{
  "schema": "ferrofinder.endpoint_parent_recovery.v4_variable_cell",
  "status": "complete",
  "input_atom_count": 16,
  "input_formula": "As2O8Tl6",
  "input_spacegroup": "P6_3",
  "input_pointgroup": "6",
  "input_is_polar_point_group": true,
  "input_energy_eV": -78.64525548547559,
  "input_cartesian_polarization_e_A2": [
    1.2594438099931097e-11,
    0.0005514794409478728,
    3.9147649703406077e-11
  ],
  "input_reduced_polarization": [
    1.4946449555980582e-09,
    0.03982770587365218,
    1.919621257827688e-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": "P6_3/m",
      "spacegroup_number": 176,
      "pointgroup": "6/m",
      "has_inversion": true,
      "is_polar_point_group": false,
      "nonpolar_parent_hypothesis": true,
      "symmetry_tolerance_A": null,
      "target_reduced_polarization": [
        0.0,
        0.0,
        0.0
      ],
      "formal_class": [
        0.0,
        0.0,
        0.0
      ],
      "target_residual": 4.8683520077438335e-16,
      "parent_symmetrization_rmsd_A": 0.4128024431172261,
      "parent_cell_rmsd_A": 0.0,
      "energy_eV": -74.31978120723464,
      "reduced_polarization": [
        1.1812931982334496e-16,
        4.722565644761731e-16,
        5.264391728414144e-18
      ],
      "cartesian_polarization_e_A2": [
        2.719760603092417e-18,
        6.539161130382245e-18,
        1.0735897117470066e-19
      ],
      "ranking_score": 0.4128024431172271
    },
    {
      "candidate_id": "inversion_parent_endpoint_01",
      "source": "same_species_inversion_center_projection_from_endpoint",
      "spacegroup": "P2_1/m",
      "spacegroup_number": 11,
      "pointgroup": "2/m",
      "has_inversion": true,
      "is_polar_point_group": false,
      "nonpolar_parent_hypothesis": true,
      "symmetry_tolerance_A": null,
      "target_reduced_polarization": [
        0.0,
        0.0,
        0.0
      ],
      "formal_class": [
        0.0,
        0.0,
        0.0
      ],
      "target_residual": 1.4794571165603693e-15,
      "parent_symmetrization_rmsd_A": 0.5822040554549167,
      "parent_cell_rmsd_A": 0.0,
      "energy_eV": -64.99729498008426,
      "reduced_polarization": [
        2.2513759015719166e-16,
        1.4498928629968359e-15,
        -1.8951810222290917e-16
      ],
      "cartesian_polarization_e_A2": [
        7.533021144091497e-18,
        2.0076127609669026e-17,
        -3.864922962289224e-18
      ],
      "ranking_score": 0.5822040554549197
    },
    {
      "candidate_id": "inversion_parent_endpoint_02",
      "source": "same_species_inversion_center_projection_from_endpoint",
      "spacegroup": "P-1",
      "spacegroup_number": 2,
      "pointgroup": "-1",
      "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": 1.0377118289958719e-15,
      "parent_symmetrization_rmsd_A": 0.8807221503369451,
      "parent_cell_rmsd_A": 0.0,
      "energy_eV": -55.85704169831386,
      "reduced_polarization": [
        -9.560447515060242e-16,
        2.3898604802679144e-16,
        -3.251306537444267e-16
      ],
      "cartesian_polarization_e_A2": [
        -1.8685089392297012e-17,
        3.309150985955868e-18,
        -6.630527187967175e-18
      ],
      "ranking_score": 0.8807221503369472
    },
    {
      "candidate_id": "bec_projection_00",
      "source": "MACEField_BEC_backprojection",
      "spacegroup": "P6_3",
      "spacegroup_number": 173,
      "pointgroup": "6",
      "has_inversion": false,
      "is_polar_point_group": true,
      "nonpolar_parent_hypothesis": false,
      "symmetry_tolerance_A": null,
      "target_reduced_polarization": [
        0.0,
        0.0,
        0.0
      ],
      "formal_class": [
        0.0,
        0.0,
        0.0
      ],
      "target_residual": 0.00014660598156600123,
      "parent_symmetrization_rmsd_A": 0.006065486000954326,
      "parent_cell_rmsd_A": 0.005917157782351317,
      "energy_eV": -78.63130053924674,
      "reduced_polarization": [
        -2.337992982671286e-12,
        0.0001466059815660012,
        -7.32385644316707e-13
      ],
      "cartesian_polarization_e_A2": [
        -4.642312934725414e-14,
        2.031836941132923e-06,
        -1.5105839058126546e-14
      ],
      "ranking_score": 0.5078379874096741
    },
    {
      "candidate_id": "inversion_parent_bec_00_00",
      "source": "same_species_inversion_center_projection_after_BEC",
      "spacegroup": "P6_3/m",
      "spacegroup_number": 176,
      "pointgroup": "6/m",
      "has_inversion": true,
      "is_polar_point_group": false,
      "nonpolar_parent_hypothesis": true,
      "symmetry_tolerance_A": null,
      "target_reduced_polarization": [
        0.0,
        0.0,
        0.0
      ],
      "formal_class": [
        0.0,
        0.0,
        0.0
      ],
      "target_residual": 4.239747390359554e-15,
      "parent_symmetrization_rmsd_A": 0.4128038307394114,
      "parent_cell_rmsd_A": 0.005917157782351317,
      "energy_eV": -74.28138495055859,
      "reduced_polarization": [
        -6.064229438357406e-16,
        -4.100570252515611e-15,
        -8.905238634839056e-16
      ],
      "cartesian_polarization_e_A2": [
        -3.791564543919012e-18,
        -5.683049238186023e-17,
        -1.814406712172565e-17
      ],
      "ranking_score": 0.41428312018500774
    },
    {
      "candidate_id": "inversion_parent_bec_00_01",
      "source": "same_species_inversion_center_projection_after_BEC",
      "spacegroup": "P2_1/m",
      "spacegroup_number": 11,
      "pointgroup": "2/m",
      "has_inversion": true,
      "is_polar_point_group": false,
      "nonpolar_parent_hypothesis": true,
      "symmetry_tolerance_A": null,
      "target_reduced_polarization": [
        0.0,
        0.0,
        0.0
      ],
      "formal_class": [
        0.0,
        0.0,
        0.0
      ],
      "target_residual": 2.18115438633483e-15,
      "parent_symmetrization_rmsd_A": 0.5822049894339223,
      "parent_cell_rmsd_A": 0.005917157782351317,
      "energy_eV": -65.08692650100825,
      "reduced_polarization": [
        8.777896263869539e-16,
        -8.258960790385543e-16,
        1.8179151507878092e-15
      ],
      "cartesian_polarization_e_A2": [
        -7.332742750032052e-19,
        -1.1446232585415887e-17,
        3.7039293256869216e-17
      ],
      "ranking_score": 0.5836842788795145
    },
    {
      "candidate_id": "bec_projection_01",
      "source": "MACEField_BEC_backprojection",
      "spacegroup": "P6_3",
      "spacegroup_number": 173,
      "pointgroup": "6",
      "has_inversion": false,
      "is_polar_point_group": true,
      "nonpolar_parent_hypothesis": false,
      "symmetry_tolerance_A": null,
      "target_reduced_polarization": [
        0.0,
        0.5,
        0.0
      ],
      "formal_class": [
        0.0,
        0.5,
        0.0
      ],
      "target_residual": 7.125801174601185e-05,
      "parent_symmetrization_rmsd_A": 0.06980943268925296,
      "parent_cell_rmsd_A": 0.06696310052720597,
      "energy_eV": -77.21280303478255,
      "reduced_polarization": [
        3.579092447119955e-12,
        0.500071258011746,
        -5.646279390849435e-12
      ],
      "cartesian_polarization_e_A2": [
        -3.759352663336652e-13,
        0.006853644116195515,
        -2.589984090756786e-13
      ],
      "ranking_score": 0.5866927238445465
    },
    {
      "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": 1.1130869904918646e-06,
      "parent_symmetrization_rmsd_A": 0.18470289295412032,
      "parent_cell_rmsd_A": 0.2213780090867138,
      "energy_eV": -69.89413131524451,
      "reduced_polarization": [
        6.708898168074237e-07,
        -8.306623647283617e-07,
        0.5000003144352683
      ],
      "cartesian_polarization_e_A2": [
        -0.005886452741194834,
        0.0004008225219538497,
        0.010194940026479754
      ],
      "ranking_score": 0.7400496213997798
    },
    {
      "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": 1.21485216671361e-06,
      "parent_symmetrization_rmsd_A": 0.1847012198842849,
      "parent_cell_rmsd_A": 0.2156115189643989,
      "energy_eV": -69.89436815236556,
      "reduced_polarization": [
        0.49999956420126274,
        -8.562107089210509e-07,
        -7.435378063668984e-07
      ],
      "cartesian_polarization_e_A2": [
        0.011772395385541914,
        0.0004008213482003003,
        6.122280323950019e-07
      ],
      "ranking_score": 0.738606529329718
    },
    {
      "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": 9.966655240780204e-05,
      "parent_symmetrization_rmsd_A": 0.21042044730378948,
      "parent_cell_rmsd_A": 0.2748765185992233,
      "energy_eV": -70.02032709222928,
      "reduced_polarization": [
        1.3032286447958459e-05,
        0.4999224444956295,
        0.499938773168295
      ],
      "cartesian_polarization_e_A2": [
        -0.006131286058958138,
        0.0073262059387570674,
        0.010597566723085386
      ],
      "ranking_score": 0.7793389100584109
    },
    {
      "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": 9.78521225933798e-05,
      "parent_symmetrization_rmsd_A": 0.21049970900991574,
      "parent_cell_rmsd_A": 0.2674985695251133,
      "energy_eV": -70.02386153152854,
      "reduced_polarization": [
        0.4999317486884913,
        0.49993077707714395,
        -1.1179594117588084e-05
      ],
      "cartesian_polarization_e_A2": [
        0.012247796496299897,
        0.007326543201433486,
        1.3864591829755548e-05
      ],
      "ranking_score": 0.7775700556363808
    },
    {
      "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": 1.020533253994993e-06,
      "parent_symmetrization_rmsd_A": 0.1846992952194181,
      "parent_cell_rmsd_A": 0.13854783856561123,
      "energy_eV": -69.89417282720515,
      "reduced_polarization": [
        0.5000004116707107,
        -8.73967181223491e-07,
        0.49999967106730997
      ],
      "cartesian_polarization_e_A2": [
        0.005885573669819424,
        0.0004008212202393636,
        0.010195229935290723
      ],
      "ranking_score": 0.7193382959273289
    },
    {
      "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": 0.00012674189236034652,
      "parent_symmetrization_rmsd_A": 0.21040039786069856,
      "parent_cell_rmsd_A": 0.1849929515627364,
      "energy_eV": -70.02078049978965,
      "reduced_polarization": [
        0.49993528009835875,
        0.49991997096674023,
        0.49992603923035733
      ],
      "cartesian_polarization_e_A2": [
        0.0061076628834458215,
        0.00732607113963553,
        0.010610580314761761
      ],
      "ranking_score": 0.7569021195361033
    }
  ],
  "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": [
              1.4946449555980582e-09,
              0.03982770587365218,
              1.919621257827688e-09
            ],
            "branch_aligned_reduced_polarization": [
              1.4946449555980582e-09,
              0.03982770587365218,
              1.919621257827688e-09
            ],
            "target_residual": 0.03982770587365226,
            "energy_eV": -78.64525548547559,
            "max_atomic_step_A": 0.009028996378262303,
            "max_log_strain_component": 0.0013760817713697768,
            "step_scale": 1.0,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 3.625512780854663,
            "cell_principal_stretches": [
              1.0013770290063313,
              0.9995475004542109,
              0.9995474969506065
            ],
            "cell_volume_ratio": 1.0004709852357059,
            "cell_rmsd_from_input_A": 0.005917157782351317
          },
          {
            "iteration": 1,
            "reduced_polarization": [
              -2.337992982671286e-12,
              0.0001466059815660012,
              -7.32385644316707e-13
            ],
            "branch_aligned_reduced_polarization": [
              -2.337992982671286e-12,
              0.0001466059815660012,
              -7.32385644316707e-13
            ],
            "target_residual": 0.00014660598156600123,
            "energy_eV": -78.63130053924674
          }
        ],
        "iterations": 1
      },
      "parent": {
        "candidate_id": "inversion_parent_endpoint_00",
        "source": "same_species_inversion_center_projection_from_endpoint",
        "spacegroup": "P6_3/m",
        "spacegroup_number": 176,
        "pointgroup": "6/m",
        "has_inversion": true,
        "is_polar_point_group": false,
        "nonpolar_parent_hypothesis": true,
        "symmetry_tolerance_A": null,
        "target_reduced_polarization": [
          0.0,
          0.0,
          0.0
        ],
        "formal_class": [
          0.0,
          0.0,
          0.0
        ],
        "target_residual": 4.8683520077438335e-16,
        "parent_symmetrization_rmsd_A": 0.4128024431172261,
        "parent_cell_rmsd_A": 0.0,
        "energy_eV": -74.31978120723464,
        "reduced_polarization": [
          1.1812931982334496e-16,
          4.722565644761731e-16,
          5.264391728414144e-18
        ],
        "cartesian_polarization_e_A2": [
          2.719760603092417e-18,
          6.539161130382245e-18,
          1.0735897117470066e-19
        ],
        "ranking_score": 0.4128024431172271
      },
      "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": [
          -78.64525548547559,
          -78.39789309931237,
          -77.85412286902894,
          -77.16563843920022,
          -76.40873563905525,
          -75.65697566466696,
          -75.00295482896573,
          -74.5148729633517,
          -74.31978120723463
        ],
        "cartesian_polarizations_e_A2": [
          [
            1.2594461718904755e-11,
            0.0005514794409478721,
            3.91476574824582e-11
          ],
          [
            1.0441587098814705e-11,
            -0.0026911937064164394,
            3.274363398382394e-11
          ],
          [
            7.566837931703873e-12,
            -0.005779610705982343,
            2.7768107014150512e-11
          ],
          [
            5.207950696694255e-12,
            -0.008477352934042608,
            2.2142212530681555e-11
          ],
          [
            3.6927632254895095e-12,
            -0.010030928517773449,
            1.5766024149068926e-11
          ],
          [
            2.5079051729914467e-12,
            -0.009515793427736313,
            1.0020112991204542e-11
          ],
          [
            1.3780410377511497e-12,
            -0.006993019927257892,
            5.7550956462757315e-12
          ],
          [
            4.905137274940677e-13,
            -0.003582517580910001,
            2.779103999082288e-12
          ],
          [
            1.6211204647379802e-17,
            2.2684743600168973e-17,
            9.832292443416336e-18
          ]
        ],
        "raw_reduced_polarization": [
          [
            1.4946461493239199e-09,
            0.03982770587365213,
            1.9196216392767384e-09
          ],
          [
            1.246210384830353e-09,
            -0.19435732944813278,
            1.6055976879860747e-09
          ],
          [
            1.002143016374665e-09,
            -0.41740202475441684,
            1.3616206571236297e-09
          ],
          [
            7.640366769019425e-10,
            -0.6122322867809414,
            1.0857525851810398e-09
          ],
          [
            5.433633342493753e-10,
            -0.7244311228698611,
            7.730935404110397e-10
          ],
          [
            3.5217068518363966e-10,
            -0.6872281968352428,
            4.913404010069619e-10
          ],
          [
            1.9962152399477918e-10,
            -0.5050341321023821,
            2.8220350460684904e-10
          ],
          [
            8.896737251491804e-11,
            -0.25872851443823497,
            1.362745185156834e-10
          ],
          [
            9.294889138307384e-16,
            1.6382864506677825e-15,
            4.821305424605953e-16
          ]
        ],
        "unwrapped_reduced_polarization": [
          [
            1.4946461493239199e-09,
            0.03982770587365213,
            1.9196216392767384e-09
          ],
          [
            1.246210384830353e-09,
            -0.19435732944813278,
            1.6055976879860747e-09
          ],
          [
            1.002143016374665e-09,
            -0.41740202475441684,
            1.3616206571236297e-09
          ],
          [
            7.640366769019425e-10,
            -0.6122322867809414,
            1.0857525851810398e-09
          ],
          [
            5.433633342493753e-10,
            -0.7244311228698611,
            7.730935404110397e-10
          ],
          [
            3.5217068518363966e-10,
            -0.6872281968352428,
            4.913404010069619e-10
          ],
          [
            1.9962152399477918e-10,
            -0.5050341321023821,
            2.8220350460684904e-10
          ],
          [
            8.896737251491804e-11,
            -0.25872851443823497,
            1.362745185156834e-10
          ],
          [
            9.294889138251244e-16,
            1.6653345369377348e-15,
            4.821305424716208e-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": [
          [
            1.4946461845966041e-09,
            0.03982770587365214,
            1.9196216838324176e-09
          ],
          [
            1.2462103571309058e-09,
            -0.19435732944813278,
            1.6055976548301487e-09
          ],
          [
            1.0021430352225025e-09,
            -0.41740202475441684,
            1.36162070507595e-09
          ],
          [
            7.640367227779166e-10,
            0.38776771321905856,
            1.0857525989393935e-09
          ],
          [
            5.433633543105998e-10,
            0.2755688771301389,
            7.730935891459012e-10
          ],
          [
            3.5217073701687696e-10,
            0.31277180316475717,
            4.913404128004117e-10
          ],
          [
            1.9962154151897948e-10,
            0.4949658678976179,
            2.8220348280427743e-10
          ],
          [
            8.896738901142953e-11,
            -0.25872851443823497,
            1.3627454720221976e-10
          ],
          [
            8.881784197001252e-16,
            1.6653345369377348e-15,
            4.440892098500626e-16
          ]
        ]
      },
      "reflected": {
        "reached": true,
        "construction": "reflect_displacements_about_reconstructed_parent",
        "energies_eV": [
          -74.31978120723463,
          -74.51487296335173,
          -75.00295482896573,
          -75.65697566466693,
          -76.40873563905524,
          -77.16563843920024,
          -77.85412286902894,
          -78.39789309931237,
          -78.6452554854756
        ],
        "cartesian_polarizations_e_A2": [
          [
            1.6211204647379802e-17,
            2.2684743600168973e-17,
            9.832292443416336e-18
          ],
          [
            -4.905094689215444e-13,
            0.0035825175809100153,
            -2.77906760439106e-12
          ],
          [
            -1.3780184565808792e-12,
            0.006993019927257912,
            -5.7550967735449285e-12
          ],
          [
            -2.507874289394072e-12,
            0.009515793427736318,
            -1.0020179585079702e-11
          ],
          [
            -3.6927214270633985e-12,
            0.01003092851777358,
            -1.5765990845421408e-11
          ],
          [
            -5.207941177532144e-12,
            0.008477352934042622,
            -2.214219021343542e-11
          ],
          [
            -7.566861407532238e-12,
            0.005779610705982351,
            -2.7768092332811203e-11
          ],
          [
            -1.0441552153469587e-11,
            0.0026911937064164697,
            -3.2743587148472765e-11
          ],
          [
            -1.259442227342943e-11,
            -0.0005514794409478722,
            -3.914763434659991e-11
          ]
        ],
        "raw_reduced_polarization": [
          [
            9.294889138307384e-16,
            1.6382864506677825e-15,
            4.821305424605953e-16
          ],
          [
            -8.896629935635551e-11,
            0.258728514438236,
            -1.3627273388688747e-10
          ],
          [
            -1.996205927027661e-10,
            0.5050341321023836,
            -2.8220355988296217e-10
          ],
          [
            -3.5217100641253194e-10,
            0.6872281968352432,
            -4.91343666465281e-10
          ],
          [
            -5.433607427118662e-10,
            0.7244311228698705,
            -7.730919073528556e-10
          ],
          [
            -7.640357254943033e-10,
            0.6122322867809424,
            -1.0857514908456093e-09
          ],
          [
            -1.0021436533444312e-09,
            0.41740202475441746,
            -1.3616199372180607e-09
          ],
          [
            -1.246207752548855e-09,
            0.19435732944813497,
            -1.605595391395183e-09
          ],
          [
            -1.4946439069974985e-09,
            -0.039827705873652135,
            -1.9196205048003208e-09
          ]
        ],
        "unwrapped_reduced_polarization": [
          [
            9.294889138307384e-16,
            1.6382864506677825e-15,
            4.821305424605953e-16
          ],
          [
            -8.896629935635551e-11,
            0.258728514438236,
            -1.3627273388688747e-10
          ],
          [
            -1.996205927027661e-10,
            0.5050341321023836,
            -2.8220355988296217e-10
          ],
          [
            -3.5217100641253194e-10,
            0.6872281968352432,
            -4.91343666465281e-10
          ],
          [
            -5.433607427118662e-10,
            0.7244311228698705,
            -7.730919073528556e-10
          ],
          [
            -7.640357254943033e-10,
            0.6122322867809424,
            -1.0857514908456093e-09
          ],
          [
            -1.0021436533444312e-09,
            0.41740202475441746,
            -1.3616199372180607e-09
          ],
          [
            -1.246207752548855e-09,
            0.19435732944813497,
            -1.605595391395183e-09
          ],
          [
            -1.4946439069974985e-09,
            -0.03982770587365214,
            -1.9196205048003208e-09
          ]
        ],
        "gauge_integer_shift": [
          0,
          0,
          0
        ],
        "expected_opposite_endpoint_reduced_polarization": [
          -1.4946442903460922e-09,
          -0.03982770587364885,
          -1.919620675015654e-09
        ],
        "actual_opposite_endpoint_branch_residual": 3.3156726781251273e-15
      },
      "pnp_branch": {
        "construction": "incoming_path_concatenated_with_parent_reflection",
        "reduced_polarization": [
          [
            1.4946461493239199e-09,
            0.03982770587365213,
            1.9196216392767384e-09
          ],
          [
            1.246210384830353e-09,
            -0.19435732944813278,
            1.6055976879860747e-09
          ],
          [
            1.002143016374665e-09,
            -0.41740202475441684,
            1.3616206571236297e-09
          ],
          [
            7.640366769019425e-10,
            -0.6122322867809414,
            1.0857525851810398e-09
          ],
          [
            5.433633342493753e-10,
            -0.7244311228698611,
            7.730935404110397e-10
          ],
          [
            3.5217068518363966e-10,
            -0.6872281968352428,
            4.913404010069619e-10
          ],
          [
            1.9962152399477918e-10,
            -0.5050341321023821,
            2.8220350460684904e-10
          ],
          [
            8.896737251491804e-11,
            -0.25872851443823497,
            1.362745185156834e-10
          ],
          [
            9.294889138307384e-16,
            1.6382864506677825e-15,
            4.821305424605953e-16
          ],
          [
            -8.896629935635551e-11,
            0.258728514438236,
            -1.3627273388688747e-10
          ],
          [
            -1.996205927027661e-10,
            0.5050341321023836,
            -2.8220355988296217e-10
          ],
          [
            -3.5217100641253194e-10,
            0.6872281968352432,
            -4.91343666465281e-10
          ],
          [
            -5.433607427118662e-10,
            0.7244311228698705,
            -7.730919073528556e-10
          ],
          [
            -7.640357254943033e-10,
            0.6122322867809424,
            -1.0857514908456093e-09
          ],
          [
            -1.0021436533444312e-09,
            0.41740202475441746,
            -1.3616199372180607e-09
          ],
          [
            -1.246207752548855e-09,
            0.19435732944813497,
            -1.605595391395183e-09
          ],
          [
            -1.4946439069974985e-09,
            -0.039827705873652135,
            -1.9196205048003208e-09
          ]
        ],
        "unwrapped_reduced_polarization": [
          [
            1.4946461493239199e-09,
            0.03982770587365213,
            1.9196216392767384e-09
          ],
          [
            1.246210384830353e-09,
            -0.19435732944813278,
            1.6055976879860747e-09
          ],
          [
            1.002143016374665e-09,
            -0.41740202475441684,
            1.3616206571236297e-09
          ],
          [
            7.640366769019425e-10,
            -0.6122322867809414,
            1.0857525851810398e-09
          ],
          [
            5.433633342493753e-10,
            -0.7244311228698611,
            7.730935404110397e-10
          ],
          [
            3.5217068518363966e-10,
            -0.6872281968352428,
            4.913404010069619e-10
          ],
          [
            1.9962152399477918e-10,
            -0.5050341321023821,
            2.8220350460684904e-10
          ],
          [
            8.896737251491804e-11,
            -0.25872851443823497,
            1.362745185156834e-10
          ],
          [
            9.294889138251244e-16,
            1.6653345369377348e-15,
            4.821305424716208e-16
          ],
          [
            -8.896629935635551e-11,
            0.258728514438236,
            -1.3627273388688747e-10
          ],
          [
            -1.996205927027661e-10,
            0.5050341321023836,
            -2.8220355988296217e-10
          ],
          [
            -3.5217100641253194e-10,
            0.6872281968352432,
            -4.91343666465281e-10
          ],
          [
            -5.433607427118662e-10,
            0.7244311228698705,
            -7.730919073528556e-10
          ],
          [
            -7.640357254943033e-10,
            0.6122322867809424,
            -1.0857514908456093e-09
          ],
          [
            -1.0021436533444312e-09,
            0.41740202475441746,
            -1.3616199372180607e-09
          ],
          [
            -1.246207752548855e-09,
            0.19435732944813497,
            -1.605595391395183e-09
          ],
          [
            -1.4946439069974985e-09,
            -0.03982770587365214,
            -1.9196205048003208e-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": [
          [
            1.4946461845966041e-09,
            0.03982770587365214,
            1.9196216838324176e-09
          ],
          [
            1.2462103571309058e-09,
            -0.19435732944813278,
            1.6055976548301487e-09
          ],
          [
            1.0021430352225025e-09,
            -0.41740202475441684,
            1.36162070507595e-09
          ],
          [
            7.640367227779166e-10,
            0.38776771321905856,
            1.0857525989393935e-09
          ],
          [
            5.433633543105998e-10,
            0.2755688771301389,
            7.730935891459012e-10
          ],
          [
            3.5217073701687696e-10,
            0.31277180316475717,
            4.913404128004117e-10
          ],
          [
            1.9962154151897948e-10,
            0.4949658678976179,
            2.8220348280427743e-10
          ],
          [
            8.896738901142953e-11,
            -0.25872851443823497,
            1.3627454720221976e-10
          ],
          [
            8.881784197001252e-16,
            1.6653345369377348e-15,
            4.440892098500626e-16
          ],
          [
            -8.896627878840491e-11,
            0.2587285144382361,
            -1.3627271533422913e-10
          ],
          [
            -1.9962059782940855e-10,
            -0.49496586789761654,
            -2.8220353831542866e-10
          ],
          [
            -3.521710145726331e-10,
            -0.31277180316475683,
            -4.913436879583344e-10
          ],
          [
            -5.433607452864919e-10,
            -0.27556887713012945,
            -7.730919238113643e-10
          ],
          [
            -7.640357235771944e-10,
            -0.38776771321905756,
            -1.0857514887163688e-09
          ],
          [
            -1.002143645845166e-09,
            0.41740202475441746,
            -1.3616199279198327e-09
          ],
          [
            -1.246207748106798e-09,
            0.194357329448135,
            -1.6055953788729482e-09
          ],
          [
            -1.4946439086394037e-09,
            -0.03982770587365214,
            -1.9196205180982417e-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": [
              1.4946449555980582e-09,
              0.03982770587365218,
              1.919621257827688e-09
            ],
            "branch_aligned_reduced_polarization": [
              1.4946449555980582e-09,
              0.0398277058736522,
              1.919621257827688e-09
            ],
            "target_residual": 0.4601722941263478,
            "energy_eV": -78.64525548547559,
            "max_atomic_step_A": 0.10432169982936267,
            "max_log_strain_component": 0.015899351763958663,
            "step_scale": 1.0,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 3.625512780854663,
            "cell_principal_stretches": [
              1.0052431347263053,
              1.0052430940147266,
              0.9842263757188944
            ],
            "cell_volume_ratio": 0.9945742552550938,
            "cell_rmsd_from_input_A": 0.06828215867468504
          },
          {
            "iteration": 1,
            "reduced_polarization": [
              -2.6218485680380564e-11,
              0.5091176531374385,
              2.882133187826315e-10
            ],
            "branch_aligned_reduced_polarization": [
              -2.6218485680380564e-11,
              0.5091176531374385,
              2.882133187826315e-10
            ],
            "target_residual": 0.009117653137438512,
            "energy_eV": -77.1489320700692,
            "max_atomic_step_A": 0.0018577278117459046,
            "max_log_strain_component": 0.00030745035137148987,
            "step_scale": 1.0,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 3.625512780854663,
            "cell_principal_stretches": [
              1.0051414865250778,
              1.0051414466047879,
              0.9845290229860584
            ],
            "cell_volume_ratio": 0.9946788948019717,
            "cell_rmsd_from_input_A": 0.06696310052720597
          },
          {
            "iteration": 2,
            "reduced_polarization": [
              3.579092447119955e-12,
              0.500071258011746,
              -5.646279390849435e-12
            ],
            "branch_aligned_reduced_polarization": [
              3.579092447119955e-12,
              0.500071258011746,
              -5.646279390849435e-12
            ],
            "target_residual": 7.125801174601185e-05,
            "energy_eV": -77.21280303478255
          }
        ],
        "iterations": 2
      },
      "parent": {
        "candidate_id": "bec_projection_01",
        "source": "MACEField_BEC_backprojection",
        "spacegroup": "P6_3",
        "spacegroup_number": 173,
        "pointgroup": "6",
        "has_inversion": false,
        "is_polar_point_group": true,
        "nonpolar_parent_hypothesis": false,
        "symmetry_tolerance_A": null,
        "target_reduced_polarization": [
          0.0,
          0.5,
          0.0
        ],
        "formal_class": [
          0.0,
          0.5,
          0.0
        ],
        "target_residual": 7.125801174601185e-05,
        "parent_symmetrization_rmsd_A": 0.06980943268925296,
        "parent_cell_rmsd_A": 0.06696310052720597,
        "energy_eV": -77.21280303478255,
        "reduced_polarization": [
          3.579092447119955e-12,
          0.500071258011746,
          -5.646279390849435e-12
        ],
        "cartesian_polarization_e_A2": [
          -3.759352663336652e-13,
          0.006853644116195515,
          -2.589984090756786e-13
        ],
        "ranking_score": 0.5866927238445465
      },
      "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": [
              1.4946449555980582e-09,
              0.03982770587365218,
              1.919621257827688e-09
            ],
            "branch_aligned_reduced_polarization": [
              1.4946449555980582e-09,
              0.03982770587365218,
              1.9196212397432078e-09
            ],
            "target_residual": 0.5015837360157693,
            "energy_eV": -78.64525548547559,
            "max_atomic_step_A": 0.12000000000000001,
            "max_log_strain_component": 0.010712982391328925,
            "step_scale": 0.5149451090007038,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 3.625512780854663,
            "cell_principal_stretches": [
              1.0131176014909296,
              0.9997669603968948,
              0.9875217375449353
            ],
            "cell_volume_ratio": 1.000242503712317,
            "cell_rmsd_from_input_A": 0.0833903306073964
          },
          {
            "iteration": 1,
            "reduced_polarization": [
              -0.0012830449737392616,
              0.02214449246711251,
              0.2484774533236188
            ],
            "branch_aligned_reduced_polarization": [
              -0.0012830449737392616,
              0.02214449246711251,
              0.2484774533236188
            ],
            "target_residual": 0.25249874502183767,
            "energy_eV": -77.01205179122915,
            "max_atomic_step_A": 0.12,
            "max_log_strain_component": 0.011967931275701687,
            "step_scale": 0.9495811928838138,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 3.625512780854663,
            "cell_principal_stretches": [
              1.027971086821738,
              0.9993919204989782,
              0.9739980670657562
            ],
            "cell_volume_ratio": 1.0006330169183564,
            "cell_rmsd_from_input_A": 0.17553488625644872
          },
          {
            "iteration": 2,
            "reduced_polarization": [
              -0.003283560049089105,
              -0.001827823556389967,
              0.4443108015933178
            ],
            "branch_aligned_reduced_polarization": [
              -0.003283560049089105,
              -0.001827823556389967,
              0.4443108015933178
            ],
            "target_residual": 0.05581585370419485,
            "energy_eV": -70.86243965810155,
            "max_atomic_step_A": 0.02821716094560703,
            "max_log_strain_component": 0.00524915005809852,
            "step_scale": 1.0,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 3.625512780854663,
            "cell_principal_stretches": [
              1.0340803787866093,
              0.9994947489626856,
              0.9680405012815333
            ],
            "cell_volume_ratio": 1.0005259159471158,
            "cell_rmsd_from_input_A": 0.21428412685598208
          },
          {
            "iteration": 3,
            "reduced_polarization": [
              0.0003521510383657921,
              -0.0037165592131250848,
              0.4921325983232578
            ],
            "branch_aligned_reduced_polarization": [
              0.0003521510383657921,
              -0.0037165592131250848,
              0.4921325983232578
            ],
            "target_residual": 0.008708204859883193,
            "energy_eV": -69.96419940571208,
            "max_atomic_step_A": 0.004905300339545419,
            "max_log_strain_component": 0.0009090557592321444,
            "step_scale": 1.0,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 3.625512780854663,
            "cell_principal_stretches": [
              1.035098104435982,
              0.9995873546590867,
              0.9669059102844777
            ],
            "cell_volume_ratio": 1.0004294819191535,
            "cell_rmsd_from_input_A": 0.22133898172836505
          },
          {
            "iteration": 4,
            "reduced_polarization": [
              0.0001415007544081013,
              -0.0003458217055952364,
              0.49892980420345484
            ],
            "branch_aligned_reduced_polarization": [
              0.0001415007544081013,
              -0.0003458217055952364,
              0.49892980420345484
            ],
            "target_residual": 0.0011335493630635536,
            "energy_eV": -69.90140326627444,
            "max_atomic_step_A": 0.0007442021184706491,
            "max_log_strain_component": 8.628377593732183e-05,
            "step_scale": 1.0,
            "strain_jacobian_refreshed": true,
            "strain_jacobian_frobenius_norm": 3.137450695986546,
            "cell_principal_stretches": [
              1.035024713265854,
              0.9995553576979295,
              0.9668172910874631
            ],
            "cell_volume_ratio": 1.0002348449230378,
            "cell_rmsd_from_input_A": 0.2213780090867138
          },
          {
            "iteration": 5,
            "reduced_polarization": [
              6.708898168074237e-07,
              -8.306623647283617e-07,
              0.5000003144352683
            ],
            "branch_aligned_reduced_polarization": [
              6.708898168074237e-07,
              -8.306623647283617e-07,
              0.5000003144352683
            ],
            "target_residual": 1.1130869904918646e-06,
            "energy_eV": -69.89413131524451
          }
        ],
        "iterations": 5
      },
      "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": 1.1130869904918646e-06,
        "parent_symmetrization_rmsd_A": 0.18470289295412032,
        "parent_cell_rmsd_A": 0.2213780090867138,
        "energy_eV": -69.89413131524451,
        "reduced_polarization": [
          6.708898168074237e-07,
          -8.306623647283617e-07,
          0.5000003144352683
        ],
        "cartesian_polarization_e_A2": [
          -0.005886452741194834,
          0.0004008225219538497,
          0.010194940026479754
        ],
        "ranking_score": 0.7400496213997798
      },
      "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": [
              1.4946449555980582e-09,
              0.03982770587365218,
              1.919621257827688e-09
            ],
            "branch_aligned_reduced_polarization": [
              1.494644963351277e-09,
              0.03982770587365218,
              1.919621257827688e-09
            ],
            "target_residual": 0.5015837364394037,
            "energy_eV": -78.64525548547559,
            "max_atomic_step_A": 0.11999999999999998,
            "max_log_strain_component": 0.012767366177147936,
            "step_scale": 0.5149445488514213,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 3.625512780854663,
            "cell_principal_stretches": [
              1.013117602026103,
              0.9997669624114259,
              0.9875217351603554
            ],
            "cell_volume_ratio": 1.0002425038408824,
            "cell_rmsd_from_input_A": 0.08034450468593836
          },
          {
            "iteration": 1,
            "reduced_polarization": [
              0.2497603864929621,
              0.02214440340014742,
              0.001283196355338742
            ],
            "branch_aligned_reduced_polarization": [
              0.24976038649296206,
              0.02214440340014742,
              0.001283196355338742
            ],
            "target_residual": 0.25122079006918707,
            "energy_eV": -77.01207474843972,
            "max_atomic_step_A": 0.12,
            "max_log_strain_component": 0.014142165466787602,
            "step_scale": 0.9495753503267479,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 3.625512780854663,
            "cell_principal_stretches": [
              1.0279709899789844,
              0.9993919322812101,
              0.9739981407302695
            ],
            "cell_volume_ratio": 1.000633010126858,
            "cell_rmsd_from_input_A": 0.17000708076953414
          },
          {
            "iteration": 2,
            "reduced_polarization": [
              0.44759354891016007,
              -0.0018278801634082989,
              0.0032831685043195266
            ],
            "branch_aligned_reduced_polarization": [
              0.44759354891016007,
              -0.0018278801634082989,
              0.0032831685043195266
            ],
            "target_residual": 0.0525409978697714,
            "energy_eV": -70.86258500063198,
            "max_atomic_step_A": 0.02821704753614411,
            "max_log_strain_component": 0.006048775406425065,
            "step_scale": 1.0,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 3.625512780854663,
            "cell_principal_stretches": [
              1.0340803114130475,
              0.9994947638757351,
              0.9680405398421755
            ],
            "cell_volume_ratio": 1.0005259055428215,
            "cell_rmsd_from_input_A": 0.20884001478231476
          },
          {
            "iteration": 3,
            "reduced_polarization": [
              0.4917802767978144,
              -0.003716682909967391,
              -0.00035219619992228775
            ],
            "branch_aligned_reduced_polarization": [
              0.4917802767978144,
              -0.003716682909967391,
              -0.00035219619992228775
            ],
            "target_residual": 0.009027824961585813,
            "energy_eV": -69.96430234890241,
            "max_atomic_step_A": 0.004905417287263445,
            "max_log_strain_component": 0.0010824721974833028,
            "step_scale": 1.0,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 3.625512780854663,
            "cell_principal_stretches": [
              1.0350980606502418,
              0.9995873729492405,
              0.9669059194969178
            ],
            "cell_volume_ratio": 1.0004294674373397,
            "cell_rmsd_from_input_A": 0.21563949635926266
          },
          {
            "iteration": 4,
            "reduced_polarization": [
              0.49878827221008265,
              -0.0003458395491826163,
              -0.0001415131724349531
            ],
            "branch_aligned_reduced_polarization": [
              0.49878827221008265,
              -0.0003458395491826163,
              -0.0001415131724349531
            ],
            "target_residual": 0.0012680359650299453,
            "energy_eV": -69.90150146148515,
            "max_atomic_step_A": 0.0007425757354740604,
            "max_log_strain_component": 8.093252942749619e-05,
            "step_scale": 1.0,
            "strain_jacobian_refreshed": true,
            "strain_jacobian_frobenius_norm": 3.1766013438871274,
            "cell_principal_stretches": [
              1.0350296845261746,
              0.9995458157160055,
              0.9668222545885681
            ],
            "cell_volume_ratio": 1.000235235609735,
            "cell_rmsd_from_input_A": 0.2156115189643989
          },
          {
            "iteration": 5,
            "reduced_polarization": [
              0.49999956420126274,
              -8.562107089210509e-07,
              -7.435378063668984e-07
            ],
            "branch_aligned_reduced_polarization": [
              0.49999956420126274,
              -8.562107089210509e-07,
              -7.435378063668984e-07
            ],
            "target_residual": 1.21485216671361e-06,
            "energy_eV": -69.89436815236556
          }
        ],
        "iterations": 5
      },
      "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": 1.21485216671361e-06,
        "parent_symmetrization_rmsd_A": 0.1847012198842849,
        "parent_cell_rmsd_A": 0.2156115189643989,
        "energy_eV": -69.89436815236556,
        "reduced_polarization": [
          0.49999956420126274,
          -8.562107089210509e-07,
          -7.435378063668984e-07
        ],
        "cartesian_polarization_e_A2": [
          0.011772395385541914,
          0.0004008213482003003,
          6.122280323950019e-07
        ],
        "ranking_score": 0.738606529329718
      },
      "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": [
              1.4946449555980582e-09,
              0.03982770587365218,
              1.919621257827688e-09
            ],
            "branch_aligned_reduced_polarization": [
              1.4946449555980582e-09,
              0.0398277058736522,
              1.9196212397432078e-09
            ],
            "target_residual": 0.6795281733393287,
            "energy_eV": -78.64525548547559,
            "max_atomic_step_A": 0.12,
            "max_log_strain_component": 0.009784037568367526,
            "step_scale": 0.4702931534659794,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 3.625512780854663,
            "cell_principal_stretches": [
              1.0102332032620664,
              1.0024623920283477,
              0.9849157227702093
            ],
            "cell_volume_ratio": 0.9974446322437993,
            "cell_rmsd_from_input_A": 0.08254012058155757
          },
          {
            "iteration": 1,
            "reduced_polarization": [
              -0.000959200603494918,
              0.2579752705836774,
              0.22682740796801384
            ],
            "branch_aligned_reduced_polarization": [
              -0.000959200603494918,
              0.2579752705836774,
              0.22682740796801382
            ],
            "target_residual": 0.36496596382719837,
            "energy_eV": -77.36207959672024,
            "max_atomic_step_A": 0.12,
            "max_log_strain_component": 0.010725114327447246,
            "step_scale": 0.8015410081600364,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 3.625512780854663,
            "cell_principal_stretches": [
              1.0215803816606643,
              1.0047149613166293,
              0.969525544372274
            ],
            "cell_volume_ratio": 0.9951182009554015,
            "cell_rmsd_from_input_A": 0.1697587218689269
          },
          {
            "iteration": 2,
            "reduced_polarization": [
              -0.0027115507136765502,
              0.4345534006419533,
              0.40882252047948586
            ],
            "branch_aligned_reduced_polarization": [
              -0.0027115507136765502,
              0.4345534006419533,
              0.40882252047948586
            ],
            "target_residual": 0.11226728217303246,
            "energy_eV": -73.34687850318915,
            "max_atomic_step_A": 0.05932941864364085,
            "max_log_strain_component": 0.009971460697670924,
            "step_scale": 1.0,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 3.625512780854663,
            "cell_principal_stretches": [
              1.0323380612848965,
              1.0062723169760548,
              0.9563952210365885
            ],
            "cell_volume_ratio": 0.993515992301922,
            "cell_rmsd_from_input_A": 0.24773124137122193
          },
          {
            "iteration": 3,
            "reduced_polarization": [
              0.0028258306276709704,
              0.4821652274411379,
              0.4723273899206445
            ],
            "branch_aligned_reduced_polarization": [
              0.0028258306276709704,
              0.4821652274411379,
              0.4723273899206445
            ],
            "target_residual": 0.03304296868573816,
            "energy_eV": -70.27003384066384,
            "max_atomic_step_A": 0.020597725707180686,
            "max_log_strain_component": 0.004042333882986427,
            "step_scale": 1.0,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 3.625512780854663,
            "cell_principal_stretches": [
              1.0369492161376919,
              1.006942060674587,
              0.9508505712114831
            ],
            "cell_volume_ratio": 0.9928285135295937,
            "cell_rmsd_from_input_A": 0.28173427899987713
          },
          {
            "iteration": 4,
            "reduced_polarization": [
              0.0003744398571058507,
              0.4959460168631281,
              0.4922088194565484
            ],
            "branch_aligned_reduced_polarization": [
              0.0003744398571058507,
              0.4959460168631281,
              0.4922088194565484
            ],
            "target_residual": 0.008790760987610243,
            "energy_eV": -70.07216893626168,
            "max_atomic_step_A": 0.005672070813287747,
            "max_log_strain_component": 0.0011959071476399144,
            "step_scale": 1.0,
            "strain_jacobian_refreshed": true,
            "strain_jacobian_frobenius_norm": 3.855212568374606,
            "cell_principal_stretches": [
              1.0351782074717057,
              1.0067812547458157,
              0.9500477921247503
            ],
            "cell_volume_ratio": 0.9901379227312228,
            "cell_rmsd_from_input_A": 0.2748765185992233
          },
          {
            "iteration": 5,
            "reduced_polarization": [
              1.3032286447958459e-05,
              0.4999224444956295,
              0.499938773168295
            ],
            "branch_aligned_reduced_polarization": [
              1.3032286447958459e-05,
              0.4999224444956295,
              0.499938773168295
            ],
            "target_residual": 9.966655240780204e-05,
            "energy_eV": -70.02032709222928
          }
        ],
        "iterations": 5
      },
      "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": 9.966655240780204e-05,
        "parent_symmetrization_rmsd_A": 0.21042044730378948,
        "parent_cell_rmsd_A": 0.2748765185992233,
        "energy_eV": -70.02032709222928,
        "reduced_polarization": [
          1.3032286447958459e-05,
          0.4999224444956295,
          0.499938773168295
        ],
        "cartesian_polarization_e_A2": [
          -0.006131286058958138,
          0.0073262059387570674,
          0.010597566723085386
        ],
        "ranking_score": 0.7793389100584109
      },
      "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": [
              1.4946449555980582e-09,
              0.03982770587365218,
              1.919621257827688e-09
            ],
            "branch_aligned_reduced_polarization": [
              1.494644963351277e-09,
              0.0398277058736522,
              1.919621257827688e-09
            ],
            "target_residual": 0.6795281736520282,
            "energy_eV": -78.64525548547559,
            "max_atomic_step_A": 0.12,
            "max_log_strain_component": 0.011660281088649593,
            "step_scale": 0.4702926287530935,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 3.625512780854663,
            "cell_principal_stretches": [
              1.0102332158131386,
              1.0024623738321654,
              0.9849157315758862
            ],
            "cell_volume_ratio": 0.9974446354485759,
            "cell_rmsd_from_input_A": 0.07996881126200811
          },
          {
            "iteration": 1,
            "reduced_polarization": [
              0.22778644029925815,
              0.25797492342005746,
              0.0009591899712891766
            ],
            "branch_aligned_reduced_polarization": [
              0.22778644029925815,
              0.25797492342005746,
              0.0009591899712891766
            ],
            "target_residual": 0.3642489256317408,
            "energy_eV": -77.36209475332166,
            "max_atomic_step_A": 0.12000000000000001,
            "max_log_strain_component": 0.012675361777871898,
            "step_scale": 0.8015435759114399,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 3.625512780854663,
            "cell_principal_stretches": [
              1.0215804493825733,
              1.0047149410531044,
              0.9695254908948535
            ],
            "cell_volume_ratio": 0.995118191964051,
            "cell_rmsd_from_input_A": 0.16503429577332218
          },
          {
            "iteration": 2,
            "reduced_polarization": [
              0.4115339854869745,
              0.434553422615549,
              0.0027107699279360115
            ],
            "branch_aligned_reduced_polarization": [
              0.4115339854869745,
              0.434553422615549,
              0.0027107699279360115
            ],
            "target_residual": 0.11007651197580694,
            "energy_eV": -73.34691527754703,
            "max_atomic_step_A": 0.05932712114998928,
            "max_log_strain_component": 0.011692203667675677,
            "step_scale": 1.0,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 3.625512780854663,
            "cell_principal_stretches": [
              1.032338219317388,
              1.0062723106309637,
              0.9563950487918598
            ],
            "cell_volume_ratio": 0.9935159591966671,
            "cell_rmsd_from_input_A": 0.24160415949540676
          },
          {
            "iteration": 3,
            "reduced_polarization": [
              0.4695013993355399,
              0.4821651465353475,
              -0.0028256680650128175
            ],
            "branch_aligned_reduced_polarization": [
              0.4695013993355399,
              0.4821651465353475,
              -0.0028256680650128175
            ],
            "target_residual": 0.03544334973742559,
            "energy_eV": -70.27010294249668,
            "max_atomic_step_A": 0.020597624315722738,
            "max_log_strain_component": 0.0049521371812021805,
            "step_scale": 1.0,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 3.625512780854663,
            "cell_principal_stretches": [
              1.0369493539336236,
              1.0069420508223046,
              0.9508504221418205
            ],
            "cell_volume_ratio": 0.9928284800975383,
            "cell_rmsd_from_input_A": 0.273465174059408
          },
          {
            "iteration": 4,
            "reduced_polarization": [
              0.4918343008038852,
              0.49594596937647367,
              -0.0003744652756986193
            ],
            "branch_aligned_reduced_polarization": [
              0.4918343008038852,
              0.49594596937647367,
              -0.0003744652756986193
            ],
            "target_residual": 0.009124364739565351,
            "energy_eV": -70.07224619838394,
            "max_atomic_step_A": 0.0058281238430371585,
            "max_log_strain_component": 0.0014186483228163021,
            "step_scale": 1.0,
            "strain_jacobian_refreshed": true,
            "strain_jacobian_frobenius_norm": 3.860153371642989,
            "cell_principal_stretches": [
              1.0353634024789753,
              1.0064326474304253,
              0.9501370603010316
            ],
            "cell_volume_ratio": 0.9900651737577459,
            "cell_rmsd_from_input_A": 0.2674985695251133
          },
          {
            "iteration": 5,
            "reduced_polarization": [
              0.4999317486884913,
              0.49993077707714395,
              -1.1179594117588084e-05
            ],
            "branch_aligned_reduced_polarization": [
              0.4999317486884913,
              0.49993077707714395,
              -1.1179594117588084e-05
            ],
            "target_residual": 9.78521225933798e-05,
            "energy_eV": -70.02386153152854
          }
        ],
        "iterations": 5
      },
      "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": 9.78521225933798e-05,
        "parent_symmetrization_rmsd_A": 0.21049970900991574,
        "parent_cell_rmsd_A": 0.2674985695251133,
        "energy_eV": -70.02386153152854,
        "reduced_polarization": [
          0.4999317486884913,
          0.49993077707714395,
          -1.1179594117588084e-05
        ],
        "cartesian_polarization_e_A2": [
          0.012247796496299897,
          0.007326543201433486,
          1.3864591829755548e-05
        ],
        "ranking_score": 0.7775700556363808
      },
      "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": [
              1.4946449555980582e-09,
              0.03982770587365218,
              1.919621257827688e-09
            ],
            "branch_aligned_reduced_polarization": [
              1.494644963351277e-09,
              0.03982770587365218,
              1.9196212397432078e-09
            ],
            "target_residual": 0.7082275359945361,
            "energy_eV": -78.64525548547559,
            "max_atomic_step_A": 0.12000000000000001,
            "max_log_strain_component": 0.011400688568392912,
            "step_scale": 0.5149439891342767,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 3.625512780854663,
            "cell_principal_stretches": [
              1.0131175568169615,
              0.9997669613829805,
              0.987521779850535
            ],
            "cell_volume_ratio": 1.0002425034431968,
            "cell_rmsd_from_input_A": 0.05203865565621212
          },
          {
            "iteration": 1,
            "reduced_polarization": [
              0.24847729960397688,
              0.02214416691477223,
              0.24976020461709772
            ],
            "branch_aligned_reduced_polarization": [
              0.2484772996039769,
              0.02214416691477223,
              0.2497602046170977
            ],
            "target_residual": 0.3554911927687291,
            "energy_eV": -77.0121039444193,
            "max_atomic_step_A": 0.11999999999999998,
            "max_log_strain_component": 0.012527110710335966,
            "step_scale": 0.9495839353780476,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 3.625512780854663,
            "cell_principal_stretches": [
              1.0279709719943826,
              0.9993919394549683,
              0.9739981399485187
            ],
            "cell_volume_ratio": 1.0006329990000782,
            "cell_rmsd_from_input_A": 0.10982942255235555
          },
          {
            "iteration": 2,
            "reduced_polarization": [
              0.44431091999114064,
              -0.0018284035914842573,
              0.4475948072769931
            ],
            "branch_aligned_reduced_polarization": [
              0.44431091999114064,
              -0.0018284035914842573,
              0.4475948072769931
            ],
            "target_residual": 0.0764913126849186,
            "energy_eV": -70.86258919610233,
            "max_atomic_step_A": 0.02821748749175467,
            "max_log_strain_component": 0.005227609841007775,
            "step_scale": 1.0,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 3.625512780854663,
            "cell_principal_stretches": [
              1.0340803106293823,
              0.9994947875546888,
              0.9680404906999099
            ],
            "cell_volume_ratio": 1.000525877696591,
            "cell_rmsd_from_input_A": 0.13419976556591212
          },
          {
            "iteration": 3,
            "reduced_polarization": [
              0.49213250783809026,
              -0.003716569855755355,
              0.49178032877965533
            ],
            "branch_aligned_reduced_polarization": [
              0.49213250783809026,
              -0.003716569855755355,
              0.49178032877965533
            ],
            "target_residual": 0.011969683345059007,
            "energy_eV": -69.96430080764831,
            "max_atomic_step_A": 0.0049054399663654,
            "max_log_strain_component": 0.000965817870721791,
            "step_scale": 1.0,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 3.625512780854663,
            "cell_principal_stretches": [
              1.0350980620184982,
              0.9995873958001497,
              0.9669058704699826
            ],
            "cell_volume_ratio": 1.0004294409031806,
            "cell_rmsd_from_input_A": 0.13853362468383648
          },
          {
            "iteration": 4,
            "reduced_polarization": [
              0.4989297738239002,
              -0.0003458286513319647,
              0.49878826612357535
            ],
            "branch_aligned_reduced_polarization": [
              0.4989297738239002,
              -0.0003458286513319647,
              0.49878826612357535
            ],
            "target_residual": 0.0016532635940364768,
            "energy_eV": -69.90150072241916,
            "max_atomic_step_A": 0.0007390788396620104,
            "max_log_strain_component": 7.398276577817423e-05,
            "step_scale": 1.0,
            "strain_jacobian_refreshed": true,
            "strain_jacobian_frobenius_norm": 3.2002230945651435,
            "cell_principal_stretches": [
              1.0350180967097167,
              0.9995697230643127,
              0.96681084388524
            ],
            "cell_volume_ratio": 1.0002361557066985,
            "cell_rmsd_from_input_A": 0.13854783856561123
          },
          {
            "iteration": 5,
            "reduced_polarization": [
              0.5000004116707107,
              -8.73967181223491e-07,
              0.49999967106730997
            ],
            "branch_aligned_reduced_polarization": [
              0.5000004116707107,
              -8.73967181223491e-07,
              0.49999967106730997
            ],
            "target_residual": 1.020533253994993e-06,
            "energy_eV": -69.89417282720515
          }
        ],
        "iterations": 5
      },
      "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": 1.020533253994993e-06,
        "parent_symmetrization_rmsd_A": 0.1846992952194181,
        "parent_cell_rmsd_A": 0.13854783856561123,
        "energy_eV": -69.89417282720515,
        "reduced_polarization": [
          0.5000004116707107,
          -8.73967181223491e-07,
          0.49999967106730997
        ],
        "cartesian_polarization_e_A2": [
          0.005885573669819424,
          0.0004008212202393636,
          0.010195229935290723
        ],
        "ranking_score": 0.7193382959273289
      },
      "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": [
              1.4946449555980582e-09,
              0.03982770587365218,
              1.919621257827688e-09
            ],
            "branch_aligned_reduced_polarization": [
              1.494644963351277e-09,
              0.0398277058736522,
              1.9196212397432078e-09
            ],
            "target_residual": 0.8436578316279887,
            "energy_eV": -78.64525548547559,
            "max_atomic_step_A": 0.12,
            "max_log_strain_component": 0.01041211532581279,
            "step_scale": 0.4702923116239155,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 3.625512780854663,
            "cell_principal_stretches": [
              1.010233173918264,
              1.0024623844096403,
              0.984915763607259
            ],
            "cell_volume_ratio": 0.9974446370474168,
            "cell_rmsd_from_input_A": 0.057054207443697935
          },
          {
            "iteration": 1,
            "reduced_polarization": [
              0.22682723459203624,
              0.25797454638560013,
              0.22778622183127836
            ],
            "branch_aligned_reduced_polarization": [
              0.22682723459203624,
              0.25797454638560013,
              0.2277862218312784
            ],
            "target_residual": 0.45530212055598906,
            "energy_eV": -77.3621138462745,
            "max_atomic_step_A": 0.12,
            "max_log_strain_component": 0.01122907715666214,
            "step_scale": 0.8015365471976047,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 3.625512780854663,
            "cell_principal_stretches": [
              1.021580256922351,
              1.0047149565071367,
              0.9695256661047527
            ],
            "cell_volume_ratio": 0.9951181996304997,
            "cell_rmsd_from_input_A": 0.11552127293633245
          },
          {
            "iteration": 2,
            "reduced_polarization": [
              0.40882113860965924,
              0.43455180980187286,
              0.41153271958421345
            ],
            "branch_aligned_reduced_polarization": [
              0.40882113860965924,
              0.43455180980187286,
              0.41153271958421345
            ],
            "target_residual": 0.14291084657510994,
            "energy_eV": -73.34702283250505,
            "max_atomic_step_A": 0.05933198661299524,
            "max_log_strain_component": 0.010280017941293622,
            "step_scale": 1.0,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 3.625512780854663,
            "cell_principal_stretches": [
              1.0323380929919432,
              1.006272362886267,
              0.9563950941976733
            ],
            "cell_volume_ratio": 0.9935159363828628,
            "cell_rmsd_from_input_A": 0.16581811835829782
          },
          {
            "iteration": 3,
            "reduced_polarization": [
              0.4723272096609758,
              0.4821650991229342,
              0.4695007724593052
            ],
            "branch_aligned_reduced_polarization": [
              0.4723272096609758,
              0.4821650991229342,
              0.4695007724593052
            ],
            "target_residual": 0.044878390067174076,
            "energy_eV": -70.27012496194769,
            "max_atomic_step_A": 0.020597885434661668,
            "max_log_strain_component": 0.004535089988053688,
            "step_scale": 1.0,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 3.625512780854663,
            "cell_principal_stretches": [
              1.0369492655341137,
              1.0069421113724013,
              0.9508504196340756
            ],
            "cell_volume_ratio": 0.9928284525422633,
            "cell_rmsd_from_input_A": 0.18736070140797334
          },
          {
            "iteration": 4,
            "reduced_polarization": [
              0.4922087376620053,
              0.4959459430626108,
              0.4918342303690649
            ],
            "branch_aligned_reduced_polarization": [
              0.4922087376620053,
              0.4959459430626108,
              0.4918342303690649
            ],
            "target_residual": 0.01199245346609903,
            "energy_eV": -70.07225519504,
            "max_atomic_step_A": 0.005645433370852899,
            "max_log_strain_component": 0.0011158283584001903,
            "step_scale": 1.0,
            "strain_jacobian_refreshed": true,
            "strain_jacobian_frobenius_norm": 3.9799070896241195,
            "cell_principal_stretches": [
              1.035185636034715,
              1.0067857839152607,
              0.9500498612162355
            ],
            "cell_volume_ratio": 0.9901516388366276,
            "cell_rmsd_from_input_A": 0.1849929515627364
          },
          {
            "iteration": 5,
            "reduced_polarization": [
              0.49993528009835875,
              0.49991997096674023,
              0.49992603923035733
            ],
            "branch_aligned_reduced_polarization": [
              0.49993528009835875,
              0.49991997096674023,
              0.49992603923035733
            ],
            "target_residual": 0.00012674189236034652,
            "energy_eV": -70.02078049978965
          }
        ],
        "iterations": 5
      },
      "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": 0.00012674189236034652,
        "parent_symmetrization_rmsd_A": 0.21040039786069856,
        "parent_cell_rmsd_A": 0.1849929515627364,
        "energy_eV": -70.02078049978965,
        "reduced_polarization": [
          0.49993528009835875,
          0.49991997096674023,
          0.49992603923035733
        ],
        "cartesian_polarization_e_A2": [
          0.0061076628834458215,
          0.00732607113963553,
          0.010610580314761761
        ],
        "ranking_score": 0.7569021195361033
      },
      "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
        ],
        "endpoint_rmsd_A": 0.4128024431172261,
        "minimum_distance_A_by_image": [
          1.7276084736820088,
          1.7083353978433244,
          1.6914544389485457,
          1.6770378352561288,
          1.665149595997305,
          1.655844179730393,
          1.6491653077759212,
          1.6451449697591634,
          1.6438026721610208
        ],
        "minimum_distance_A": 1.6438026721610208,
        "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": [
          387.7958494562615,
          387.7958494562615,
          387.7958494562615,
          387.7958494562615,
          387.7958494562615,
          387.7958494562615,
          387.7958494562615,
          387.7958494562615,
          387.7958494562615
        ],
        "cell_deformation_log_strain_norm": 0.0
      },
      "parent_reduced_polarization": [
        9.294889138307384e-16,
        1.6382864506677825e-15,
        4.821305424605953e-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": [
          -78.64525548547559,
          -78.39789309931237,
          -77.85412286902894,
          -77.16563843920022,
          -76.40873563905525,
          -75.65697566466696,
          -75.00295482896573,
          -74.5148729633517,
          -74.31978120723463
        ],
        "cartesian_polarizations_e_A2": [
          [
            1.2594461718904755e-11,
            0.0005514794409478721,
            3.91476574824582e-11
          ],
          [
            1.0441587098814705e-11,
            -0.0026911937064164394,
            3.274363398382394e-11
          ],
          [
            7.566837931703873e-12,
            -0.005779610705982343,
            2.7768107014150512e-11
          ],
          [
            5.207950696694255e-12,
            -0.008477352934042608,
            2.2142212530681555e-11
          ],
          [
            3.6927632254895095e-12,
            -0.010030928517773449,
            1.5766024149068926e-11
          ],
          [
            2.5079051729914467e-12,
            -0.009515793427736313,
            1.0020112991204542e-11
          ],
          [
            1.3780410377511497e-12,
            -0.006993019927257892,
            5.7550956462757315e-12
          ],
          [
            4.905137274940677e-13,
            -0.003582517580910001,
            2.779103999082288e-12
          ],
          [
            1.6211204647379802e-17,
            2.2684743600168973e-17,
            9.832292443416336e-18
          ]
        ],
        "raw_reduced_polarization": [
          [
            1.4946461493239199e-09,
            0.03982770587365213,
            1.9196216392767384e-09
          ],
          [
            1.246210384830353e-09,
            -0.19435732944813278,
            1.6055976879860747e-09
          ],
          [
            1.002143016374665e-09,
            -0.41740202475441684,
            1.3616206571236297e-09
          ],
          [
            7.640366769019425e-10,
            -0.6122322867809414,
            1.0857525851810398e-09
          ],
          [
            5.433633342493753e-10,
            -0.7244311228698611,
            7.730935404110397e-10
          ],
          [
            3.5217068518363966e-10,
            -0.6872281968352428,
            4.913404010069619e-10
          ],
          [
            1.9962152399477918e-10,
            -0.5050341321023821,
            2.8220350460684904e-10
          ],
          [
            8.896737251491804e-11,
            -0.25872851443823497,
            1.362745185156834e-10
          ],
          [
            9.294889138307384e-16,
            1.6382864506677825e-15,
            4.821305424605953e-16
          ]
        ],
        "unwrapped_reduced_polarization": [
          [
            1.4946461493239199e-09,
            0.03982770587365213,
            1.9196216392767384e-09
          ],
          [
            1.246210384830353e-09,
            -0.19435732944813278,
            1.6055976879860747e-09
          ],
          [
            1.002143016374665e-09,
            -0.41740202475441684,
            1.3616206571236297e-09
          ],
          [
            7.640366769019425e-10,
            -0.6122322867809414,
            1.0857525851810398e-09
          ],
          [
            5.433633342493753e-10,
            -0.7244311228698611,
            7.730935404110397e-10
          ],
          [
            3.5217068518363966e-10,
            -0.6872281968352428,
            4.913404010069619e-10
          ],
          [
            1.9962152399477918e-10,
            -0.5050341321023821,
            2.8220350460684904e-10
          ],
          [
            8.896737251491804e-11,
            -0.25872851443823497,
            1.362745185156834e-10
          ],
          [
            9.294889138251244e-16,
            1.6653345369377348e-15,
            4.821305424716208e-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": [
          [
            1.4946461845966041e-09,
            0.03982770587365214,
            1.9196216838324176e-09
          ],
          [
            1.2462103571309058e-09,
            -0.19435732944813278,
            1.6055976548301487e-09
          ],
          [
            1.0021430352225025e-09,
            -0.41740202475441684,
            1.36162070507595e-09
          ],
          [
            7.640367227779166e-10,
            0.38776771321905856,
            1.0857525989393935e-09
          ],
          [
            5.433633543105998e-10,
            0.2755688771301389,
            7.730935891459012e-10
          ],
          [
            3.5217073701687696e-10,
            0.31277180316475717,
            4.913404128004117e-10
          ],
          [
            1.9962154151897948e-10,
            0.4949658678976179,
            2.8220348280427743e-10
          ],
          [
            8.896738901142953e-11,
            -0.25872851443823497,
            1.3627454720221976e-10
          ],
          [
            8.881784197001252e-16,
            1.6653345369377348e-15,
            4.440892098500626e-16
          ]
        ]
      },
      "reflected": {
        "reached": true,
        "construction": "reflect_displacements_about_reconstructed_parent",
        "energies_eV": [
          -74.31978120723463,
          -74.51487296335173,
          -75.00295482896573,
          -75.65697566466693,
          -76.40873563905524,
          -77.16563843920024,
          -77.85412286902894,
          -78.39789309931237,
          -78.6452554854756
        ],
        "cartesian_polarizations_e_A2": [
          [
            1.6211204647379802e-17,
            2.2684743600168973e-17,
            9.832292443416336e-18
          ],
          [
            -4.905094689215444e-13,
            0.0035825175809100153,
            -2.77906760439106e-12
          ],
          [
            -1.3780184565808792e-12,
            0.006993019927257912,
            -5.7550967735449285e-12
          ],
          [
            -2.507874289394072e-12,
            0.009515793427736318,
            -1.0020179585079702e-11
          ],
          [
            -3.6927214270633985e-12,
            0.01003092851777358,
            -1.5765990845421408e-11
          ],
          [
            -5.207941177532144e-12,
            0.008477352934042622,
            -2.214219021343542e-11
          ],
          [
            -7.566861407532238e-12,
            0.005779610705982351,
            -2.7768092332811203e-11
          ],
          [
            -1.0441552153469587e-11,
            0.0026911937064164697,
            -3.2743587148472765e-11
          ],
          [
            -1.259442227342943e-11,
            -0.0005514794409478722,
            -3.914763434659991e-11
          ]
        ],
        "raw_reduced_polarization": [
          [
            9.294889138307384e-16,
            1.6382864506677825e-15,
            4.821305424605953e-16
          ],
          [
            -8.896629935635551e-11,
            0.258728514438236,
            -1.3627273388688747e-10
          ],
          [
            -1.996205927027661e-10,
            0.5050341321023836,
            -2.8220355988296217e-10
          ],
          [
            -3.5217100641253194e-10,
            0.6872281968352432,
            -4.91343666465281e-10
          ],
          [
            -5.433607427118662e-10,
            0.7244311228698705,
            -7.730919073528556e-10
          ],
          [
            -7.640357254943033e-10,
            0.6122322867809424,
            -1.0857514908456093e-09
          ],
          [
            -1.0021436533444312e-09,
            0.41740202475441746,
            -1.3616199372180607e-09
          ],
          [
            -1.246207752548855e-09,
            0.19435732944813497,
            -1.605595391395183e-09
          ],
          [
            -1.4946439069974985e-09,
            -0.039827705873652135,
            -1.9196205048003208e-09
          ]
        ],
        "unwrapped_reduced_polarization": [
          [
            9.294889138307384e-16,
            1.6382864506677825e-15,
            4.821305424605953e-16
          ],
          [
            -8.896629935635551e-11,
            0.258728514438236,
            -1.3627273388688747e-10
          ],
          [
            -1.996205927027661e-10,
            0.5050341321023836,
            -2.8220355988296217e-10
          ],
          [
            -3.5217100641253194e-10,
            0.6872281968352432,
            -4.91343666465281e-10
          ],
          [
            -5.433607427118662e-10,
            0.7244311228698705,
            -7.730919073528556e-10
          ],
          [
            -7.640357254943033e-10,
            0.6122322867809424,
            -1.0857514908456093e-09
          ],
          [
            -1.0021436533444312e-09,
            0.41740202475441746,
            -1.3616199372180607e-09
          ],
          [
            -1.246207752548855e-09,
            0.19435732944813497,
            -1.605595391395183e-09
          ],
          [
            -1.4946439069974985e-09,
            -0.03982770587365214,
            -1.9196205048003208e-09
          ]
        ],
        "gauge_integer_shift": [
          0,
          0,
          0
        ],
        "expected_opposite_endpoint_reduced_polarization": [
          -1.4946442903460922e-09,
          -0.03982770587364885,
          -1.919620675015654e-09
        ],
        "actual_opposite_endpoint_branch_residual": 3.3156726781251273e-15
      },
      "pnp_branch": {
        "construction": "incoming_path_concatenated_with_parent_reflection",
        "reduced_polarization": [
          [
            1.4946461493239199e-09,
            0.03982770587365213,
            1.9196216392767384e-09
          ],
          [
            1.246210384830353e-09,
            -0.19435732944813278,
            1.6055976879860747e-09
          ],
          [
            1.002143016374665e-09,
            -0.41740202475441684,
            1.3616206571236297e-09
          ],
          [
            7.640366769019425e-10,
            -0.6122322867809414,
            1.0857525851810398e-09
          ],
          [
            5.433633342493753e-10,
            -0.7244311228698611,
            7.730935404110397e-10
          ],
          [
            3.5217068518363966e-10,
            -0.6872281968352428,
            4.913404010069619e-10
          ],
          [
            1.9962152399477918e-10,
            -0.5050341321023821,
            2.8220350460684904e-10
          ],
          [
            8.896737251491804e-11,
            -0.25872851443823497,
            1.362745185156834e-10
          ],
          [
            9.294889138307384e-16,
            1.6382864506677825e-15,
            4.821305424605953e-16
          ],
          [
            -8.896629935635551e-11,
            0.258728514438236,
            -1.3627273388688747e-10
          ],
          [
            -1.996205927027661e-10,
            0.5050341321023836,
            -2.8220355988296217e-10
          ],
          [
            -3.5217100641253194e-10,
            0.6872281968352432,
            -4.91343666465281e-10
          ],
          [
            -5.433607427118662e-10,
            0.7244311228698705,
            -7.730919073528556e-10
          ],
          [
            -7.640357254943033e-10,
            0.6122322867809424,
            -1.0857514908456093e-09
          ],
          [
            -1.0021436533444312e-09,
            0.41740202475441746,
            -1.3616199372180607e-09
          ],
          [
            -1.246207752548855e-09,
            0.19435732944813497,
            -1.605595391395183e-09
          ],
          [
            -1.4946439069974985e-09,
            -0.039827705873652135,
            -1.9196205048003208e-09
          ]
        ],
        "unwrapped_reduced_polarization": [
          [
            1.4946461493239199e-09,
            0.03982770587365213,
            1.9196216392767384e-09
          ],
          [
            1.246210384830353e-09,
            -0.19435732944813278,
            1.6055976879860747e-09
          ],
          [
            1.002143016374665e-09,
            -0.41740202475441684,
            1.3616206571236297e-09
          ],
          [
            7.640366769019425e-10,
            -0.6122322867809414,
            1.0857525851810398e-09
          ],
          [
            5.433633342493753e-10,
            -0.7244311228698611,
            7.730935404110397e-10
          ],
          [
            3.5217068518363966e-10,
            -0.6872281968352428,
            4.913404010069619e-10
          ],
          [
            1.9962152399477918e-10,
            -0.5050341321023821,
            2.8220350460684904e-10
          ],
          [
            8.896737251491804e-11,
            -0.25872851443823497,
            1.362745185156834e-10
          ],
          [
            9.294889138251244e-16,
            1.6653345369377348e-15,
            4.821305424716208e-16
          ],
          [
            -8.896629935635551e-11,
            0.258728514438236,
            -1.3627273388688747e-10
          ],
          [
            -1.996205927027661e-10,
            0.5050341321023836,
            -2.8220355988296217e-10
          ],
          [
            -3.5217100641253194e-10,
            0.6872281968352432,
            -4.91343666465281e-10
          ],
          [
            -5.433607427118662e-10,
            0.7244311228698705,
            -7.730919073528556e-10
          ],
          [
            -7.640357254943033e-10,
            0.6122322867809424,
            -1.0857514908456093e-09
          ],
          [
            -1.0021436533444312e-09,
            0.41740202475441746,
            -1.3616199372180607e-09
          ],
          [
            -1.246207752548855e-09,
            0.19435732944813497,
            -1.605595391395183e-09
          ],
          [
            -1.4946439069974985e-09,
            -0.03982770587365214,
            -1.9196205048003208e-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": [
          [
            1.4946461845966041e-09,
            0.03982770587365214,
            1.9196216838324176e-09
          ],
          [
            1.2462103571309058e-09,
            -0.19435732944813278,
            1.6055976548301487e-09
          ],
          [
            1.0021430352225025e-09,
            -0.41740202475441684,
            1.36162070507595e-09
          ],
          [
            7.640367227779166e-10,
            0.38776771321905856,
            1.0857525989393935e-09
          ],
          [
            5.433633543105998e-10,
            0.2755688771301389,
            7.730935891459012e-10
          ],
          [
            3.5217073701687696e-10,
            0.31277180316475717,
            4.913404128004117e-10
          ],
          [
            1.9962154151897948e-10,
            0.4949658678976179,
            2.8220348280427743e-10
          ],
          [
            8.896738901142953e-11,
            -0.25872851443823497,
            1.3627454720221976e-10
          ],
          [
            8.881784197001252e-16,
            1.6653345369377348e-15,
            4.440892098500626e-16
          ],
          [
            -8.896627878840491e-11,
            0.2587285144382361,
            -1.3627271533422913e-10
          ],
          [
            -1.9962059782940855e-10,
            -0.49496586789761654,
            -2.8220353831542866e-10
          ],
          [
            -3.521710145726331e-10,
            -0.31277180316475683,
            -4.913436879583344e-10
          ],
          [
            -5.433607452864919e-10,
            -0.27556887713012945,
            -7.730919238113643e-10
          ],
          [
            -7.640357235771944e-10,
            -0.38776771321905756,
            -1.0857514887163688e-09
          ],
          [
            -1.002143645845166e-09,
            0.41740202475441746,
            -1.3616199279198327e-09
          ],
          [
            -1.246207748106798e-09,
            0.194357329448135,
            -1.6055953788729482e-09
          ],
          [
            -1.4946439086394037e-09,
            -0.03982770587365214,
            -1.9196205180982417e-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": "P6_3/m",
        "spacegroup_number": 176,
        "pointgroup": "6/m",
        "has_inversion": true,
        "is_polar_point_group": false,
        "nonpolar_parent_hypothesis": true,
        "symmetry_tolerance_A": null,
        "target_reduced_polarization": [
          0.0,
          0.0,
          0.0
        ],
        "formal_class": [
          0.0,
          0.0,
          0.0
        ],
        "target_residual": 4.8683520077438335e-16,
        "parent_symmetrization_rmsd_A": 0.4128024431172261,
        "parent_cell_rmsd_A": 0.0,
        "energy_eV": -74.31978120723464,
        "reduced_polarization": [
          1.1812931982334496e-16,
          4.722565644761731e-16,
          5.264391728414144e-18
        ],
        "cartesian_polarization_e_A2": [
          2.719760603092417e-18,
          6.539161130382245e-18,
          1.0735897117470066e-19
        ],
        "ranking_score": 0.4128024431172271
      }
    }
  ],
  "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": 141,
      "full_response": 34,
      "energy_polarization": 107
    },
    "model_evaluations_for_recovery_and_path_properties": {
      "total": 166,
      "full_response": 59,
      "energy_polarization": 107
    },
    "elapsed_seconds": 292.6320273880265
  }
}