{
  "schema": "ferrofinder.endpoint_parent_recovery.v4_variable_cell",
  "status": "complete",
  "input_atom_count": 60,
  "input_formula": "Al12F42Na2Rb4",
  "input_spacegroup": "C2",
  "input_pointgroup": "2",
  "input_is_polar_point_group": true,
  "input_energy_eV": -323.79642228336274,
  "input_cartesian_polarization_e_A2": [
    -2.5699272812811592e-11,
    0.0007890566163449523,
    -9.081849202275064e-11
  ],
  "input_reduced_polarization": [
    -4.335464397057429e-09,
    0.09160314318502097,
    -7.842917015458688e-09
  ],
  "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,
        0.5,
        0.0
      ],
      "target_reduced_polarization": [
        0.0,
        0.5,
        0.0
      ]
    },
    {
      "orbit_id": 2,
      "representative_formal_class": [
        0.0,
        0.0,
        0.5
      ],
      "target_reduced_polarization": [
        0.0,
        0.0,
        -0.5
      ]
    },
    {
      "orbit_id": 3,
      "representative_formal_class": [
        0.5,
        0.0,
        0.0
      ],
      "target_reduced_polarization": [
        -0.5,
        0.0,
        0.0
      ]
    },
    {
      "orbit_id": 4,
      "representative_formal_class": [
        0.0,
        0.5,
        0.5
      ],
      "target_reduced_polarization": [
        0.0,
        0.5,
        -0.5
      ]
    },
    {
      "orbit_id": 5,
      "representative_formal_class": [
        0.5,
        0.5,
        0.0
      ],
      "target_reduced_polarization": [
        -0.5,
        0.5,
        0.0
      ]
    },
    {
      "orbit_id": 6,
      "representative_formal_class": [
        0.5,
        0.0,
        0.5
      ],
      "target_reduced_polarization": [
        -0.5,
        0.0,
        -0.5
      ]
    },
    {
      "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": "C2/m",
      "spacegroup_number": 12,
      "pointgroup": "2/m",
      "has_inversion": true,
      "is_polar_point_group": false,
      "nonpolar_parent_hypothesis": true,
      "symmetry_tolerance_A": null,
      "target_reduced_polarization": [
        0.0,
        0.0,
        0.0
      ],
      "formal_class": [
        0.0,
        0.0,
        0.0
      ],
      "target_residual": 3.6847954287622854e-15,
      "parent_symmetrization_rmsd_A": 0.2125394622113827,
      "parent_cell_rmsd_A": 0.0,
      "energy_eV": -323.7815632500804,
      "reduced_polarization": [
        -1.798622727097208e-15,
        3.1978882314505917e-15,
        -3.4085846996465534e-16
      ],
      "cartesian_polarization_e_A2": [
        -2.511198118890025e-17,
        2.7546160313092422e-17,
        -3.947032994784478e-18
      ],
      "ranking_score": 0.21253946221139008
    },
    {
      "candidate_id": "bec_projection_00",
      "source": "MACEField_BEC_backprojection",
      "spacegroup": "C2",
      "spacegroup_number": 5,
      "pointgroup": "2",
      "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": 4.07215265139821e-05,
      "parent_symmetrization_rmsd_A": 0.007863484514546083,
      "parent_cell_rmsd_A": 0.002107810680927672,
      "energy_eV": -323.76940221290363,
      "reduced_polarization": [
        7.32430890321808e-14,
        4.07215265139821e-05,
        -3.960487262129377e-14
      ],
      "cartesian_polarization_e_A2": [
        1.2901873407923527e-15,
        3.508401631013692e-07,
        -4.468224493442961e-16
      ],
      "ranking_score": 0.508471880237806
    },
    {
      "candidate_id": "inversion_parent_bec_00_00",
      "source": "same_species_inversion_center_projection_after_BEC",
      "spacegroup": "C2/m",
      "spacegroup_number": 12,
      "pointgroup": "2/m",
      "has_inversion": true,
      "is_polar_point_group": false,
      "nonpolar_parent_hypothesis": true,
      "symmetry_tolerance_A": null,
      "target_reduced_polarization": [
        0.0,
        0.0,
        0.0
      ],
      "formal_class": [
        0.0,
        0.0,
        0.0
      ],
      "target_residual": 3.211910465461858e-15,
      "parent_symmetrization_rmsd_A": 0.212539529222671,
      "parent_cell_rmsd_A": 0.002107810680927672,
      "energy_eV": -323.7790704654419,
      "reduced_polarization": [
        7.934771383429367e-16,
        3.1120638386834783e-15,
        -4.267942161238048e-17
      ],
      "cartesian_polarization_e_A2": [
        1.2035647657742138e-17,
        2.6812280339570237e-17,
        -4.939291585013363e-19
      ],
      "ranking_score": 0.21306648189290933
    },
    {
      "candidate_id": "bec_projection_01",
      "source": "MACEField_BEC_backprojection",
      "spacegroup": "C2",
      "spacegroup_number": 5,
      "pointgroup": "2",
      "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": 1.2275611527332746e-08,
      "parent_symmetrization_rmsd_A": 0.035256559169018056,
      "parent_cell_rmsd_A": 0.009439150816691234,
      "energy_eV": -323.3266923581721,
      "reduced_polarization": [
        -2.0087928191273864e-14,
        0.5000000122756115,
        -3.014574250748603e-14
      ],
      "cartesian_polarization_e_A2": [
        6.76863238323349e-14,
        0.004303049201711957,
        -1.7452748027361618e-13
      ],
      "ranking_score": 0.5376163714244139
    },
    {
      "candidate_id": "bec_projection_02",
      "source": "MACEField_BEC_backprojection",
      "spacegroup": "P1",
      "spacegroup_number": 1,
      "pointgroup": "1",
      "has_inversion": false,
      "is_polar_point_group": true,
      "nonpolar_parent_hypothesis": false,
      "symmetry_tolerance_A": null,
      "target_reduced_polarization": [
        0.0,
        0.0,
        -0.5
      ],
      "formal_class": [
        0.0,
        0.0,
        0.5
      ],
      "target_residual": 3.0568413455324526e-06,
      "parent_symmetrization_rmsd_A": 0.06386176479954749,
      "parent_cell_rmsd_A": 0.007896248442330825,
      "energy_eV": -321.4988231639086,
      "reduced_polarization": [
        5.293768243731967e-07,
        2.2922465992083735e-06,
        -0.49999804816888077
      ],
      "cartesian_polarization_e_A2": [
        0.002480289359617283,
        4.8768280735209965e-06,
        -0.005787498869763803
      ],
      "ranking_score": 0.5658419405928212
    },
    {
      "candidate_id": "bec_projection_03",
      "source": "MACEField_BEC_backprojection",
      "spacegroup": "P1",
      "spacegroup_number": 1,
      "pointgroup": "1",
      "has_inversion": false,
      "is_polar_point_group": true,
      "nonpolar_parent_hypothesis": false,
      "symmetry_tolerance_A": null,
      "target_reduced_polarization": [
        -0.5,
        0.0,
        0.0
      ],
      "formal_class": [
        0.5,
        0.0,
        0.0
      ],
      "target_residual": 1.8274618000243612e-05,
      "parent_symmetrization_rmsd_A": 0.07620113118852294,
      "parent_cell_rmsd_A": 0.003880853098487959,
      "energy_eV": -321.4388227601314,
      "reduced_polarization": [
        -0.49998247737588236,
        5.154138055251191e-06,
        -5.95120151056097e-07
      ],
      "cartesian_polarization_e_A2": [
        -0.007450437218356666,
        -2.027076163973183e-06,
        -6.352277015366275e-08
      ],
      "ranking_score": 0.5772078936991454
    },
    {
      "candidate_id": "bec_projection_04",
      "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": [
        0.0,
        0.5,
        -0.5
      ],
      "formal_class": [
        0.0,
        0.5,
        0.5
      ],
      "target_residual": 4.018620475789917e-06,
      "parent_symmetrization_rmsd_A": 0.07255156654103057,
      "parent_cell_rmsd_A": 0.012152015993294334,
      "energy_eV": -321.11447005566504,
      "reduced_polarization": [
        6.435490545812861e-07,
        0.5000017988664298,
        -0.499996464574324
      ],
      "cartesian_polarization_e_A2": [
        0.0024780376928744056,
        0.004307919469704996,
        -0.005805071083058423
      ],
      "ranking_score": 0.5755976077803058
    },
    {
      "candidate_id": "bec_projection_05",
      "source": "MACEField_BEC_backprojection",
      "spacegroup": "P1",
      "spacegroup_number": 1,
      "pointgroup": "1",
      "has_inversion": false,
      "is_polar_point_group": true,
      "nonpolar_parent_hypothesis": false,
      "symmetry_tolerance_A": null,
      "target_reduced_polarization": [
        -0.5,
        0.5,
        0.0
      ],
      "formal_class": [
        0.5,
        0.5,
        0.0
      ],
      "target_residual": 0.00017881171684688566,
      "parent_symmetrization_rmsd_A": 0.08440441446676357,
      "parent_cell_rmsd_A": 0.010233221508632553,
      "energy_eV": -320.86007291189503,
      "reduced_polarization": [
        -0.4998527663793177,
        0.49989857912531094,
        3.1140327253725558e-06
      ],
      "cartesian_polarization_e_A2": [
        -0.007448730064365971,
        0.004299988585172684,
        -8.050097124535165e-07
      ],
      "ranking_score": 0.5873203432776155
    },
    {
      "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,
        0.0,
        -0.5
      ],
      "formal_class": [
        0.5,
        0.0,
        0.5
      ],
      "target_residual": 5.250082039407014e-06,
      "parent_symmetrization_rmsd_A": 0.07681763637521706,
      "parent_cell_rmsd_A": 0.008501771293020433,
      "energy_eV": -320.77380382307314,
      "reduced_polarization": [
        -0.4999970831459729,
        3.3047790428046175e-06,
        -0.4999971480253361
      ],
      "cartesian_polarization_e_A2": [
        -0.004970386229089729,
        1.0049939009999975e-05,
        -0.005787546520165692
      ],
      "ranking_score": 0.578953579362551
    },
    {
      "candidate_id": "bec_projection_07",
      "source": "MACEField_BEC_backprojection",
      "spacegroup": "P1",
      "spacegroup_number": 1,
      "pointgroup": "1",
      "has_inversion": false,
      "is_polar_point_group": true,
      "nonpolar_parent_hypothesis": false,
      "symmetry_tolerance_A": null,
      "target_reduced_polarization": [
        -0.5,
        0.5,
        -0.5
      ],
      "formal_class": [
        0.5,
        0.5,
        0.5
      ],
      "target_residual": 0.0002411474732687868,
      "parent_symmetrization_rmsd_A": 0.08456237068216516,
      "parent_cell_rmsd_A": 0.012683736833144527,
      "energy_eV": -320.3504376029648,
      "reduced_polarization": [
        -0.4998459070722684,
        0.49989480426950206,
        -0.4998472212980418
      ],
      "cartesian_polarization_e_A2": [
        -0.00497133403007559,
        0.004312154608558232,
        -0.005804333513820939
      ],
      "ranking_score": 0.5882155998369889
    }
  ],
  "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": [
              -4.335464397057429e-09,
              0.09160314318502097,
              -7.842917015458688e-09
            ],
            "branch_aligned_reduced_polarization": [
              -4.335464397057429e-09,
              0.09160314318502097,
              -7.842917015458688e-09
            ],
            "target_residual": 0.0916031431850214,
            "energy_eV": -323.79642228336274,
            "max_atomic_step_A": 0.01189955067685686,
            "max_log_strain_component": 0.00031538977539921436,
            "step_scale": 1.0,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 0.41461402957126836,
            "cell_principal_stretches": [
              1.0003154395159837,
              1.0000805514115443,
              0.9997180972316829
            ],
            "cell_volume_ratio": 1.0001140019302075,
            "cell_rmsd_from_input_A": 0.002107810680927672
          },
          {
            "iteration": 1,
            "reduced_polarization": [
              7.32430890321808e-14,
              4.07215265139821e-05,
              -3.960487262129377e-14
            ],
            "branch_aligned_reduced_polarization": [
              7.32430890321808e-14,
              4.07215265139821e-05,
              -3.960487262129377e-14
            ],
            "target_residual": 4.07215265139821e-05,
            "energy_eV": -323.76940221290363
          }
        ],
        "iterations": 1
      },
      "parent": {
        "candidate_id": "inversion_parent_endpoint_00",
        "source": "same_species_inversion_center_projection_from_endpoint",
        "spacegroup": "C2/m",
        "spacegroup_number": 12,
        "pointgroup": "2/m",
        "has_inversion": true,
        "is_polar_point_group": false,
        "nonpolar_parent_hypothesis": true,
        "symmetry_tolerance_A": null,
        "target_reduced_polarization": [
          0.0,
          0.0,
          0.0
        ],
        "formal_class": [
          0.0,
          0.0,
          0.0
        ],
        "target_residual": 3.6847954287622854e-15,
        "parent_symmetrization_rmsd_A": 0.2125394622113827,
        "parent_cell_rmsd_A": 0.0,
        "energy_eV": -323.7815632500804,
        "reduced_polarization": [
          -1.798622727097208e-15,
          3.1978882314505917e-15,
          -3.4085846996465534e-16
        ],
        "cartesian_polarization_e_A2": [
          -2.511198118890025e-17,
          2.7546160313092422e-17,
          -3.947032994784478e-18
        ],
        "ranking_score": 0.21253946221139008
      },
      "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": [
          -323.79642228336274,
          -323.8010535155031,
          -323.80101306487626,
          -323.79809682104343,
          -323.7937674791524,
          -323.78919129201233,
          -323.7852228192652,
          -323.782520971938,
          -323.7815632500803
        ],
        "cartesian_polarizations_e_A2": [
          [
            -2.5699264361035258e-11,
            0.0007890566163449593,
            -9.081848655328909e-11
          ],
          [
            -2.249560306346312e-11,
            0.0006824893804544956,
            -7.926022221065182e-11
          ],
          [
            -1.9279633683374867e-11,
            0.0005794067586751256,
            -6.778331609104387e-11
          ],
          [
            -1.6058713980414846e-11,
            0.00047923849613722917,
            -5.637888027450505e-11
          ],
          [
            -1.283860413854166e-11,
            0.00038134097591009387,
            -4.503171730765902e-11
          ],
          [
            -9.622241940940463e-12,
            0.000285033282076523,
            -3.372939028591391e-11
          ],
          [
            -6.410401953993215e-12,
            0.00018966719165338882,
            -2.2464066478467753e-11
          ],
          [
            -3.203528037447419e-12,
            9.475212248096349e-05,
            -1.122513952372864e-11
          ],
          [
            1.2781744652676453e-18,
            4.0151478220266364e-17,
            -1.0488621524923847e-17
          ]
        ],
        "raw_reduced_polarization": [
          [
            -4.335463672657803e-09,
            0.0916031431850218,
            -7.842916543126103e-09
          ],
          [
            -3.78819679652919e-09,
            0.07923154200217532,
            -6.844766209829106e-09
          ],
          [
            -3.2424429143034784e-09,
            0.06726447656334383,
            -5.853641822212689e-09
          ],
          [
            -2.6984402567607843e-09,
            0.05563574485286496,
            -4.8687758359460105e-09
          ],
          [
            -2.1561384584911673e-09,
            0.04427062810830891,
            -3.8888558270609735e-09
          ],
          [
            -1.6153771174344409e-09,
            0.03309007745413507,
            -2.9128077674772768e-09
          ],
          [
            -1.0759830313289636e-09,
            0.022018839402178896,
            -1.9399552370483605e-09
          ],
          [
            -5.376810677412459e-10,
            0.010999961299245834,
            -9.693822900020749e-10
          ],
          [
            -2.1576049805721448e-16,
            4.661264518049991e-15,
            -9.057779577084858e-16
          ]
        ],
        "unwrapped_reduced_polarization": [
          [
            -4.335463672657803e-09,
            0.0916031431850218,
            -7.842916543126103e-09
          ],
          [
            -3.78819679652919e-09,
            0.07923154200217532,
            -6.844766209829106e-09
          ],
          [
            -3.2424429143034784e-09,
            0.06726447656334383,
            -5.853641822212689e-09
          ],
          [
            -2.6984402567607843e-09,
            0.05563574485286496,
            -4.8687758359460105e-09
          ],
          [
            -2.1561384584911673e-09,
            0.04427062810830891,
            -3.8888558270609735e-09
          ],
          [
            -1.6153771174344409e-09,
            0.03309007745413507,
            -2.9128077674772768e-09
          ],
          [
            -1.0759830313289636e-09,
            0.022018839402178896,
            -1.9399552370483605e-09
          ],
          [
            -5.376810677412459e-10,
            0.010999961299245834,
            -9.693822900020749e-10
          ],
          [
            -2.1576049809503432e-16,
            4.661201979949681e-15,
            -9.057779577816118e-16
          ]
        ],
        "berry_integer_shifts": [
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ]
        ],
        "folded_reduced_polarization": [
          [
            -4.335463654747684e-09,
            0.09160314318502183,
            -7.842916538436384e-09
          ],
          [
            -3.788196811793654e-09,
            0.0792315420021753,
            -6.844766198277341e-09
          ],
          [
            -3.242442925266431e-09,
            0.06726447656334389,
            -5.853641849018487e-09
          ],
          [
            -2.698440249027101e-09,
            0.05563574485286493,
            -4.868775826949445e-09
          ],
          [
            -2.1561384344614964e-09,
            0.04427062810830895,
            -3.888855848455108e-09
          ],
          [
            -1.6153771098537106e-09,
            0.03309007745413506,
            -2.9128077727591517e-09
          ],
          [
            -1.0759830249007507e-09,
            0.022018839402178858,
            -1.9399552519949737e-09
          ],
          [
            -5.376810663371145e-10,
            0.010999961299245853,
            -9.693822966561072e-10
          ],
          [
            -2.220446049250313e-16,
            4.6629367034256575e-15,
            -8.881784197001252e-16
          ]
        ]
      },
      "reflected": {
        "reached": true,
        "construction": "reflect_displacements_about_reconstructed_parent",
        "energies_eV": [
          -323.78156325008035,
          -323.782520971938,
          -323.7852228192652,
          -323.7891912920124,
          -323.7937674791523,
          -323.7980968210435,
          -323.80101306487626,
          -323.80105351550327,
          -323.7964222833628
        ],
        "cartesian_polarizations_e_A2": [
          [
            6.777005335794398e-19,
            4.035446268070621e-17,
            -1.6285926409864518e-18
          ],
          [
            3.203516259795978e-12,
            -9.47521224809111e-05,
            1.122511880545506e-11
          ],
          [
            6.410381806310767e-12,
            -0.00018966719165332908,
            2.246406111024077e-11
          ],
          [
            9.62222763589905e-12,
            -0.0002850332820764435,
            3.372936298309842e-11
          ],
          [
            1.2838577318837569e-11,
            -0.0003813409759100337,
            4.5031707575727666e-11
          ],
          [
            1.6058692579874976e-11,
            -0.0004792384961371624,
            5.6378886976522385e-11
          ],
          [
            1.9279624150043958e-11,
            -0.0005794067586750455,
            6.778329749601566e-11
          ],
          [
            2.2495583110308773e-11,
            -0.0006824893804544119,
            7.926018749288008e-11
          ],
          [
            2.5699259874726215e-11,
            -0.0007890566163448818,
            9.081848509855029e-11
          ]
        ],
        "raw_reduced_polarization": [
          [
            -1.3423195854565266e-18,
            4.68482938552444e-15,
            -1.406422486297586e-16
          ],
          [
            5.376796817755206e-10,
            -0.010999961299239754,
            9.693805008102838e-10
          ],
          [
            1.075981524980492e-09,
            -0.02201883940217196,
            1.939954773458206e-09
          ],
          [
            1.6153753725708032e-09,
            -0.033090077454125844,
            2.912805409656624e-09
          ],
          [
            2.1561363789632837e-09,
            -0.04427062810830192,
            3.88885498662938e-09
          ],
          [
            2.6984390133411334e-09,
            -0.055635744852857216,
            4.868776414719833e-09
          ],
          [
            3.242441739984215e-09,
            -0.06726447656333454,
            5.853640216380441e-09
          ],
          [
            3.788194459476847e-09,
            -0.0792315420021656,
            6.844763211666544e-09
          ],
          [
            4.33546332978028e-09,
            -0.0916031431850128,
            7.842916417497551e-09
          ]
        ],
        "unwrapped_reduced_polarization": [
          [
            -1.3423195854565266e-18,
            4.68482938552444e-15,
            -1.406422486297586e-16
          ],
          [
            5.376796817755206e-10,
            -0.010999961299239754,
            9.693805008102838e-10
          ],
          [
            1.075981524980492e-09,
            -0.02201883940217196,
            1.939954773458206e-09
          ],
          [
            1.6153753725708032e-09,
            -0.033090077454125844,
            2.912805409656624e-09
          ],
          [
            2.1561363789632837e-09,
            -0.04427062810830192,
            3.88885498662938e-09
          ],
          [
            2.6984390133411334e-09,
            -0.055635744852857216,
            4.868776414719833e-09
          ],
          [
            3.242441739984215e-09,
            -0.06726447656333454,
            5.853640216380441e-09
          ],
          [
            3.788194459476847e-09,
            -0.0792315420021656,
            6.844763211666544e-09
          ],
          [
            4.33546332978028e-09,
            -0.0916031431850128,
            7.842916417497551e-09
          ]
        ],
        "gauge_integer_shift": [
          0,
          0,
          0
        ],
        "expected_opposite_endpoint_reduced_polarization": [
          4.335463241136806e-09,
          -0.09160314318501248,
          7.842914731570187e-09
        ],
        "actual_opposite_endpoint_branch_residual": 1.7181648451836007e-15
      },
      "pnp_branch": {
        "construction": "incoming_path_concatenated_with_parent_reflection",
        "reduced_polarization": [
          [
            -4.335463672657803e-09,
            0.0916031431850218,
            -7.842916543126103e-09
          ],
          [
            -3.78819679652919e-09,
            0.07923154200217532,
            -6.844766209829106e-09
          ],
          [
            -3.2424429143034784e-09,
            0.06726447656334383,
            -5.853641822212689e-09
          ],
          [
            -2.6984402567607843e-09,
            0.05563574485286496,
            -4.8687758359460105e-09
          ],
          [
            -2.1561384584911673e-09,
            0.04427062810830891,
            -3.8888558270609735e-09
          ],
          [
            -1.6153771174344409e-09,
            0.03309007745413507,
            -2.9128077674772768e-09
          ],
          [
            -1.0759830313289636e-09,
            0.022018839402178896,
            -1.9399552370483605e-09
          ],
          [
            -5.376810677412459e-10,
            0.010999961299245834,
            -9.693822900020749e-10
          ],
          [
            -2.1576049805721448e-16,
            4.661264518049991e-15,
            -9.057779577084858e-16
          ],
          [
            5.376796817755206e-10,
            -0.010999961299239754,
            9.693805008102838e-10
          ],
          [
            1.075981524980492e-09,
            -0.02201883940217196,
            1.939954773458206e-09
          ],
          [
            1.6153753725708032e-09,
            -0.033090077454125844,
            2.912805409656624e-09
          ],
          [
            2.1561363789632837e-09,
            -0.04427062810830192,
            3.88885498662938e-09
          ],
          [
            2.6984390133411334e-09,
            -0.055635744852857216,
            4.868776414719833e-09
          ],
          [
            3.242441739984215e-09,
            -0.06726447656333454,
            5.853640216380441e-09
          ],
          [
            3.788194459476847e-09,
            -0.0792315420021656,
            6.844763211666544e-09
          ],
          [
            4.33546332978028e-09,
            -0.0916031431850128,
            7.842916417497551e-09
          ]
        ],
        "unwrapped_reduced_polarization": [
          [
            -4.335463672657803e-09,
            0.0916031431850218,
            -7.842916543126103e-09
          ],
          [
            -3.78819679652919e-09,
            0.07923154200217532,
            -6.844766209829106e-09
          ],
          [
            -3.2424429143034784e-09,
            0.06726447656334383,
            -5.853641822212689e-09
          ],
          [
            -2.6984402567607843e-09,
            0.05563574485286496,
            -4.8687758359460105e-09
          ],
          [
            -2.1561384584911673e-09,
            0.04427062810830891,
            -3.8888558270609735e-09
          ],
          [
            -1.6153771174344409e-09,
            0.03309007745413507,
            -2.9128077674772768e-09
          ],
          [
            -1.0759830313289636e-09,
            0.022018839402178896,
            -1.9399552370483605e-09
          ],
          [
            -5.376810677412459e-10,
            0.010999961299245834,
            -9.693822900020749e-10
          ],
          [
            -2.1576049809503432e-16,
            4.661201979949681e-15,
            -9.057779577816118e-16
          ],
          [
            5.376796817755206e-10,
            -0.010999961299239754,
            9.693805008102838e-10
          ],
          [
            1.075981524980492e-09,
            -0.02201883940217196,
            1.939954773458206e-09
          ],
          [
            1.6153753725708032e-09,
            -0.033090077454125844,
            2.912805409656624e-09
          ],
          [
            2.1561363789632837e-09,
            -0.04427062810830192,
            3.88885498662938e-09
          ],
          [
            2.6984390133411334e-09,
            -0.055635744852857216,
            4.868776414719833e-09
          ],
          [
            3.242441739984215e-09,
            -0.06726447656333454,
            5.853640216380441e-09
          ],
          [
            3.788194459476847e-09,
            -0.0792315420021656,
            6.844763211666544e-09
          ],
          [
            4.33546332978028e-09,
            -0.0916031431850128,
            7.842916417497551e-09
          ]
        ],
        "berry_integer_shifts": [
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ]
        ],
        "folded_reduced_polarization": [
          [
            -4.335463654747684e-09,
            0.09160314318502183,
            -7.842916538436384e-09
          ],
          [
            -3.788196811793654e-09,
            0.0792315420021753,
            -6.844766198277341e-09
          ],
          [
            -3.242442925266431e-09,
            0.06726447656334389,
            -5.853641849018487e-09
          ],
          [
            -2.698440249027101e-09,
            0.05563574485286493,
            -4.868775826949445e-09
          ],
          [
            -2.1561384344614964e-09,
            0.04427062810830895,
            -3.888855848455108e-09
          ],
          [
            -1.6153771098537106e-09,
            0.03309007745413506,
            -2.9128077727591517e-09
          ],
          [
            -1.0759830249007507e-09,
            0.022018839402178858,
            -1.9399552519949737e-09
          ],
          [
            -5.376810663371145e-10,
            0.010999961299245853,
            -9.693822966561072e-10
          ],
          [
            -2.220446049250313e-16,
            4.6629367034256575e-15,
            -8.881784197001252e-16
          ],
          [
            5.376796785583338e-10,
            -0.010999961299239747,
            9.693804647881166e-10
          ],
          [
            1.0759815260996675e-09,
            -0.022018839402171975,
            1.9399547523946126e-09
          ],
          [
            1.6153753890080225e-09,
            -0.033090077454125844,
            2.9128054412908e-09
          ],
          [
            2.156136380548901e-09,
            -0.0442706281083019,
            3.88885501578784e-09
          ],
          [
            2.698439027781774e-09,
            -0.055635744852857216,
            4.8687763820609575e-09
          ],
          [
            3.2424417595322552e-09,
            -0.06726447656333456,
            5.8536402391951015e-09
          ],
          [
            3.788194424814151e-09,
            -0.07923154200216559,
            6.844763200675175e-09
          ],
          [
            4.335463321680777e-09,
            -0.09160314318501278,
            7.842916427414082e-09
          ]
        ]
      },
      "incoming_structure_ids": [
        "incoming_00_000",
        "incoming_00_001",
        "incoming_00_002",
        "incoming_00_003",
        "incoming_00_004",
        "incoming_00_005",
        "incoming_00_006",
        "incoming_00_007",
        "incoming_00_008"
      ],
      "reflected_structure_ids": [
        "reflected_00_001",
        "reflected_00_002",
        "reflected_00_003",
        "reflected_00_004",
        "reflected_00_005",
        "reflected_00_006",
        "reflected_00_007",
        "reflected_00_008"
      ]
    },
    {
      "orbit_id": 1,
      "formal_class": [
        0.0,
        0.5,
        0.0
      ],
      "formal_classes_in_orbit": [
        [
          0.0,
          0.5,
          0.0
        ]
      ],
      "target_reduced_polarization": [
        0.0,
        0.5,
        0.0
      ],
      "bec_backprojection": {
        "converged_to_target": true,
        "history": [
          {
            "iteration": 0,
            "reduced_polarization": [
              -4.335464397057429e-09,
              0.09160314318502097,
              -7.842917015458688e-09
            ],
            "branch_aligned_reduced_polarization": [
              -4.335464397057429e-09,
              0.09160314318502094,
              -7.842917015458688e-09
            ],
            "target_residual": 0.40839685681497917,
            "energy_eV": -323.79642228336274,
            "max_atomic_step_A": 0.05305209973604813,
            "max_log_strain_component": 0.00140611106198029,
            "step_scale": 1.0,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 0.41461402957126836,
            "cell_principal_stretches": [
              1.0012577825300648,
              0.9996409543231974,
              0.9985948770489934
            ],
            "cell_volume_ratio": 0.999491900099652,
            "cell_rmsd_from_input_A": 0.009401818009184335
          },
          {
            "iteration": 1,
            "reduced_polarization": [
              -1.9561835299943688e-11,
              0.4984227576949792,
              -1.4985806631713824e-11
            ],
            "branch_aligned_reduced_polarization": [
              -1.9561835299943688e-11,
              0.4984227576949792,
              -1.4985806631713824e-11
            ],
            "target_residual": 0.0015772423050208209,
            "energy_eV": -323.3304788631176,
            "max_atomic_step_A": 0.00020798105627489014,
            "max_log_strain_component": 5.581190556747045e-06,
            "step_scale": 1.0,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 0.41461402957126836,
            "cell_principal_stretches": [
              1.001262778120109,
              0.9996395294420641,
              0.9985893037162487
            ],
            "cell_volume_ratio": 0.9994898838443041,
            "cell_rmsd_from_input_A": 0.009439150816691234
          },
          {
            "iteration": 2,
            "reduced_polarization": [
              -2.0087928191273864e-14,
              0.5000000122756115,
              -3.014574250748603e-14
            ],
            "branch_aligned_reduced_polarization": [
              -2.0087928191273864e-14,
              0.5000000122756115,
              -3.014574250748603e-14
            ],
            "target_residual": 1.2275611527332746e-08,
            "energy_eV": -323.3266923581721
          }
        ],
        "iterations": 2
      },
      "parent": {
        "candidate_id": "bec_projection_01",
        "source": "MACEField_BEC_backprojection",
        "spacegroup": "C2",
        "spacegroup_number": 5,
        "pointgroup": "2",
        "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": 1.2275611527332746e-08,
        "parent_symmetrization_rmsd_A": 0.035256559169018056,
        "parent_cell_rmsd_A": 0.009439150816691234,
        "energy_eV": -323.3266923581721,
        "reduced_polarization": [
          -2.0087928191273864e-14,
          0.5000000122756115,
          -3.014574250748603e-14
        ],
        "cartesian_polarization_e_A2": [
          6.76863238323349e-14,
          0.004303049201711957,
          -1.7452748027361618e-13
        ],
        "ranking_score": 0.5376163714244139
      },
      "branch_status": "awaiting_branch_sampling"
    },
    {
      "orbit_id": 2,
      "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": [
              -4.335464397057429e-09,
              0.09160314318502097,
              -7.842917015458688e-09
            ],
            "branch_aligned_reduced_polarization": [
              -4.335464397057429e-09,
              0.09160314318502097,
              -7.842917038036745e-09
            ],
            "target_residual": 0.5083218744048484,
            "energy_eV": -323.79642228336274,
            "max_atomic_step_A": 0.09592278022993166,
            "max_log_strain_component": 0.0011168680510964483,
            "step_scale": 1.0,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 0.41461402957126836,
            "cell_principal_stretches": [
              1.0014049070747382,
              0.999982160560813,
              0.9987287229182006
            ],
            "cell_volume_ratio": 1.000114002175563,
            "cell_rmsd_from_input_A": 0.007803905157957797
          },
          {
            "iteration": 1,
            "reduced_polarization": [
              0.0010620504171126235,
              0.0004837881056049492,
              -0.49424603965636077
            ],
            "branch_aligned_reduced_polarization": [
              0.0010620504171126235,
              0.0004837881056049492,
              -0.49424603965636077
            ],
            "target_residual": 0.00587112098800449,
            "energy_eV": -321.5510613868965,
            "max_atomic_step_A": 0.0010770458779996003,
            "max_log_strain_component": 1.4321578812231e-05,
            "step_scale": 1.0,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 0.41461402957126836,
            "cell_principal_stretches": [
              1.001421449971309,
              0.9999821908996508,
              0.9987128469019616
            ],
            "cell_volume_ratio": 1.0001146557900644,
            "cell_rmsd_from_input_A": 0.007896248442330825
          },
          {
            "iteration": 2,
            "reduced_polarization": [
              5.293768243731967e-07,
              2.2922465992083735e-06,
              -0.49999804816888077
            ],
            "branch_aligned_reduced_polarization": [
              5.293768243731967e-07,
              2.2922465992083735e-06,
              -0.49999804816888077
            ],
            "target_residual": 3.0568413455324526e-06,
            "energy_eV": -321.4988231639086
          }
        ],
        "iterations": 2
      },
      "parent": {
        "candidate_id": "bec_projection_02",
        "source": "MACEField_BEC_backprojection",
        "spacegroup": "P1",
        "spacegroup_number": 1,
        "pointgroup": "1",
        "has_inversion": false,
        "is_polar_point_group": true,
        "nonpolar_parent_hypothesis": false,
        "symmetry_tolerance_A": null,
        "target_reduced_polarization": [
          0.0,
          0.0,
          -0.5
        ],
        "formal_class": [
          0.0,
          0.0,
          0.5
        ],
        "target_residual": 3.0568413455324526e-06,
        "parent_symmetrization_rmsd_A": 0.06386176479954749,
        "parent_cell_rmsd_A": 0.007896248442330825,
        "energy_eV": -321.4988231639086,
        "reduced_polarization": [
          5.293768243731967e-07,
          2.2922465992083735e-06,
          -0.49999804816888077
        ],
        "cartesian_polarization_e_A2": [
          0.002480289359617283,
          4.8768280735209965e-06,
          -0.005787498869763803
        ],
        "ranking_score": 0.5658419405928212
      },
      "branch_status": "awaiting_branch_sampling"
    },
    {
      "orbit_id": 3,
      "formal_class": [
        0.5,
        0.0,
        0.0
      ],
      "formal_classes_in_orbit": [
        [
          0.5,
          0.0,
          0.0
        ]
      ],
      "target_reduced_polarization": [
        -0.5,
        0.0,
        0.0
      ],
      "bec_backprojection": {
        "converged_to_target": true,
        "history": [
          {
            "iteration": 0,
            "reduced_polarization": [
              -4.335464397057429e-09,
              0.09160314318502097,
              -7.842917015458688e-09
            ],
            "branch_aligned_reduced_polarization": [
              -4.33546437639265e-09,
              0.09160314318502097,
              -7.842917015458688e-09
            ],
            "target_residual": 0.5083218778548796,
            "energy_eV": -323.79642228336274,
            "max_atomic_step_A": 0.11412768189966911,
            "max_log_strain_component": 0.0003153897863217243,
            "step_scale": 1.0,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 0.41461402957126836,
            "cell_principal_stretches": [
              1.0005436029372459,
              0.9999641283614071,
              0.9996064899635816
            ],
            "cell_volume_ratio": 1.000114001972618,
            "cell_rmsd_from_input_A": 0.0037821079732191735
          },
          {
            "iteration": 1,
            "reduced_polarization": [
              -0.488841648630363,
              0.0022155115315801595,
              -0.00034991780353884006
            ],
            "branch_aligned_reduced_polarization": [
              -0.488841648630363,
              0.0022155115315801595,
              -0.00034991780353884006
            ],
            "target_residual": 0.011381552578803914,
            "energy_eV": -321.55333315207037,
            "max_atomic_step_A": 0.00279855825254353,
            "max_log_strain_component": 8.607533394680377e-06,
            "step_scale": 1.0,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 0.41461402957126836,
            "cell_principal_stretches": [
              1.0005579566622864,
              0.9999627459946265,
              0.9995966416164238
            ],
            "cell_volume_ratio": 1.0001171134658184,
            "cell_rmsd_from_input_A": 0.003880853098487959
          },
          {
            "iteration": 2,
            "reduced_polarization": [
              -0.49998247737588236,
              5.154138055251191e-06,
              -5.95120151056097e-07
            ],
            "branch_aligned_reduced_polarization": [
              -0.49998247737588236,
              5.154138055251191e-06,
              -5.95120151056097e-07
            ],
            "target_residual": 1.8274618000243612e-05,
            "energy_eV": -321.4388227601314
          }
        ],
        "iterations": 2
      },
      "parent": {
        "candidate_id": "bec_projection_03",
        "source": "MACEField_BEC_backprojection",
        "spacegroup": "P1",
        "spacegroup_number": 1,
        "pointgroup": "1",
        "has_inversion": false,
        "is_polar_point_group": true,
        "nonpolar_parent_hypothesis": false,
        "symmetry_tolerance_A": null,
        "target_reduced_polarization": [
          -0.5,
          0.0,
          0.0
        ],
        "formal_class": [
          0.5,
          0.0,
          0.0
        ],
        "target_residual": 1.8274618000243612e-05,
        "parent_symmetrization_rmsd_A": 0.07620113118852294,
        "parent_cell_rmsd_A": 0.003880853098487959,
        "energy_eV": -321.4388227601314,
        "reduced_polarization": [
          -0.49998247737588236,
          5.154138055251191e-06,
          -5.95120151056097e-07
        ],
        "cartesian_polarization_e_A2": [
          -0.007450437218356666,
          -2.027076163973183e-06,
          -6.352277015366275e-08
        ],
        "ranking_score": 0.5772078936991454
      },
      "branch_status": "awaiting_branch_sampling"
    },
    {
      "orbit_id": 4,
      "formal_class": [
        0.0,
        0.5,
        0.5
      ],
      "formal_classes_in_orbit": [
        [
          0.0,
          0.5,
          0.5
        ]
      ],
      "target_reduced_polarization": [
        0.0,
        0.5,
        -0.5
      ],
      "bec_backprojection": {
        "converged_to_target": true,
        "history": [
          {
            "iteration": 0,
            "reduced_polarization": [
              -4.335464397057429e-09,
              0.09160314318502097,
              -7.842917015458688e-09
            ],
            "branch_aligned_reduced_polarization": [
              -4.335464397057429e-09,
              0.09160314318502094,
              -7.842917038036745e-09
            ],
            "target_residual": 0.6455911901609543,
            "energy_eV": -323.79642228336274,
            "max_atomic_step_A": 0.10936812978502013,
            "max_log_strain_component": 0.001406110931936742,
            "step_scale": 1.0,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 0.41461402957126836,
            "cell_principal_stretches": [
              1.0016848826514153,
              0.9998670711822707,
              0.9979433618275003
            ],
            "cell_volume_ratio": 0.9994919003448552,
            "cell_rmsd_from_input_A": 0.012030686130513075
          },
          {
            "iteration": 1,
            "reduced_polarization": [
              0.0006748595446956003,
              0.4969694377273918,
              -0.49367289367649564
            ],
            "branch_aligned_reduced_polarization": [
              0.0006748595446956003,
              0.4969694377273918,
              -0.49367289367649564
            ],
            "target_residual": 0.007047837790567518,
            "energy_eV": -321.1778815045897,
            "max_atomic_step_A": 0.0012757864101911594,
            "max_log_strain_component": 1.559225932766857e-05,
            "step_scale": 1.0,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 0.41461402957126836,
            "cell_principal_stretches": [
              1.0017029045830268,
              0.9998670810794208,
              0.9979214310246461
            ],
            "cell_volume_ratio": 0.9994879274858458,
            "cell_rmsd_from_input_A": 0.012152015993294334
          },
          {
            "iteration": 2,
            "reduced_polarization": [
              6.435490545812861e-07,
              0.5000017988664298,
              -0.499996464574324
            ],
            "branch_aligned_reduced_polarization": [
              6.435490545812861e-07,
              0.5000017988664298,
              -0.499996464574324
            ],
            "target_residual": 4.018620475789917e-06,
            "energy_eV": -321.11447005566504
          }
        ],
        "iterations": 2
      },
      "parent": {
        "candidate_id": "bec_projection_04",
        "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": [
          0.0,
          0.5,
          -0.5
        ],
        "formal_class": [
          0.0,
          0.5,
          0.5
        ],
        "target_residual": 4.018620475789917e-06,
        "parent_symmetrization_rmsd_A": 0.07255156654103057,
        "parent_cell_rmsd_A": 0.012152015993294334,
        "energy_eV": -321.11447005566504,
        "reduced_polarization": [
          6.435490545812861e-07,
          0.5000017988664298,
          -0.499996464574324
        ],
        "cartesian_polarization_e_A2": [
          0.0024780376928744056,
          0.004307919469704996,
          -0.005805071083058423
        ],
        "ranking_score": 0.5755976077803058
      },
      "branch_status": "awaiting_branch_sampling"
    },
    {
      "orbit_id": 5,
      "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": [
              -4.335464397057429e-09,
              0.09160314318502097,
              -7.842917015458688e-09
            ],
            "branch_aligned_reduced_polarization": [
              -4.33546437639265e-09,
              0.09160314318502094,
              -7.842917015458688e-09
            ],
            "target_residual": 0.6455911928774201,
            "energy_eV": -323.79642228336274,
            "max_atomic_step_A": 0.12,
            "max_log_strain_component": 0.0013530949604825566,
            "step_scale": 0.9622959434567128,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 0.41461402957126836,
            "cell_principal_stretches": [
              1.001233127433604,
              0.9997135271381081,
              0.9985661084628277
            ],
            "cell_volume_ratio": 0.999511052883548,
            "cell_rmsd_from_input_A": 0.009537174926850576
          },
          {
            "iteration": 1,
            "reduced_polarization": [
              -0.46879155153250196,
              0.4754478059259394,
              0.0005315916568385651
            ],
            "branch_aligned_reduced_polarization": [
              -0.46879155153250196,
              0.4754478059259394,
              0.0005315916568385651
            ],
            "target_residual": 0.0397122157438796,
            "energy_eV": -321.2484977468477,
            "max_atomic_step_A": 0.008316657238693475,
            "max_log_strain_component": 9.836180912248372e-05,
            "step_scale": 1.0,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 0.41461402957126836,
            "cell_principal_stretches": [
              1.0013232060411614,
              0.9996925993400111,
              0.9984616820913021
            ],
            "cell_volume_ratio": 0.9994755187121723,
            "cell_rmsd_from_input_A": 0.010233221508632553
          },
          {
            "iteration": 2,
            "reduced_polarization": [
              -0.4998527663793177,
              0.49989857912531094,
              3.1140327253725558e-06
            ],
            "branch_aligned_reduced_polarization": [
              -0.4998527663793177,
              0.49989857912531094,
              3.1140327253725558e-06
            ],
            "target_residual": 0.00017881171684688566,
            "energy_eV": -320.86007291189503
          }
        ],
        "iterations": 2
      },
      "parent": {
        "candidate_id": "bec_projection_05",
        "source": "MACEField_BEC_backprojection",
        "spacegroup": "P1",
        "spacegroup_number": 1,
        "pointgroup": "1",
        "has_inversion": false,
        "is_polar_point_group": true,
        "nonpolar_parent_hypothesis": false,
        "symmetry_tolerance_A": null,
        "target_reduced_polarization": [
          -0.5,
          0.5,
          0.0
        ],
        "formal_class": [
          0.5,
          0.5,
          0.0
        ],
        "target_residual": 0.00017881171684688566,
        "parent_symmetrization_rmsd_A": 0.08440441446676357,
        "parent_cell_rmsd_A": 0.010233221508632553,
        "energy_eV": -320.86007291189503,
        "reduced_polarization": [
          -0.4998527663793177,
          0.49989857912531094,
          3.1140327253725558e-06
        ],
        "cartesian_polarization_e_A2": [
          -0.007448730064365971,
          0.004299988585172684,
          -8.050097124535165e-07
        ],
        "ranking_score": 0.5873203432776155
      },
      "branch_status": "awaiting_branch_sampling"
    },
    {
      "orbit_id": 6,
      "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": [
              -4.335464397057429e-09,
              0.09160314318502097,
              -7.842917015458688e-09
            ],
            "branch_aligned_reduced_polarization": [
              -4.33546437639265e-09,
              0.09160314318502097,
              -7.842917038036745e-09
            ],
            "target_residual": 0.7130155143213884,
            "energy_eV": -323.79642228336274,
            "max_atomic_step_A": 0.11664259561057694,
            "max_log_strain_component": 0.0013614808404322294,
            "step_scale": 1.0,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 0.41461402957126836,
            "cell_principal_stretches": [
              1.0014854388127417,
              1.0000484781194283,
              0.9985821881821765
            ],
            "cell_volume_ratio": 1.0001140022179735,
            "cell_rmsd_from_input_A": 0.008393123354807523
          },
          {
            "iteration": 1,
            "reduced_polarization": [
              -0.4939377212570096,
              0.0005417193223319257,
              -0.4937816479857597
            ],
            "branch_aligned_reduced_polarization": [
              -0.4939377212570096,
              0.0005417193223319257,
              -0.4937816479857597
            ],
            "target_residual": 0.008701297900595512,
            "energy_eV": -320.84988472076634,
            "max_atomic_step_A": 0.0014933030499648982,
            "max_log_strain_component": 1.819419437015013e-05,
            "step_scale": 1.0,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 0.41461402957126836,
            "cell_principal_stretches": [
              1.001504707696615,
              1.0000487598264078,
              0.9985634378849613
            ],
            "cell_volume_ratio": 1.00011474701928,
            "cell_rmsd_from_input_A": 0.008501771293020433
          },
          {
            "iteration": 2,
            "reduced_polarization": [
              -0.4999970831459729,
              3.3047790428046175e-06,
              -0.4999971480253361
            ],
            "branch_aligned_reduced_polarization": [
              -0.4999970831459729,
              3.3047790428046175e-06,
              -0.4999971480253361
            ],
            "target_residual": 5.250082039407014e-06,
            "energy_eV": -320.77380382307314
          }
        ],
        "iterations": 2
      },
      "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,
          0.0,
          -0.5
        ],
        "formal_class": [
          0.5,
          0.0,
          0.5
        ],
        "target_residual": 5.250082039407014e-06,
        "parent_symmetrization_rmsd_A": 0.07681763637521706,
        "parent_cell_rmsd_A": 0.008501771293020433,
        "energy_eV": -320.77380382307314,
        "reduced_polarization": [
          -0.4999970831459729,
          3.3047790428046175e-06,
          -0.4999971480253361
        ],
        "cartesian_polarization_e_A2": [
          -0.004970386229089729,
          1.0049939009999975e-05,
          -0.005787546520165692
        ],
        "ranking_score": 0.578953579362551
      },
      "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": [
              -4.335464397057429e-09,
              0.09160314318502097,
              -7.842917015458688e-09
            ],
            "branch_aligned_reduced_polarization": [
              -4.33546437639265e-09,
              0.09160314318502094,
              -7.842917038036745e-09
            ],
            "target_residual": 0.8165708667825305,
            "energy_eV": -323.79642228336274,
            "max_atomic_step_A": 0.12,
            "max_log_strain_component": 0.0013195027413841374,
            "step_scale": 0.9384058694547197,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 0.41461402957126836,
            "cell_principal_stretches": [
              1.0017249711282274,
              0.9997383959975867,
              0.9980631065244966
            ],
            "cell_volume_ratio": 0.999523188878763,
            "cell_rmsd_from_input_A": 0.011661572594204982
          },
          {
            "iteration": 1,
            "reduced_polarization": [
              -0.46219095344746447,
              0.4690189122737396,
              -0.462804334589848
            ],
            "branch_aligned_reduced_polarization": [
              -0.46219095344746447,
              0.4690189122737396,
              -0.462804334589848
            ],
            "target_residual": 0.06142368698814832,
            "energy_eV": -320.8645723010713,
            "max_atomic_step_A": 0.010165084662081457,
            "max_log_strain_component": 0.00011718398869530377,
            "step_scale": 1.0,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 0.41461402957126836,
            "cell_principal_stretches": [
              1.0018757335922952,
              0.999714710360164,
              0.9978942937112157
            ],
            "cell_volume_ratio": 0.9994808546553026,
            "cell_rmsd_from_input_A": 0.012683736833144527
          },
          {
            "iteration": 2,
            "reduced_polarization": [
              -0.4998459070722684,
              0.49989480426950206,
              -0.4998472212980418
            ],
            "branch_aligned_reduced_polarization": [
              -0.4998459070722684,
              0.49989480426950206,
              -0.4998472212980418
            ],
            "target_residual": 0.0002411474732687868,
            "energy_eV": -320.3504376029648
          }
        ],
        "iterations": 2
      },
      "parent": {
        "candidate_id": "bec_projection_07",
        "source": "MACEField_BEC_backprojection",
        "spacegroup": "P1",
        "spacegroup_number": 1,
        "pointgroup": "1",
        "has_inversion": false,
        "is_polar_point_group": true,
        "nonpolar_parent_hypothesis": false,
        "symmetry_tolerance_A": null,
        "target_reduced_polarization": [
          -0.5,
          0.5,
          -0.5
        ],
        "formal_class": [
          0.5,
          0.5,
          0.5
        ],
        "target_residual": 0.0002411474732687868,
        "parent_symmetrization_rmsd_A": 0.08456237068216516,
        "parent_cell_rmsd_A": 0.012683736833144527,
        "energy_eV": -320.3504376029648,
        "reduced_polarization": [
          -0.4998459070722684,
          0.49989480426950206,
          -0.4998472212980418
        ],
        "cartesian_polarization_e_A2": [
          -0.00497133403007559,
          0.004312154608558232,
          -0.005804333513820939
        ],
        "ranking_score": 0.5882155998369889
      },
      "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,
          40,
          41,
          42,
          43,
          44,
          45,
          46,
          47,
          48,
          49,
          50,
          51,
          52,
          53,
          54,
          55,
          56,
          57,
          58,
          59
        ],
        "endpoint_rmsd_A": 0.2125394622113827,
        "minimum_distance_A_by_image": [
          1.7598764143663603,
          1.759407696848093,
          1.7590958032396362,
          1.7587342909527224,
          1.7567281488720163,
          1.7551662308571112,
          1.7540497236049342,
          1.7533794779942715,
          1.7531560058534188
        ],
        "minimum_distance_A": 1.7531560058534188,
        "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": [
          820.2225610710977,
          820.2225610710977,
          820.2225610710977,
          820.2225610710977,
          820.2225610710977,
          820.2225610710977,
          820.2225610710977,
          820.2225610710977,
          820.2225610710977
        ],
        "cell_deformation_log_strain_norm": 0.0
      },
      "parent_reduced_polarization": [
        -2.1576049805721448e-16,
        4.661264518049991e-15,
        -9.057779577084858e-16
      ],
      "incoming": {
        "reached": true,
        "construction": "variable_cell_linear_interpolation",
        "continuation_fractions": [
          0.0,
          0.125,
          0.25,
          0.375,
          0.5,
          0.625,
          0.75,
          0.875,
          1.0
        ],
        "energies_eV": [
          -323.79642228336274,
          -323.8010535155031,
          -323.80101306487626,
          -323.79809682104343,
          -323.7937674791524,
          -323.78919129201233,
          -323.7852228192652,
          -323.782520971938,
          -323.7815632500803
        ],
        "cartesian_polarizations_e_A2": [
          [
            -2.5699264361035258e-11,
            0.0007890566163449593,
            -9.081848655328909e-11
          ],
          [
            -2.249560306346312e-11,
            0.0006824893804544956,
            -7.926022221065182e-11
          ],
          [
            -1.9279633683374867e-11,
            0.0005794067586751256,
            -6.778331609104387e-11
          ],
          [
            -1.6058713980414846e-11,
            0.00047923849613722917,
            -5.637888027450505e-11
          ],
          [
            -1.283860413854166e-11,
            0.00038134097591009387,
            -4.503171730765902e-11
          ],
          [
            -9.622241940940463e-12,
            0.000285033282076523,
            -3.372939028591391e-11
          ],
          [
            -6.410401953993215e-12,
            0.00018966719165338882,
            -2.2464066478467753e-11
          ],
          [
            -3.203528037447419e-12,
            9.475212248096349e-05,
            -1.122513952372864e-11
          ],
          [
            1.2781744652676453e-18,
            4.0151478220266364e-17,
            -1.0488621524923847e-17
          ]
        ],
        "raw_reduced_polarization": [
          [
            -4.335463672657803e-09,
            0.0916031431850218,
            -7.842916543126103e-09
          ],
          [
            -3.78819679652919e-09,
            0.07923154200217532,
            -6.844766209829106e-09
          ],
          [
            -3.2424429143034784e-09,
            0.06726447656334383,
            -5.853641822212689e-09
          ],
          [
            -2.6984402567607843e-09,
            0.05563574485286496,
            -4.8687758359460105e-09
          ],
          [
            -2.1561384584911673e-09,
            0.04427062810830891,
            -3.8888558270609735e-09
          ],
          [
            -1.6153771174344409e-09,
            0.03309007745413507,
            -2.9128077674772768e-09
          ],
          [
            -1.0759830313289636e-09,
            0.022018839402178896,
            -1.9399552370483605e-09
          ],
          [
            -5.376810677412459e-10,
            0.010999961299245834,
            -9.693822900020749e-10
          ],
          [
            -2.1576049805721448e-16,
            4.661264518049991e-15,
            -9.057779577084858e-16
          ]
        ],
        "unwrapped_reduced_polarization": [
          [
            -4.335463672657803e-09,
            0.0916031431850218,
            -7.842916543126103e-09
          ],
          [
            -3.78819679652919e-09,
            0.07923154200217532,
            -6.844766209829106e-09
          ],
          [
            -3.2424429143034784e-09,
            0.06726447656334383,
            -5.853641822212689e-09
          ],
          [
            -2.6984402567607843e-09,
            0.05563574485286496,
            -4.8687758359460105e-09
          ],
          [
            -2.1561384584911673e-09,
            0.04427062810830891,
            -3.8888558270609735e-09
          ],
          [
            -1.6153771174344409e-09,
            0.03309007745413507,
            -2.9128077674772768e-09
          ],
          [
            -1.0759830313289636e-09,
            0.022018839402178896,
            -1.9399552370483605e-09
          ],
          [
            -5.376810677412459e-10,
            0.010999961299245834,
            -9.693822900020749e-10
          ],
          [
            -2.1576049809503432e-16,
            4.661201979949681e-15,
            -9.057779577816118e-16
          ]
        ],
        "berry_integer_shifts": [
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ]
        ],
        "folded_reduced_polarization": [
          [
            -4.335463654747684e-09,
            0.09160314318502183,
            -7.842916538436384e-09
          ],
          [
            -3.788196811793654e-09,
            0.0792315420021753,
            -6.844766198277341e-09
          ],
          [
            -3.242442925266431e-09,
            0.06726447656334389,
            -5.853641849018487e-09
          ],
          [
            -2.698440249027101e-09,
            0.05563574485286493,
            -4.868775826949445e-09
          ],
          [
            -2.1561384344614964e-09,
            0.04427062810830895,
            -3.888855848455108e-09
          ],
          [
            -1.6153771098537106e-09,
            0.03309007745413506,
            -2.9128077727591517e-09
          ],
          [
            -1.0759830249007507e-09,
            0.022018839402178858,
            -1.9399552519949737e-09
          ],
          [
            -5.376810663371145e-10,
            0.010999961299245853,
            -9.693822966561072e-10
          ],
          [
            -2.220446049250313e-16,
            4.6629367034256575e-15,
            -8.881784197001252e-16
          ]
        ]
      },
      "reflected": {
        "reached": true,
        "construction": "reflect_displacements_about_reconstructed_parent",
        "energies_eV": [
          -323.78156325008035,
          -323.782520971938,
          -323.7852228192652,
          -323.7891912920124,
          -323.7937674791523,
          -323.7980968210435,
          -323.80101306487626,
          -323.80105351550327,
          -323.7964222833628
        ],
        "cartesian_polarizations_e_A2": [
          [
            6.777005335794398e-19,
            4.035446268070621e-17,
            -1.6285926409864518e-18
          ],
          [
            3.203516259795978e-12,
            -9.47521224809111e-05,
            1.122511880545506e-11
          ],
          [
            6.410381806310767e-12,
            -0.00018966719165332908,
            2.246406111024077e-11
          ],
          [
            9.62222763589905e-12,
            -0.0002850332820764435,
            3.372936298309842e-11
          ],
          [
            1.2838577318837569e-11,
            -0.0003813409759100337,
            4.5031707575727666e-11
          ],
          [
            1.6058692579874976e-11,
            -0.0004792384961371624,
            5.6378886976522385e-11
          ],
          [
            1.9279624150043958e-11,
            -0.0005794067586750455,
            6.778329749601566e-11
          ],
          [
            2.2495583110308773e-11,
            -0.0006824893804544119,
            7.926018749288008e-11
          ],
          [
            2.5699259874726215e-11,
            -0.0007890566163448818,
            9.081848509855029e-11
          ]
        ],
        "raw_reduced_polarization": [
          [
            -1.3423195854565266e-18,
            4.68482938552444e-15,
            -1.406422486297586e-16
          ],
          [
            5.376796817755206e-10,
            -0.010999961299239754,
            9.693805008102838e-10
          ],
          [
            1.075981524980492e-09,
            -0.02201883940217196,
            1.939954773458206e-09
          ],
          [
            1.6153753725708032e-09,
            -0.033090077454125844,
            2.912805409656624e-09
          ],
          [
            2.1561363789632837e-09,
            -0.04427062810830192,
            3.88885498662938e-09
          ],
          [
            2.6984390133411334e-09,
            -0.055635744852857216,
            4.868776414719833e-09
          ],
          [
            3.242441739984215e-09,
            -0.06726447656333454,
            5.853640216380441e-09
          ],
          [
            3.788194459476847e-09,
            -0.0792315420021656,
            6.844763211666544e-09
          ],
          [
            4.33546332978028e-09,
            -0.0916031431850128,
            7.842916417497551e-09
          ]
        ],
        "unwrapped_reduced_polarization": [
          [
            -1.3423195854565266e-18,
            4.68482938552444e-15,
            -1.406422486297586e-16
          ],
          [
            5.376796817755206e-10,
            -0.010999961299239754,
            9.693805008102838e-10
          ],
          [
            1.075981524980492e-09,
            -0.02201883940217196,
            1.939954773458206e-09
          ],
          [
            1.6153753725708032e-09,
            -0.033090077454125844,
            2.912805409656624e-09
          ],
          [
            2.1561363789632837e-09,
            -0.04427062810830192,
            3.88885498662938e-09
          ],
          [
            2.6984390133411334e-09,
            -0.055635744852857216,
            4.868776414719833e-09
          ],
          [
            3.242441739984215e-09,
            -0.06726447656333454,
            5.853640216380441e-09
          ],
          [
            3.788194459476847e-09,
            -0.0792315420021656,
            6.844763211666544e-09
          ],
          [
            4.33546332978028e-09,
            -0.0916031431850128,
            7.842916417497551e-09
          ]
        ],
        "gauge_integer_shift": [
          0,
          0,
          0
        ],
        "expected_opposite_endpoint_reduced_polarization": [
          4.335463241136806e-09,
          -0.09160314318501248,
          7.842914731570187e-09
        ],
        "actual_opposite_endpoint_branch_residual": 1.7181648451836007e-15
      },
      "pnp_branch": {
        "construction": "incoming_path_concatenated_with_parent_reflection",
        "reduced_polarization": [
          [
            -4.335463672657803e-09,
            0.0916031431850218,
            -7.842916543126103e-09
          ],
          [
            -3.78819679652919e-09,
            0.07923154200217532,
            -6.844766209829106e-09
          ],
          [
            -3.2424429143034784e-09,
            0.06726447656334383,
            -5.853641822212689e-09
          ],
          [
            -2.6984402567607843e-09,
            0.05563574485286496,
            -4.8687758359460105e-09
          ],
          [
            -2.1561384584911673e-09,
            0.04427062810830891,
            -3.8888558270609735e-09
          ],
          [
            -1.6153771174344409e-09,
            0.03309007745413507,
            -2.9128077674772768e-09
          ],
          [
            -1.0759830313289636e-09,
            0.022018839402178896,
            -1.9399552370483605e-09
          ],
          [
            -5.376810677412459e-10,
            0.010999961299245834,
            -9.693822900020749e-10
          ],
          [
            -2.1576049805721448e-16,
            4.661264518049991e-15,
            -9.057779577084858e-16
          ],
          [
            5.376796817755206e-10,
            -0.010999961299239754,
            9.693805008102838e-10
          ],
          [
            1.075981524980492e-09,
            -0.02201883940217196,
            1.939954773458206e-09
          ],
          [
            1.6153753725708032e-09,
            -0.033090077454125844,
            2.912805409656624e-09
          ],
          [
            2.1561363789632837e-09,
            -0.04427062810830192,
            3.88885498662938e-09
          ],
          [
            2.6984390133411334e-09,
            -0.055635744852857216,
            4.868776414719833e-09
          ],
          [
            3.242441739984215e-09,
            -0.06726447656333454,
            5.853640216380441e-09
          ],
          [
            3.788194459476847e-09,
            -0.0792315420021656,
            6.844763211666544e-09
          ],
          [
            4.33546332978028e-09,
            -0.0916031431850128,
            7.842916417497551e-09
          ]
        ],
        "unwrapped_reduced_polarization": [
          [
            -4.335463672657803e-09,
            0.0916031431850218,
            -7.842916543126103e-09
          ],
          [
            -3.78819679652919e-09,
            0.07923154200217532,
            -6.844766209829106e-09
          ],
          [
            -3.2424429143034784e-09,
            0.06726447656334383,
            -5.853641822212689e-09
          ],
          [
            -2.6984402567607843e-09,
            0.05563574485286496,
            -4.8687758359460105e-09
          ],
          [
            -2.1561384584911673e-09,
            0.04427062810830891,
            -3.8888558270609735e-09
          ],
          [
            -1.6153771174344409e-09,
            0.03309007745413507,
            -2.9128077674772768e-09
          ],
          [
            -1.0759830313289636e-09,
            0.022018839402178896,
            -1.9399552370483605e-09
          ],
          [
            -5.376810677412459e-10,
            0.010999961299245834,
            -9.693822900020749e-10
          ],
          [
            -2.1576049809503432e-16,
            4.661201979949681e-15,
            -9.057779577816118e-16
          ],
          [
            5.376796817755206e-10,
            -0.010999961299239754,
            9.693805008102838e-10
          ],
          [
            1.075981524980492e-09,
            -0.02201883940217196,
            1.939954773458206e-09
          ],
          [
            1.6153753725708032e-09,
            -0.033090077454125844,
            2.912805409656624e-09
          ],
          [
            2.1561363789632837e-09,
            -0.04427062810830192,
            3.88885498662938e-09
          ],
          [
            2.6984390133411334e-09,
            -0.055635744852857216,
            4.868776414719833e-09
          ],
          [
            3.242441739984215e-09,
            -0.06726447656333454,
            5.853640216380441e-09
          ],
          [
            3.788194459476847e-09,
            -0.0792315420021656,
            6.844763211666544e-09
          ],
          [
            4.33546332978028e-09,
            -0.0916031431850128,
            7.842916417497551e-09
          ]
        ],
        "berry_integer_shifts": [
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ]
        ],
        "folded_reduced_polarization": [
          [
            -4.335463654747684e-09,
            0.09160314318502183,
            -7.842916538436384e-09
          ],
          [
            -3.788196811793654e-09,
            0.0792315420021753,
            -6.844766198277341e-09
          ],
          [
            -3.242442925266431e-09,
            0.06726447656334389,
            -5.853641849018487e-09
          ],
          [
            -2.698440249027101e-09,
            0.05563574485286493,
            -4.868775826949445e-09
          ],
          [
            -2.1561384344614964e-09,
            0.04427062810830895,
            -3.888855848455108e-09
          ],
          [
            -1.6153771098537106e-09,
            0.03309007745413506,
            -2.9128077727591517e-09
          ],
          [
            -1.0759830249007507e-09,
            0.022018839402178858,
            -1.9399552519949737e-09
          ],
          [
            -5.376810663371145e-10,
            0.010999961299245853,
            -9.693822966561072e-10
          ],
          [
            -2.220446049250313e-16,
            4.6629367034256575e-15,
            -8.881784197001252e-16
          ],
          [
            5.376796785583338e-10,
            -0.010999961299239747,
            9.693804647881166e-10
          ],
          [
            1.0759815260996675e-09,
            -0.022018839402171975,
            1.9399547523946126e-09
          ],
          [
            1.6153753890080225e-09,
            -0.033090077454125844,
            2.9128054412908e-09
          ],
          [
            2.156136380548901e-09,
            -0.0442706281083019,
            3.88885501578784e-09
          ],
          [
            2.698439027781774e-09,
            -0.055635744852857216,
            4.8687763820609575e-09
          ],
          [
            3.2424417595322552e-09,
            -0.06726447656333456,
            5.8536402391951015e-09
          ],
          [
            3.788194424814151e-09,
            -0.07923154200216559,
            6.844763200675175e-09
          ],
          [
            4.335463321680777e-09,
            -0.09160314318501278,
            7.842916427414082e-09
          ]
        ]
      },
      "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": "C2/m",
        "spacegroup_number": 12,
        "pointgroup": "2/m",
        "has_inversion": true,
        "is_polar_point_group": false,
        "nonpolar_parent_hypothesis": true,
        "symmetry_tolerance_A": null,
        "target_reduced_polarization": [
          0.0,
          0.0,
          0.0
        ],
        "formal_class": [
          0.0,
          0.0,
          0.0
        ],
        "target_residual": 3.6847954287622854e-15,
        "parent_symmetrization_rmsd_A": 0.2125394622113827,
        "parent_cell_rmsd_A": 0.0,
        "energy_eV": -323.7815632500804,
        "reduced_polarization": [
          -1.798622727097208e-15,
          3.1978882314505917e-15,
          -3.4085846996465534e-16
        ],
        "cartesian_polarization_e_A2": [
          -2.511198118890025e-17,
          2.7546160313092422e-17,
          -3.947032994784478e-18
        ],
        "ranking_score": 0.21253946221139008
      }
    }
  ],
  "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": 48,
      "full_response": 16,
      "energy_polarization": 32
    },
    "model_evaluations_for_recovery_and_path_properties": {
      "total": 73,
      "full_response": 41,
      "energy_polarization": 32
    },
    "elapsed_seconds": 922.8977880870225
  }
}
