{
  "schema": "ferrofinder.endpoint_parent_recovery.v4_variable_cell",
  "status": "complete",
  "input_atom_count": 22,
  "input_formula": "Ga2Na6P8Sr6",
  "input_spacegroup": "P6_3mc",
  "input_pointgroup": "6mm",
  "input_is_polar_point_group": true,
  "input_energy_eV": -83.26996189457662,
  "input_cartesian_polarization_e_A2": [
    -1.709396363262364e-11,
    0.0005718772465176018,
    1.4055789913836568e-12
  ],
  "input_reduced_polarization": [
    -9.850173858380219e-10,
    0.04404365609868856,
    9.818580558610348e-11
  ],
  "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": [
        0.5,
        0.5,
        0.0
      ],
      "target_reduced_polarization": [
        -0.5,
        0.5,
        0.0
      ]
    }
  ],
  "parent_candidates": [
    {
      "candidate_id": "inversion_parent_endpoint_00",
      "source": "same_species_inversion_center_projection_from_endpoint",
      "spacegroup": "P6_3/mmc",
      "spacegroup_number": 194,
      "pointgroup": "6/mmm",
      "has_inversion": true,
      "is_polar_point_group": false,
      "nonpolar_parent_hypothesis": true,
      "symmetry_tolerance_A": null,
      "target_reduced_polarization": [
        0.0,
        0.0,
        0.0
      ],
      "formal_class": [
        0.0,
        0.0,
        0.0
      ],
      "target_residual": 9.465530891637482e-15,
      "parent_symmetrization_rmsd_A": 0.7318859637289283,
      "parent_cell_rmsd_A": 0.0,
      "energy_eV": -80.77779544639127,
      "reduced_polarization": [
        -3.0707867906731036e-15,
        5.22928283449193e-15,
        7.267815667974739e-15
      ],
      "cartesian_polarization_e_A2": [
        -1.1082938379488041e-16,
        6.78987198962361e-17,
        1.0404242196898672e-16
      ],
      "ranking_score": 0.7318859637289473
    },
    {
      "candidate_id": "bec_projection_00",
      "source": "MACEField_BEC_backprojection",
      "spacegroup": "P6_3mc",
      "spacegroup_number": 186,
      "pointgroup": "6mm",
      "has_inversion": false,
      "is_polar_point_group": true,
      "nonpolar_parent_hypothesis": false,
      "symmetry_tolerance_A": null,
      "target_reduced_polarization": [
        0.0,
        0.0,
        0.0
      ],
      "formal_class": [
        0.0,
        0.0,
        0.0
      ],
      "target_residual": 4.8503278585723514e-05,
      "parent_symmetrization_rmsd_A": 0.005883335463007772,
      "parent_cell_rmsd_A": 0.0009064034697018341,
      "energy_eV": -83.2672193276863,
      "reduced_polarization": [
        -2.8466095990904203e-12,
        -4.850327858572342e-05,
        8.957576991798866e-13
      ],
      "cartesian_polarization_e_A2": [
        -5.443782667061977e-14,
        -6.297027845017971e-07,
        1.2820371280324972e-14
      ],
      "ranking_score": 0.5062069428876047
    },
    {
      "candidate_id": "inversion_parent_bec_00_00",
      "source": "same_species_inversion_center_projection_after_BEC",
      "spacegroup": "P6_3/mmc",
      "spacegroup_number": 194,
      "pointgroup": "6/mmm",
      "has_inversion": true,
      "is_polar_point_group": false,
      "nonpolar_parent_hypothesis": true,
      "symmetry_tolerance_A": null,
      "target_reduced_polarization": [
        0.0,
        0.0,
        0.0
      ],
      "formal_class": [
        0.0,
        0.0,
        0.0
      ],
      "target_residual": 1.1537010140093088e-14,
      "parent_symmetrization_rmsd_A": 0.7318861153621008,
      "parent_cell_rmsd_A": 0.0009064034697018341,
      "energy_eV": -80.7737110290158,
      "reduced_polarization": [
        -7.141993384016232e-15,
        -7.714992936940806e-16,
        -9.027697509061137e-15
      ],
      "cartesian_polarization_e_A2": [
        -4.343444264129151e-17,
        -1.0016132261926702e-17,
        -1.2920895506897077e-16
      ],
      "ranking_score": 0.7321127162295493
    },
    {
      "candidate_id": "bec_projection_01",
      "source": "MACEField_BEC_backprojection",
      "spacegroup": "P6_3mc",
      "spacegroup_number": 186,
      "pointgroup": "6mm",
      "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": 8.478452932281222e-06,
      "parent_symmetrization_rmsd_A": 0.06196458523805881,
      "parent_cell_rmsd_A": 0.009523814744173287,
      "energy_eV": -83.13869835453934,
      "reduced_polarization": [
        -2.1834618205038788e-14,
        0.5000084784529323,
        -3.322814419551186e-15
      ],
      "cartesian_polarization_e_A2": [
        2.8843911722568327e-13,
        0.006500918538120946,
        4.1131283507153564e-14
      ],
      "ranking_score": 0.5643624958299667
    },
    {
      "candidate_id": "bec_projection_02",
      "source": "MACEField_BEC_backprojection",
      "spacegroup": "Cc",
      "spacegroup_number": 9,
      "pointgroup": "m",
      "has_inversion": false,
      "is_polar_point_group": true,
      "nonpolar_parent_hypothesis": false,
      "symmetry_tolerance_A": null,
      "target_reduced_polarization": [
        -0.5,
        0.0,
        0.0
      ],
      "formal_class": [
        0.5,
        0.0,
        0.0
      ],
      "target_residual": 6.55368924066776e-05,
      "parent_symmetrization_rmsd_A": 0.10624153458200716,
      "parent_cell_rmsd_A": 0.03785087879083227,
      "energy_eV": -82.85424905854313,
      "reduced_polarization": [
        -0.49995096260853183,
        4.347894322711309e-05,
        4.1931918793245246e-10
      ],
      "cartesian_polarization_e_A2": [
        -0.00826215234872493,
        -3.681311131690447e-05,
        -9.700861242107308e-11
      ],
      "ranking_score": 0.6158353280645286
    },
    {
      "candidate_id": "bec_projection_03",
      "source": "MACEField_BEC_backprojection",
      "spacegroup": "Cc",
      "spacegroup_number": 9,
      "pointgroup": "m",
      "has_inversion": false,
      "is_polar_point_group": true,
      "nonpolar_parent_hypothesis": false,
      "symmetry_tolerance_A": null,
      "target_reduced_polarization": [
        -0.5,
        0.5,
        0.0
      ],
      "formal_class": [
        0.5,
        0.5,
        0.0
      ],
      "target_residual": 8.539986181182947e-05,
      "parent_symmetrization_rmsd_A": 0.12028943677458867,
      "parent_cell_rmsd_A": 0.03784755208659656,
      "energy_eV": -82.65955919535203,
      "reduced_polarization": [
        -0.4999669530595444,
        0.4999212533430195,
        -1.1764437660662004e-08
      ],
      "cartesian_polarization_e_A2": [
        -0.00825384370519526,
        0.006463240981806531,
        1.7565022344131979e-09
      ],
      "ranking_score": 0.6299221245198614
    }
  ],
  "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": [
              -9.850173858380219e-10,
              0.04404365609868856,
              9.818580558610348e-11
            ],
            "branch_aligned_reduced_polarization": [
              -9.850173858380219e-10,
              0.04404365609868856,
              9.818580558610348e-11
            ],
            "target_residual": 0.044043656098688565,
            "energy_eV": -83.26996189457662,
            "max_atomic_step_A": 0.009713534461358194,
            "max_log_strain_component": 0.0001461409190731655,
            "step_scale": 1.0,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 0.5799214376857585,
            "cell_principal_stretches": [
              1.0001461515981775,
              1.0000632600325914,
              1.0000632401661638
            ],
            "cell_volume_ratio": 1.0002726742862986,
            "cell_rmsd_from_input_A": 0.0009064034697018341
          },
          {
            "iteration": 1,
            "reduced_polarization": [
              -2.8466095990904203e-12,
              -4.850327858572342e-05,
              8.957576991798866e-13
            ],
            "branch_aligned_reduced_polarization": [
              -2.8466095990904203e-12,
              -4.850327858572342e-05,
              8.957576991798866e-13
            ],
            "target_residual": 4.8503278585723514e-05,
            "energy_eV": -83.2672193276863
          }
        ],
        "iterations": 1
      },
      "parent": {
        "candidate_id": "bec_projection_00",
        "source": "MACEField_BEC_backprojection",
        "spacegroup": "P6_3mc",
        "spacegroup_number": 186,
        "pointgroup": "6mm",
        "has_inversion": false,
        "is_polar_point_group": true,
        "nonpolar_parent_hypothesis": false,
        "symmetry_tolerance_A": null,
        "target_reduced_polarization": [
          0.0,
          0.0,
          0.0
        ],
        "formal_class": [
          0.0,
          0.0,
          0.0
        ],
        "target_residual": 4.8503278585723514e-05,
        "parent_symmetrization_rmsd_A": 0.005883335463007772,
        "parent_cell_rmsd_A": 0.0009064034697018341,
        "energy_eV": -83.2672193276863,
        "reduced_polarization": [
          -2.8466095990904203e-12,
          -4.850327858572342e-05,
          8.957576991798866e-13
        ],
        "cartesian_polarization_e_A2": [
          -5.443782667061977e-14,
          -6.297027845017971e-07,
          1.2820371280324972e-14
        ],
        "ranking_score": 0.5062069428876047
      },
      "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": [
          -83.26996189457662,
          -83.26977633515166,
          -83.26954616069793,
          -83.26927121283633,
          -83.26895133312209,
          -83.26858636310214,
          -83.26817614437013,
          -83.26772051861829,
          -83.2672193276863
        ],
        "cartesian_polarizations_e_A2": [
          [
            -1.709390922746191e-11,
            0.0005718772465176047,
            1.4055477446006267e-12
          ],
          [
            -1.4959403146004413e-11,
            0.000500383813179907,
            1.2301165827899696e-12
          ],
          [
            -1.2826204090255171e-11,
            0.0004288702091983651,
            1.0550527189647996e-12
          ],
          [
            -1.0694300319532943e-11,
            0.0003573365313753257,
            8.803258455378688e-13
          ],
          [
            -8.56376725518728e-12,
            0.00028578287458956347,
            7.060019040229356e-13
          ],
          [
            -6.434536383533515e-12,
            0.0002142093319617455,
            5.321371711548731e-13
          ],
          [
            -4.30654041627002e-12,
            0.00014261599501543386,
            3.5870416644343025e-13
          ],
          [
            -2.17987098261289e-12,
            7.100295383442518e-05,
            1.8552765561067199e-13
          ],
          [
            -5.439524340686562e-14,
            -6.297027844655611e-07,
            1.2854661629778624e-14
          ]
        ],
        "raw_reduced_polarization": [
          [
            -9.850151859247297e-10,
            0.04404365609868878,
            9.818362286241268e-11
          ],
          [
            -8.619829355223413e-10,
            0.038538132438372875,
            8.593010761490957e-11
          ],
          [
            -7.390258708393403e-10,
            0.03303088114876005,
            7.37019339223813e-11
          ],
          [
            -6.16144352595691e-10,
            0.02752190960770348,
            6.149698664886522e-11
          ],
          [
            -4.933406529217562e-10,
            0.022011225045370363,
            4.931987455824938e-11
          ],
          [
            -3.7060867317131746e-10,
            0.016498834556974894,
            3.717453168076339e-11
          ],
          [
            -2.479453140247885e-10,
            0.01098474511516821,
            2.5059040732216388e-11
          ],
          [
            -1.253622529458572e-10,
            0.005468963582147816,
            1.2961161090985033e-11
          ],
          [
            -2.8428350419922212e-12,
            -4.850327858293232e-05,
            8.981535307960634e-13
          ]
        ],
        "unwrapped_reduced_polarization": [
          [
            -9.850151859247297e-10,
            0.04404365609868878,
            9.818362286241268e-11
          ],
          [
            -8.619829355223413e-10,
            0.038538132438372875,
            8.593010761490957e-11
          ],
          [
            -7.390258708393403e-10,
            0.03303088114876005,
            7.37019339223813e-11
          ],
          [
            -6.16144352595691e-10,
            0.02752190960770348,
            6.149698664886522e-11
          ],
          [
            -4.933406529217562e-10,
            0.022011225045370363,
            4.931987455824938e-11
          ],
          [
            -3.7060867317131746e-10,
            0.016498834556974894,
            3.717453168076339e-11
          ],
          [
            -2.479453140247885e-10,
            0.01098474511516821,
            2.5059040732216388e-11
          ],
          [
            -1.253622529458572e-10,
            0.005468963582147816,
            1.2961161090985033e-11
          ],
          [
            -2.842835041992213e-12,
            -4.8503278582931984e-05,
            8.981535307960636e-13
          ]
        ],
        "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": [
          [
            -9.850151805324003e-10,
            0.044043656098688766,
            9.818357238344788e-11
          ],
          [
            -8.619829294786996e-10,
            0.038538132438372896,
            8.593015188296249e-11
          ],
          [
            -7.390258960349172e-10,
            0.03303088114876007,
            7.370193344513609e-11
          ],
          [
            -6.161443577568093e-10,
            0.02752190960770351,
            6.149702969082682e-11
          ],
          [
            -4.933406461127277e-10,
            0.022011225045370342,
            4.931988151213318e-11
          ],
          [
            -3.706086548760368e-10,
            0.016498834556974873,
            3.7174485711943817e-11
          ],
          [
            -2.4794533093341897e-10,
            0.010984745115168226,
            2.5059065933419333e-11
          ],
          [
            -1.2536227611548156e-10,
            0.005468963582147768,
            1.2961187678683928e-11
          ],
          [
            -2.842837076855176e-12,
            -4.8503278582912035e-05,
            8.981704269217516e-13
          ]
        ]
      },
      "reflected": {
        "reached": true,
        "construction": "reflect_displacements_about_reconstructed_parent",
        "energies_eV": [
          -83.2672193276863,
          -83.2675292676324,
          -83.26779337298102,
          -83.26801144159461,
          -83.2681832715483,
          -83.26830866116346,
          -83.26838740903648,
          -83.26841931406281,
          -83.26840417545564
        ],
        "cartesian_polarizations_e_A2": [
          [
            -5.4391607657047666e-14,
            -6.297027844396853e-07,
            1.285473458796895e-14
          ],
          [
            2.0501201227685763e-12,
            -7.213002002189712e-05,
            -1.5940883990152798e-13
          ],
          [
            4.1532170355870506e-12,
            -0.0001436560854966103,
            -3.313202278692406e-13
          ],
          [
            6.2552799446324964e-12,
            -0.00021520769035653767,
            -5.029600683940314e-13
          ],
          [
            8.355885971637895e-12,
            -0.0002867846285154904,
            -6.742569702761554e-13
          ],
          [
            1.0455471871933625e-11,
            -0.00035838669669888145,
            -8.45291968217813e-13
          ],
          [
            1.255382851459024e-11,
            -0.00043001369448774637,
            -1.0159427805609973e-12
          ],
          [
            1.4651010388846643e-11,
            -0.0005016654243577027,
            -1.1864863463092817e-12
          ],
          [
            1.6746969177421106e-11,
            -0.0005733416917153388,
            -1.3564341629338557e-12
          ]
        ],
        "raw_reduced_polarization": [
          [
            -2.842612500160493e-12,
            -4.850327858093923e-05,
            8.981586283077544e-13
          ],
          [
            1.1842302826433472e-10,
            -0.005555775237171748,
            -1.1136295925041816e-11
          ],
          [
            2.3962438369606463e-10,
            -0.011064856247381672,
            -2.3145838857397446e-11
          ],
          [
            3.607816909826824e-10,
            -0.016575730133061115,
            -3.513610600657799e-11
          ],
          [
            4.818718706853516e-10,
            -0.022088380932108954,
            -4.710211153444233e-11
          ],
          [
            6.029185296372481e-10,
            -0.027602792899979262,
            -5.904951857163004e-11
          ],
          [
            7.239132984014197e-10,
            -0.03311895051305446,
            -7.096978637840148e-11
          ],
          [
            8.44849812604817e-10,
            -0.03863683847162866,
            -8.28822631368937e-11
          ],
          [
            9.657422238196527e-10,
            -0.04415644170269233,
            -9.475282558190997e-11
          ]
        ],
        "unwrapped_reduced_polarization": [
          [
            -2.842612500160493e-12,
            -4.850327858093923e-05,
            8.981586283077544e-13
          ],
          [
            1.1842302826433472e-10,
            -0.005555775237171748,
            -1.1136295925041816e-11
          ],
          [
            2.3962438369606463e-10,
            -0.011064856247381672,
            -2.3145838857397446e-11
          ],
          [
            3.607816909826824e-10,
            -0.016575730133061115,
            -3.513610600657799e-11
          ],
          [
            4.818718706853516e-10,
            -0.022088380932108954,
            -4.710211153444233e-11
          ],
          [
            6.029185296372481e-10,
            -0.027602792899979262,
            -5.904951857163004e-11
          ],
          [
            7.239132984014197e-10,
            -0.03311895051305446,
            -7.096978637840148e-11
          ],
          [
            8.44849812604817e-10,
            -0.03863683847162866,
            -8.28822631368937e-11
          ],
          [
            9.657422238196527e-10,
            -0.04415644170269233,
            -9.475282558190997e-11
          ]
        ],
        "gauge_integer_shift": [
          0,
          0,
          0
        ],
        "expected_opposite_endpoint_reduced_polarization": [
          9.793317897022248e-10,
          -0.04414065038567003,
          -9.638771481968628e-11
        ],
        "actual_opposite_endpoint_branch_residual": 1.5791317022311284e-05
      },
      "pnp_branch": {
        "construction": "incoming_path_concatenated_with_parent_reflection",
        "reduced_polarization": [
          [
            -9.850151859247297e-10,
            0.04404365609868878,
            9.818362286241268e-11
          ],
          [
            -8.619829355223413e-10,
            0.038538132438372875,
            8.593010761490957e-11
          ],
          [
            -7.390258708393403e-10,
            0.03303088114876005,
            7.37019339223813e-11
          ],
          [
            -6.16144352595691e-10,
            0.02752190960770348,
            6.149698664886522e-11
          ],
          [
            -4.933406529217562e-10,
            0.022011225045370363,
            4.931987455824938e-11
          ],
          [
            -3.7060867317131746e-10,
            0.016498834556974894,
            3.717453168076339e-11
          ],
          [
            -2.479453140247885e-10,
            0.01098474511516821,
            2.5059040732216388e-11
          ],
          [
            -1.253622529458572e-10,
            0.005468963582147816,
            1.2961161090985033e-11
          ],
          [
            -2.8428350419922212e-12,
            -4.850327858293232e-05,
            8.981535307960634e-13
          ],
          [
            1.1842302826433472e-10,
            -0.005555775237171748,
            -1.1136295925041816e-11
          ],
          [
            2.3962438369606463e-10,
            -0.011064856247381672,
            -2.3145838857397446e-11
          ],
          [
            3.607816909826824e-10,
            -0.016575730133061115,
            -3.513610600657799e-11
          ],
          [
            4.818718706853516e-10,
            -0.022088380932108954,
            -4.710211153444233e-11
          ],
          [
            6.029185296372481e-10,
            -0.027602792899979262,
            -5.904951857163004e-11
          ],
          [
            7.239132984014197e-10,
            -0.03311895051305446,
            -7.096978637840148e-11
          ],
          [
            8.44849812604817e-10,
            -0.03863683847162866,
            -8.28822631368937e-11
          ],
          [
            9.657422238196527e-10,
            -0.04415644170269233,
            -9.475282558190997e-11
          ]
        ],
        "unwrapped_reduced_polarization": [
          [
            -9.850151859247297e-10,
            0.04404365609868878,
            9.818362286241268e-11
          ],
          [
            -8.619829355223413e-10,
            0.038538132438372875,
            8.593010761490957e-11
          ],
          [
            -7.390258708393403e-10,
            0.03303088114876005,
            7.37019339223813e-11
          ],
          [
            -6.16144352595691e-10,
            0.02752190960770348,
            6.149698664886522e-11
          ],
          [
            -4.933406529217562e-10,
            0.022011225045370363,
            4.931987455824938e-11
          ],
          [
            -3.7060867317131746e-10,
            0.016498834556974894,
            3.717453168076339e-11
          ],
          [
            -2.479453140247885e-10,
            0.01098474511516821,
            2.5059040732216388e-11
          ],
          [
            -1.253622529458572e-10,
            0.005468963582147816,
            1.2961161090985033e-11
          ],
          [
            -2.842835041992213e-12,
            -4.8503278582931984e-05,
            8.981535307960636e-13
          ],
          [
            1.1842302826433472e-10,
            -0.005555775237171748,
            -1.1136295925041816e-11
          ],
          [
            2.3962438369606463e-10,
            -0.011064856247381672,
            -2.3145838857397446e-11
          ],
          [
            3.607816909826824e-10,
            -0.016575730133061115,
            -3.513610600657799e-11
          ],
          [
            4.818718706853516e-10,
            -0.022088380932108954,
            -4.710211153444233e-11
          ],
          [
            6.029185296372481e-10,
            -0.027602792899979262,
            -5.904951857163004e-11
          ],
          [
            7.239132984014197e-10,
            -0.03311895051305446,
            -7.096978637840148e-11
          ],
          [
            8.44849812604817e-10,
            -0.03863683847162866,
            -8.28822631368937e-11
          ],
          [
            9.657422238196527e-10,
            -0.04415644170269233,
            -9.475282558190997e-11
          ]
        ],
        "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": [
          [
            -9.850151805324003e-10,
            0.044043656098688766,
            9.818357238344788e-11
          ],
          [
            -8.619829294786996e-10,
            0.038538132438372896,
            8.593015188296249e-11
          ],
          [
            -7.390258960349172e-10,
            0.03303088114876007,
            7.370193344513609e-11
          ],
          [
            -6.161443577568093e-10,
            0.02752190960770351,
            6.149702969082682e-11
          ],
          [
            -4.933406461127277e-10,
            0.022011225045370342,
            4.931988151213318e-11
          ],
          [
            -3.706086548760368e-10,
            0.016498834556974873,
            3.7174485711943817e-11
          ],
          [
            -2.4794533093341897e-10,
            0.010984745115168226,
            2.5059065933419333e-11
          ],
          [
            -1.2536227611548156e-10,
            0.005468963582147768,
            1.2961187678683928e-11
          ],
          [
            -2.842837076855176e-12,
            -4.8503278582912035e-05,
            8.981704269217516e-13
          ],
          [
            1.1842304914466695e-10,
            -0.005555775237171767,
            -1.1136314093107558e-11
          ],
          [
            2.3962443140845835e-10,
            -0.011064856247381682,
            -2.31458185950828e-11
          ],
          [
            3.6078173781817213e-10,
            -0.01657573013306113,
            -3.513611623873203e-11
          ],
          [
            4.818718757348961e-10,
            -0.022088380932108964,
            -4.7102099998141966e-11
          ],
          [
            6.029184929090547e-10,
            -0.027602792899979245,
            -5.904954303304066e-11
          ],
          [
            7.239132626679634e-10,
            -0.03311895051305447,
            -7.096978560383604e-11
          ],
          [
            8.448498567403817e-10,
            -0.03863683847162869,
            -8.288225661345905e-11
          ],
          [
            9.6574226393642e-10,
            -0.04415644170269234,
            -9.475281670390245e-11
          ]
        ]
      },
      "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": [
              -9.850173858380219e-10,
              0.04404365609868856,
              9.818580558610348e-11
            ],
            "branch_aligned_reduced_polarization": [
              -9.850173858380219e-10,
              0.044043656098688544,
              9.818580558610348e-11
            ],
            "target_residual": 0.45595634390131146,
            "energy_eV": -83.26996189457662,
            "max_atomic_step_A": 0.1005581291761106,
            "max_log_strain_component": 0.0015129052639424741,
            "step_scale": 1.0,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 0.5799214376857585,
            "cell_principal_stretches": [
              0.9993455491757421,
              0.9993453436586949,
              0.9984882386003011
            ],
            "cell_volume_ratio": 0.9971815382851019,
            "cell_rmsd_from_input_A": 0.009372739143809861
          },
          {
            "iteration": 1,
            "reduced_polarization": [
              -8.526983147429733e-11,
              0.49316449607893426,
              4.9245103454958205e-11
            ],
            "branch_aligned_reduced_polarization": [
              -8.526983147429733e-11,
              0.49316449607893426,
              4.9245103454958205e-11
            ],
            "target_residual": 0.006835503921065745,
            "energy_eV": -83.14283699477127,
            "max_atomic_step_A": 0.0015236718339950415,
            "max_log_strain_component": 2.4411709462720384e-05,
            "step_scale": 1.0,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 0.5799214376857585,
            "cell_principal_stretches": [
              0.9993349926984626,
              0.9993347838674707,
              0.998463864093031
            ],
            "cell_volume_ratio": 0.9971361257569854,
            "cell_rmsd_from_input_A": 0.009523814744173287
          },
          {
            "iteration": 2,
            "reduced_polarization": [
              -2.1834618205038788e-14,
              0.5000084784529323,
              -3.322814419551186e-15
            ],
            "branch_aligned_reduced_polarization": [
              -2.1834618205038788e-14,
              0.5000084784529323,
              -3.322814419551186e-15
            ],
            "target_residual": 8.478452932281222e-06,
            "energy_eV": -83.13869835453934
          }
        ],
        "iterations": 2
      },
      "parent": {
        "candidate_id": "bec_projection_01",
        "source": "MACEField_BEC_backprojection",
        "spacegroup": "P6_3mc",
        "spacegroup_number": 186,
        "pointgroup": "6mm",
        "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": 8.478452932281222e-06,
        "parent_symmetrization_rmsd_A": 0.06196458523805881,
        "parent_cell_rmsd_A": 0.009523814744173287,
        "energy_eV": -83.13869835453934,
        "reduced_polarization": [
          -2.1834618205038788e-14,
          0.5000084784529323,
          -3.322814419551186e-15
        ],
        "cartesian_polarization_e_A2": [
          2.8843911722568327e-13,
          0.006500918538120946,
          4.1131283507153564e-14
        ],
        "ranking_score": 0.5643624958299667
      },
      "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
        ],
        [
          0.0,
          0.0,
          0.5
        ],
        [
          0.5,
          0.0,
          0.5
        ]
      ],
      "target_reduced_polarization": [
        -0.5,
        0.0,
        0.0
      ],
      "bec_backprojection": {
        "converged_to_target": true,
        "history": [
          {
            "iteration": 0,
            "reduced_polarization": [
              -9.850173858380219e-10,
              0.04404365609868856,
              9.818580558610348e-11
            ],
            "branch_aligned_reduced_polarization": [
              -9.850174009784496e-10,
              0.04404365609868856,
              9.818580558610348e-11
            ],
            "target_residual": 0.5019360941967833,
            "energy_eV": -83.26996189457662,
            "max_atomic_step_A": 0.12,
            "max_log_strain_component": 0.004364505136400868,
            "step_scale": 0.9827272700772844,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 0.5799214376857585,
            "cell_principal_stretches": [
              1.00447757461803,
              1.0000621599132151,
              0.9957472583294414
            ],
            "cell_volume_ratio": 1.0002679636844745,
            "cell_rmsd_from_input_A": 0.036509873240451664
          },
          {
            "iteration": 1,
            "reduced_polarization": [
              -0.4837927654712932,
              0.010750075818526954,
              5.395938456399204e-08
            ],
            "branch_aligned_reduced_polarization": [
              -0.4837927654712932,
              0.010750075818526954,
              5.395938456399204e-08
            ],
            "target_residual": 0.019448356773144,
            "energy_eV": -82.88204286213161,
            "max_atomic_step_A": 0.004529752601022925,
            "max_log_strain_component": 0.00015919594444541748,
            "step_scale": 1.0,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 0.5799214376857585,
            "cell_principal_stretches": [
              1.0046666033514748,
              1.000079598054635,
              0.9956173768314635
            ],
            "cell_volume_ratio": 1.0003431472499398,
            "cell_rmsd_from_input_A": 0.03785087879083227
          },
          {
            "iteration": 2,
            "reduced_polarization": [
              -0.49995096260853183,
              4.347894322711309e-05,
              4.1931918793245246e-10
            ],
            "branch_aligned_reduced_polarization": [
              -0.49995096260853183,
              4.347894322711309e-05,
              4.1931918793245246e-10
            ],
            "target_residual": 6.55368924066776e-05,
            "energy_eV": -82.85424905854313
          }
        ],
        "iterations": 2
      },
      "parent": {
        "candidate_id": "bec_projection_02",
        "source": "MACEField_BEC_backprojection",
        "spacegroup": "Cc",
        "spacegroup_number": 9,
        "pointgroup": "m",
        "has_inversion": false,
        "is_polar_point_group": true,
        "nonpolar_parent_hypothesis": false,
        "symmetry_tolerance_A": null,
        "target_reduced_polarization": [
          -0.5,
          0.0,
          0.0
        ],
        "formal_class": [
          0.5,
          0.0,
          0.0
        ],
        "target_residual": 6.55368924066776e-05,
        "parent_symmetrization_rmsd_A": 0.10624153458200716,
        "parent_cell_rmsd_A": 0.03785087879083227,
        "energy_eV": -82.85424905854313,
        "reduced_polarization": [
          -0.49995096260853183,
          4.347894322711309e-05,
          4.1931918793245246e-10
        ],
        "cartesian_polarization_e_A2": [
          -0.00826215234872493,
          -3.681311131690447e-05,
          -9.700861242107308e-11
        ],
        "ranking_score": 0.6158353280645286
      },
      "branch_status": "awaiting_branch_sampling"
    },
    {
      "orbit_id": 3,
      "formal_class": [
        0.5,
        0.5,
        0.0
      ],
      "formal_classes_in_orbit": [
        [
          0.5,
          0.5,
          0.0
        ],
        [
          0.0,
          0.5,
          0.5
        ],
        [
          0.5,
          0.5,
          0.5
        ]
      ],
      "target_reduced_polarization": [
        -0.5,
        0.5,
        0.0
      ],
      "bec_backprojection": {
        "converged_to_target": true,
        "history": [
          {
            "iteration": 0,
            "reduced_polarization": [
              -9.850173858380219e-10,
              0.04404365609868856,
              9.818580558610348e-11
            ],
            "branch_aligned_reduced_polarization": [
              -9.850174009784496e-10,
              0.044043656098688544,
              9.818580558610348e-11
            ],
            "target_residual": 0.6766802690775264,
            "energy_eV": -83.26996189457662,
            "max_atomic_step_A": 0.12,
            "max_log_strain_component": 0.00363863781260874,
            "step_scale": 0.8192884290957293,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 0.5799214376857585,
            "cell_principal_stretches": [
              1.0027714490536896,
              0.9994636794667595,
              0.9954667616011981
            ],
            "cell_volume_ratio": 0.9976902781043152,
            "cell_rmsd_from_input_A": 0.03129442783886549
          },
          {
            "iteration": 1,
            "reduced_polarization": [
              -0.4133658451407598,
              0.4189764178446633,
              -8.743038000626042e-08
            ],
            "branch_aligned_reduced_polarization": [
              -0.4133658451407598,
              0.4189764178446633,
              -8.743038000626042e-08
            ],
            "target_residual": 0.11861828549370058,
            "energy_eV": -82.8722400927327,
            "max_atomic_step_A": 0.02734568442813065,
            "max_log_strain_component": 0.0007628966693319294,
            "step_scale": 1.0,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 0.5799214376857585,
            "cell_principal_stretches": [
              1.0033477747475519,
              0.9993476864945184,
              0.99451278242942
            ],
            "cell_volume_ratio": 0.9971912812734991,
            "cell_rmsd_from_input_A": 0.03784755208659656
          },
          {
            "iteration": 2,
            "reduced_polarization": [
              -0.4999669530595444,
              0.4999212533430195,
              -1.1764437660662004e-08
            ],
            "branch_aligned_reduced_polarization": [
              -0.4999669530595444,
              0.4999212533430195,
              -1.1764437660662004e-08
            ],
            "target_residual": 8.539986181182947e-05,
            "energy_eV": -82.65955919535203
          }
        ],
        "iterations": 2
      },
      "parent": {
        "candidate_id": "bec_projection_03",
        "source": "MACEField_BEC_backprojection",
        "spacegroup": "Cc",
        "spacegroup_number": 9,
        "pointgroup": "m",
        "has_inversion": false,
        "is_polar_point_group": true,
        "nonpolar_parent_hypothesis": false,
        "symmetry_tolerance_A": null,
        "target_reduced_polarization": [
          -0.5,
          0.5,
          0.0
        ],
        "formal_class": [
          0.5,
          0.5,
          0.0
        ],
        "target_residual": 8.539986181182947e-05,
        "parent_symmetrization_rmsd_A": 0.12028943677458867,
        "parent_cell_rmsd_A": 0.03784755208659656,
        "energy_eV": -82.65955919535203,
        "reduced_polarization": [
          -0.4999669530595444,
          0.4999212533430195,
          -1.1764437660662004e-08
        ],
        "cartesian_polarization_e_A2": [
          -0.00825384370519526,
          0.006463240981806531,
          1.7565022344131979e-09
        ],
        "ranking_score": 0.6299221245198614
      },
      "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
        ],
        "endpoint_rmsd_A": 0.005883335463007772,
        "minimum_distance_A_by_image": [
          2.435257094068625,
          2.435728024950297,
          2.4361995920374357,
          2.4366717950384733,
          2.4371446336615814,
          2.437618107614661,
          2.43809221660535,
          2.4385669603410256,
          2.439042338528798
        ],
        "minimum_distance_A": 2.435257094068625,
        "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": [
          570.4913181636166,
          570.5107606334725,
          570.530203765933,
          570.5496475610204,
          570.5690920187554,
          570.588537139162,
          570.6079829222625,
          570.6274293680796,
          570.6468764766369
        ],
        "cell_deformation_log_strain_norm": 0.00017134121665039848
      },
      "parent_reduced_polarization": [
        -2.8428350419922212e-12,
        -4.850327858293232e-05,
        8.981535307960634e-13
      ],
      "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": [
          -83.26996189457662,
          -83.26977633515166,
          -83.26954616069793,
          -83.26927121283633,
          -83.26895133312209,
          -83.26858636310214,
          -83.26817614437013,
          -83.26772051861829,
          -83.2672193276863
        ],
        "cartesian_polarizations_e_A2": [
          [
            -1.709390922746191e-11,
            0.0005718772465176047,
            1.4055477446006267e-12
          ],
          [
            -1.4959403146004413e-11,
            0.000500383813179907,
            1.2301165827899696e-12
          ],
          [
            -1.2826204090255171e-11,
            0.0004288702091983651,
            1.0550527189647996e-12
          ],
          [
            -1.0694300319532943e-11,
            0.0003573365313753257,
            8.803258455378688e-13
          ],
          [
            -8.56376725518728e-12,
            0.00028578287458956347,
            7.060019040229356e-13
          ],
          [
            -6.434536383533515e-12,
            0.0002142093319617455,
            5.321371711548731e-13
          ],
          [
            -4.30654041627002e-12,
            0.00014261599501543386,
            3.5870416644343025e-13
          ],
          [
            -2.17987098261289e-12,
            7.100295383442518e-05,
            1.8552765561067199e-13
          ],
          [
            -5.439524340686562e-14,
            -6.297027844655611e-07,
            1.2854661629778624e-14
          ]
        ],
        "raw_reduced_polarization": [
          [
            -9.850151859247297e-10,
            0.04404365609868878,
            9.818362286241268e-11
          ],
          [
            -8.619829355223413e-10,
            0.038538132438372875,
            8.593010761490957e-11
          ],
          [
            -7.390258708393403e-10,
            0.03303088114876005,
            7.37019339223813e-11
          ],
          [
            -6.16144352595691e-10,
            0.02752190960770348,
            6.149698664886522e-11
          ],
          [
            -4.933406529217562e-10,
            0.022011225045370363,
            4.931987455824938e-11
          ],
          [
            -3.7060867317131746e-10,
            0.016498834556974894,
            3.717453168076339e-11
          ],
          [
            -2.479453140247885e-10,
            0.01098474511516821,
            2.5059040732216388e-11
          ],
          [
            -1.253622529458572e-10,
            0.005468963582147816,
            1.2961161090985033e-11
          ],
          [
            -2.8428350419922212e-12,
            -4.850327858293232e-05,
            8.981535307960634e-13
          ]
        ],
        "unwrapped_reduced_polarization": [
          [
            -9.850151859247297e-10,
            0.04404365609868878,
            9.818362286241268e-11
          ],
          [
            -8.619829355223413e-10,
            0.038538132438372875,
            8.593010761490957e-11
          ],
          [
            -7.390258708393403e-10,
            0.03303088114876005,
            7.37019339223813e-11
          ],
          [
            -6.16144352595691e-10,
            0.02752190960770348,
            6.149698664886522e-11
          ],
          [
            -4.933406529217562e-10,
            0.022011225045370363,
            4.931987455824938e-11
          ],
          [
            -3.7060867317131746e-10,
            0.016498834556974894,
            3.717453168076339e-11
          ],
          [
            -2.479453140247885e-10,
            0.01098474511516821,
            2.5059040732216388e-11
          ],
          [
            -1.253622529458572e-10,
            0.005468963582147816,
            1.2961161090985033e-11
          ],
          [
            -2.842835041992213e-12,
            -4.8503278582931984e-05,
            8.981535307960636e-13
          ]
        ],
        "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": [
          [
            -9.850151805324003e-10,
            0.044043656098688766,
            9.818357238344788e-11
          ],
          [
            -8.619829294786996e-10,
            0.038538132438372896,
            8.593015188296249e-11
          ],
          [
            -7.390258960349172e-10,
            0.03303088114876007,
            7.370193344513609e-11
          ],
          [
            -6.161443577568093e-10,
            0.02752190960770351,
            6.149702969082682e-11
          ],
          [
            -4.933406461127277e-10,
            0.022011225045370342,
            4.931988151213318e-11
          ],
          [
            -3.706086548760368e-10,
            0.016498834556974873,
            3.7174485711943817e-11
          ],
          [
            -2.4794533093341897e-10,
            0.010984745115168226,
            2.5059065933419333e-11
          ],
          [
            -1.2536227611548156e-10,
            0.005468963582147768,
            1.2961187678683928e-11
          ],
          [
            -2.842837076855176e-12,
            -4.8503278582912035e-05,
            8.981704269217516e-13
          ]
        ]
      },
      "reflected": {
        "reached": true,
        "construction": "reflect_displacements_about_reconstructed_parent",
        "energies_eV": [
          -83.2672193276863,
          -83.2675292676324,
          -83.26779337298102,
          -83.26801144159461,
          -83.2681832715483,
          -83.26830866116346,
          -83.26838740903648,
          -83.26841931406281,
          -83.26840417545564
        ],
        "cartesian_polarizations_e_A2": [
          [
            -5.4391607657047666e-14,
            -6.297027844396853e-07,
            1.285473458796895e-14
          ],
          [
            2.0501201227685763e-12,
            -7.213002002189712e-05,
            -1.5940883990152798e-13
          ],
          [
            4.1532170355870506e-12,
            -0.0001436560854966103,
            -3.313202278692406e-13
          ],
          [
            6.2552799446324964e-12,
            -0.00021520769035653767,
            -5.029600683940314e-13
          ],
          [
            8.355885971637895e-12,
            -0.0002867846285154904,
            -6.742569702761554e-13
          ],
          [
            1.0455471871933625e-11,
            -0.00035838669669888145,
            -8.45291968217813e-13
          ],
          [
            1.255382851459024e-11,
            -0.00043001369448774637,
            -1.0159427805609973e-12
          ],
          [
            1.4651010388846643e-11,
            -0.0005016654243577027,
            -1.1864863463092817e-12
          ],
          [
            1.6746969177421106e-11,
            -0.0005733416917153388,
            -1.3564341629338557e-12
          ]
        ],
        "raw_reduced_polarization": [
          [
            -2.842612500160493e-12,
            -4.850327858093923e-05,
            8.981586283077544e-13
          ],
          [
            1.1842302826433472e-10,
            -0.005555775237171748,
            -1.1136295925041816e-11
          ],
          [
            2.3962438369606463e-10,
            -0.011064856247381672,
            -2.3145838857397446e-11
          ],
          [
            3.607816909826824e-10,
            -0.016575730133061115,
            -3.513610600657799e-11
          ],
          [
            4.818718706853516e-10,
            -0.022088380932108954,
            -4.710211153444233e-11
          ],
          [
            6.029185296372481e-10,
            -0.027602792899979262,
            -5.904951857163004e-11
          ],
          [
            7.239132984014197e-10,
            -0.03311895051305446,
            -7.096978637840148e-11
          ],
          [
            8.44849812604817e-10,
            -0.03863683847162866,
            -8.28822631368937e-11
          ],
          [
            9.657422238196527e-10,
            -0.04415644170269233,
            -9.475282558190997e-11
          ]
        ],
        "unwrapped_reduced_polarization": [
          [
            -2.842612500160493e-12,
            -4.850327858093923e-05,
            8.981586283077544e-13
          ],
          [
            1.1842302826433472e-10,
            -0.005555775237171748,
            -1.1136295925041816e-11
          ],
          [
            2.3962438369606463e-10,
            -0.011064856247381672,
            -2.3145838857397446e-11
          ],
          [
            3.607816909826824e-10,
            -0.016575730133061115,
            -3.513610600657799e-11
          ],
          [
            4.818718706853516e-10,
            -0.022088380932108954,
            -4.710211153444233e-11
          ],
          [
            6.029185296372481e-10,
            -0.027602792899979262,
            -5.904951857163004e-11
          ],
          [
            7.239132984014197e-10,
            -0.03311895051305446,
            -7.096978637840148e-11
          ],
          [
            8.44849812604817e-10,
            -0.03863683847162866,
            -8.28822631368937e-11
          ],
          [
            9.657422238196527e-10,
            -0.04415644170269233,
            -9.475282558190997e-11
          ]
        ],
        "gauge_integer_shift": [
          0,
          0,
          0
        ],
        "expected_opposite_endpoint_reduced_polarization": [
          9.793317897022248e-10,
          -0.04414065038567003,
          -9.638771481968628e-11
        ],
        "actual_opposite_endpoint_branch_residual": 1.5791317022311284e-05
      },
      "pnp_branch": {
        "construction": "incoming_path_concatenated_with_parent_reflection",
        "reduced_polarization": [
          [
            -9.850151859247297e-10,
            0.04404365609868878,
            9.818362286241268e-11
          ],
          [
            -8.619829355223413e-10,
            0.038538132438372875,
            8.593010761490957e-11
          ],
          [
            -7.390258708393403e-10,
            0.03303088114876005,
            7.37019339223813e-11
          ],
          [
            -6.16144352595691e-10,
            0.02752190960770348,
            6.149698664886522e-11
          ],
          [
            -4.933406529217562e-10,
            0.022011225045370363,
            4.931987455824938e-11
          ],
          [
            -3.7060867317131746e-10,
            0.016498834556974894,
            3.717453168076339e-11
          ],
          [
            -2.479453140247885e-10,
            0.01098474511516821,
            2.5059040732216388e-11
          ],
          [
            -1.253622529458572e-10,
            0.005468963582147816,
            1.2961161090985033e-11
          ],
          [
            -2.8428350419922212e-12,
            -4.850327858293232e-05,
            8.981535307960634e-13
          ],
          [
            1.1842302826433472e-10,
            -0.005555775237171748,
            -1.1136295925041816e-11
          ],
          [
            2.3962438369606463e-10,
            -0.011064856247381672,
            -2.3145838857397446e-11
          ],
          [
            3.607816909826824e-10,
            -0.016575730133061115,
            -3.513610600657799e-11
          ],
          [
            4.818718706853516e-10,
            -0.022088380932108954,
            -4.710211153444233e-11
          ],
          [
            6.029185296372481e-10,
            -0.027602792899979262,
            -5.904951857163004e-11
          ],
          [
            7.239132984014197e-10,
            -0.03311895051305446,
            -7.096978637840148e-11
          ],
          [
            8.44849812604817e-10,
            -0.03863683847162866,
            -8.28822631368937e-11
          ],
          [
            9.657422238196527e-10,
            -0.04415644170269233,
            -9.475282558190997e-11
          ]
        ],
        "unwrapped_reduced_polarization": [
          [
            -9.850151859247297e-10,
            0.04404365609868878,
            9.818362286241268e-11
          ],
          [
            -8.619829355223413e-10,
            0.038538132438372875,
            8.593010761490957e-11
          ],
          [
            -7.390258708393403e-10,
            0.03303088114876005,
            7.37019339223813e-11
          ],
          [
            -6.16144352595691e-10,
            0.02752190960770348,
            6.149698664886522e-11
          ],
          [
            -4.933406529217562e-10,
            0.022011225045370363,
            4.931987455824938e-11
          ],
          [
            -3.7060867317131746e-10,
            0.016498834556974894,
            3.717453168076339e-11
          ],
          [
            -2.479453140247885e-10,
            0.01098474511516821,
            2.5059040732216388e-11
          ],
          [
            -1.253622529458572e-10,
            0.005468963582147816,
            1.2961161090985033e-11
          ],
          [
            -2.842835041992213e-12,
            -4.8503278582931984e-05,
            8.981535307960636e-13
          ],
          [
            1.1842302826433472e-10,
            -0.005555775237171748,
            -1.1136295925041816e-11
          ],
          [
            2.3962438369606463e-10,
            -0.011064856247381672,
            -2.3145838857397446e-11
          ],
          [
            3.607816909826824e-10,
            -0.016575730133061115,
            -3.513610600657799e-11
          ],
          [
            4.818718706853516e-10,
            -0.022088380932108954,
            -4.710211153444233e-11
          ],
          [
            6.029185296372481e-10,
            -0.027602792899979262,
            -5.904951857163004e-11
          ],
          [
            7.239132984014197e-10,
            -0.03311895051305446,
            -7.096978637840148e-11
          ],
          [
            8.44849812604817e-10,
            -0.03863683847162866,
            -8.28822631368937e-11
          ],
          [
            9.657422238196527e-10,
            -0.04415644170269233,
            -9.475282558190997e-11
          ]
        ],
        "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": [
          [
            -9.850151805324003e-10,
            0.044043656098688766,
            9.818357238344788e-11
          ],
          [
            -8.619829294786996e-10,
            0.038538132438372896,
            8.593015188296249e-11
          ],
          [
            -7.390258960349172e-10,
            0.03303088114876007,
            7.370193344513609e-11
          ],
          [
            -6.161443577568093e-10,
            0.02752190960770351,
            6.149702969082682e-11
          ],
          [
            -4.933406461127277e-10,
            0.022011225045370342,
            4.931988151213318e-11
          ],
          [
            -3.706086548760368e-10,
            0.016498834556974873,
            3.7174485711943817e-11
          ],
          [
            -2.4794533093341897e-10,
            0.010984745115168226,
            2.5059065933419333e-11
          ],
          [
            -1.2536227611548156e-10,
            0.005468963582147768,
            1.2961187678683928e-11
          ],
          [
            -2.842837076855176e-12,
            -4.8503278582912035e-05,
            8.981704269217516e-13
          ],
          [
            1.1842304914466695e-10,
            -0.005555775237171767,
            -1.1136314093107558e-11
          ],
          [
            2.3962443140845835e-10,
            -0.011064856247381682,
            -2.31458185950828e-11
          ],
          [
            3.6078173781817213e-10,
            -0.01657573013306113,
            -3.513611623873203e-11
          ],
          [
            4.818718757348961e-10,
            -0.022088380932108964,
            -4.7102099998141966e-11
          ],
          [
            6.029184929090547e-10,
            -0.027602792899979245,
            -5.904954303304066e-11
          ],
          [
            7.239132626679634e-10,
            -0.03311895051305447,
            -7.096978560383604e-11
          ],
          [
            8.448498567403817e-10,
            -0.03863683847162869,
            -8.288225661345905e-11
          ],
          [
            9.6574226393642e-10,
            -0.04415644170269234,
            -9.475281670390245e-11
          ]
        ]
      },
      "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": "P6_3mc",
        "spacegroup_number": 186,
        "pointgroup": "6mm",
        "has_inversion": false,
        "is_polar_point_group": true,
        "nonpolar_parent_hypothesis": false,
        "symmetry_tolerance_A": null,
        "target_reduced_polarization": [
          0.0,
          0.0,
          0.0
        ],
        "formal_class": [
          0.0,
          0.0,
          0.0
        ],
        "target_residual": 4.8503278585723514e-05,
        "parent_symmetrization_rmsd_A": 0.005883335463007772,
        "parent_cell_rmsd_A": 0.0009064034697018341,
        "energy_eV": -83.2672193276863,
        "reduced_polarization": [
          -2.8466095990904203e-12,
          -4.850327858572342e-05,
          8.957576991798866e-13
        ],
        "cartesian_polarization_e_A2": [
          -5.443782667061977e-14,
          -6.297027845017971e-07,
          1.2820371280324972e-14
        ],
        "ranking_score": 0.5062069428876047
      }
    }
  ],
  "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": 40,
      "full_response": 8,
      "energy_polarization": 32
    },
    "model_evaluations_for_recovery_and_path_properties": {
      "total": 65,
      "full_response": 33,
      "energy_polarization": 32
    },
    "elapsed_seconds": 175.42460521502653
  }
}