0043623224496816765
          },
          {
            "iteration": 3,
            "reduced_polarization": [
              0.5000003822237207,
              1.227944790930918e-16,
              -0.49999867513350504
            ],
            "branch_aligned_reduced_polarization": [
              0.5000003822237207,
              1.227944790930918e-16,
              -0.49999867513350504
            ],
            "target_residual": 1.378900359744401e-06,
            "energy_eV": -241.92022212444945
          }
        ],
        "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": 1.378900359744401e-06,
        "parent_symmetrization_rmsd_A": 0.11491857994393156,
        "parent_cell_rmsd_A": 0.0043623224496816765,
        "energy_eV": -241.92022212444945,
        "reduced_polarization": [
          0.5000003822237207,
          1.227944790930918e-16,
          -0.49999867513350504
        ],
        "cartesian_polarization_e_A2": [
          0.006995383948613977,
          3.268695560004536e-16,
          -0.008424899200210107
        ],
        "ranking_score": 0.6160119183570715
      },
      "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": [
              1.4636376871550856e-15,
              -6.7009724475262425e-16,
              -0.02671201566078685
            ],
            "branch_aligned_reduced_polarization": [
              1.4636376871550856e-15,
              -6.661338147750939e-16,
              -0.026712015660786848
            ],
            "target_residual": 0.6884776801900514,
            "energy_eV": -246.2005182693247,
            "max_atomic_step_A": 0.12,
            "max_log_strain_component": 0.0008509935598049445,
            "step_scale": 0.6757838421149643,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 0.11819268475247496,
            "cell_principal_stretches": [
              1.0012651882999097,
              0.99999392982148,
              0.9994147973324118
            ],
            "cell_volume_ratio": 1.0006731709390937,
            "cell_rmsd_from_input_A": 0.0077265497623205896
          },
          {
            "iteration": 1,
            "reduced_polarization": [
              -3.703140528150165e-14,
              -0.33452816793043455,
              -0.3524619802534291
            ],
            "branch_aligned_reduced_polarization": [
              -3.703140528150165e-14,
              -0.33452816793043455,
              -0.3524619802534291
            ],
            "target_residual": 0.22169437178060702,
            "energy_eV": -242.24113596364415,
            "max_atomic_step_A": 0.050980329715492184,
            "max_log_strain_component": 0.00040477508644567984,
            "step_scale": 1.0,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 0.11819268475247496,
            "cell_principal_stretches": [
              1.001819071228471,
              0.9999916579031397,
              0.9991161263083184
            ],
            "cell_volume_ratio": 1.0009252398226316,
            "cell_rmsd_from_input_A": 0.01131046992371901
          },
          {
            "iteration": 2,
            "reduced_polarization": [
              -4.693539454043477e-15,
              -0.49785666435443443,
              -0.5074876808518568
            ],
            "branch_aligned_reduced_polarization": [
              -4.693539454043477e-15,
              -0.49785666435443443,
              -0.5074876808518568
            ],
            "target_residual": 0.00778840498618395,
            "energy_eV": -237.86678789062773,
            "max_atomic_step_A": 0.001972081197170529,
            "max_log_strain_component": 1.3552979677999643e-05,
            "step_scale": 1.0,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 0.11819268475247496,
            "cell_principal_stretches": [
              1.001816840604338,
              0.9999917751376013,
              0.9991052485645509
            ],
            "cell_volume_ratio": 1.0009122311150653,
            "cell_rmsd_from_input_A": 0.011352382120221377
          },
          {
            "iteration": 3,
            "reduced_polarization": [
              -5.546703054504272e-15,
              -0.5000012989394568,
              -0.49999881312961597
            ],
            "branch_aligned_reduced_polarization": [
              -5.546703054504272e-15,
              -0.5000012989394568,
              -0.49999881312961597
            ],
            "target_residual": 1.7595184059415241e-06,
            "energy_eV": -237.8759254741254
          }
        ],
        "iterations": 3
      },
      "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": 1.7595184059415241e-06,
        "parent_symmetrization_rmsd_A": 0.12337378125565751,
        "parent_cell_rmsd_A": 0.011352382120221377,
        "energy_eV": -237.8759254741254,
        "reduced_polarization": [
          -5.546703054504272e-15,
          -0.5000012989394568,
          -0.49999881312961597
        ],
        "cartesian_polarization_e_A2": [
          4.902210327230416e-16,
          -0.013067738177377868,
          -0.008444093686828167
        ],
        "ranking_score": 0.6262153958225247
      },
      "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": [
              1.4636376871550856e-15,
              -6.7009724475262425e-16,
              -0.02671201566078685
            ],
            "branch_aligned_reduced_polarization": [
              1.4432899320127035e-15,
              -6.661338147750939e-16,
              -0.02671201566078685
            ],
            "target_residual": 0.7076111444717784,
            "energy_eV": -246.2005182693247,
            "max_atomic_step_A": 0.12000000000000001,
            "max_log_strain_component": 0.0008647008735827524,
            "step_scale": 0.6866689787363606,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 0.11819268475247496,
            "cell_principal_stretches": [
              1.000884313907854,
              1.0000004278129961,
              0.9990774825917709
            ],
            "cell_volume_ratio": 0.9999614085009533,
            "cell_rmsd_from_input_A": 0.0074368593651628415
          },
          {
            "iteration": 1,
            "reduced_polarization": [
              0.3339626051737512,
              -0.33782297188407706,
              -0.009072857329780963
            ],
            "branch_aligned_reduced_polarization": [
              0.3339626051737512,
              -0.33782297188407706,
              -0.009072857329780963
            ],
            "target_residual": 0.23227596016231866,
            "energy_eV": -243.0542986118652,
            "max_atomic_step_A": 0.0542087413734308,
            "max_log_strain_component": 0.0004319521328901445,
            "step_scale": 1.0,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 0.11819268475247496,
            "cell_principal_stretches": [
              1.001330723063544,
              1.000000639932094,
              0.9986134364498563
            ],
            "cell_volume_ratio": 0.9999429542764846,
            "cell_rmsd_from_input_A": 0.011161527298150523
          },
          {
            "iteration": 2,
            "reduced_polarization": [
              0.49485572071434836,
              -0.49858510224233016,
              0.0005927977859293498
            ],
            "branch_aligned_reduced_polarization": [
              0.49485572071434836,
              -0.49858510224233016,
              0.0005927977859293498
            ],
            "target_residual": 0.005368142532426506,
            "energy_eV": -238.79058164477036,
            "max_atomic_step_A": 0.0010519645510874802,
            "max_log_strain_component": 4.674102500439626e-06,
            "step_scale": 1.0,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 0.11819268475247496,
            "cell_principal_stretches": [
              1.0013367634006005,
              1.0000006303919942,
              0.9986084351827579
            ],
            "cell_volume_ratio": 0.9999439687467159,
            "cell_rmsd_from_input_A": 0.011201254520728725
          },
          {
            "iteration": 3,
            "reduced_polarization": [
              0.49999691389301526,
              -0.4999991409124903,
              -3.0301026916439734e-06
            ],
            "branch_aligned_reduced_polarization": [
              0.49999691389301526,
              -0.4999991409124903,
              -3.0301026916439734e-06
            ],
            "target_residual": 4.409490899465222e-06,
            "energy_eV": -238.72102537296058
          }
        ],
        "iterations": 3
      },
      "parent": {
        "candidate_id": "bec_projection_06",
        "source": "MACEField_BEC_backprojection",
        "spacegroup": "P1",
        "spacegroup_number": 1,
        "pointgroup": "1",
        "has_inversion": false,
        "is_polar_point_group": true,
        "nonpolar_parent_hypothesis": false,
        "symmetry_tolerance_A": null,
        "target_reduced_polarization": [
          0.5,
          -0.5,
          0.0
        ],
        "formal_class": [
          0.5,
          0.5,
          0.0
        ],
        "target_residual": 4.409490899465222e-06,
        "parent_symmetrization_rmsd_A": 0.1006680479447973,
        "parent_cell_rmsd_A": 0.011201254520728725,
        "energy_eV": -238.72102537296058,
        "reduced_polarization": [
          0.49999691389301526,
          -0.4999991409124903,
          -3.0301026916439734e-06
        ],
        "cartesian_polarization_e_A2": [
          0.0070059447286611185,
          -0.013070110721227832,
          -1.4186757957238304e-05
        ],
        "ranking_score": 0.6034771805567785
      },
      "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": [
              1.4636376871550856e-15,
              -6.7009724475262425e-16,
              -0.02671201566078685
            ],
            "branch_aligned_reduced_polarization": [
              1.4432899320127035e-15,
              -6.661338147750939e-16,
              -0.026712015660786848
            ],
            "target_residual": 0.8508827863577175,
            "energy_eV": -246.2005182693247,
            "max_atomic_step_A": 0.12,
            "max_log_strain_component": 0.0007015894161199551,
            "step_scale": 0.5571402812142048,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 0.11819268475247496,
            "cell_principal_stretches": [
              1.0010721748124596,
              0.9999938652703957,
              0.9994894640670849
            ],
            "cell_volume_ratio": 1.000554953324028,
            "cell_rmsd_from_input_A": 0.006441712599157915
          },
          {
            "iteration": 1,
            "reduced_polarization": [
              0.2732960897576353,
              -0.27609222652776333,
              -0.2935240744357146
            ],
            "branch_aligned_reduced_polarization": [
              0.2732960897576353,
              -0.27609222652776333,
              -0.2935240744357146
            ],
            "target_residual": 0.3796862675658693,
            "energy_eV": -243.17858055366875,
            "max_atomic_step_A": 0.08414372057783177,
            "max_log_strain_component": 0.0005558135339856039,
            "step_scale": 1.0,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 0.11819268475247496,
            "cell_principal_stretches": [
              1.0018812838176854,
              0.9999895352382101,
              0.9990580971427593
            ],
            "cell_volume_ratio": 1.000927134400197,
            "cell_rmsd_from_input_A": 0.011473594837417654
          },
          {
            "iteration": 2,
            "reduced_polarization": [
              0.4905352096739928,
              -0.493895100863467,
              -0.512127291623225
            ],
            "branch_aligned_reduced_polarization": [
              0.4905352096739928,
              -0.493895100863467,
              -0.512127291623225
            ],
            "target_residual": 0.016550626921578073,
            "energy_eV": -236.42703032176104,
            "max_atomic_step_A": 0.0037118833564754664,
            "max_log_strain_component": 2.2295986071561897e-05,
            "step_scale": 1.0,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 0.11819268475247496,
            "cell_principal_stretches": [
              1.0018874524379437,
              0.9999897541769532,
              0.9990303667513518
            ],
            "cell_volume_ratio": 1.0009057338445473,
            "cell_rmsd_from_input_A": 0.011615354722151751
          },
          {
            "iteration": 3,
            "reduced_polarization": [
              0.4999877408443399,
              -0.5000026020314859,
              -0.5000085576166678
            ],
            "branch_aligned_reduced_polarization": [
              0.4999877408443399,
              -0.5000026020314859,
              -0.5000085576166678
            ],
            "target_residual": 1.5175317735931813e-05,
            "energy_eV": -236.31272196534428
          }
        ],
        "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": 1.5175317735931813e-05,
        "parent_symmetrization_rmsd_A": 0.1362054110129262,
        "parent_cell_rmsd_A": 0.011615354722151751,
        "energy_eV": -236.31272196534428,
        "reduced_polarization": [
          0.4999877408443399,
          -0.5000026020314859,
          -0.5000085576166678
        ],
        "cartesian_polarization_e_A2": [
          0.006995560170051361,
          -0.013067983655282686,
          -0.008441571622520265
        ],
        "ranking_score": 0.639139600328936
      },
      "branch_status": "awaiting_branch_sampling"
    }
  ],
  "sampled_polarization_branches": [
    {
      "orbit_id": 0,
      "candidate_id": "inversion_parent_endpoint_00",
      "formal_class": [
        0.0,
        0.0,
        0.0
      ],
      "construction": "MACEField-BEC-parent plus variable-cell P-N-P path and symmetric log-strain continuation beyond both polar endpoints",
      "geometry_diagnostics": {
        "collision_aware": false,
        "permutations_tested": 1,
        "selected_order": [
          0,
          1,
          2,
          3,
          4,
          5,
          6,
          7,
          8,
          9,
          10,
          11,
          12,
          13,
          14,
          15,
          16,
          17,
          18,
          19,
          20,
          21,
          22,
          23,
          24,
          25,
          26,
          27,
          28,
          29,
          30,
          31,
          32,
          33,
          34,
          35,
          36,
          37,
          38,
          39
        ],
        "endpoint_rmsd_A": 0.0477586508086499,
        "minimum_distance_A_by_image": [
          0.9943030991780639,
          0.9943886651886726,
          0.9944746097589596,
          0.9945609327907864,
          0.9946476341856149,
          0.9947347138445122,
          0.9948221716681448,
          0.994910007556787,
          0.9949982214103116
        ],
        "minimum_distance_A": 0.9943030991780639,
        "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": [
          402.496011045199,
          402.496011045199,
          402.496011045199,
          402.496011045199,
          402.496011045199,
          402.496011045199,
          402.496011045199,
          402.496011045199,
          402.496011045199
        ],
        "cell_deformation_log_strain_norm": 0.0
      },
      "parent_reduced_polarization": [
        -1.6961563656205985e-15,
        -8.534506247144644e-16,
        -2.6304300953774632e-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": [
          -246.20051826932468,
          -246.2019507675797,
          -246.203196873077,
          -246.2042548500275,
          -246.20512297267092,
          -246.205799579371,
          -246.2062834731964,
          -246.20657405021734,
          -246.20667094994658
        ],
        "cartesian_polarizations_e_A2": [
          [
            4.779579109308331e-18,
            -2.1946085668615386e-17,
            -0.0004502191267995526
          ],
          [
            2.475247758360898e-17,
            -2.1842647715738958e-17,
            -0.00039452078423788084
          ],
          [
            -4.345371137131426e-17,
            9.119779511938365e-18,
            -0.00033859558370507475
          ],
          [
            -9.297127967479235e-18,
            -2.858335431151949e-17,
            -0.00028247260502094716
          ],
          [
            -3.917028014392035e-17,
            -1.792924516524745e-18,
            -0.00022618240831002556
          ],
          [
            -7.368550745035293e-18,
            3.482411080173062e-18,
            -0.00016975677823639622
          ],
          [
            -5.913827549917342e-17,
            -3.568609374236752e-18,
            -0.0001132285792750543
          ],
          [
            -4.877027221346307e-17,
            7.447532607102786e-18,
            -5.663156021069768e-05
          ],
          [
            -2.376516875023686e-17,
            -2.2308118503682884e-17,
            -4.4334727700335963e-17
          ]
        ],
        "raw_reduced_polarization": [
          [
            3.4112585592979464e-16,
            -8.396001895374908e-16,
            -0.026712015660787087
          ],
          [
            1.766622103952075e-15,
            -8.356429223440698e-16,
            -0.02340736930032789
          ],
          [
            -3.1013577023962975e-15,
            3.488990575532856e-16,
            -0.020089263197007937
          ],
          [
            -6.635502129086306e-16,
            -1.0935248344486722e-15,
            -0.016759422689792226
          ],
          [
            -2.795642678051275e-15,
            -6.859263135263083e-17,
            -0.013419660945817343
          ],
          [
            -5.259047130252525e-16,
            1.3322799551184063e-16,
            -0.010071863785552264
          ],
          [
            -4.220788982983676e-15,
            -1.3652571817302482e-16,
            -0.006717981095882061
          ],
          [
            -3.4808087641746843e-15,
            2.849232379263126e-16,
            -0.003360015230797757
          ],
          [
            -1.6961563656205985e-15,
            -8.534506247144644e-16,
            -2.6304300953774632e-15
          ]
        ],
        "unwrapped_reduced_polarization": [
          [
            3.4112585592979464e-16,
            -8.396001895374908e-16,
            -0.026712015660787087
          ],
          [
            1.766622103952075e-15,
            -8.356429223440698e-16,
            -0.02340736930032789
          ],
          [
            -3.1013577023962975e-15,
            3.4889905755328556e-16,
            -0.020089263197007937
          ],
          [
            -6.635502129086306e-16,
            -1.0935248344486722e-15,
            -0.016759422689792226
          ],
          [
            -2.795642678051275e-15,
            -6.859263135263092e-17,
            -0.013419660945817343
          ],
          [
            -5.259047130252524e-16,
            1.3322799551184063e-16,
            -0.010071863785552264
          ],
          [
            -4.220788982983676e-15,
            -1.3652571817302482e-16,
            -0.006717981095882061
          ],
          [
            -3.4808087641746843e-15,
            2.849232379263126e-16,
            -0.003360015230797757
          ],
          [
            -1.6961563656205986e-15,
            -8.534506247144645e-16,
            -2.6302744704498338e-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": [
          [
            3.3306690738754696e-16,
            -8.326672684688674e-16,
            -0.02671201566078707
          ],
          [
            1.7763568394002505e-15,
            -8.326672684688674e-16,
            -0.023407369300327885
          ],
          [
            -3.1086244689504383e-15,
            3.3306690738754696e-16,
            -0.020089263197007934
          ],
          [
            -6.661338147750939e-16,
            -1.1102230246251565e-15,
            -0.016759422689792247
          ],
          [
            -2.7755575615628914e-15,
            -5.551115123125783e-17,
            -0.013419660945817369
          ],
          [
            -4.996003610813204e-16,
            1.1102230246251565e-16,
            -0.010071863785552249
          ],
          [
            -4.218847493575595e-15,
            -1.1102230246251565e-16,
            -0.006717981095882064
          ],
          [
            -3.497202527569243e-15,
            3.3306690738754696e-16,
            -0.0033600152307977638
          ],
          [
            -1.7208456881689926e-15,
            -8.326672684688674e-16,
            -2.609024107869118e-15
          ]
        ]
      },
      "reflected": {
        "reached": true,
        "construction": "reflect_displacements_about_reconstructed_parent",
        "energies_eV": [
          -246.20667094994658,
          -246.20657405021737,
          -246.20628347319635,
          -246.20579957937096,
          -246.20512297267086,
          -246.20425485002744,
          -246.203196873077,
          -246.20195076757975,
          -246.20051826932462
        ],
        "cartesian_polarizations_e_A2": [
          [
            -1.9935073987505378e-17,
            3.4996507389858e-18,
            -1.982111911312779e-17
          ],
          [
            -6.045012849900675e-17,
            -2.241155645655931e-18,
            5.663156021074125e-05
          ],
          [
            -1.8005260643595943e-17,
            -3.306566560283135e-17,
            0.00011322857927504217
          ],
          [
            -8.561322600946715e-19,
            -6.102839219709227e-18,
            0.00016975677823631918
          ],
          [
            4.48822754330953e-18,
            1.4136520226445103e-17,
            0.00022618240830998433
          ],
          [
            3.588812086964643e-17,
            2.348041530294906e-17,
            0.0002824726050209707
          ],
          [
            6.38028522232192e-18,
            -5.396013208386972e-18,
            0.00033859558370509497
          ],
          [
            3.4276046343392977e-18,
            -2.017040081090338e-18,
            0.0003945207842378834
          ],
          [
            -4.1473408772325794e-17,
            5.533930478888876e-18,
            0.0004502191267995651
          ]
        ],
        "raw_reduced_polarization": [
          [
            -1.4227966566695578e-15,
            1.3388754004407747e-16,
            -1.1760096642893714e-15
          ],
          [
            -4.314417933815494e-15,
            -8.574078919078854e-17,
            0.003360015230800342
          ],
          [
            -1.2850629329105403e-15,
            -1.265006412830249e-15,
            0.006717981095881341
          ],
          [
            -6.110346608661275e-17,
            -2.3347876441183953e-16,
            0.010071863785547693
          ],
          [
            3.2033164998511895e-16,
            5.408265164342046e-16,
            0.013419660945814897
          ],
          [
            2.5613899612055376e-15,
            8.98299652906569e-16,
            0.016759422689793625
          ],
          [
            4.553706943153308e-16,
            -2.0643743859012928e-16,
            0.020089263197009138
          ],
          [
            2.446333741815875e-16,
            -7.716671027170968e-17,
            0.02340736930032804
          ],
          [
            -2.9600204834423683e-15,
            2.1171379484802397e-16,
            0.026712015660787833
          ]
        ],
        "unwrapped_reduced_polarization": [
          [
            -1.4227966566695578e-15,
            1.3388754004407747e-16,
            -1.1760096642893714e-15
          ],
          [
            -4.314417933815494e-15,
            -8.574078919078852e-17,
            0.003360015230800342
          ],
          [
            -1.28506293291054e-15,
            -1.265006412830249e-15,
            0.006717981095881341
          ],
          [
            -6.110346608661282e-17,
            -2.3347876441183953e-16,
            0.010071863785547693
          ],
          [
            3.2033164998511895e-16,
            5.408265164342046e-16,
            0.013419660945814897
          ],
          [
            2.5613899612055376e-15,
            8.98299652906569e-16,
            0.016759422689793625
          ],
          [
            4.553706943153307e-16,
            -2.0643743859012938e-16,
            0.020089263197009138
          ],
          [
            2.446333741815875e-16,
            -7.716671027170968e-17,
            0.02340736930032804
          ],
          [
            -2.9600204834423683e-15,
            2.11713794848024e-16,
            0.026712015660787833
          ]
        ],
        "gauge_integer_shift": [
          0,
          0,
          0
        ],
        "expected_opposite_endpoint_reduced_polarization": [
          -3.733438587170992e-15,
          -8.67301059891438e-16,
          0.026712015660781827
        ],
        "actual_opposite_endpoint_branch_residual": 6.150596085584845e-15
      },
      "pnp_branch": {
        "construction": "incoming_path_concatenated_with_parent_reflection",
        "reduced_polarization": [
          [
            3.4112585592979464e-16,
            -8.396001895374908e-16,
            -0.026712015660787087
          ],
          [
            1.766622103952075e-15,
            -8.356429223440698e-16,
            -0.02340736930032789
          ],
          [
            -3.1013577023962975e-15,
            3.488990575532856e-16,
            -0.020089263197007937
          ],
          [
            -6.635502129086306e-16,
            -1.0935248344486722e-15,
            -0.016759422689792226
          ],
          [
            -2.795642678051275e-15,
            -6.859263135263083e-17,
            -0.013419660945817343
          ],
          [
            -5.259047130252525e-16,
            1.3322799551184063e-16,
            -0.010071863785552264
          ],
          [
            -4.220788982983676e-15,
            -1.3652571817302482e-16,
            -0.006717981095882061
          ],
          [
            -3.4808087641746843e-15,
            2.849232379263126e-16,
            -0.003360015230797757
          ],
          [
            -1.6961563656205985e-15,
            -8.534506247144644e-16,
            -2.6304300953774632e-15
          ],
          [
            -4.314417933815494e-15,
            -8.574078919078854e-17,
            0.003360015230800342
          ],
          [
            -1.2850629329105403e-15,
            -1.265006412830249e-15,
            0.006717981095881341
          ],
          [
            -6.110346608661275e-17,
            -2.3347876441183953e-16,
            0.010071863785547693
          ],
          [
            3.2033164998511895e-16,
            5.408265164342046e-16,
            0.013419660945814897
          ],
          [
            2.5613899612055376e-15,
            8.98299652906569e-16,
            0.016759422689793625
          ],
          [
            4.553706943153308e-16,
            -2.0643743859012928e-16,
            0.020089263197009138
          ],
          [
            2.446333741815875e-16,
            -7.716671027170968e-17,
            0.02340736930032804
          ],
          [
            -2.9600204834423683e-15,
            2.1171379484802397e-16,
            0.026712015660787833
          ]
        ],
        "unwrapped_reduced_polarization": [
          [
            3.4112585592979464e-16,
            -8.396001895374908e-16,
            -0.026712015660787087
          ],
          [
            1.766622103952075e-15,
            -8.356429223440698e-16,
            -0.02340736930032789
          ],
          [
            -3.1013577023962975e-15,
            3.4889905755328556e-16,
            -0.020089263197007937
          ],
          [
            -6.635502129086306e-16,
            -1.0935248344486722e-15,
            -0.016759422689792226
          ],
          [
            -2.795642678051275e-15,
            -6.859263135263092e-17,
            -0.013419660945817343
          ],
          [
            -5.259047130252524e-16,
            1.3322799551184063e-16,
            -0.010071863785552264
          ],
          [
            -4.220788982983676e-15,
            -1.3652571817302482e-16,
            -0.006717981095882061
          ],
          [
            -3.4808087641746843e-15,
            2.849232379263126e-16,
            -0.003360015230797757
          ],
          [
            -1.6961563656205986e-15,
            -8.534506247144645e-16,
            -2.6302744704498338e-15
          ],
          [
            -4.314417933815494e-15,
            -8.57407891907885e-17,
            0.003360015230800342
          ],
          [
            -1.28506293291054e-15,
            -1.265006412830249e-15,
            0.006717981095881341
          ],
          [
            -6.110346608661282e-17,
            -2.3347876441183953e-16,
            0.010071863785547693
          ],
          [
            3.2033164998511895e-16,
            5.408265164342046e-16,
            0.013419660945814897
          ],
          [
            2.5613899612055376e-15,
            8.98299652906569e-16,
            0.016759422689793625
          ],
          [
            4.553706943153307e-16,
            -2.0643743859012938e-16,
            0.020089263197009138
          ],
          [
            2.446333741815875e-16,
            -7.716671027170968e-17,
            0.02340736930032804
          ],
          [
            -2.9600204834423683e-15,
            2.11713794848024e-16,
            0.026712015660787833
          ]
        ],
        "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": [
          [
            3.3306690738754696e-16,
            -8.326672684688674e-16,
            -0.02671201566078707
          ],
          [
            1.7763568394002505e-15,
            -8.326672684688674e-16,
            -0.023407369300327885
          ],
          [
            -3.1086244689504383e-15,
            3.3306690738754696e-16,
            -0.020089263197007934
          ],
          [
            -6.661338147750939e-16,
            -1.1102230246251565e-15,
            -0.016759422689792247
          ],
          [
            -2.7755575615628914e-15,
            -5.551115123125783e-17,
            -0.013419660945817369
          ],
          [
            -4.996003610813204e-16,
            1.1102230246251565e-16,
            -0.010071863785552249
          ],
          [
            -4.218847493575595e-15,
            -1.1102230246251565e-16,
            -0.006717981095882064
          ],
          [
            -3.497202527569243e-15,
            3.3306690738754696e-16,
            -0.0033600152307977638
          ],
          [
            -1.7208456881689926e-15,
            -8.326672684688674e-16,
            -2.609024107869118e-15
          ],
          [
            -4.3298697960381105e-15,
            -1.1102230246251565e-16,
            0.0033600152308003173
          ],
          [
            -1.27675647831893e-15,
            -1.27675647831893e-15,
            0.006717981095881287
          ],
          [
            -5.551115123125783e-17,
            -2.220446049250313e-16,
            0.010071863785547697
          ],
          [
            3.3306690738754696e-16,
            5.551115123125783e-16,
            0.013419660945814926
          ],
          [
            2.55351295663786e-15,
            8.881784197001252e-16,
            0.01675942268979358
          ],
          [
            4.440892098500626e-16,
            -2.220446049250313e-16,
            0.0200892631970091
          ],
          [
            2.220446049250313e-16,
            -5.551115123125783e-17,
            0.02340736930032805
          ],
          [
            -2.942091015256665e-15,
            2.220446049250313e-16,
            0.026712015660787847
          ]
        ]
      },
      "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": "Imma",
        "spacegroup_number": 74,
        "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": 1.1159375881937921e-15,
        "parent_symmetrization_rmsd_A": 0.0477586508086499,
        "parent_cell_rmsd_A": 0.0,
        "energy_eV": -246.2066709499466,
        "reduced_polarization": [
          -9.316683919422624e-16,
          5.902923563519672e-16,
          -1.6989891768913237e-16
        ],
        "cartesian_polarization_e_A2": [
          -1.3053782659754087e-17,
          1.542949463740045e-17,
          -2.8635705870178556e-18
        ],
        "ranking_score": 0.04775865080865213
      }
    }
  ],
  "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": 20,
      "energy_polarization": 35
    },
    "model_evaluations_for_recovery_and_path_properties": {
      "total": 80,
      "full_response": 45,
      "energy_polarization": 35
    },
    "elapsed_seconds": 1188.5056218089885
  }
}