{
  "schema": "ferrofinder.endpoint_parent_recovery.v4_variable_cell",
  "status": "complete",
  "input_atom_count": 28,
  "input_formula": "Ba4Cl20La4",
  "input_spacegroup": "P2_1",
  "input_pointgroup": "2",
  "input_is_polar_point_group": true,
  "input_energy_eV": -131.12716413193058,
  "input_cartesian_polarization_e_A2": [
    3.2417188084821945e-17,
    -0.0021356292951045693,
    -1.7845904895414307e-17
  ],
  "input_reduced_polarization": [
    4.0357706137985266e-15,
    -0.15177429120251115,
    -1.441066878410653e-15
  ],
  "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": [
        0.5,
        0.0,
        0.0
      ],
      "target_reduced_polarization": [
        0.5,
        0.0,
        0.0
      ]
    },
    {
      "orbit_id": 3,
      "representative_formal_class": [
        0.0,
        0.0,
        0.5
      ],
      "target_reduced_polarization": [
        0.0,
        0.0,
        -0.5
      ]
    },
    {
      "orbit_id": 4,
      "representative_formal_class": [
        0.5,
        0.5,
        0.0
      ],
      "target_reduced_polarization": [
        0.5,
        -0.5,
        0.0
      ]
    },
    {
      "orbit_id": 5,
      "representative_formal_class": [
        0.0,
        0.5,
        0.5
      ],
      "target_reduced_polarization": [
        0.0,
        -0.5,
        -0.5
      ]
    },
    {
      "orbit_id": 6,
      "representative_formal_class": [
        0.5,
        0.0,
        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": "P2_1/c",
      "spacegroup_number": 14,
      "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": 8.309159579663046e-15,
      "parent_symmetrization_rmsd_A": 0.8150456608173575,
      "parent_cell_rmsd_A": 0.0,
      "energy_eV": -127.90027221490107,
      "reduced_polarization": [
        4.158043342284071e-15,
        7.121896353195488e-15,
        -1.0155790556791093e-15
      ],
      "cartesian_polarization_e_A2": [
        3.340427501055601e-17,
        1.0021282503166805e-16,
        -1.3098486824026655e-17
      ],
      "ranking_score": 0.8150456608173742
    },
    {
      "candidate_id": "bec_projection_00",
      "source": "MACEField_BEC_backprojection",
      "spacegroup": "P2_1",
      "spacegroup_number": 4,
      "pointgroup": "2",
      "has_inversion": false,
      "is_polar_point_group": true,
      "nonpolar_parent_hypothesis": false,
      "symmetry_tolerance_A": null,
      "target_reduced_polarization": [
        0.0,
        0.0,
        0.0
      ],
      "formal_class": [
        0.0,
        0.0,
        0.0
      ],
      "target_residual": 3.458840907359854e-06,
      "parent_symmetrization_rmsd_A": 0.047921781142931365,
      "parent_cell_rmsd_A": 0.05379183301846588,
      "energy_eV": -131.06317121386633,
      "reduced_polarization": [
        5.001703392550363e-15,
        -3.458840907359854e-06,
        7.759400865455864e-16
      ],
      "cartesian_polarization_e_A2": [
        3.990771874254629e-17,
        -4.853353683977895e-08,
        6.7238365236272965e-18
      ],
      "ranking_score": 0.5613766570793626
    },
    {
      "candidate_id": "inversion_parent_bec_00_00",
      "source": "same_species_inversion_center_projection_after_BEC",
      "spacegroup": "P2_1/c",
      "spacegroup_number": 14,
      "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": 4.354636108648712e-15,
      "parent_symmetrization_rmsd_A": 0.8150690222214957,
      "parent_cell_rmsd_A": 0.05379183301846588,
      "energy_eV": -127.86133797000879,
      "reduced_polarization": [
        -4.954203802564967e-16,
        3.418021953935367e-15,
        -2.6522707644562917e-15
      ],
      "cartesian_polarization_e_A2": [
        -3.979889364274191e-18,
        4.7960776128069846e-17,
        -2.9538241375472515e-17
      ],
      "ranking_score": 0.8285169804761208
    },
    {
      "candidate_id": "bec_projection_01",
      "source": "MACEField_BEC_backprojection",
      "spacegroup": "P2_1",
      "spacegroup_number": 4,
      "pointgroup": "2",
      "has_inversion": false,
      "is_polar_point_group": true,
      "nonpolar_parent_hypothesis": false,
      "symmetry_tolerance_A": null,
      "target_reduced_polarization": [
        0.0,
        -0.5,
        0.0
      ],
      "formal_class": [
        0.0,
        0.5,
        0.0
      ],
      "target_residual": 4.360443968931538e-05,
      "parent_symmetrization_rmsd_A": 0.10933322797236183,
      "parent_cell_rmsd_A": 0.11891282712347716,
      "energy_eV": -130.63488691123365,
      "reduced_polarization": [
        2.3103917972523727e-15,
        -0.4999563955603107,
        -1.3504230073987328e-15
      ],
      "cartesian_polarization_e_A2": [
        1.8509201235384192e-16,
        -0.007079301375281429,
        -1.2463236861483823e-16
      ],
      "ranking_score": 0.6391486436326097
    },
    {
      "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": [
        0.5,
        0.0,
        0.0
      ],
      "formal_class": [
        0.5,
        0.0,
        0.0
      ],
      "target_residual": 7.911251584609837e-06,
      "parent_symmetrization_rmsd_A": 0.09458475685509514,
      "parent_cell_rmsd_A": 0.08400419857489737,
      "energy_eV": -130.82251244556028,
      "reduced_polarization": [
        0.4999951863088373,
        -4.6581193450268676e-06,
        4.209299608350807e-06
      ],
      "cartesian_polarization_e_A2": [
        0.003988491655554353,
        1.3877425017325016e-05,
        -0.0001974476393903906
      ],
      "ranking_score": 0.6156016290019887
    },
    {
      "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": [
        0.0,
        0.0,
        -0.5
      ],
      "formal_class": [
        0.0,
        0.0,
        0.5
      ],
      "target_residual": 0.0005656447945974505,
      "parent_symmetrization_rmsd_A": 0.11454006964538539,
      "parent_cell_rmsd_A": 0.06234121262382818,
      "energy_eV": -130.37952457935455,
      "reduced_polarization": [
        -1.594630209122331e-06,
        -0.00040822965918961595,
        -0.49960846451480406
      ],
      "cartesian_polarization_e_A2": [
        -5.267547574089144e-06,
        -1.7266692549477754e-05,
        -0.0056003538739404215
      ],
      "ranking_score": 0.6312566623905373
    },
    {
      "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": [
        0.5,
        -0.5,
        0.0
      ],
      "formal_class": [
        0.5,
        0.5,
        0.0
      ],
      "target_residual": 0.0007415107105564628,
      "parent_symmetrization_rmsd_A": 0.13962751509111462,
      "parent_cell_rmsd_A": 0.1366639907764741,
      "energy_eV": -130.3437536247157,
      "reduced_polarization": [
        0.49983851941192975,
        -0.5004528914732076,
        -0.0005644922205330119
      ],
      "cartesian_polarization_e_A2": [
        0.00406084668984731,
        -0.007072423378663965,
        -0.0001711349432546947
      ],
      "ranking_score": 0.675276534206346
    },
    {
      "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": [
        0.0,
        -0.5,
        -0.5
      ],
      "formal_class": [
        0.0,
        0.5,
        0.5
      ],
      "target_residual": 7.776910871810939e-06,
      "parent_symmetrization_rmsd_A": 0.1516090999830722,
      "parent_cell_rmsd_A": 0.12366429854398998,
      "energy_eV": -129.8786714672505,
      "reduced_polarization": [
        3.947475575676201e-06,
        -0.49999767126262706,
        -0.4999937171056403
      ],
      "cartesian_polarization_e_A2": [
        -1.993256699985805e-05,
        -0.007092704108533055,
        -0.005720940632993728
      ],
      "ranking_score": 0.6825407284408134
    },
    {
      "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": 3.5005070085217314e-06,
      "parent_symmetrization_rmsd_A": 0.14573161723843325,
      "parent_cell_rmsd_A": 0.08077098517867771,
      "energy_eV": -130.114207713743,
      "reduced_polarization": [
        0.5000004375402514,
        -1.2405859833797495e-06,
        -0.5000032439257487
      ],
      "cartesian_polarization_e_A2": [
        0.003981902576637846,
        3.820639826226702e-05,
        -0.005801187098561812
      ],
      "ranking_score": 0.6659313645471198
    },
    {
      "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": 2.4723513318779027e-05,
      "parent_symmetrization_rmsd_A": 0.17936113083096125,
      "parent_cell_rmsd_A": 0.13330942191867962,
      "energy_eV": -129.53944379408617,
      "reduced_polarization": [
        0.5000156642081903,
        -0.5000099595551762,
        -0.5000163307058416
      ],
      "cartesian_polarization_e_A2": [
        0.004042133206255971,
        -0.007040732824445188,
        -0.005885545440936707
      ],
      "ranking_score": 0.7127379333372688
    }
  ],
  "formal_branches": [
    {
      "orbit_id": 0,
      "formal_class": [
        0.0,
        0.0,
        0.0
      ],
      "formal_classes_in_orbit": [
        [
          0.0,
          0.0,
          0.0
        ]
      ],
      "target_reduced_polarization": [
        0.0,
        0.0,
        0.0
      ],
      "bec_backprojection": {
        "converged_to_target": true,
        "history": [
          {
            "iteration": 0,
            "reduced_polarization": [
              4.0357706137985266e-15,
              -0.15177429120251115,
              -1.441066878410653e-15
            ],
            "branch_aligned_reduced_polarization": [
              4.0357706137985266e-15,
              -0.15177429120251115,
              -1.441066878410653e-15
            ],
            "target_residual": 0.15177429120251115,
            "energy_eV": -131.12716413193058,
            "max_atomic_step_A": 0.044942189472461494,
            "max_log_strain_component": 0.0049536173790207146,
            "step_scale": 1.0,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 1.3359161831261426,
            "cell_principal_stretches": [
              1.0049659068256152,
              1.0023527026838834,
              1.0004298773891627
            ],
            "cell_volume_ratio": 1.007763321328114,
            "cell_rmsd_from_input_A": 0.05338824418608775
          },
          {
            "iteration": 1,
            "reduced_polarization": [
              -3.5021309562518392e-15,
              -0.0011259031936378843,
              -3.491098976265515e-15
            ],
            "branch_aligned_reduced_polarization": [
              -3.5021309562518392e-15,
              -0.0011259031936378843,
              -3.491098976265515e-15
            ],
            "target_residual": 0.0011259031936378843,
            "energy_eV": -131.06418448294855,
            "max_atomic_step_A": 0.0003370567216749989,
            "max_log_strain_component": 3.726900049745593e-05,
            "step_scale": 1.0,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 1.3359161831261426,
            "cell_principal_stretches": [
              1.0050033615984433,
              1.0023704244237528,
              1.000433112311922
            ],
            "cell_volume_ratio": 1.0078219572389155,
            "cell_rmsd_from_input_A": 0.05379183301846588
          },
          {
            "iteration": 2,
            "reduced_polarization": [
              5.001703392550363e-15,
              -3.458840907359854e-06,
              7.759400865455864e-16
            ],
            "branch_aligned_reduced_polarization": [
              5.001703392550363e-15,
              -3.458840907359854e-06,
              7.759400865455864e-16
            ],
            "target_residual": 3.458840907359854e-06,
            "energy_eV": -131.06317121386633
          }
        ],
        "iterations": 2
      },
      "parent": {
        "candidate_id": "bec_projection_00",
        "source": "MACEField_BEC_backprojection",
        "spacegroup": "P2_1",
        "spacegroup_number": 4,
        "pointgroup": "2",
        "has_inversion": false,
        "is_polar_point_group": true,
        "nonpolar_parent_hypothesis": false,
        "symmetry_tolerance_A": null,
        "target_reduced_polarization": [
          0.0,
          0.0,
          0.0
        ],
        "formal_class": [
          0.0,
          0.0,
          0.0
        ],
        "target_residual": 3.458840907359854e-06,
        "parent_symmetrization_rmsd_A": 0.047921781142931365,
        "parent_cell_rmsd_A": 0.05379183301846588,
        "energy_eV": -131.06317121386633,
        "reduced_polarization": [
          5.001703392550363e-15,
          -3.458840907359854e-06,
          7.759400865455864e-16
        ],
        "cartesian_polarization_e_A2": [
          3.990771874254629e-17,
          -4.853353683977895e-08,
          6.7238365236272965e-18
        ],
        "ranking_score": 0.5613766570793626
      },
      "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": [
          -131.12716413193056,
          -131.12736631694753,
          -131.12515320345094,
          -131.12056448989887,
          -131.11363680611623,
          -131.1044038666484,
          -131.09289667000047,
          -131.07914366839367,
          -131.06317121386638
        ],
        "cartesian_polarizations_e_A2": [
          [
            1.2926138313184199e-18,
            -0.002135629295104575,
            4.5923044116294406e-17
          ],
          [
            -1.6419781035271725e-17,
            -0.0018673438344146006,
            3.6314482365901244e-17
          ],
          [
            3.542688459932355e-17,
            -0.0015994332969811913,
            1.7873727255363857e-17
          ],
          [
            5.636538113569807e-17,
            -0.0013319022568419466,
            2.18009671216371e-17
          ],
          [
            5.462494170060476e-19,
            -0.0010647546010239925,
            2.700813188939901e-17
          ],
          [
            6.969594134584737e-18,
            -0.0007979934959918481,
            9.30058814603981e-18
          ],
          [
            4.336568581893022e-17,
            -0.000531621316784006,
            -2.1379096187673035e-17
          ],
          [
            2.798752234133274e-17,
            -0.0002656395721531272,
            -6.037897508166307e-18
          ],
          [
            3.295845879789565e-18,
            -4.853353684613745e-08,
            1.9503012529226458e-17
          ]
        ],
        "raw_reduced_polarization": [
          [
            1.5550784941131958e-16,
            -0.1517742912025115,
            4.0796665187018845e-15
          ],
          [
            -1.742202864491151e-15,
            -0.13275432337178164,
            3.0157807580653046e-15
          ],
          [
            4.9405214958966775e-15,
            -0.11374768119240429,
            1.5103762170239928e-15
          ],
          [
            7.688236351068345e-15,
            -0.09475471107190994,
            1.8945564189393576e-15
          ],
          [
            7.666688874091698e-16,
            -0.07577571099724364,
            2.0943604954269306e-15
          ],
          [
            1.5278380785002353e-15,
            -0.056810928060926115,
            5.675150027858089e-16
          ],
          [
            5.954507796066457e-15,
            -0.037860553324904615,
            -1.9460080881527984e-15
          ],
          [
            3.8126122402768206e-15,
            -0.01892471638899547,
            -5.505010285444076e-16
          ],
          [
            4.1091461541771665e-16,
            -3.4588409078130056e-06,
            1.7541189528012837e-15
          ]
        ],
        "unwrapped_reduced_polarization": [
          [
            1.5550784941131958e-16,
            -0.1517742912025115,
            4.0796665187018845e-15
          ],
          [
            -1.7422028644911509e-15,
            -0.13275432337178164,
            3.0157807580653046e-15
          ],
          [
            4.9405214958966775e-15,
            -0.11374768119240429,
            1.5103762170239928e-15
          ],
          [
            7.688236351068345e-15,
            -0.09475471107190994,
            1.8945564189393576e-15
          ],
          [
            7.666688874091699e-16,
            -0.07577571099724364,
            2.0943604954269306e-15
          ],
          [
            1.5278380785002353e-15,
            -0.056810928060926115,
            5.67515002785809e-16
          ],
          [
            5.954507796066457e-15,
            -0.037860553324904615,
            -1.9460080881527984e-15
          ],
          [
            3.8126122402768206e-15,
            -0.01892471638899547,
            -5.505010285444076e-16
          ],
          [
            4.109146154177166e-16,
            -3.458840907813454e-06,
            1.7541189528012837e-15
          ]
        ],
        "berry_integer_shifts": [
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ]
        ],
        "folded_reduced_polarization": [
          [
            1.1102230246251565e-16,
            -0.1517742912025115,
            4.107825191113079e-15
          ],
          [
            -1.7208456881689926e-15,
            -0.1327543233717816,
            2.9976021664879227e-15
          ],
          [
            4.9960036108132044e-15,
            -0.1137476811924043,
            1.5543122344752192e-15
          ],
          [
            7.66053886991358e-15,
            -0.09475471107190991,
            1.887379141862766e-15
          ],
          [
            7.771561172376096e-16,
            -0.07577571099724367,
            2.1094237467877974e-15
          ],
          [
            1.5543122344752192e-15,
            -0.056810928060926136,
            5.551115123125783e-16
          ],
          [
            5.995204332975845e-15,
            -0.03786055332490462,
            -1.942890293094024e-15
          ],
          [
            3.774758283725532e-15,
            -0.018924716388995455,
            -5.551115123125783e-16
          ],
          [
            4.440892098500626e-16,
            -3.4588409077995763e-06,
            1.7763568394002505e-15
          ]
        ]
      },
      "reflected": {
        "reached": true,
        "construction": "reflect_displacements_about_reconstructed_parent",
        "energies_eV": [
          -131.06317121386638,
          -131.05631658264522,
          -131.04760990890838,
          -131.03702376428066,
          -131.0245298383786,
          -131.01009885670584,
          -130.99370047933039,
          -130.9753031969465,
          -130.9548742429805
        ],
        "cartesian_polarizations_e_A2": [
          [
            3.489399093013056e-17,
            -4.853353684355674e-08,
            1.444264538832314e-17
          ],
          [
            1.6331890295929225e-17,
            0.0002484360024857464,
            4.894120531748205e-18
          ],
          [
            -4.088898177970253e-18,
            0.0004966076602284916,
            -2.770325870293369e-17
          ],
          [
            -9.994429172860886e-18,
            0.0007443888855756603,
            -1.299587631135655e-17
          ],
          [
            -1.6668410781784537e-17,
            0.0009917020638832517,
            -1.8104266392200436e-18
          ],
          [
            -1.1732372847258661e-17,
            0.0012384698275237417,
            -4.362536774430068e-17
          ],
          [
            -4.9805617942549325e-17,
            0.0014846153408985094,
            -7.287101400699525e-18
          ],
          [
            -6.292423237539784e-17,
            0.0017300625688476093,
            1.4791890446455463e-18
          ],
          [
            -6.842235880445502e-17,
            0.0019747365361198204,
            -2.0822833719056728e-17
          ]
        ],
        "raw_reduced_polarization": [
          [
            4.37232970892954e-15,
            -3.458840907629086e-06,
            1.4422877116514515e-15
          ],
          [
            1.757721232550278e-15,
            0.017699098254639223,
            6.352865756231471e-16
          ],
          [
            -9.998313342176337e-16,
            0.03536698060825875,
            -2.2682225070990784e-15
          ],
          [
            -1.8613444763446576e-15,
            0.05299469687435123,
            -9.293236598233816e-16
          ],
          [
            -2.7349592787839038e-15,
            0.07057675911042531,
            5.4849884552148444e-17
          ],
          [
            -2.070480203514785e-15,
            0.08810770465735158,
            -3.658851272098766e-15
          ],
          [
            -6.696425386609887e-15,
            0.10558211637122253,
            -6.497981973706688e-16
          ],
          [
            -8.121547064644718e-15,
            0.12299464163235466,
            -1.8828036976990373e-17
          ],
          [
            -8.511433722918772e-15,
            0.14034001067896593,
            -2.1472142907176813e-15
          ]
        ],
        "unwrapped_reduced_polarization": [
          [
            4.37232970892954e-15,
            -3.458840907629086e-06,
            1.4422877116514515e-15
          ],
          [
            1.757721232550278e-15,
            0.017699098254639223,
            6.352865756231471e-16
          ],
          [
            -9.998313342176339e-16,
            0.03536698060825875,
            -2.2682225070990784e-15
          ],
          [
            -1.8613444763446576e-15,
            0.05299469687435123,
            -9.293236598233816e-16
          ],
          [
            -2.7349592787839038e-15,
            0.07057675911042531,
            5.4849884552148395e-17
          ],
          [
            -2.070480203514785e-15,
            0.08810770465735158,
            -3.658851272098766e-15
          ],
          [
            -6.696425386609887e-15,
            0.10558211637122253,
            -6.49798197370669e-16
          ],
          [
            -8.121547064644718e-15,
            0.12299464163235466,
            -1.8828036976990358e-17
          ],
          [
            -8.511433722918772e-15,
            0.14034001067896593,
            -2.1472142907176813e-15
          ]
        ],
        "gauge_integer_shift": [
          0,
          0,
          0
        ],
        "expected_opposite_endpoint_reduced_polarization": [
          6.601720401638818e-16,
          0.15176739286751373,
          -5.904041638944437e-16
        ],
        "actual_opposite_endpoint_branch_residual": 0.011427382188547802
      },
      "pnp_branch": {
        "construction": "incoming_path_concatenated_with_parent_reflection",
        "reduced_polarization": [
          [
            1.5550784941131958e-16,
            -0.1517742912025115,
            4.0796665187018845e-15
          ],
          [
            -1.742202864491151e-15,
            -0.13275432337178164,
            3.0157807580653046e-15
          ],
          [
            4.9405214958966775e-15,
            -0.11374768119240429,
            1.5103762170239928e-15
          ],
          [
            7.688236351068345e-15,
            -0.09475471107190994,
            1.8945564189393576e-15
          ],
          [
            7.666688874091698e-16,
            -0.07577571099724364,
            2.0943604954269306e-15
          ],
          [
            1.5278380785002353e-15,
            -0.056810928060926115,
            5.675150027858089e-16
          ],
          [
            5.954507796066457e-15,
            -0.037860553324904615,
            -1.9460080881527984e-15
          ],
          [
            3.8126122402768206e-15,
            -0.01892471638899547,
            -5.505010285444076e-16
          ],
          [
            4.1091461541771665e-16,
            -3.4588409078130056e-06,
            1.7541189528012837e-15
          ],
          [
            1.757721232550278e-15,
            0.017699098254639223,
            6.352865756231471e-16
          ],
          [
            -9.998313342176337e-16,
            0.03536698060825875,
            -2.2682225070990784e-15
          ],
          [
            -1.8613444763446576e-15,
            0.05299469687435123,
            -9.293236598233816e-16
          ],
          [
            -2.7349592787839038e-15,
            0.07057675911042531,
            5.4849884552148444e-17
          ],
          [
            -2.070480203514785e-15,
            0.08810770465735158,
            -3.658851272098766e-15
          ],
          [
            -6.696425386609887e-15,
            0.10558211637122253,
            -6.497981973706688e-16
          ],
          [
            -8.121547064644718e-15,
            0.12299464163235466,
            -1.8828036976990373e-17
          ],
          [
            -8.511433722918772e-15,
            0.14034001067896593,
            -2.1472142907176813e-15
          ]
        ],
        "unwrapped_reduced_polarization": [
          [
            1.5550784941131958e-16,
            -0.1517742912025115,
            4.0796665187018845e-15
          ],
          [
            -1.7422028644911509e-15,
            -0.13275432337178164,
            3.0157807580653046e-15
          ],
          [
            4.9405214958966775e-15,
            -0.11374768119240429,
            1.5103762170239928e-15
          ],
          [
            7.688236351068345e-15,
            -0.09475471107190994,
            1.8945564189393576e-15
          ],
          [
            7.666688874091699e-16,
            -0.07577571099724364,
            2.0943604954269306e-15
          ],
          [
            1.5278380785002353e-15,
            -0.056810928060926115,
            5.67515002785809e-16
          ],
          [
            5.954507796066457e-15,
            -0.037860553324904615,
            -1.9460080881527984e-15
          ],
          [
            3.8126122402768206e-15,
            -0.01892471638899547,
            -5.505010285444076e-16
          ],
          [
            4.109146154177166e-16,
            -3.458840907813454e-06,
            1.7541189528012837e-15
          ],
          [
            1.757721232550278e-15,
            0.017699098254639223,
            6.352865756231472e-16
          ],
          [
            -9.998313342176339e-16,
            0.03536698060825875,
            -2.2682225070990784e-15
          ],
          [
            -1.8613444763446576e-15,
            0.05299469687435123,
            -9.293236598233816e-16
          ],
          [
            -2.7349592787839038e-15,
            0.07057675911042531,
            5.4849884552148395e-17
          ],
          [
            -2.070480203514785e-15,
            0.08810770465735158,
            -3.658851272098766e-15
          ],
          [
            -6.696425386609887e-15,
            0.10558211637122253,
            -6.49798197370669e-16
          ],
          [
            -8.121547064644718e-15,
            0.12299464163235466,
            -1.8828036976990358e-17
          ],
          [
            -8.511433722918772e-15,
            0.14034001067896593,
            -2.1472142907176813e-15
          ]
        ],
        "berry_integer_shifts": [
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            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": [
          [
            1.1102230246251565e-16,
            -0.1517742912025115,
            4.107825191113079e-15
          ],
          [
            -1.7208456881689926e-15,
            -0.1327543233717816,
            2.9976021664879227e-15
          ],
          [
            4.9960036108132044e-15,
            -0.1137476811924043,
            1.5543122344752192e-15
          ],
          [
            7.66053886991358e-15,
            -0.09475471107190991,
            1.887379141862766e-15
          ],
          [
            7.771561172376096e-16,
            -0.07577571099724367,
            2.1094237467877974e-15
          ],
          [
            1.5543122344752192e-15,
            -0.056810928060926136,
            5.551115123125783e-16
          ],
          [
            5.995204332975845e-15,
            -0.03786055332490462,
            -1.942890293094024e-15
          ],
          [
            3.774758283725532e-15,
            -0.018924716388995455,
            -5.551115123125783e-16
          ],
          [
            4.440892098500626e-16,
            -3.4588409077995763e-06,
            1.7763568394002505e-15
          ],
          [
            1.7763568394002505e-15,
            0.017699098254639223,
            6.661338147750939e-16
          ],
          [
            -9.992007221626409e-16,
            0.035366980608258713,
            -2.275957200481571e-15
          ],
          [
            -1.887379141862766e-15,
            0.05299469687435121,
            -9.43689570931383e-16
          ],
          [
            -2.7200464103316335e-15,
            0.07057675911042527,
            0.0
          ],
          [
            -2.0539125955565396e-15,
            0.08810770465735163,
            -3.6637359812630166e-15
          ],
          [
            -6.716849298982197e-15,
            0.1055821163712225,
            -6.661338147750939e-16
          ],
          [
            -8.104628079763643e-15,
            0.12299464163235463,
            0.0
          ],
          [
            -8.493206138382448e-15,
            0.14034001067896595,
            -2.1649348980190553e-15
          ]
        ]
      },
      "incoming_structure_ids": [
        "incoming_00_000",
        "incoming_00_001",
        "incoming_00_002",
        "incoming_00_003",
        "incoming_00_004",
        "incoming_00_005",
        "incoming_00_006",
        "incoming_00_007",
        "incoming_00_008"
      ],
      "reflected_structure_ids": [
        "reflected_00_001",
        "reflected_00_002",
        "reflected_00_003",
        "reflected_00_004",
        "reflected_00_005",
        "reflected_00_006",
        "reflected_00_007",
        "reflected_00_008"
      ]
    },
    {
      "orbit_id": 1,
      "formal_class": [
        0.0,
        0.5,
        0.0
      ],
      "formal_classes_in_orbit": [
        [
          0.0,
          0.5,
          0.0
        ]
      ],
      "target_reduced_polarization": [
        0.0,
        -0.5,
        0.0
      ],
      "bec_backprojection": {
        "converged_to_target": true,
        "history": [
          {
            "iteration": 0,
            "reduced_polarization": [
              4.0357706137985266e-15,
              -0.15177429120251115,
              -1.441066878410653e-15
            ],
            "branch_aligned_reduced_polarization": [
              4.0357706137985266e-15,
              -0.15177429120251118,
              -1.441066878410653e-15
            ],
            "target_residual": 0.3482257087974888,
            "energy_eV": -131.12716413193058,
            "max_atomic_step_A": 0.10311381235888817,
            "max_log_strain_component": 0.011365409182635714,
            "step_scale": 1.0,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 1.3359161831261426,
            "cell_principal_stretches": [
              0.999014402070567,
              0.9946228886077774,
              0.98869893309086
            ],
            "cell_volume_ratio": 0.982413368950903,
            "cell_rmsd_from_input_A": 0.12060081944834875
          },
          {
            "iteration": 1,
            "reduced_polarization": [
              -4.768073211187403e-14,
              -0.5049995848592828,
              2.6452964177701433e-14
            ],
            "branch_aligned_reduced_polarization": [
              -4.768073211187403e-14,
              -0.5049995848592828,
              2.6452964177701433e-14
            ],
            "target_residual": 0.004999584859282757,
            "energy_eV": -130.61974186420775,
            "max_atomic_step_A": 0.0014486465023196328,
            "max_log_strain_component": 0.00016078907232397555,
            "step_scale": 1.0,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 1.3359161831261426,
            "cell_principal_stretches": [
              0.9990283387760446,
              0.9946987578504278,
              0.9888579178562837
            ],
            "cell_volume_ratio": 0.9826600013058666,
            "cell_rmsd_from_input_A": 0.11891282712347716
          },
          {
            "iteration": 2,
            "reduced_polarization": [
              2.3103917972523727e-15,
              -0.4999563955603107,
              -1.3504230073987328e-15
            ],
            "branch_aligned_reduced_polarization": [
              2.3103917972523727e-15,
              -0.4999563955603107,
              -1.3504230073987328e-15
            ],
            "target_residual": 4.360443968931538e-05,
            "energy_eV": -130.63488691123365
          }
        ],
        "iterations": 2
      },
      "parent": {
        "candidate_id": "bec_projection_01",
        "source": "MACEField_BEC_backprojection",
        "spacegroup": "P2_1",
        "spacegroup_number": 4,
        "pointgroup": "2",
        "has_inversion": false,
        "is_polar_point_group": true,
        "nonpolar_parent_hypothesis": false,
        "symmetry_tolerance_A": null,
        "target_reduced_polarization": [
          0.0,
          -0.5,
          0.0
        ],
        "formal_class": [
          0.0,
          0.5,
          0.0
        ],
        "target_residual": 4.360443968931538e-05,
        "parent_symmetrization_rmsd_A": 0.10933322797236183,
        "parent_cell_rmsd_A": 0.11891282712347716,
        "energy_eV": -130.63488691123365,
        "reduced_polarization": [
          2.3103917972523727e-15,
          -0.4999563955603107,
          -1.3504230073987328e-15
        ],
        "cartesian_polarization_e_A2": [
          1.8509201235384192e-16,
          -0.007079301375281429,
          -1.2463236861483823e-16
        ],
        "ranking_score": 0.6391486436326097
      },
      "branch_status": "awaiting_branch_sampling"
    },
    {
      "orbit_id": 2,
      "formal_class": [
        0.5,
        0.0,
        0.0
      ],
      "formal_classes_in_orbit": [
        [
          0.5,
          0.0,
          0.0
        ]
      ],
      "target_reduced_polarization": [
        0.5,
        0.0,
        0.0
      ],
      "bec_backprojection": {
        "converged_to_target": true,
        "history": [
          {
            "iteration": 0,
            "reduced_polarization": [
              4.0357706137985266e-15,
              -0.15177429120251115,
              -1.441066878410653e-15
            ],
            "branch_aligned_reduced_polarization": [
              4.052314039881821e-15,
              -0.15177429120251115,
              -1.441066878410653e-15
            ],
            "target_residual": 0.5225279279330634,
            "energy_eV": -131.12716413193058,
            "max_atomic_step_A": 0.10367229384995168,
            "max_log_strain_component": 0.004953617379015646,
            "step_scale": 1.0,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 1.3359161831261426,
            "cell_principal_stretches": [
              1.0095259942898682,
              1.0011120825253865,
              0.9971450522192469
            ],
            "cell_volume_ratio": 1.007763321328056,
            "cell_rmsd_from_input_A": 0.08378383231048102
          },
          {
            "iteration": 1,
            "reduced_polarization": [
              0.5015119269825131,
              -0.0017872142799238641,
              0.002892174756465929
            ],
            "branch_aligned_reduced_polarization": [
              0.5015119269825131,
              -0.0017872142799238641,
              0.002892174756465929
            ],
            "target_residual": 0.003720851099513896,
            "energy_eV": -130.8224197198282,
            "max_atomic_step_A": 0.0012043604470829395,
            "max_log_strain_component": 6.177284361325924e-05,
            "step_scale": 1.0,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 1.3359161831261426,
            "cell_principal_stretches": [
              1.0095516949218586,
              1.0011345253065884,
              0.9971934760617539
            ],
            "cell_volume_ratio": 1.0078605113836419,
            "cell_rmsd_from_input_A": 0.08400419857489737
          },
          {
            "iteration": 2,
            "reduced_polarization": [
              0.4999951863088373,
              -4.6581193450268676e-06,
              4.209299608350807e-06
            ],
            "branch_aligned_reduced_polarization": [
              0.4999951863088373,
              -4.6581193450268676e-06,
              4.209299608350807e-06
            ],
            "target_residual": 7.911251584609837e-06,
            "energy_eV": -130.82251244556028
          }
        ],
        "iterations": 2
      },
      "parent": {
        "candidate_id": "bec_projection_02",
        "source": "MACEField_BEC_backprojection",
        "spacegroup": "P1",
        "spacegroup_number": 1,
        "pointgroup": "1",
        "has_inversion": false,
        "is_polar_point_group": true,
        "nonpolar_parent_hypothesis": false,
        "symmetry_tolerance_A": null,
        "target_reduced_polarization": [
          0.5,
          0.0,
          0.0
        ],
        "formal_class": [
          0.5,
          0.0,
          0.0
        ],
        "target_residual": 7.911251584609837e-06,
        "parent_symmetrization_rmsd_A": 0.09458475685509514,
        "parent_cell_rmsd_A": 0.08400419857489737,
        "energy_eV": -130.82251244556028,
        "reduced_polarization": [
          0.4999951863088373,
          -4.6581193450268676e-06,
          4.209299608350807e-06
        ],
        "cartesian_polarization_e_A2": [
          0.003988491655554353,
          1.3877425017325016e-05,
          -0.0001974476393903906
        ],
        "ranking_score": 0.6156016290019887
      },
      "branch_status": "awaiting_branch_sampling"
    },
    {
      "orbit_id": 3,
      "formal_class": [
        0.0,
        0.0,
        0.5
      ],
      "formal_classes_in_orbit": [
        [
          0.0,
          0.0,
          0.5
        ]
      ],
      "target_reduced_polarization": [
        0.0,
        0.0,
        -0.5
      ],
      "bec_backprojection": {
        "converged_to_target": true,
        "history": [
          {
            "iteration": 0,
            "reduced_polarization": [
              4.0357706137985266e-15,
              -0.15177429120251115,
              -1.441066878410653e-15
            ],
            "branch_aligned_reduced_polarization": [
              4.0357706137985266e-15,
              -0.15177429120251115,
              -1.4432899320127035e-15
            ],
            "target_residual": 0.5225279279330658,
            "energy_eV": -131.12716413193058,
            "max_atomic_step_A": 0.12,
            "max_log_strain_component": 0.0036098044294308506,
            "step_scale": 0.7287208827895104,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 1.3359161831261426,
            "cell_principal_stretches": [
              1.0048393490430205,
              1.0012484604940073,
              0.9995601855669467
            ],
            "cell_volume_ratio": 1.0056513566763294,
            "cell_rmsd_from_input_A": 0.0442679899877791
          },
          {
            "iteration": 1,
            "reduced_polarization": [
              -0.0004120208341126609,
              -0.043554133641612605,
              -0.36293949935227243
            ],
            "branch_aligned_reduced_polarization": [
              -0.0004120208341126609,
              -0.043554133641612605,
              -0.36293949935227243
            ],
            "target_residual": 0.14381485721664825,
            "energy_eV": -130.74196114092172,
            "max_atomic_step_A": 0.04709094200952737,
            "max_log_strain_component": 0.0014873109030539657,
            "step_scale": 1.0,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 1.3359161831261426,
            "cell_principal_stretches": [
              1.0067899896585626,
              1.001779160047579,
              0.9994129153844805
            ],
            "cell_volume_ratio": 1.0079891076607226,
            "cell_rmsd_from_input_A": 0.06234121262382818
          },
          {
            "iteration": 2,
            "reduced_polarization": [
              -1.594630209122331e-06,
              -0.00040822965918961595,
              -0.49960846451480406
            ],
            "branch_aligned_reduced_polarization": [
              -1.594630209122331e-06,
              -0.00040822965918961595,
              -0.49960846451480406
            ],
            "target_residual": 0.0005656447945974505,
            "energy_eV": -130.37952457935455
          }
        ],
        "iterations": 2
      },
      "parent": {
        "candidate_id": "bec_projection_03",
        "source": "MACEField_BEC_backprojection",
        "spacegroup": "P1",
        "spacegroup_number": 1,
        "pointgroup": "1",
        "has_inversion": false,
        "is_polar_point_group": true,
        "nonpolar_parent_hypothesis": false,
        "symmetry_tolerance_A": null,
        "target_reduced_polarization": [
          0.0,
          0.0,
          -0.5
        ],
        "formal_class": [
          0.0,
          0.0,
          0.5
        ],
        "target_residual": 0.0005656447945974505,
        "parent_symmetrization_rmsd_A": 0.11454006964538539,
        "parent_cell_rmsd_A": 0.06234121262382818,
        "energy_eV": -130.37952457935455,
        "reduced_polarization": [
          -1.594630209122331e-06,
          -0.00040822965918961595,
          -0.49960846451480406
        ],
        "cartesian_polarization_e_A2": [
          -5.267547574089144e-06,
          -1.7266692549477754e-05,
          -0.0056003538739404215
        ],
        "ranking_score": 0.6312566623905373
      },
      "branch_status": "awaiting_branch_sampling"
    },
    {
      "orbit_id": 4,
      "formal_class": [
        0.5,
        0.5,
        0.0
      ],
      "formal_classes_in_orbit": [
        [
          0.5,
          0.5,
          0.0
        ]
      ],
      "target_reduced_polarization": [
        0.5,
        -0.5,
        0.0
      ],
      "bec_backprojection": {
        "converged_to_target": true,
        "history": [
          {
            "iteration": 0,
            "reduced_polarization": [
              4.0357706137985266e-15,
              -0.15177429120251115,
              -1.441066878410653e-15
            ],
            "branch_aligned_reduced_polarization": [
              4.052314039881821e-15,
              -0.15177429120251118,
              -1.441066878410653e-15
            ],
            "target_residual": 0.6093120253757589,
            "energy_eV": -131.12716413193058,
            "max_atomic_step_A": 0.12,
            "max_log_strain_component": 0.009722114381480318,
            "step_scale": 0.8554126142972144,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 1.3359161831261426,
            "cell_principal_stretches": [
              1.000341690908791,
              0.9970658651435151,
              0.9874979407317421
            ],
            "cell_volume_ratio": 0.9849369176388809,
            "cell_rmsd_from_input_A": 0.11626293541654963
          },
          {
            "iteration": 1,
            "reduced_polarization": [
              0.4174847208617557,
              -0.45167717844944993,
              -0.004992479959201488
            ],
            "branch_aligned_reduced_polarization": [
              0.4174847208617557,
              -0.45167717844944993,
              -0.004992479959201488
            ],
            "target_residual": 0.09575380530303593,
            "energy_eV": -130.5709508183164,
            "max_atomic_step_A": 0.02131814748227045,
            "max_log_strain_component": 0.0016286571625060752,
            "step_scale": 1.0,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 1.3359161831261426,
            "cell_principal_stretches": [
              1.0005166609275378,
              0.9966645335865904,
              0.9852146451530934
            ],
            "cell_volume_ratio": 0.982435818881082,
            "cell_rmsd_from_input_A": 0.1366639907764741
          },
          {
            "iteration": 2,
            "reduced_polarization": [
              0.49983851941192975,
              -0.5004528914732076,
              -0.0005644922205330119
            ],
            "branch_aligned_reduced_polarization": [
              0.49983851941192975,
              -0.5004528914732076,
              -0.0005644922205330119
            ],
            "target_residual": 0.0007415107105564628,
            "energy_eV": -130.3437536247157
          }
        ],
        "iterations": 2
      },
      "parent": {
        "candidate_id": "bec_projection_04",
        "source": "MACEField_BEC_backprojection",
        "spacegroup": "P1",
        "spacegroup_number": 1,
        "pointgroup": "1",
        "has_inversion": false,
        "is_polar_point_group": true,
        "nonpolar_parent_hypothesis": false,
        "symmetry_tolerance_A": null,
        "target_reduced_polarization": [
          0.5,
          -0.5,
          0.0
        ],
        "formal_class": [
          0.5,
          0.5,
          0.0
        ],
        "target_residual": 0.0007415107105564628,
        "parent_symmetrization_rmsd_A": 0.13962751509111462,
        "parent_cell_rmsd_A": 0.1366639907764741,
        "energy_eV": -130.3437536247157,
        "reduced_polarization": [
          0.49983851941192975,
          -0.5004528914732076,
          -0.0005644922205330119
        ],
        "cartesian_polarization_e_A2": [
          0.00406084668984731,
          -0.007072423378663965,
          -0.0001711349432546947
        ],
        "ranking_score": 0.675276534206346
      },
      "branch_status": "awaiting_branch_sampling"
    },
    {
      "orbit_id": 5,
      "formal_class": [
        0.0,
        0.5,
        0.5
      ],
      "formal_classes_in_orbit": [
        [
          0.0,
          0.5,
          0.5
        ]
      ],
      "target_reduced_polarization": [
        0.0,
        -0.5,
        -0.5
      ],
      "bec_backprojection": {
        "converged_to_target": true,
        "history": [
          {
            "iteration": 0,
            "reduced_polarization": [
              4.0357706137985266e-15,
              -0.15177429120251115,
              -1.441066878410653e-15
            ],
            "branch_aligned_reduced_polarization": [
              4.0357706137985266e-15,
              -0.15177429120251118,
              -1.4432899320127035e-15
            ],
            "target_residual": 0.609312025375761,
            "energy_eV": -131.12716413193058,
            "max_atomic_step_A": 0.12,
            "max_log_strain_component": 0.006816152025374399,
            "step_scale": 0.599727815851939,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 1.3359161831261426,
            "cell_principal_stretches": [
              0.9996665988550657,
              0.9971002630520361,
              0.9926237069017482
            ],
            "cell_volume_ratio": 0.9894153770274483,
            "cell_rmsd_from_input_A": 0.07460491805503128
          },
          {
            "iteration": 1,
            "reduced_polarization": [
              0.0018345374470427162,
              -0.3621799386978853,
              -0.29800261491091645
            ],
            "branch_aligned_reduced_polarization": [
              0.0018345374470427162,
              -0.3621799386978853,
              -0.29800261491091645
            ],
            "target_residual": 0.24454177231669597,
            "energy_eV": -130.70121221649032,
            "max_atomic_step_A": 0.07635542740895757,
            "max_log_strain_component": 0.0045106142288563085,
            "step_scale": 1.0,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 1.3359161831261426,
            "cell_principal_stretches": [
              0.999446375705276,
              0.995237590975682,
              0.9877207896234798
            ],
            "cell_volume_ratio": 0.9824726372060818,
            "cell_rmsd_from_input_A": 0.12360651986370011
          },
          {
            "iteration": 2,
            "reduced_polarization": [
              0.0009091536892466028,
              -0.49998146274458843,
              -0.4981501227186364
            ],
            "branch_aligned_reduced_polarization": [
              0.0009091536892466028,
              -0.49998146274458843,
              -0.4981501227186364
            ],
            "target_residual": 0.0020612981387014544,
            "energy_eV": -129.88451431327005,
            "max_atomic_step_A": 0.0005945816995797317,
            "max_log_strain_component": 1.8272571350336546e-05,
            "step_scale": 1.0,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 1.3359161831261426,
            "cell_principal_stretches": [
              0.9994473740107355,
              0.9952459304254883,
              0.9877090008405465
            ],
            "cell_volume_ratio": 0.9824701247986977,
            "cell_rmsd_from_input_A": 0.12366429854398998
          },
          {
            "iteration": 3,
            "reduced_polarization": [
              3.947475575676201e-06,
              -0.49999767126262706,
              -0.4999937171056403
            ],
            "branch_aligned_reduced_polarization": [
              3.947475575676201e-06,
              -0.49999767126262706,
              -0.4999937171056403
            ],
            "target_residual": 7.776910871810939e-06,
            "energy_eV": -129.8786714672505
          }
        ],
        "iterations": 3
      },
      "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": [
          0.0,
          -0.5,
          -0.5
        ],
        "formal_class": [
          0.0,
          0.5,
          0.5
        ],
        "target_residual": 7.776910871810939e-06,
        "parent_symmetrization_rmsd_A": 0.1516090999830722,
        "parent_cell_rmsd_A": 0.12366429854398998,
        "energy_eV": -129.8786714672505,
        "reduced_polarization": [
          3.947475575676201e-06,
          -0.49999767126262706,
          -0.4999937171056403
        ],
        "cartesian_polarization_e_A2": [
          -1.993256699985805e-05,
          -0.007092704108533055,
          -0.005720940632993728
        ],
        "ranking_score": 0.6825407284408134
      },
      "branch_status": "awaiting_branch_sampling"
    },
    {
      "orbit_id": 6,
      "formal_class": [
        0.5,
        0.0,
        0.5
      ],
      "formal_classes_in_orbit": [
        [
          0.5,
          0.0,
          0.5
        ]
      ],
      "target_reduced_polarization": [
        0.5,
        0.0,
        -0.5
      ],
      "bec_backprojection": {
        "converged_to_target": true,
        "history": [
          {
            "iteration": 0,
            "reduced_polarization": [
              4.0357706137985266e-15,
              -0.15177429120251115,
              -1.441066878410653e-15
            ],
            "branch_aligned_reduced_polarization": [
              4.052314039881821e-15,
              -0.15177429120251115,
              -1.4432899320127035e-15
            ],
            "target_residual": 0.7232118883633062,
            "energy_eV": -131.12716413193058,
            "max_atomic_step_A": 0.12000000000000001,
            "max_log_strain_component": 0.003400694617902075,
            "step_scale": 0.6398309623000927,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 1.3359161831261426,
            "cell_principal_stretches": [
              1.0059718549786862,
              1.0012614423832626,
              0.9977358570178936
            ],
            "cell_volume_ratio": 1.004960293255229,
            "cell_rmsd_from_input_A": 0.04968337138539639
          },
          {
            "iteration": 1,
            "reduced_polarization": [
              0.3190799114035306,
              -0.05776041510423876,
              -0.31793248803290697
            ],
            "branch_aligned_reduced_polarization": [
              0.3190799114035306,
              -0.05776041510423876,
              -0.31793248803290697
            ],
            "target_residual": 0.2630910924464298,
            "energy_eV": -130.74107618549465,
            "max_atomic_step_A": 0.07139900373192588,
            "max_log_strain_component": 0.0020373765303868395,
            "step_scale": 1.0,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 1.3359161831261426,
            "cell_principal_stretches": [
              1.0095818907636347,
              1.0020822826864253,
              0.9965183643946116
            ],
            "cell_volume_ratio": 1.008161810182013,
            "cell_rmsd_from_input_A": 0.0801206571066878
          },
          {
            "iteration": 2,
            "reduced_polarization": [
              0.49779719404177053,
              -0.001671656578801,
              -0.4984790076815667
            ],
            "branch_aligned_reduced_polarization": [
              0.49779719404177053,
              -0.001671656578801,
              -0.4984790076815667
            ],
            "target_residual": 0.00315597963234761,
            "energy_eV": -130.12278976101607,
            "max_atomic_step_A": 0.0009171896628512577,
            "max_log_strain_component": 5.9844436816150205e-05,
            "step_scale": 1.0,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 1.3359161831261426,
            "cell_principal_stretches": [
              1.0096521989298994,
              1.0021060292438864,
              0.9965184548631132
            ],
            "cell_volume_ratio": 1.0082560032757968,
            "cell_rmsd_from_input_A": 0.08077098517867771
          },
          {
            "iteration": 3,
            "reduced_polarization": [
              0.5000004375402514,
              -1.2405859833797495e-06,
              -0.5000032439257487
            ],
            "branch_aligned_reduced_polarization": [
              0.5000004375402514,
              -1.2405859833797495e-06,
              -0.5000032439257487
            ],
            "target_residual": 3.5005070085217314e-06,
            "energy_eV": -130.114207713743
          }
        ],
        "iterations": 3
      },
      "parent": {
        "candidate_id": "bec_projection_06",
        "source": "MACEField_BEC_backprojection",
        "spacegroup": "P1",
        "spacegroup_number": 1,
        "pointgroup": "1",
        "has_inversion": false,
        "is_polar_point_group": true,
        "nonpolar_parent_hypothesis": false,
        "symmetry_tolerance_A": null,
        "target_reduced_polarization": [
          0.5,
          0.0,
          -0.5
        ],
        "formal_class": [
          0.5,
          0.0,
          0.5
        ],
        "target_residual": 3.5005070085217314e-06,
        "parent_symmetrization_rmsd_A": 0.14573161723843325,
        "parent_cell_rmsd_A": 0.08077098517867771,
        "energy_eV": -130.114207713743,
        "reduced_polarization": [
          0.5000004375402514,
          -1.2405859833797495e-06,
          -0.5000032439257487
        ],
        "cartesian_polarization_e_A2": [
          0.003981902576637846,
          3.820639826226702e-05,
          -0.005801187098561812
        ],
        "ranking_score": 0.6659313645471198
      },
      "branch_status": "awaiting_branch_sampling"
    },
    {
      "orbit_id": 7,
      "formal_class": [
        0.5,
        0.5,
        0.5
      ],
      "formal_classes_in_orbit": [
        [
          0.5,
          0.5,
          0.5
        ]
      ],
      "target_reduced_polarization": [
        0.5,
        -0.5,
        -0.5
      ],
      "bec_backprojection": {
        "converged_to_target": true,
        "history": [
          {
            "iteration": 0,
            "reduced_polarization": [
              4.0357706137985266e-15,
              -0.15177429120251115,
              -1.441066878410653e-15
            ],
            "branch_aligned_reduced_polarization": [
              4.052314039881821e-15,
              -0.15177429120251118,
              -1.4432899320127035e-15
            ],
            "target_residual": 0.7882012079840451,
            "energy_eV": -131.12716413193058,
            "max_atomic_step_A": 0.12,
            "max_log_strain_component": 0.006239978446190922,
            "step_scale": 0.5490324497699318,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 1.3359161831261426,
            "cell_principal_stretches": [
              1.0007946682419258,
              0.9973622480552737,
              0.9921364203511417
            ],
            "cell_volume_ratio": 0.990305750229283,
            "cell_rmsd_from_input_A": 0.07310259207989912
          },
          {
            "iteration": 1,
            "reduced_polarization": [
              0.27118655958550275,
              -0.34451416529386625,
              -0.2751622611600064
            ],
            "branch_aligned_reduced_polarization": [
              0.27118655958550275,
              -0.34451416529386625,
              -0.2751622611600064
            ],
            "target_residual": 0.35648764931658294,
            "energy_eV": -130.69038408264345,
            "max_atomic_step_A": 0.09256523793346072,
            "max_log_strain_component": 0.005123187472588659,
            "step_scale": 1.0,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 1.3359161831261426,
            "cell_principal_stretches": [
              1.0015501760038028,
              0.9952466058932061,
              0.9855811030211175
            ],
            "cell_volume_ratio": 0.9824168094395217,
            "cell_rmsd_from_input_A": 0.13303899737714908
          },
          {
            "iteration": 2,
            "reduced_polarization": [
              0.49577445869168396,
              -0.4999397056440295,
              -0.4995932190687931
            ],
            "branch_aligned_reduced_polarization": [
              0.49577445869168396,
              -0.4999397056440295,
              -0.4995932190687931
            ],
            "target_residual": 0.004245504149525785,
            "energy_eV": -129.546798398981,
            "max_atomic_step_A": 0.0008842058900843516,
            "max_log_strain_component": 4.358208246966137e-05,
            "step_scale": 1.0,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 1.3359161831261426,
            "cell_principal_stretches": [
              1.001579128331665,
              0.9952565303499099,
              0.9855343956701343
            ],
            "cell_volume_ratio": 0.9824084462691651,
            "cell_rmsd_from_input_A": 0.13330942191867962
          },
          {
            "iteration": 3,
            "reduced_polarization": [
              0.5000156642081903,
              -0.5000099595551762,
              -0.5000163307058416
            ],
            "branch_aligned_reduced_polarization": [
              0.5000156642081903,
              -0.5000099595551762,
              -0.5000163307058416
            ],
            "target_residual": 2.4723513318779027e-05,
            "energy_eV": -129.53944379408617
          }
        ],
        "iterations": 3
      },
      "parent": {
        "candidate_id": "bec_projection_07",
        "source": "MACEField_BEC_backprojection",
        "spacegroup": "P1",
        "spacegroup_number": 1,
        "pointgroup": "1",
        "has_inversion": false,
        "is_polar_point_group": true,
        "nonpolar_parent_hypothesis": false,
        "symmetry_tolerance_A": null,
        "target_reduced_polarization": [
          0.5,
          -0.5,
          -0.5
        ],
        "formal_class": [
          0.5,
          0.5,
          0.5
        ],
        "target_residual": 2.4723513318779027e-05,
        "parent_symmetrization_rmsd_A": 0.17936113083096125,
        "parent_cell_rmsd_A": 0.13330942191867962,
        "energy_eV": -129.53944379408617,
        "reduced_polarization": [
          0.5000156642081903,
          -0.5000099595551762,
          -0.5000163307058416
        ],
        "cartesian_polarization_e_A2": [
          0.004042133206255971,
          -0.007040732824445188,
          -0.005885545440936707
        ],
        "ranking_score": 0.7127379333372688
      },
      "branch_status": "awaiting_branch_sampling"
    }
  ],
  "sampled_polarization_branches": [
    {
      "orbit_id": 0,
      "candidate_id": "bec_projection_00",
      "formal_class": [
        0.0,
        0.0,
        0.0
      ],
      "construction": "MACEField-BEC-parent plus variable-cell P-N-P path and symmetric log-strain continuation beyond both polar endpoints",
      "geometry_diagnostics": {
        "collision_aware": false,
        "permutations_tested": 1,
        "selected_order": [
          0,
          1,
          2,
          3,
          4,
          5,
          6,
          7,
          8,
          9,
          10,
          11,
          12,
          13,
          14,
          15,
          16,
          17,
          18,
          19,
          20,
          21,
          22,
          23,
          24,
          25,
          26,
          27
        ],
        "endpoint_rmsd_A": 0.047921781142931365,
        "minimum_distance_A_by_image": [
          2.7183704315561643,
          2.7183927740033433,
          2.7184327977324725,
          2.7184905662643493,
          2.7185661429269525,
          2.718659590851619,
          2.718770972969288,
          2.7189003520067145,
          2.719047790482698
        ],
        "minimum_distance_A": 2.7183704315561643,
        "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": [
          885.7382355075982,
          886.6013121079644,
          887.4652297030935,
          888.3299891124642,
          889.1955911563538,
          890.0620366558363,
          890.9293264327898,
          891.7974613098886,
          892.6664421106102
        ],
        "cell_deformation_log_strain_norm": 0.005540945184338843
      },
      "parent_reduced_polarization": [
        4.1091461541771665e-16,
        -3.4588409078130056e-06,
        1.7541189528012837e-15
      ],
      "incoming": {
        "reached": true,
        "construction": "variable_cell_linear_interpolation",
        "continuation_fractions": [
          0.0,
          0.125,
          0.25,
          0.375,
          0.5,
          0.625,
          0.75,
          0.875,
          1.0
        ],
        "energies_eV": [
          -131.12716413193056,
          -131.12736631694753,
          -131.12515320345094,
          -131.12056448989887,
          -131.11363680611623,
          -131.1044038666484,
          -131.09289667000047,
          -131.07914366839367,
          -131.06317121386638
        ],
        "cartesian_polarizations_e_A2": [
          [
            1.2926138313184199e-18,
            -0.002135629295104575,
            4.5923044116294406e-17
          ],
          [
            -1.6419781035271725e-17,
            -0.0018673438344146006,
            3.6314482365901244e-17
          ],
          [
            3.542688459932355e-17,
            -0.0015994332969811913,
            1.7873727255363857e-17
          ],
          [
            5.636538113569807e-17,
            -0.0013319022568419466,
            2.18009671216371e-17
          ],
          [
            5.462494170060476e-19,
            -0.0010647546010239925,
            2.700813188939901e-17
          ],
          [
            6.969594134584737e-18,
            -0.0007979934959918481,
            9.30058814603981e-18
          ],
          [
            4.336568581893022e-17,
            -0.000531621316784006,
            -2.1379096187673035e-17
          ],
          [
            2.798752234133274e-17,
            -0.0002656395721531272,
            -6.037897508166307e-18
          ],
          [
            3.295845879789565e-18,
            -4.853353684613745e-08,
            1.9503012529226458e-17
          ]
        ],
        "raw_reduced_polarization": [
          [
            1.5550784941131958e-16,
            -0.1517742912025115,
            4.0796665187018845e-15
          ],
          [
            -1.742202864491151e-15,
            -0.13275432337178164,
            3.0157807580653046e-15
          ],
          [
            4.9405214958966775e-15,
            -0.11374768119240429,
            1.5103762170239928e-15
          ],
          [
            7.688236351068345e-15,
            -0.09475471107190994,
            1.8945564189393576e-15
          ],
          [
            7.666688874091698e-16,
            -0.07577571099724364,
            2.0943604954269306e-15
          ],
          [
            1.5278380785002353e-15,
            -0.056810928060926115,
            5.675150027858089e-16
          ],
          [
            5.954507796066457e-15,
            -0.037860553324904615,
            -1.9460080881527984e-15
          ],
          [
            3.8126122402768206e-15,
            -0.01892471638899547,
            -5.505010285444076e-16
          ],
          [
            4.1091461541771665e-16,
            -3.4588409078130056e-06,
            1.7541189528012837e-15
          ]
        ],
        "unwrapped_reduced_polarization": [
          [
            1.5550784941131958e-16,
            -0.1517742912025115,
            4.0796665187018845e-15
          ],
          [
            -1.7422028644911509e-15,
            -0.13275432337178164,
            3.0157807580653046e-15
          ],
          [
            4.9405214958966775e-15,
            -0.11374768119240429,
            1.5103762170239928e-15
          ],
          [
            7.688236351068345e-15,
            -0.09475471107190994,
            1.8945564189393576e-15
          ],
          [
            7.666688874091699e-16,
            -0.07577571099724364,
            2.0943604954269306e-15
          ],
          [
            1.5278380785002353e-15,
            -0.056810928060926115,
            5.67515002785809e-16
          ],
          [
            5.954507796066457e-15,
            -0.037860553324904615,
            -1.9460080881527984e-15
          ],
          [
            3.8126122402768206e-15,
            -0.01892471638899547,
            -5.505010285444076e-16
          ],
          [
            4.109146154177166e-16,
            -3.458840907813454e-06,
            1.7541189528012837e-15
          ]
        ],
        "berry_integer_shifts": [
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ]
        ],
        "folded_reduced_polarization": [
          [
            1.1102230246251565e-16,
            -0.1517742912025115,
            4.107825191113079e-15
          ],
          [
            -1.7208456881689926e-15,
            -0.1327543233717816,
            2.9976021664879227e-15
          ],
          [
            4.9960036108132044e-15,
            -0.1137476811924043,
            1.5543122344752192e-15
          ],
          [
            7.66053886991358e-15,
            -0.09475471107190991,
            1.887379141862766e-15
          ],
          [
            7.771561172376096e-16,
            -0.07577571099724367,
            2.1094237467877974e-15
          ],
          [
            1.5543122344752192e-15,
            -0.056810928060926136,
            5.551115123125783e-16
          ],
          [
            5.995204332975845e-15,
            -0.03786055332490462,
            -1.942890293094024e-15
          ],
          [
            3.774758283725532e-15,
            -0.018924716388995455,
            -5.551115123125783e-16
          ],
          [
            4.440892098500626e-16,
            -3.4588409077995763e-06,
            1.7763568394002505e-15
          ]
        ]
      },
      "reflected": {
        "reached": true,
        "construction": "reflect_displacements_about_reconstructed_parent",
        "energies_eV": [
          -131.06317121386638,
          -131.05631658264522,
          -131.04760990890838,
          -131.03702376428066,
          -131.0245298383786,
          -131.01009885670584,
          -130.99370047933039,
          -130.9753031969465,
          -130.9548742429805
        ],
        "cartesian_polarizations_e_A2": [
          [
            3.489399093013056e-17,
            -4.853353684355674e-08,
            1.444264538832314e-17
          ],
          [
            1.6331890295929225e-17,
            0.0002484360024857464,
            4.894120531748205e-18
          ],
          [
            -4.088898177970253e-18,
            0.0004966076602284916,
            -2.770325870293369e-17
          ],
          [
            -9.994429172860886e-18,
            0.0007443888855756603,
            -1.299587631135655e-17
          ],
          [
            -1.6668410781784537e-17,
            0.0009917020638832517,
            -1.8104266392200436e-18
          ],
          [
            -1.1732372847258661e-17,
            0.0012384698275237417,
            -4.362536774430068e-17
          ],
          [
            -4.9805617942549325e-17,
            0.0014846153408985094,
            -7.287101400699525e-18
          ],
          [
            -6.292423237539784e-17,
            0.0017300625688476093,
            1.4791890446455463e-18
          ],
          [
            -6.842235880445502e-17,
            0.0019747365361198204,
            -2.0822833719056728e-17
          ]
        ],
        "raw_reduced_polarization": [
          [
            4.37232970892954e-15,
            -3.458840907629086e-06,
            1.4422877116514515e-15
          ],
          [
            1.757721232550278e-15,
            0.017699098254639223,
            6.352865756231471e-16
          ],
          [
            -9.998313342176337e-16,
            0.03536698060825875,
            -2.2682225070990784e-15
          ],
          [
            -1.8613444763446576e-15,
            0.05299469687435123,
            -9.293236598233816e-16
          ],
          [
            -2.7349592787839038e-15,
            0.07057675911042531,
            5.4849884552148444e-17
          ],
          [
            -2.070480203514785e-15,
            0.08810770465735158,
            -3.658851272098766e-15
          ],
          [
            -6.696425386609887e-15,
            0.10558211637122253,
            -6.497981973706688e-16
          ],
          [
            -8.121547064644718e-15,
            0.12299464163235466,
            -1.8828036976990373e-17
          ],
          [
            -8.511433722918772e-15,
            0.14034001067896593,
            -2.1472142907176813e-15
          ]
        ],
        "unwrapped_reduced_polarization": [
          [
            4.37232970892954e-15,
            -3.458840907629086e-06,
            1.4422877116514515e-15
          ],
          [
            1.757721232550278e-15,
            0.017699098254639223,
            6.352865756231471e-16
          ],
          [
            -9.998313342176339e-16,
            0.03536698060825875,
            -2.2682225070990784e-15
          ],
          [
            -1.8613444763446576e-15,
            0.05299469687435123,
            -9.293236598233816e-16
          ],
          [
            -2.7349592787839038e-15,
            0.07057675911042531,
            5.4849884552148395e-17
          ],
          [
            -2.070480203514785e-15,
            0.08810770465735158,
            -3.658851272098766e-15
          ],
          [
            -6.696425386609887e-15,
            0.10558211637122253,
            -6.49798197370669e-16
          ],
          [
            -8.121547064644718e-15,
            0.12299464163235466,
            -1.8828036976990358e-17
          ],
          [
            -8.511433722918772e-15,
            0.14034001067896593,
            -2.1472142907176813e-15
          ]
        ],
        "gauge_integer_shift": [
          0,
          0,
          0
        ],
        "expected_opposite_endpoint_reduced_polarization": [
          6.601720401638818e-16,
          0.15176739286751373,
          -5.904041638944437e-16
        ],
        "actual_opposite_endpoint_branch_residual": 0.011427382188547802
      },
      "pnp_branch": {
        "construction": "incoming_path_concatenated_with_parent_reflection",
        "reduced_polarization": [
          [
            1.5550784941131958e-16,
            -0.1517742912025115,
            4.0796665187018845e-15
          ],
          [
            -1.742202864491151e-15,
            -0.13275432337178164,
            3.0157807580653046e-15
          ],
          [
            4.9405214958966775e-15,
            -0.11374768119240429,
            1.5103762170239928e-15
          ],
          [
            7.688236351068345e-15,
            -0.09475471107190994,
            1.8945564189393576e-15
          ],
          [
            7.666688874091698e-16,
            -0.07577571099724364,
            2.0943604954269306e-15
          ],
          [
            1.5278380785002353e-15,
            -0.056810928060926115,
            5.675150027858089e-16
          ],
          [
            5.954507796066457e-15,
            -0.037860553324904615,
            -1.9460080881527984e-15
          ],
          [
            3.8126122402768206e-15,
            -0.01892471638899547,
            -5.505010285444076e-16
          ],
          [
            4.1091461541771665e-16,
            -3.4588409078130056e-06,
            1.7541189528012837e-15
          ],
          [
            1.757721232550278e-15,
            0.017699098254639223,
            6.352865756231471e-16
          ],
          [
            -9.998313342176337e-16,
            0.03536698060825875,
            -2.2682225070990784e-15
          ],
          [
            -1.8613444763446576e-15,
            0.05299469687435123,
            -9.293236598233816e-16
          ],
          [
            -2.7349592787839038e-15,
            0.07057675911042531,
            5.4849884552148444e-17
          ],
          [
            -2.070480203514785e-15,
            0.08810770465735158,
            -3.658851272098766e-15
          ],
          [
            -6.696425386609887e-15,
            0.10558211637122253,
            -6.497981973706688e-16
          ],
          [
            -8.121547064644718e-15,
            0.12299464163235466,
            -1.8828036976990373e-17
          ],
          [
            -8.511433722918772e-15,
            0.14034001067896593,
            -2.1472142907176813e-15
          ]
        ],
        "unwrapped_reduced_polarization": [
          [
            1.5550784941131958e-16,
            -0.1517742912025115,
            4.0796665187018845e-15
          ],
          [
            -1.7422028644911509e-15,
            -0.13275432337178164,
            3.0157807580653046e-15
          ],
          [
            4.9405214958966775e-15,
            -0.11374768119240429,
            1.5103762170239928e-15
          ],
          [
            7.688236351068345e-15,
            -0.09475471107190994,
            1.8945564189393576e-15
          ],
          [
            7.666688874091699e-16,
            -0.07577571099724364,
            2.0943604954269306e-15
          ],
          [
            1.5278380785002353e-15,
            -0.056810928060926115,
            5.67515002785809e-16
          ],
          [
            5.954507796066457e-15,
            -0.037860553324904615,
            -1.9460080881527984e-15
          ],
          [
            3.8126122402768206e-15,
            -0.01892471638899547,
            -5.505010285444076e-16
          ],
          [
            4.109146154177166e-16,
            -3.458840907813454e-06,
            1.7541189528012837e-15
          ],
          [
            1.757721232550278e-15,
            0.017699098254639223,
            6.352865756231472e-16
          ],
          [
            -9.998313342176339e-16,
            0.03536698060825875,
            -2.2682225070990784e-15
          ],
          [
            -1.8613444763446576e-15,
            0.05299469687435123,
            -9.293236598233816e-16
          ],
          [
            -2.7349592787839038e-15,
            0.07057675911042531,
            5.4849884552148395e-17
          ],
          [
            -2.070480203514785e-15,
            0.08810770465735158,
            -3.658851272098766e-15
          ],
          [
            -6.696425386609887e-15,
            0.10558211637122253,
            -6.49798197370669e-16
          ],
          [
            -8.121547064644718e-15,
            0.12299464163235466,
            -1.8828036976990358e-17
          ],
          [
            -8.511433722918772e-15,
            0.14034001067896593,
            -2.1472142907176813e-15
          ]
        ],
        "berry_integer_shifts": [
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            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": [
          [
            1.1102230246251565e-16,
            -0.1517742912025115,
            4.107825191113079e-15
          ],
          [
            -1.7208456881689926e-15,
            -0.1327543233717816,
            2.9976021664879227e-15
          ],
          [
            4.9960036108132044e-15,
            -0.1137476811924043,
            1.5543122344752192e-15
          ],
          [
            7.66053886991358e-15,
            -0.09475471107190991,
            1.887379141862766e-15
          ],
          [
            7.771561172376096e-16,
            -0.07577571099724367,
            2.1094237467877974e-15
          ],
          [
            1.5543122344752192e-15,
            -0.056810928060926136,
            5.551115123125783e-16
          ],
          [
            5.995204332975845e-15,
            -0.03786055332490462,
            -1.942890293094024e-15
          ],
          [
            3.774758283725532e-15,
            -0.018924716388995455,
            -5.551115123125783e-16
          ],
          [
            4.440892098500626e-16,
            -3.4588409077995763e-06,
            1.7763568394002505e-15
          ],
          [
            1.7763568394002505e-15,
            0.017699098254639223,
            6.661338147750939e-16
          ],
          [
            -9.992007221626409e-16,
            0.035366980608258713,
            -2.275957200481571e-15
          ],
          [
            -1.887379141862766e-15,
            0.05299469687435121,
            -9.43689570931383e-16
          ],
          [
            -2.7200464103316335e-15,
            0.07057675911042527,
            0.0
          ],
          [
            -2.0539125955565396e-15,
            0.08810770465735163,
            -3.6637359812630166e-15
          ],
          [
            -6.716849298982197e-15,
            0.1055821163712225,
            -6.661338147750939e-16
          ],
          [
            -8.104628079763643e-15,
            0.12299464163235463,
            0.0
          ],
          [
            -8.493206138382448e-15,
            0.14034001067896595,
            -2.1649348980190553e-15
          ]
        ]
      },
      "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": "bec_projection_00",
        "source": "MACEField_BEC_backprojection",
        "spacegroup": "P2_1",
        "spacegroup_number": 4,
        "pointgroup": "2",
        "has_inversion": false,
        "is_polar_point_group": true,
        "nonpolar_parent_hypothesis": false,
        "symmetry_tolerance_A": null,
        "target_reduced_polarization": [
          0.0,
          0.0,
          0.0
        ],
        "formal_class": [
          0.0,
          0.0,
          0.0
        ],
        "target_residual": 3.458840907359854e-06,
        "parent_symmetrization_rmsd_A": 0.047921781142931365,
        "parent_cell_rmsd_A": 0.05379183301846588,
        "energy_eV": -131.06317121386633,
        "reduced_polarization": [
          5.001703392550363e-15,
          -3.458840907359854e-06,
          7.759400865455864e-16
        ],
        "cartesian_polarization_e_A2": [
          3.990771874254629e-17,
          -4.853353683977895e-08,
          6.7238365236272965e-18
        ],
        "ranking_score": 0.5613766570793626
      }
    }
  ],
  "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": 52,
      "full_response": 20,
      "energy_polarization": 32
    },
    "model_evaluations_for_recovery_and_path_properties": {
      "total": 77,
      "full_response": 45,
      "energy_polarization": 32
    },
    "elapsed_seconds": 328.9578275110107
  }
}