{
  "schema": "ferrofinder.endpoint_parent_recovery.v4_variable_cell",
  "status": "complete",
  "input_atom_count": 24,
  "input_formula": "Ge8K4N12",
  "input_spacegroup": "Cmc2_1",
  "input_pointgroup": "mm2",
  "input_is_polar_point_group": true,
  "input_energy_eV": -141.38640382576563,
  "input_cartesian_polarization_e_A2": [
    7.180905028401303e-18,
    -1.1363874049613999e-17,
    0.001066108828954427
  ],
  "input_reduced_polarization": [
    2.302879751357545e-16,
    -6.111146963671413e-16,
    0.06492632512262175
  ],
  "input_formal_targets": [
    {
      "orbit_id": 0,
      "representative_formal_class": [
        0.0,
        0.0,
        0.0
      ],
      "target_reduced_polarization": [
        0.0,
        0.0,
        0.0
      ]
    },
    {
      "orbit_id": 1,
      "representative_formal_class": [
        0.0,
        0.0,
        0.5
      ],
      "target_reduced_polarization": [
        0.0,
        0.0,
        0.5
      ]
    },
    {
      "orbit_id": 2,
      "representative_formal_class": [
        0.0,
        0.5,
        0.0
      ],
      "target_reduced_polarization": [
        0.0,
        -0.5,
        0.0
      ]
    },
    {
      "orbit_id": 3,
      "representative_formal_class": [
        0.5,
        0.0,
        0.0
      ],
      "target_reduced_polarization": [
        0.5,
        0.0,
        0.0
      ]
    },
    {
      "orbit_id": 4,
      "representative_formal_class": [
        0.0,
        0.5,
        0.5
      ],
      "target_reduced_polarization": [
        0.0,
        -0.5,
        0.5
      ]
    },
    {
      "orbit_id": 5,
      "representative_formal_class": [
        0.5,
        0.0,
        0.5
      ],
      "target_reduced_polarization": [
        0.5,
        0.0,
        0.5
      ]
    },
    {
      "orbit_id": 6,
      "representative_formal_class": [
        0.5,
        0.5,
        0.0
      ],
      "target_reduced_polarization": [
        0.5,
        -0.5,
        0.0
      ]
    },
    {
      "orbit_id": 7,
      "representative_formal_class": [
        0.5,
        0.5,
        0.5
      ],
      "target_reduced_polarization": [
        0.5,
        -0.5,
        0.5
      ]
    }
  ],
  "parent_candidates": [
    {
      "candidate_id": "inversion_parent_endpoint_00",
      "source": "same_species_inversion_center_projection_from_endpoint",
      "spacegroup": "Cmcm",
      "spacegroup_number": 63,
      "pointgroup": "mmm",
      "has_inversion": true,
      "is_polar_point_group": false,
      "nonpolar_parent_hypothesis": true,
      "symmetry_tolerance_A": null,
      "target_reduced_polarization": [
        0.0,
        0.0,
        0.0
      ],
      "formal_class": [
        0.0,
        0.0,
        0.0
      ],
      "target_residual": 9.927371598046309e-15,
      "parent_symmetrization_rmsd_A": 0.4409445565951117,
      "parent_cell_rmsd_A": 0.0,
      "energy_eV": -129.8316506253975,
      "reduced_polarization": [
        -1.7311010643618293e-15,
        -2.3071522804440123e-15,
        9.499107553107495e-15
      ],
      "cartesian_polarization_e_A2": [
        -5.39796849158916e-17,
        -4.2902237639027887e-17,
        1.559780629879988e-16
      ],
      "ranking_score": 0.4409445565951316
    },
    {
      "candidate_id": "inversion_parent_endpoint_01",
      "source": "same_species_inversion_center_projection_from_endpoint",
      "spacegroup": "Cmcm",
      "spacegroup_number": 63,
      "pointgroup": "mmm",
      "has_inversion": true,
      "is_polar_point_group": false,
      "nonpolar_parent_hypothesis": true,
      "symmetry_tolerance_A": null,
      "target_reduced_polarization": [
        0.0,
        0.0,
        0.0
      ],
      "formal_class": [
        0.0,
        0.0,
        0.0
      ],
      "target_residual": 4.5342386351032685e-15,
      "parent_symmetrization_rmsd_A": 0.5352888326174108,
      "parent_cell_rmsd_A": 0.0,
      "energy_eV": -128.00932474294575,
      "reduced_polarization": [
        3.918974694398746e-15,
        -3.1318548735160145e-16,
        2.2589537833337253e-15
      ],
      "cartesian_polarization_e_A2": [
        1.2220258167017128e-16,
        -5.823784722553006e-18,
        3.709266723572792e-17
      ],
      "ranking_score": 0.5352888326174199
    },
    {
      "candidate_id": "inversion_parent_endpoint_02",
      "source": "same_species_inversion_center_projection_from_endpoint",
      "spacegroup": "Cmce",
      "spacegroup_number": 64,
      "pointgroup": "mmm",
      "has_inversion": true,
      "is_polar_point_group": false,
      "nonpolar_parent_hypothesis": true,
      "symmetry_tolerance_A": null,
      "target_reduced_polarization": [
        0.0,
        0.0,
        0.0
      ],
      "formal_class": [
        0.0,
        0.0,
        0.0
      ],
      "target_residual": 5.3191469194109665e-15,
      "parent_symmetrization_rmsd_A": 0.5723568078836101,
      "parent_cell_rmsd_A": 0.0,
      "energy_eV": -131.86341607146517,
      "reduced_polarization": [
        4.993199827371192e-15,
        1.8220196520073308e-15,
        2.0377394808600403e-16
      ],
      "cartesian_polarization_e_A2": [
        1.5569937478083872e-16,
        3.388104060402714e-17,
        3.3460265116667905e-18
      ],
      "ranking_score": 0.5723568078836208
    },
    {
      "candidate_id": "bec_projection_00",
      "source": "MACEField_BEC_backprojection",
      "spacegroup": "Cmc2_1",
      "spacegroup_number": 36,
      "pointgroup": "mm2",
      "has_inversion": false,
      "is_polar_point_group": true,
      "nonpolar_parent_hypothesis": false,
      "symmetry_tolerance_A": null,
      "target_reduced_polarization": [
        0.0,
        0.0,
        0.0
      ],
      "formal_class": [
        0.0,
        0.0,
        0.0
      ],
      "target_residual": 0.00017865470027207895,
      "parent_symmetrization_rmsd_A": 0.005262234774149632,
      "parent_cell_rmsd_A": 0.0034613881295732195,
      "energy_eV": -141.37425909164836,
      "reduced_polarization": [
        2.9052109209161045e-15,
        -8.17783869060451e-16,
        0.00017865470027207895
      ],
      "cartesian_polarization_e_A2": [
        9.056672776413683e-17,
        -1.5193160573603427e-17,
        2.9358355764529375e-06
      ],
      "ranking_score": 0.5064848912070871
    },
    {
      "candidate_id": "inversion_parent_bec_00_00",
      "source": "same_species_inversion_center_projection_after_BEC",
      "spacegroup": "Cmcm",
      "spacegroup_number": 63,
      "pointgroup": "mmm",
      "has_inversion": true,
      "is_polar_point_group": false,
      "nonpolar_parent_hypothesis": true,
      "symmetry_tolerance_A": null,
      "target_reduced_polarization": [
        0.0,
        0.0,
        0.0
      ],
      "formal_class": [
        0.0,
        0.0,
        0.0
      ],
      "target_residual": 1.913753517275059e-15,
      "parent_symmetrization_rmsd_A": 0.44094463872307965,
      "parent_cell_rmsd_A": 0.0034613881295732195,
      "energy_eV": -129.79761270900795,
      "reduced_polarization": [
        1.5115162422151612e-16,
        -1.4604629238236137e-16,
        1.9021766983798385e-15
      ],
      "cartesian_polarization_e_A2": [
        4.7119463454607635e-18,
        -2.713255516314525e-18,
        3.1258500421755147e-17
      ],
      "ranking_score": 0.4418099857554768
    },
    {
      "candidate_id": "bec_projection_01",
      "source": "MACEField_BEC_backprojection",
      "spacegroup": "Cmc2_1",
      "spacegroup_number": 36,
      "pointgroup": "mm2",
      "has_inversion": false,
      "is_polar_point_group": true,
      "nonpolar_parent_hypothesis": false,
      "symmetry_tolerance_A": null,
      "target_reduced_polarization": [
        0.0,
        0.0,
        0.5
      ],
      "formal_class": [
        0.0,
        0.0,
        0.5
      ],
      "target_residual": 4.3365678037421423e-07,
      "parent_symmetrization_rmsd_A": 0.03485122484850547,
      "parent_cell_rmsd_A": 0.022733541614007285,
      "energy_eV": -140.98820822540307,
      "reduced_polarization": [
        -1.9775965307337265e-15,
        6.6706764287573764e-15,
        0.5000004336567804
      ],
      "cartesian_polarization_e_A2": [
        -7.474085056384842e-17,
        1.322021472816342e-16,
        0.008168406931825245
      ],
      "ranking_score": 0.5405354775655681
    },
    {
      "candidate_id": "bec_projection_02",
      "source": "MACEField_BEC_backprojection",
      "spacegroup": "Cm",
      "spacegroup_number": 8,
      "pointgroup": "m",
      "has_inversion": false,
      "is_polar_point_group": true,
      "nonpolar_parent_hypothesis": false,
      "symmetry_tolerance_A": null,
      "target_reduced_polarization": [
        0.0,
        -0.5,
        0.0
      ],
      "formal_class": [
        0.0,
        0.5,
        0.0
      ],
      "target_residual": 6.846038217379479e-05,
      "parent_symmetrization_rmsd_A": 0.04601153349289619,
      "parent_cell_rmsd_A": 0.052622421470350525,
      "energy_eV": -140.7047557797841,
      "reduced_polarization": [
        1.5302985836434291e-15,
        -0.499935454050794,
        2.2817632841206717e-05
      ],
      "cartesian_polarization_e_A2": [
        3.2338601202602153e-17,
        -0.009291034184978586,
        0.00012079625118380156
      ],
      "ranking_score": 0.5593040596248314
    },
    {
      "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,
        0.0,
        0.0
      ],
      "formal_class": [
        0.5,
        0.0,
        0.0
      ],
      "target_residual": 3.395931646216268e-05,
      "parent_symmetrization_rmsd_A": 0.06728860145183493,
      "parent_cell_rmsd_A": 0.04798689513804643,
      "energy_eV": -139.55712465337217,
      "reduced_polarization": [
        0.49996610719675577,
        -7.314498886596802e-15,
        -2.1243970498267102e-06
      ],
      "cartesian_polarization_e_A2": [
        0.01558707720228571,
        -1.328753993442044e-16,
        0.00010971683615905426
      ],
      "ranking_score": 0.5793532438692709
    },
    {
      "candidate_id": "bec_projection_04",
      "source": "MACEField_BEC_backprojection",
      "spacegroup": "Cm",
      "spacegroup_number": 8,
      "pointgroup": "m",
      "has_inversion": false,
      "is_polar_point_group": true,
      "nonpolar_parent_hypothesis": false,
      "symmetry_tolerance_A": null,
      "target_reduced_polarization": [
        0.0,
        -0.5,
        0.5
      ],
      "formal_class": [
        0.0,
        0.5,
        0.5
      ],
      "target_residual": 0.0005726493543380182,
      "parent_symmetrization_rmsd_A": 0.05977574056244689,
      "parent_cell_rmsd_A": 0.0606792182035065,
      "energy_eV": -140.37943439007253,
      "reduced_polarization": [
        -1.3019928209626166e-15,
        -0.49957458067350696,
        0.49961666505550634
      ],
      "cartesian_polarization_e_A2": [
        2.002100071130597e-17,
        -0.009463439901094491,
        0.008288906797849523
      ],
      "ranking_score": 0.5760908438219996
    },
    {
      "candidate_id": "bec_projection_05",
      "source": "MACEField_BEC_backprojection",
      "spacegroup": "Cc",
      "spacegroup_number": 9,
      "pointgroup": "m",
      "has_inversion": false,
      "is_polar_point_group": true,
      "nonpolar_parent_hypothesis": false,
      "symmetry_tolerance_A": null,
      "target_reduced_polarization": [
        0.5,
        0.0,
        0.5
      ],
      "formal_class": [
        0.5,
        0.0,
        0.5
      ],
      "target_residual": 6.701179722283354e-05,
      "parent_symmetrization_rmsd_A": 0.07747550498590446,
      "parent_cell_rmsd_A": 0.054412782658257185,
      "energy_eV": -139.1297450541752,
      "reduced_polarization": [
        0.4999509076864771,
        -1.8057660646157073e-16,
        0.49995438721977337
      ],
      "cartesian_polarization_e_A2": [
        0.015679210485885553,
        -8.185828379733495e-18,
        0.008278409626666015
      ],
      "ranking_score": 0.5912127242449144
    },
    {
      "candidate_id": "bec_projection_06",
      "source": "MACEField_BEC_backprojection",
      "spacegroup": "P1",
      "spacegroup_number": 1,
      "pointgroup": "1",
      "has_inversion": false,
      "is_polar_point_group": true,
      "nonpolar_parent_hypothesis": false,
      "symmetry_tolerance_A": null,
      "target_reduced_polarization": [
        0.5,
        -0.5,
        0.0
      ],
      "formal_class": [
        0.5,
        0.5,
        0.0
      ],
      "target_residual": 0.000289964074790676,
      "parent_symmetrization_rmsd_A": 0.08191210174637045,
      "parent_cell_rmsd_A": 0.0720055571188755,
      "energy_eV": -138.836884712296,
      "reduced_polarization": [
        0.4999107454455531,
        -0.4997305112154239,
        -5.906423763484891e-05
      ],
      "cartesian_polarization_e_A2": [
        0.015587247950427197,
        -0.009290314681283041,
        0.00023181621938255802
      ],
      "ranking_score": 0.6004934191756707
    },
    {
      "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": 3.679832613624384e-05,
      "parent_symmetrization_rmsd_A": 0.09252276648985738,
      "parent_cell_rmsd_A": 0.07992051855781356,
      "energy_eV": -138.44934514404963,
      "reduced_polarization": [
        0.49999666935642123,
        -0.4999697144826842,
        0.4999793648101367
      ],
      "cartesian_polarization_e_A2": [
        0.015683502661821426,
        -0.009479072418147532,
        0.008410175305726847
      ],
      "ranking_score": 0.6125764927815832
    }
  ],
  "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": [
              2.302879751357545e-16,
              -6.111146963671413e-16,
              0.06492632512262175
            ],
            "branch_aligned_reduced_polarization": [
              2.302879751357545e-16,
              -6.111146963671413e-16,
              0.06492632512262175
            ],
            "target_residual": 0.06492632512262175,
            "energy_eV": -141.38640382576563,
            "max_atomic_step_A": 0.006179709489722271,
            "max_log_strain_component": 0.000990679546105912,
            "step_scale": 1.0,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 4.875177885141351,
            "cell_principal_stretches": [
              1.0009911704311771,
              0.9999384734680851,
              0.9992868144114984
            ],
            "cell_volume_ratio": 1.000215734362343,
            "cell_rmsd_from_input_A": 0.0034613881295732195
          },
          {
            "iteration": 1,
            "reduced_polarization": [
              2.9052109209161045e-15,
              -8.17783869060451e-16,
              0.00017865470027207895
            ],
            "branch_aligned_reduced_polarization": [
              2.9052109209161045e-15,
              -8.17783869060451e-16,
              0.00017865470027207895
            ],
            "target_residual": 0.00017865470027207895,
            "energy_eV": -141.37425909164836
          }
        ],
        "iterations": 1
      },
      "parent": {
        "candidate_id": "inversion_parent_endpoint_00",
        "source": "same_species_inversion_center_projection_from_endpoint",
        "spacegroup": "Cmcm",
        "spacegroup_number": 63,
        "pointgroup": "mmm",
        "has_inversion": true,
        "is_polar_point_group": false,
        "nonpolar_parent_hypothesis": true,
        "symmetry_tolerance_A": null,
        "target_reduced_polarization": [
          0.0,
          0.0,
          0.0
        ],
        "formal_class": [
          0.0,
          0.0,
          0.0
        ],
        "target_residual": 9.927371598046309e-15,
        "parent_symmetrization_rmsd_A": 0.4409445565951117,
        "parent_cell_rmsd_A": 0.0,
        "energy_eV": -129.8316506253975,
        "reduced_polarization": [
          -1.7311010643618293e-15,
          -2.3071522804440123e-15,
          9.499107553107495e-15
        ],
        "cartesian_polarization_e_A2": [
          -5.39796849158916e-17,
          -4.2902237639027887e-17,
          1.559780629879988e-16
        ],
        "ranking_score": 0.4409445565951316
      },
      "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": [
          -141.38640382576563,
          -140.77263491438168,
          -139.284718814322,
          -137.27030836661731,
          -135.0686952292835,
          -133.00308135541096,
          -131.32825113210487,
          -130.22557055413233,
          -129.8316506253975
        ],
        "cartesian_polarizations_e_A2": [
          [
            7.57949894683325e-17,
            -3.695533982031797e-17,
            0.0010661088289545455
          ],
          [
            3.181130295226125e-17,
            -5.207683967437334e-17,
            -0.007107791526409326
          ],
          [
            6.900736577682579e-17,
            -1.0903538124853377e-17,
            -0.014909773558285206
          ],
          [
            8.376623614508896e-17,
            -2.793596734099645e-17,
            -0.021647746174217813
          ],
          [
            7.382761525681743e-17,
            -2.3568128799081694e-17,
            -0.02591670618880488
          ],
          [
            1.2589482369452383e-17,
            -3.483030072578346e-17,
            -0.026058973948508674
          ],
          [
            5.4191136153118024e-17,
            -1.9516102112525972e-17,
            -0.02116844727245498
          ],
          [
            1.3565192522050185e-18,
            -1.1042709450943797e-17,
            -0.011891544400965832
          ],
          [
            7.448004257193887e-17,
            -3.3700871887126587e-17,
            3.441786126487715e-17
          ]
        ],
        "raw_reduced_polarization": [
          [
            2.4307067954614203e-15,
            -1.987346144003177e-15,
            0.06492632512262897
          ],
          [
            1.0201723201089655e-15,
            -2.8005345647460757e-15,
            -0.43286648699838765
          ],
          [
            2.213031152945848e-15,
            -5.8635922585957e-16,
            -0.9080093694555407
          ],
          [
            2.6863406256315065e-15,
            -1.5023116346397133e-15,
            -1.3183537816281774
          ],
          [
            2.3676141042599363e-15,
            -1.267422519126012e-15,
            -1.578334637536088
          ],
          [
            4.037383019830754e-16,
            -1.8730679836368293e-15,
            -1.586998783794078
          ],
          [
            1.737882198086371e-15,
            -1.049516807797738e-15,
            -1.2891643447887051
          ],
          [
            4.350288307496381e-17,
            -5.93843437873487e-16,
            -0.7241983717031986
          ],
          [
            2.3885371167114772e-15,
            -1.8123307246008114e-15,
            2.096057353450758e-15
          ]
        ],
        "unwrapped_reduced_polarization": [
          [
            2.4307067954614203e-15,
            -1.987346144003177e-15,
            0.06492632512262897
          ],
          [
            1.0201723201089655e-15,
            -2.8005345647460757e-15,
            -0.43286648699838765
          ],
          [
            2.213031152945848e-15,
            -5.863592258595701e-16,
            -0.9080093694555407
          ],
          [
            2.6863406256315065e-15,
            -1.5023116346397133e-15,
            -1.3183537816281774
          ],
          [
            2.3676141042599363e-15,
            -1.267422519126012e-15,
            -1.578334637536088
          ],
          [
            4.0373830198307526e-16,
            -1.8730679836368293e-15,
            -1.586998783794078
          ],
          [
            1.737882198086371e-15,
            -1.049516807797738e-15,
            -1.2891643447887051
          ],
          [
            4.3502883074963727e-17,
            -5.93843437873487e-16,
            -1.7241983717031986
          ],
          [
            2.388537116711477e-15,
            -1.8123307246008114e-15,
            -1.999999999999998
          ]
        ],
        "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,
            -1
          ],
          [
            0,
            0,
            -2
          ]
        ],
        "folded_reduced_polarization": [
          [
            2.4424906541753444e-15,
            -1.9984014443252818e-15,
            0.06492632512262897
          ],
          [
            9.992007221626409e-16,
            -2.7755575615628914e-15,
            -0.43286648699838765
          ],
          [
            2.220446049250313e-15,
            -6.106226635438361e-16,
            0.09199063054445933
          ],
          [
            2.6645352591003757e-15,
            -1.4988010832439613e-15,
            -0.3183537816281774
          ],
          [
            2.3314683517128287e-15,
            -1.27675647831893e-15,
            0.42166536246391195
          ],
          [
            4.440892098500626e-16,
            -1.887379141862766e-15,
            0.413001216205922
          ],
          [
            1.7763568394002505e-15,
            -1.0547118733938987e-15,
            -0.2891643447887051
          ],
          [
            0.0,
            -6.106226635438361e-16,
            0.27580162829680144
          ],
          [
            2.4424906541753444e-15,
            -1.8318679906315083e-15,
            1.9984014443252818e-15
          ]
        ]
      },
      "reflected": {
        "reached": true,
        "construction": "reflect_displacements_about_reconstructed_parent",
        "energies_eV": [
          -129.83165062539754,
          -130.22557055413228,
          -131.32825113210492,
          -133.00308135541098,
          -135.0686952292835,
          -137.27030836661726,
          -139.284718814322,
          -140.77263491438168,
          -141.38640382576557
        ],
        "cartesian_polarizations_e_A2": [
          [
            -1.2285235560559638e-17,
            -3.550474638299089e-17,
            8.00185350297928e-17
          ],
          [
            5.789114078270288e-17,
            -1.2605710497805448e-17,
            0.011891544400966037
          ],
          [
            4.3376064089824227e-17,
            -1.8761365305650998e-17,
            0.021168447272455027
          ],
          [
            9.102976031764042e-18,
            -6.975695083116799e-17,
            0.026058973948508764
          ],
          [
            -5.99630576116816e-18,
            -4.603359247606236e-17,
            0.02591670618880473
          ],
          [
            1.3884291004002717e-16,
            -2.3182731280677454e-17,
            0.021647746174217743
          ],
          [
            1.129069173568679e-16,
            -6.188841816374803e-17,
            0.014909773558285206
          ],
          [
            5.130401583349986e-17,
            -1.505726693432133e-17,
            0.007107791526409302
          ],
          [
            1.4786338202659728e-16,
            -1.3001813502832032e-17,
            -0.001066108828954611
          ]
        ],
        "raw_reduced_polarization": [
          [
            -3.9398126143117947e-16,
            -1.9093376264735042e-15,
            4.8731511081054075e-15
          ],
          [
            1.8565394663234515e-15,
            -6.778968958759387e-16,
            0.724198371703211
          ],
          [
            1.3910483329185876e-15,
            -1.00892935033765e-15,
            1.289164344788708
          ],
          [
            2.9192781547355334e-16,
            -3.751317344821755e-15,
            1.5869987837940835
          ],
          [
            -1.9229847861415063e-16,
            -2.4755470507571435e-15,
            1.5783346375360787
          ],
          [
            4.452621569093773e-15,
            -1.2466970089336268e-15,
            1.3183537816281732
          ],
          [
            3.620867463654753e-15,
            -3.3281715117272203e-15,
            0.9080093694555407
          ],
          [
            1.6452937165859854e-15,
            -8.097341690441682e-16,
            0.4328664869983862
          ],
          [
            4.74190352176409e-15,
            -6.991981146847793e-16,
            -0.06492632512263295
          ]
        ],
        "unwrapped_reduced_polarization": [
          [
            -3.9398126143117947e-16,
            -1.9093376264735042e-15,
            -1.9999999999999951
          ],
          [
            1.8565394663234515e-15,
            -6.778968958759387e-16,
            -2.2758016282967892
          ],
          [
            1.3910483329185876e-15,
            -1.00892935033765e-15,
            -2.7108356552112918
          ],
          [
            2.919278154735534e-16,
            -3.751317344821755e-15,
            -2.4130012162059167
          ],
          [
            -1.9229847861415063e-16,
            -2.4755470507571435e-15,
            -2.421665362463921
          ],
          [
            4.452621569093773e-15,
            -1.2466970089336268e-15,
            -2.681646218371827
          ],
          [
            3.620867463654753e-15,
            -3.32817151172722e-15,
            -3.0919906305444593
          ],
          [
            1.6452937165859856e-15,
            -8.097341690441683e-16,
            -3.5671335130016137
          ],
          [
            4.74190352176409e-15,
            -6.991981146847793e-16,
            -4.064926325122633
          ]
        ],
        "gauge_integer_shift": [
          0,
          0,
          -2
        ],
        "expected_opposite_endpoint_reduced_polarization": [
          2.346367437961534e-15,
          -1.6373153051984459e-15,
          -0.06492632512262478
        ],
        "actual_opposite_endpoint_branch_residual": 8.397403784196595e-15
      },
      "pnp_branch": {
        "construction": "incoming_path_concatenated_with_parent_reflection",
        "reduced_polarization": [
          [
            2.4307067954614203e-15,
            -1.987346144003177e-15,
            0.06492632512262897
          ],
          [
            1.0201723201089655e-15,
            -2.8005345647460757e-15,
            -0.43286648699838765
          ],
          [
            2.213031152945848e-15,
            -5.8635922585957e-16,
            -0.9080093694555407
          ],
          [
            2.6863406256315065e-15,
            -1.5023116346397133e-15,
            -1.3183537816281774
          ],
          [
            2.3676141042599363e-15,
            -1.267422519126012e-15,
            -1.578334637536088
          ],
          [
            4.037383019830754e-16,
            -1.8730679836368293e-15,
            -1.586998783794078
          ],
          [
            1.737882198086371e-15,
            -1.049516807797738e-15,
            -1.2891643447887051
          ],
          [
            4.350288307496381e-17,
            -5.93843437873487e-16,
            -0.7241983717031986
          ],
          [
            2.3885371167114772e-15,
            -1.8123307246008114e-15,
            2.096057353450758e-15
          ],
          [
            1.8565394663234515e-15,
            -6.778968958759387e-16,
            0.724198371703211
          ],
          [
            1.3910483329185876e-15,
            -1.00892935033765e-15,
            1.289164344788708
          ],
          [
            2.9192781547355334e-16,
            -3.751317344821755e-15,
            1.5869987837940835
          ],
          [
            -1.9229847861415063e-16,
            -2.4755470507571435e-15,
            1.5783346375360787
          ],
          [
            4.452621569093773e-15,
            -1.2466970089336268e-15,
            1.3183537816281732
          ],
          [
            3.620867463654753e-15,
            -3.3281715117272203e-15,
            0.9080093694555407
          ],
          [
            1.6452937165859854e-15,
            -8.097341690441682e-16,
            0.4328664869983862
          ],
          [
            4.74190352176409e-15,
            -6.991981146847793e-16,
            -0.06492632512263295
          ]
        ],
        "unwrapped_reduced_polarization": [
          [
            2.4307067954614203e-15,
            -1.987346144003177e-15,
            0.06492632512262897
          ],
          [
            1.0201723201089655e-15,
            -2.8005345647460757e-15,
            -0.43286648699838765
          ],
          [
            2.213031152945848e-15,
            -5.863592258595701e-16,
            -0.9080093694555407
          ],
          [
            2.6863406256315065e-15,
            -1.5023116346397133e-15,
            -1.3183537816281774
          ],
          [
            2.3676141042599363e-15,
            -1.267422519126012e-15,
            -1.578334637536088
          ],
          [
            4.0373830198307526e-16,
            -1.8730679836368293e-15,
            -1.586998783794078
          ],
          [
            1.737882198086371e-15,
            -1.049516807797738e-15,
            -1.2891643447887051
          ],
          [
            4.3502883074963727e-17,
            -5.93843437873487e-16,
            -1.7241983717031986
          ],
          [
            2.388537116711477e-15,
            -1.8123307246008114e-15,
            -1.999999999999998
          ],
          [
            1.8565394663234515e-15,
            -6.778968958759387e-16,
            -2.2758016282967892
          ],
          [
            1.3910483329185876e-15,
            -1.00892935033765e-15,
            -2.7108356552112918
          ],
          [
            2.919278154735534e-16,
            -3.751317344821755e-15,
            -2.4130012162059167
          ],
          [
            -1.9229847861415063e-16,
            -2.4755470507571435e-15,
            -2.421665362463921
          ],
          [
            4.452621569093773e-15,
            -1.2466970089336268e-15,
            -2.681646218371827
          ],
          [
            3.620867463654753e-15,
            -3.32817151172722e-15,
            -3.0919906305444593
          ],
          [
            1.6452937165859856e-15,
            -8.097341690441683e-16,
            -3.5671335130016137
          ],
          [
            4.74190352176409e-15,
            -6.991981146847793e-16,
            -4.064926325122633
          ]
        ],
        "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,
            -1
          ],
          [
            0,
            0,
            -2
          ],
          [
            0,
            0,
            -3
          ],
          [
            0,
            0,
            -4
          ],
          [
            0,
            0,
            -4
          ],
          [
            0,
            0,
            -4
          ],
          [
            0,
            0,
            -4
          ],
          [
            0,
            0,
            -4
          ],
          [
            0,
            0,
            -4
          ],
          [
            0,
            0,
            -4
          ]
        ],
        "folded_reduced_polarization": [
          [
            2.4424906541753444e-15,
            -1.9984014443252818e-15,
            0.06492632512262897
          ],
          [
            9.992007221626409e-16,
            -2.7755575615628914e-15,
            -0.43286648699838765
          ],
          [
            2.220446049250313e-15,
            -6.106226635438361e-16,
            0.09199063054445933
          ],
          [
            2.6645352591003757e-15,
            -1.4988010832439613e-15,
            -0.3183537816281774
          ],
          [
            2.3314683517128287e-15,
            -1.27675647831893e-15,
            0.42166536246391195
          ],
          [
            4.440892098500626e-16,
            -1.887379141862766e-15,
            0.413001216205922
          ],
          [
            1.7763568394002505e-15,
            -1.0547118733938987e-15,
            -0.2891643447887051
          ],
          [
            0.0,
            -6.106226635438361e-16,
            0.27580162829680144
          ],
          [
            2.4424906541753444e-15,
            -1.8318679906315083e-15,
            1.9984014443252818e-15
          ],
          [
            1.887379141862766e-15,
            -6.661338147750939e-16,
            -0.2758016282967892
          ],
          [
            1.4432899320127035e-15,
            -9.992007221626409e-16,
            0.2891643447887082
          ],
          [
            3.3306690738754696e-16,
            -3.774758283725532e-15,
            -0.4130012162059167
          ],
          [
            -1.6653345369377348e-16,
            -2.4980018054066022e-15,
            -0.42166536246392106
          ],
          [
            4.440892098500626e-15,
            -1.2212453270876722e-15,
            0.31835378162817296
          ],
          [
            3.6637359812630166e-15,
            -3.3306690738754696e-15,
            -0.09199063054445933
          ],
          [
            1.6653345369377348e-15,
            -8.326672684688674e-16,
            0.43286648699838626
          ],
          [
            4.773959005888173e-15,
            -7.216449660063518e-16,
            -0.06492632512263263
          ]
        ]
      },
      "incoming_structure_ids": [
        "incoming_00_000",
        "incoming_00_001",
        "incoming_00_002",
        "incoming_00_003",
        "incoming_00_004",
        "incoming_00_005",
        "incoming_00_006",
        "incoming_00_007",
        "incoming_00_008"
      ],
      "reflected_structure_ids": [
        "reflected_00_001",
        "reflected_00_002",
        "reflected_00_003",
        "reflected_00_004",
        "reflected_00_005",
        "reflected_00_006",
        "reflected_00_007",
        "reflected_00_008"
      ]
    },
    {
      "orbit_id": 1,
      "formal_class": [
        0.0,
        0.0,
        0.5
      ],
      "formal_classes_in_orbit": [
        [
          0.0,
          0.0,
          0.5
        ]
      ],
      "target_reduced_polarization": [
        0.0,
        0.0,
        0.5
      ],
      "bec_backprojection": {
        "converged_to_target": true,
        "history": [
          {
            "iteration": 0,
            "reduced_polarization": [
              2.302879751357545e-16,
              -6.111146963671413e-16,
              0.06492632512262175
            ],
            "branch_aligned_reduced_polarization": [
              2.302879751357545e-16,
              -6.111146963671413e-16,
              0.06492632512262175
            ],
            "target_residual": 0.43507367487737825,
            "energy_eV": -141.38640382576563,
            "max_atomic_step_A": 0.041410458889984215,
            "max_log_strain_component": 0.006638579804665025,
            "step_scale": 1.0,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 4.875177885141351,
            "cell_principal_stretches": [
              1.0047922338602544,
              1.0004123892295,
              0.993383406885876
            ],
            "cell_volume_ratio": 0.9985555562918164,
            "cell_rmsd_from_input_A": 0.023160181722508735
          },
          {
            "iteration": 1,
            "reduced_polarization": [
              -5.175935400240813e-15,
              -1.4765102186547042e-15,
              0.5085847649847981
            ],
            "branch_aligned_reduced_polarization": [
              -5.175935400240813e-15,
              -1.4765102186547042e-15,
              0.5085847649847981
            ],
            "target_residual": 0.008584764984798099,
            "energy_eV": -140.97137487384788,
            "max_atomic_step_A": 0.0007905774681627917,
            "max_log_strain_component": 0.00012244265916375638,
            "step_scale": 1.0,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 4.875177885141351,
            "cell_principal_stretches": [
              1.0047036378530514,
              1.0004047815402817,
              0.9935050468385919
            ],
            "cell_volume_ratio": 0.9985821788669731,
            "cell_rmsd_from_input_A": 0.022733541614007285
          },
          {
            "iteration": 2,
            "reduced_polarization": [
              -1.9775965307337265e-15,
              6.6706764287573764e-15,
              0.5000004336567804
            ],
            "branch_aligned_reduced_polarization": [
              -1.9775965307337265e-15,
              6.6706764287573764e-15,
              0.5000004336567804
            ],
            "target_residual": 4.3365678037421423e-07,
            "energy_eV": -140.98820822540307
          }
        ],
        "iterations": 2
      },
      "parent": {
        "candidate_id": "bec_projection_01",
        "source": "MACEField_BEC_backprojection",
        "spacegroup": "Cmc2_1",
        "spacegroup_number": 36,
        "pointgroup": "mm2",
        "has_inversion": false,
        "is_polar_point_group": true,
        "nonpolar_parent_hypothesis": false,
        "symmetry_tolerance_A": null,
        "target_reduced_polarization": [
          0.0,
          0.0,
          0.5
        ],
        "formal_class": [
          0.0,
          0.0,
          0.5
        ],
        "target_residual": 4.3365678037421423e-07,
        "parent_symmetrization_rmsd_A": 0.03485122484850547,
        "parent_cell_rmsd_A": 0.022733541614007285,
        "energy_eV": -140.98820822540307,
        "reduced_polarization": [
          -1.9775965307337265e-15,
          6.6706764287573764e-15,
          0.5000004336567804
        ],
        "cartesian_polarization_e_A2": [
          -7.474085056384842e-17,
          1.322021472816342e-16,
          0.008168406931825245
        ],
        "ranking_score": 0.5405354775655681
      },
      "branch_status": "awaiting_branch_sampling"
    },
    {
      "orbit_id": 2,
      "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": [
              2.302879751357545e-16,
              -6.111146963671413e-16,
              0.06492632512262175
            ],
            "branch_aligned_reduced_polarization": [
              2.302879751357545e-16,
              -6.106226635438361e-16,
              0.06492632512262175
            ],
            "target_residual": 0.5041978061177258,
            "energy_eV": -141.38640382576563,
            "max_atomic_step_A": 0.04967805753810844,
            "max_log_strain_component": 0.012972257963316091,
            "step_scale": 1.0,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 4.875177885141351,
            "cell_principal_stretches": [
              1.013225524328989,
              0.9999384734680856,
              0.9872207656993721
            ],
            "cell_volume_ratio": 1.0002157343623472,
            "cell_rmsd_from_input_A": 0.05274259022111053
          },
          {
            "iteration": 1,
            "reduced_polarization": [
              -4.7024667389385244e-15,
              -0.5023397673672866,
              -0.01810341847689544
            ],
            "branch_aligned_reduced_polarization": [
              -4.7024667389385244e-15,
              -0.5023397673672866,
              -0.01810341847689544
            ],
            "target_residual": 0.018253993313316907,
            "energy_eV": -140.68897024151397,
            "max_atomic_step_A": 0.0017332168651452442,
            "max_log_strain_component": 0.0002780630480960632,
            "step_scale": 1.0,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 4.875177885141351,
            "cell_principal_stretches": [
              1.0131569055134706,
              0.9999557422978274,
              0.9872108047854555
            ],
            "cell_volume_ratio": 1.000155177536786,
            "cell_rmsd_from_input_A": 0.052622421470350525
          },
          {
            "iteration": 2,
            "reduced_polarization": [
              1.5302985836434291e-15,
              -0.499935454050794,
              2.2817632841206717e-05
            ],
            "branch_aligned_reduced_polarization": [
              1.5302985836434291e-15,
              -0.499935454050794,
              2.2817632841206717e-05
            ],
            "target_residual": 6.846038217379479e-05,
            "energy_eV": -140.7047557797841
          }
        ],
        "iterations": 2
      },
      "parent": {
        "candidate_id": "bec_projection_02",
        "source": "MACEField_BEC_backprojection",
        "spacegroup": "Cm",
        "spacegroup_number": 8,
        "pointgroup": "m",
        "has_inversion": false,
        "is_polar_point_group": true,
        "nonpolar_parent_hypothesis": false,
        "symmetry_tolerance_A": null,
        "target_reduced_polarization": [
          0.0,
          -0.5,
          0.0
        ],
        "formal_class": [
          0.0,
          0.5,
          0.0
        ],
        "target_residual": 6.846038217379479e-05,
        "parent_symmetrization_rmsd_A": 0.04601153349289619,
        "parent_cell_rmsd_A": 0.052622421470350525,
        "energy_eV": -140.7047557797841,
        "reduced_polarization": [
          1.5302985836434291e-15,
          -0.499935454050794,
          2.2817632841206717e-05
        ],
        "cartesian_polarization_e_A2": [
          3.2338601202602153e-17,
          -0.009291034184978586,
          0.00012079625118380156
        ],
        "ranking_score": 0.5593040596248314
      },
      "branch_status": "awaiting_branch_sampling"
    },
    {
      "orbit_id": 3,
      "formal_class": [
        0.5,
        0.0,
        0.0
      ],
      "formal_classes_in_orbit": [
        [
          0.5,
          0.0,
          0.0
        ]
      ],
      "target_reduced_polarization": [
        0.5,
        0.0,
        0.0
      ],
      "bec_backprojection": {
        "converged_to_target": true,
        "history": [
          {
            "iteration": 0,
            "reduced_polarization": [
              2.302879751357545e-16,
              -6.111146963671413e-16,
              0.06492632512262175
            ],
            "branch_aligned_reduced_polarization": [
              2.220446049250313e-16,
              -6.111146963671413e-16,
              0.06492632512262175
            ],
            "target_residual": 0.5041978061177261,
            "energy_eV": -141.38640382576563,
            "max_atomic_step_A": 0.07979770493571077,
            "max_log_strain_component": 0.0068901194197322066,
            "step_scale": 1.0,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 4.875177885141351,
            "cell_principal_stretches": [
              1.0074020119158749,
              0.9992868144114796,
              0.9935751279793393
            ],
            "cell_volume_ratio": 1.0002157343623,
            "cell_rmsd_from_input_A": 0.04703176571908867
          },
          {
            "iteration": 1,
            "reduced_polarization": [
              0.4908975835856392,
              1.7894602955648556e-14,
              -0.012442115906345934
            ],
            "branch_aligned_reduced_polarization": [
              0.4908975835856392,
              1.7894602955648556e-14,
              -0.012442115906345934
            ],
            "target_residual": 0.015416232769628639,
            "energy_eV": -139.62375845966096,
            "max_atomic_step_A": 0.001995235998314693,
            "max_log_strain_component": 0.0002126690998420304,
            "step_scale": 1.0,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 4.875177885141351,
            "cell_principal_stretches": [
              1.0074437930819613,
              0.9994398710185455,
              0.9933357706745052
            ],
            "cell_volume_ratio": 1.0001694187610084,
            "cell_rmsd_from_input_A": 0.04798689513804643
          },
          {
            "iteration": 2,
            "reduced_polarization": [
              0.49996610719675577,
              -7.314498886596802e-15,
              -2.1243970498267102e-06
            ],
            "branch_aligned_reduced_polarization": [
              0.49996610719675577,
              -7.314498886596802e-15,
              -2.1243970498267102e-06
            ],
            "target_residual": 3.395931646216268e-05,
            "energy_eV": -139.55712465337217
          }
        ],
        "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,
          0.0,
          0.0
        ],
        "formal_class": [
          0.5,
          0.0,
          0.0
        ],
        "target_residual": 3.395931646216268e-05,
        "parent_symmetrization_rmsd_A": 0.06728860145183493,
        "parent_cell_rmsd_A": 0.04798689513804643,
        "energy_eV": -139.55712465337217,
        "reduced_polarization": [
          0.49996610719675577,
          -7.314498886596802e-15,
          -2.1243970498267102e-06
        ],
        "cartesian_polarization_e_A2": [
          0.01558707720228571,
          -1.328753993442044e-16,
          0.00010971683615905426
        ],
        "ranking_score": 0.5793532438692709
      },
      "branch_status": "awaiting_branch_sampling"
    },
    {
      "orbit_id": 4,
      "formal_class": [
        0.0,
        0.5,
        0.5
      ],
      "formal_classes_in_orbit": [
        [
          0.0,
          0.5,
          0.5
        ]
      ],
      "target_reduced_polarization": [
        0.0,
        -0.5,
        0.5
      ],
      "bec_backprojection": {
        "converged_to_target": true,
        "history": [
          {
            "iteration": 0,
            "reduced_polarization": [
              2.302879751357545e-16,
              -6.111146963671413e-16,
              0.06492632512262175
            ],
            "branch_aligned_reduced_polarization": [
              2.302879751357545e-16,
              -6.106226635438361e-16,
              0.06492632512262175
            ],
            "target_residual": 0.6627888823534279,
            "energy_eV": -141.38640382576563,
            "max_atomic_step_A": 0.06488359698611341,
            "max_log_strain_component": 0.012972257963315102,
            "step_scale": 1.0,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 4.875177885141351,
            "cell_principal_stretches": [
              1.0133324113188786,
              1.0004123892295005,
              0.9850113559335006
            ],
            "cell_volume_ratio": 0.9985555562918206,
            "cell_rmsd_from_input_A": 0.05742672218727481
          },
          {
            "iteration": 1,
            "reduced_polarization": [
              -1.4093179962909532e-14,
              -0.4730548890611097,
              0.4896633249258776
            ],
            "branch_aligned_reduced_polarization": [
              -1.4093179962909532e-14,
              -0.4730548890611097,
              0.4896633249258776
            ],
            "target_residual": 0.028859761868336484,
            "energy_eV": -140.4616509282954,
            "max_atomic_step_A": 0.0030193379192651553,
            "max_log_strain_component": 0.0008010724182931244,
            "step_scale": 1.0,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 4.875177885141351,
            "cell_principal_stretches": [
              1.0141183084929006,
              1.0004247651641116,
              0.9841931538238311
            ],
            "cell_volume_ratio": 0.9985122495251293,
            "cell_rmsd_from_input_A": 0.0606792182035065
          },
          {
            "iteration": 2,
            "reduced_polarization": [
              -1.3019928209626166e-15,
              -0.49957458067350696,
              0.49961666505550634
            ],
            "branch_aligned_reduced_polarization": [
              -1.3019928209626166e-15,
              -0.49957458067350696,
              0.49961666505550634
            ],
            "target_residual": 0.0005726493543380182,
            "energy_eV": -140.37943439007253
          }
        ],
        "iterations": 2
      },
      "parent": {
        "candidate_id": "bec_projection_04",
        "source": "MACEField_BEC_backprojection",
        "spacegroup": "Cm",
        "spacegroup_number": 8,
        "pointgroup": "m",
        "has_inversion": false,
        "is_polar_point_group": true,
        "nonpolar_parent_hypothesis": false,
        "symmetry_tolerance_A": null,
        "target_reduced_polarization": [
          0.0,
          -0.5,
          0.5
        ],
        "formal_class": [
          0.0,
          0.5,
          0.5
        ],
        "target_residual": 0.0005726493543380182,
        "parent_symmetrization_rmsd_A": 0.05977574056244689,
        "parent_cell_rmsd_A": 0.0606792182035065,
        "energy_eV": -140.37943439007253,
        "reduced_polarization": [
          -1.3019928209626166e-15,
          -0.49957458067350696,
          0.49961666505550634
        ],
        "cartesian_polarization_e_A2": [
          2.002100071130597e-17,
          -0.009463439901094491,
          0.008288906797849523
        ],
        "ranking_score": 0.5760908438219996
      },
      "branch_status": "awaiting_branch_sampling"
    },
    {
      "orbit_id": 5,
      "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": [
              2.302879751357545e-16,
              -6.111146963671413e-16,
              0.06492632512262175
            ],
            "branch_aligned_reduced_polarization": [
              2.220446049250313e-16,
              -6.111146963671413e-16,
              0.06492632512262175
            ],
            "target_residual": 0.6627888823534281,
            "energy_eV": -141.38640382576563,
            "max_atomic_step_A": 0.08672502538217547,
            "max_log_strain_component": 0.0068901194197302715,
            "step_scale": 1.0,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 4.875177885141351,
            "cell_principal_stretches": [
              1.0047922338602353,
              1.004637250826632,
              0.989205871757101
            ],
            "cell_volume_ratio": 0.9985555562917733,
            "cell_rmsd_from_input_A": 0.052003203667640364
          },
          {
            "iteration": 1,
            "reduced_polarization": [
              0.47897990427810305,
              2.209224774173736e-14,
              0.4889311982669383
            ],
            "branch_aligned_reduced_polarization": [
              0.47897990427810305,
              2.209224774173736e-14,
              0.4889311982669383
            ],
            "target_residual": 0.023756321179078624,
            "energy_eV": -139.3175517419407,
            "max_atomic_step_A": 0.0037796532840677507,
            "max_log_strain_component": 0.00034672099744097597,
            "step_scale": 1.0,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 4.875177885141351,
            "cell_principal_stretches": [
              1.0049407957303682,
              1.0049007815968114,
              0.988756060461225
            ],
            "cell_volume_ratio": 0.9985109211906984,
            "cell_rmsd_from_input_A": 0.054412782658257185
          },
          {
            "iteration": 2,
            "reduced_polarization": [
              0.4999509076864771,
              -1.8057660646157073e-16,
              0.49995438721977337
            ],
            "branch_aligned_reduced_polarization": [
              0.4999509076864771,
              -1.8057660646157073e-16,
              0.49995438721977337
            ],
            "target_residual": 6.701179722283354e-05,
            "energy_eV": -139.1297450541752
          }
        ],
        "iterations": 2
      },
      "parent": {
        "candidate_id": "bec_projection_05",
        "source": "MACEField_BEC_backprojection",
        "spacegroup": "Cc",
        "spacegroup_number": 9,
        "pointgroup": "m",
        "has_inversion": false,
        "is_polar_point_group": true,
        "nonpolar_parent_hypothesis": false,
        "symmetry_tolerance_A": null,
        "target_reduced_polarization": [
          0.5,
          0.0,
          0.5
        ],
        "formal_class": [
          0.5,
          0.0,
          0.5
        ],
        "target_residual": 6.701179722283354e-05,
        "parent_symmetrization_rmsd_A": 0.07747550498590446,
        "parent_cell_rmsd_A": 0.054412782658257185,
        "energy_eV": -139.1297450541752,
        "reduced_polarization": [
          0.4999509076864771,
          -1.8057660646157073e-16,
          0.49995438721977337
        ],
        "cartesian_polarization_e_A2": [
          0.015679210485885553,
          -8.185828379733495e-18,
          0.008278409626666015
        ],
        "ranking_score": 0.5912127242449144
      },
      "branch_status": "awaiting_branch_sampling"
    },
    {
      "orbit_id": 6,
      "formal_class": [
        0.5,
        0.5,
        0.0
      ],
      "formal_classes_in_orbit": [
        [
          0.5,
          0.5,
          0.0
        ]
      ],
      "target_reduced_polarization": [
        0.5,
        -0.5,
        0.0
      ],
      "bec_backprojection": {
        "converged_to_target": true,
        "history": [
          {
            "iteration": 0,
            "reduced_polarization": [
              2.302879751357545e-16,
              -6.111146963671413e-16,
              0.06492632512262175
            ],
            "branch_aligned_reduced_polarization": [
              2.220446049250313e-16,
              -6.106226635438361e-16,
              0.06492632512262175
            ],
            "target_residual": 0.7100812824556971,
            "energy_eV": -141.38640382576563,
            "max_atomic_step_A": 0.09160050959947141,
            "max_log_strain_component": 0.01297225796331804,
            "step_scale": 1.0,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 4.875177885141351,
            "cell_principal_stretches": [
              1.0150337662342044,
              0.9997954509088794,
              0.9856030436811881
            ],
            "cell_volume_ratio": 1.0002157343623044,
            "cell_rmsd_from_input_A": 0.0705905952131831
          },
          {
            "iteration": 1,
            "reduced_polarization": [
              0.4902836225431341,
              -0.49504237129298456,
              -0.03219465192469834
            ],
            "branch_aligned_reduced_polarization": [
              0.4902836225431341,
              -0.49504237129298456,
              -0.03219465192469834
            ],
            "target_residual": 0.03399237687825607,
            "energy_eV": -138.91212863913313,
            "max_atomic_step_A": 0.0038409050304139395,
            "max_log_strain_component": 0.000548289839434161,
            "step_scale": 1.0,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 4.875177885141351,
            "cell_principal_stretches": [
              1.0151909433043178,
              0.9999077891191694,
              0.9852221059259223
            ],
            "cell_volume_ratio": 1.0000963308111739,
            "cell_rmsd_from_input_A": 0.0720055571188755
          },
          {
            "iteration": 2,
            "reduced_polarization": [
              0.4999107454455531,
              -0.4997305112154239,
              -5.906423763484891e-05
            ],
            "branch_aligned_reduced_polarization": [
              0.4999107454455531,
              -0.4997305112154239,
              -5.906423763484891e-05
            ],
            "target_residual": 0.000289964074790676,
            "energy_eV": -138.836884712296
          }
        ],
        "iterations": 2
      },
      "parent": {
        "candidate_id": "bec_projection_06",
        "source": "MACEField_BEC_backprojection",
        "spacegroup": "P1",
        "spacegroup_number": 1,
        "pointgroup": "1",
        "has_inversion": false,
        "is_polar_point_group": true,
        "nonpolar_parent_hypothesis": false,
        "symmetry_tolerance_A": null,
        "target_reduced_polarization": [
          0.5,
          -0.5,
          0.0
        ],
        "formal_class": [
          0.5,
          0.5,
          0.0
        ],
        "target_residual": 0.000289964074790676,
        "parent_symmetrization_rmsd_A": 0.08191210174637045,
        "parent_cell_rmsd_A": 0.0720055571188755,
        "energy_eV": -138.836884712296,
        "reduced_polarization": [
          0.4999107454455531,
          -0.4997305112154239,
          -5.906423763484891e-05
        ],
        "cartesian_polarization_e_A2": [
          0.015587247950427197,
          -0.009290314681283041,
          0.00023181621938255802
        ],
        "ranking_score": 0.6004934191756707
      },
      "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": [
              2.302879751357545e-16,
              -6.111146963671413e-16,
              0.06492632512262175
            ],
            "branch_aligned_reduced_polarization": [
              2.220446049250313e-16,
              -6.106226635438361e-16,
              0.06492632512262175
            ],
            "target_residual": 0.8302343660505181,
            "energy_eV": -141.38640382576563,
            "max_atomic_step_A": 0.10142072581050425,
            "max_log_strain_component": 0.012972257963317052,
            "step_scale": 1.0,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 4.875177885141351,
            "cell_principal_stretches": [
              1.0144544660935404,
              1.0012646409153305,
              0.983084377270153
            ],
            "cell_volume_ratio": 0.998555556291778,
            "cell_rmsd_from_input_A": 0.07393918762385213
          },
          {
            "iteration": 1,
            "reduced_polarization": [
              0.47737681195407133,
              -0.46433224380652915,
              0.4680066395185623
            ],
            "branch_aligned_reduced_polarization": [
              0.47737681195407133,
              -0.46433224380652915,
              0.4680066395185623
            ],
            "target_residual": 0.05298653210140806,
            "energy_eV": -138.79231504937138,
            "max_atomic_step_A": 0.007207952126661276,
            "max_log_strain_component": 0.0011906415416967186,
            "step_scale": 1.0,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 4.875177885141351,
            "cell_principal_stretches": [
              1.015719754274749,
              1.0013354477987972,
              0.9816607820578915
            ],
            "cell_volume_ratio": 0.9984238129812335,
            "cell_rmsd_from_input_A": 0.07976366393257124
          },
          {
            "iteration": 2,
            "reduced_polarization": [
              0.49977929682772587,
              -0.49874039472795534,
              0.49922444406387695
            ],
            "branch_aligned_reduced_polarization": [
              0.49977929682772587,
              -0.49874039472795534,
              0.49922444406387695
            ],
            "target_residual": 0.0014955943105235028,
            "energy_eV": -138.45618057365925,
            "max_atomic_step_A": 0.00018186834223652188,
            "max_log_strain_component": 4.106375308703838e-05,
            "step_scale": 1.0,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 4.875177885141351,
            "cell_principal_stretches": [
              1.0157598952729148,
              1.0013351707548959,
              0.9816190251513645
            ],
            "cell_volume_ratio": 0.9984205225764974,
            "cell_rmsd_from_input_A": 0.07992051855781356
          },
          {
            "iteration": 3,
            "reduced_polarization": [
              0.49999666935642123,
              -0.4999697144826842,
              0.4999793648101367
            ],
            "branch_aligned_reduced_polarization": [
              0.49999666935642123,
              -0.4999697144826842,
              0.4999793648101367
            ],
            "target_residual": 3.679832613624384e-05,
            "energy_eV": -138.44934514404963
          }
        ],
        "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": 3.679832613624384e-05,
        "parent_symmetrization_rmsd_A": 0.09252276648985738,
        "parent_cell_rmsd_A": 0.07992051855781356,
        "energy_eV": -138.44934514404963,
        "reduced_polarization": [
          0.49999666935642123,
          -0.4999697144826842,
          0.4999793648101367
        ],
        "cartesian_polarization_e_A2": [
          0.015683502661821426,
          -0.009479072418147532,
          0.008410175305726847
        ],
        "ranking_score": 0.6125764927815832
      },
      "branch_status": "awaiting_branch_sampling"
    }
  ],
  "sampled_polarization_branches": [
    {
      "orbit_id": 0,
      "candidate_id": "inversion_parent_endpoint_00",
      "formal_class": [
        0.0,
        0.0,
        0.0
      ],
      "construction": "MACEField-BEC-parent plus variable-cell P-N-P path and symmetric log-strain continuation beyond both polar endpoints",
      "geometry_diagnostics": {
        "collision_aware": false,
        "permutations_tested": 1,
        "selected_order": [
          0,
          1,
          2,
          3,
          4,
          5,
          6,
          7,
          8,
          9,
          10,
          11,
          12,
          13,
          14,
          15,
          16,
          17,
          18,
          19,
          20,
          21,
          22,
          23
        ],
        "endpoint_rmsd_A": 0.4409445565951117,
        "minimum_distance_A_by_image": [
          1.7976410964841276,
          1.7951871362555782,
          1.793057654101462,
          1.7838765700355204,
          1.7539095586204736,
          1.7302430952284766,
          1.7131383199900583,
          1.7027929834004727,
          1.6993305420913234
        ],
        "minimum_distance_A": 1.6993305420913234,
        "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": [
          324.0812000748863,
          324.0812000748863,
          324.0812000748863,
          324.0812000748863,
          324.0812000748863,
          324.0812000748863,
          324.0812000748863,
          324.0812000748863,
          324.0812000748863
        ],
        "cell_deformation_log_strain_norm": 0.0
      },
      "parent_reduced_polarization": [
        2.3885371167114772e-15,
        -1.8123307246008114e-15,
        2.096057353450758e-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": [
          -141.38640382576563,
          -140.77263491438168,
          -139.284718814322,
          -137.27030836661731,
          -135.0686952292835,
          -133.00308135541096,
          -131.32825113210487,
          -130.22557055413233,
          -129.8316506253975
        ],
        "cartesian_polarizations_e_A2": [
          [
            7.57949894683325e-17,
            -3.695533982031797e-17,
            0.0010661088289545455
          ],
          [
            3.181130295226125e-17,
            -5.207683967437334e-17,
            -0.007107791526409326
          ],
          [
            6.900736577682579e-17,
            -1.0903538124853377e-17,
            -0.014909773558285206
          ],
          [
            8.376623614508896e-17,
            -2.793596734099645e-17,
            -0.021647746174217813
          ],
          [
            7.382761525681743e-17,
            -2.3568128799081694e-17,
            -0.02591670618880488
          ],
          [
            1.2589482369452383e-17,
            -3.483030072578346e-17,
            -0.026058973948508674
          ],
          [
            5.4191136153118024e-17,
            -1.9516102112525972e-17,
            -0.02116844727245498
          ],
          [
            1.3565192522050185e-18,
            -1.1042709450943797e-17,
            -0.011891544400965832
          ],
          [
            7.448004257193887e-17,
            -3.3700871887126587e-17,
            3.441786126487715e-17
          ]
        ],
        "raw_reduced_polarization": [
          [
            2.4307067954614203e-15,
            -1.987346144003177e-15,
            0.06492632512262897
          ],
          [
            1.0201723201089655e-15,
            -2.8005345647460757e-15,
            -0.43286648699838765
          ],
          [
            2.213031152945848e-15,
            -5.8635922585957e-16,
            -0.9080093694555407
          ],
          [
            2.6863406256315065e-15,
            -1.5023116346397133e-15,
            -1.3183537816281774
          ],
          [
            2.3676141042599363e-15,
            -1.267422519126012e-15,
            -1.578334637536088
          ],
          [
            4.037383019830754e-16,
            -1.8730679836368293e-15,
            -1.586998783794078
          ],
          [
            1.737882198086371e-15,
            -1.049516807797738e-15,
            -1.2891643447887051
          ],
          [
            4.350288307496381e-17,
            -5.93843437873487e-16,
            -0.7241983717031986
          ],
          [
            2.3885371167114772e-15,
            -1.8123307246008114e-15,
            2.096057353450758e-15
          ]
        ],
        "unwrapped_reduced_polarization": [
          [
            2.4307067954614203e-15,
            -1.987346144003177e-15,
            0.06492632512262897
          ],
          [
            1.0201723201089655e-15,
            -2.8005345647460757e-15,
            -0.43286648699838765
          ],
          [
            2.213031152945848e-15,
            -5.863592258595701e-16,
            -0.9080093694555407
          ],
          [
            2.6863406256315065e-15,
            -1.5023116346397133e-15,
            -1.3183537816281774
          ],
          [
            2.3676141042599363e-15,
            -1.267422519126012e-15,
            -1.578334637536088
          ],
          [
            4.0373830198307526e-16,
            -1.8730679836368293e-15,
            -1.586998783794078
          ],
          [
            1.737882198086371e-15,
            -1.049516807797738e-15,
            -1.2891643447887051
          ],
          [
            4.3502883074963727e-17,
            -5.93843437873487e-16,
            -1.7241983717031986
          ],
          [
            2.388537116711477e-15,
            -1.8123307246008114e-15,
            -1.999999999999998
          ]
        ],
        "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,
            -1
          ],
          [
            0,
            0,
            -2
          ]
        ],
        "folded_reduced_polarization": [
          [
            2.4424906541753444e-15,
            -1.9984014443252818e-15,
            0.06492632512262897
          ],
          [
            9.992007221626409e-16,
            -2.7755575615628914e-15,
            -0.43286648699838765
          ],
          [
            2.220446049250313e-15,
            -6.106226635438361e-16,
            0.09199063054445933
          ],
          [
            2.6645352591003757e-15,
            -1.4988010832439613e-15,
            -0.3183537816281774
          ],
          [
            2.3314683517128287e-15,
            -1.27675647831893e-15,
            0.42166536246391195
          ],
          [
            4.440892098500626e-16,
            -1.887379141862766e-15,
            0.413001216205922
          ],
          [
            1.7763568394002505e-15,
            -1.0547118733938987e-15,
            -0.2891643447887051
          ],
          [
            0.0,
            -6.106226635438361e-16,
            0.27580162829680144
          ],
          [
            2.4424906541753444e-15,
            -1.8318679906315083e-15,
            1.9984014443252818e-15
          ]
        ]
      },
      "reflected": {
        "reached": true,
        "construction": "reflect_displacements_about_reconstructed_parent",
        "energies_eV": [
          -129.83165062539754,
          -130.22557055413228,
          -131.32825113210492,
          -133.00308135541098,
          -135.0686952292835,
          -137.27030836661726,
          -139.284718814322,
          -140.77263491438168,
          -141.38640382576557
        ],
        "cartesian_polarizations_e_A2": [
          [
            -1.2285235560559638e-17,
            -3.550474638299089e-17,
            8.00185350297928e-17
          ],
          [
            5.789114078270288e-17,
            -1.2605710497805448e-17,
            0.011891544400966037
          ],
          [
            4.3376064089824227e-17,
            -1.8761365305650998e-17,
            0.021168447272455027
          ],
          [
            9.102976031764042e-18,
            -6.975695083116799e-17,
            0.026058973948508764
          ],
          [
            -5.99630576116816e-18,
            -4.603359247606236e-17,
            0.02591670618880473
          ],
          [
            1.3884291004002717e-16,
            -2.3182731280677454e-17,
            0.021647746174217743
          ],
          [
            1.129069173568679e-16,
            -6.188841816374803e-17,
            0.014909773558285206
          ],
          [
            5.130401583349986e-17,
            -1.505726693432133e-17,
            0.007107791526409302
          ],
          [
            1.4786338202659728e-16,
            -1.3001813502832032e-17,
            -0.001066108828954611
          ]
        ],
        "raw_reduced_polarization": [
          [
            -3.9398126143117947e-16,
            -1.9093376264735042e-15,
            4.8731511081054075e-15
          ],
          [
            1.8565394663234515e-15,
            -6.778968958759387e-16,
            0.724198371703211
          ],
          [
            1.3910483329185876e-15,
            -1.00892935033765e-15,
            1.289164344788708
          ],
          [
            2.9192781547355334e-16,
            -3.751317344821755e-15,
            1.5869987837940835
          ],
          [
            -1.9229847861415063e-16,
            -2.4755470507571435e-15,
            1.5783346375360787
          ],
          [
            4.452621569093773e-15,
            -1.2466970089336268e-15,
            1.3183537816281732
          ],
          [
            3.620867463654753e-15,
            -3.3281715117272203e-15,
            0.9080093694555407
          ],
          [
            1.6452937165859854e-15,
            -8.097341690441682e-16,
            0.4328664869983862
          ],
          [
            4.74190352176409e-15,
            -6.991981146847793e-16,
            -0.06492632512263295
          ]
        ],
        "unwrapped_reduced_polarization": [
          [
            -3.9398126143117947e-16,
            -1.9093376264735042e-15,
            -1.9999999999999951
          ],
          [
            1.8565394663234515e-15,
            -6.778968958759387e-16,
            -2.2758016282967892
          ],
          [
            1.3910483329185876e-15,
            -1.00892935033765e-15,
            -2.7108356552112918
          ],
          [
            2.919278154735534e-16,
            -3.751317344821755e-15,
            -2.4130012162059167
          ],
          [
            -1.9229847861415063e-16,
            -2.4755470507571435e-15,
            -2.421665362463921
          ],
          [
            4.452621569093773e-15,
            -1.2466970089336268e-15,
            -2.681646218371827
          ],
          [
            3.620867463654753e-15,
            -3.32817151172722e-15,
            -3.0919906305444593
          ],
          [
            1.6452937165859856e-15,
            -8.097341690441683e-16,
            -3.5671335130016137
          ],
          [
            4.74190352176409e-15,
            -6.991981146847793e-16,
            -4.064926325122633
          ]
        ],
        "gauge_integer_shift": [
          0,
          0,
          -2
        ],
        "expected_opposite_endpoint_reduced_polarization": [
          2.346367437961534e-15,
          -1.6373153051984459e-15,
          -0.06492632512262478
        ],
        "actual_opposite_endpoint_branch_residual": 8.397403784196595e-15
      },
      "pnp_branch": {
        "construction": "incoming_path_concatenated_with_parent_reflection",
        "reduced_polarization": [
          [
            2.4307067954614203e-15,
            -1.987346144003177e-15,
            0.06492632512262897
          ],
          [
            1.0201723201089655e-15,
            -2.8005345647460757e-15,
            -0.43286648699838765
          ],
          [
            2.213031152945848e-15,
            -5.8635922585957e-16,
            -0.9080093694555407
          ],
          [
            2.6863406256315065e-15,
            -1.5023116346397133e-15,
            -1.3183537816281774
          ],
          [
            2.3676141042599363e-15,
            -1.267422519126012e-15,
            -1.578334637536088
          ],
          [
            4.037383019830754e-16,
            -1.8730679836368293e-15,
            -1.586998783794078
          ],
          [
            1.737882198086371e-15,
            -1.049516807797738e-15,
            -1.2891643447887051
          ],
          [
            4.350288307496381e-17,
            -5.93843437873487e-16,
            -0.7241983717031986
          ],
          [
            2.3885371167114772e-15,
            -1.8123307246008114e-15,
            2.096057353450758e-15
          ],
          [
            1.8565394663234515e-15,
            -6.778968958759387e-16,
            0.724198371703211
          ],
          [
            1.3910483329185876e-15,
            -1.00892935033765e-15,
            1.289164344788708
          ],
          [
            2.9192781547355334e-16,
            -3.751317344821755e-15,
            1.5869987837940835
          ],
          [
            -1.9229847861415063e-16,
            -2.4755470507571435e-15,
            1.5783346375360787
          ],
          [
            4.452621569093773e-15,
            -1.2466970089336268e-15,
            1.3183537816281732
          ],
          [
            3.620867463654753e-15,
            -3.3281715117272203e-15,
            0.9080093694555407
          ],
          [
            1.6452937165859854e-15,
            -8.097341690441682e-16,
            0.4328664869983862
          ],
          [
            4.74190352176409e-15,
            -6.991981146847793e-16,
            -0.06492632512263295
          ]
        ],
        "unwrapped_reduced_polarization": [
          [
            2.4307067954614203e-15,
            -1.987346144003177e-15,
            0.06492632512262897
          ],
          [
            1.0201723201089655e-15,
            -2.8005345647460757e-15,
            -0.43286648699838765
          ],
          [
            2.213031152945848e-15,
            -5.863592258595701e-16,
            -0.9080093694555407
          ],
          [
            2.6863406256315065e-15,
            -1.5023116346397133e-15,
            -1.3183537816281774
          ],
          [
            2.3676141042599363e-15,
            -1.267422519126012e-15,
            -1.578334637536088
          ],
          [
            4.0373830198307526e-16,
            -1.8730679836368293e-15,
            -1.586998783794078
          ],
          [
            1.737882198086371e-15,
            -1.049516807797738e-15,
            -1.2891643447887051
          ],
          [
            4.3502883074963727e-17,
            -5.93843437873487e-16,
            -1.7241983717031986
          ],
          [
            2.388537116711477e-15,
            -1.8123307246008114e-15,
            -1.999999999999998
          ],
          [
            1.8565394663234515e-15,
            -6.778968958759387e-16,
            -2.2758016282967892
          ],
          [
            1.3910483329185876e-15,
            -1.00892935033765e-15,
            -2.7108356552112918
          ],
          [
            2.919278154735534e-16,
            -3.751317344821755e-15,
            -2.4130012162059167
          ],
          [
            -1.9229847861415063e-16,
            -2.4755470507571435e-15,
            -2.421665362463921
          ],
          [
            4.452621569093773e-15,
            -1.2466970089336268e-15,
            -2.681646218371827
          ],
          [
            3.620867463654753e-15,
            -3.32817151172722e-15,
            -3.0919906305444593
          ],
          [
            1.6452937165859856e-15,
            -8.097341690441683e-16,
            -3.5671335130016137
          ],
          [
            4.74190352176409e-15,
            -6.991981146847793e-16,
            -4.064926325122633
          ]
        ],
        "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,
            -1
          ],
          [
            0,
            0,
            -2
          ],
          [
            0,
            0,
            -3
          ],
          [
            0,
            0,
            -4
          ],
          [
            0,
            0,
            -4
          ],
          [
            0,
            0,
            -4
          ],
          [
            0,
            0,
            -4
          ],
          [
            0,
            0,
            -4
          ],
          [
            0,
            0,
            -4
          ],
          [
            0,
            0,
            -4
          ]
        ],
        "folded_reduced_polarization": [
          [
            2.4424906541753444e-15,
            -1.9984014443252818e-15,
            0.06492632512262897
          ],
          [
            9.992007221626409e-16,
            -2.7755575615628914e-15,
            -0.43286648699838765
          ],
          [
            2.220446049250313e-15,
            -6.106226635438361e-16,
            0.09199063054445933
          ],
          [
            2.6645352591003757e-15,
            -1.4988010832439613e-15,
            -0.3183537816281774
          ],
          [
            2.3314683517128287e-15,
            -1.27675647831893e-15,
            0.42166536246391195
          ],
          [
            4.440892098500626e-16,
            -1.887379141862766e-15,
            0.413001216205922
          ],
          [
            1.7763568394002505e-15,
            -1.0547118733938987e-15,
            -0.2891643447887051
          ],
          [
            0.0,
            -6.106226635438361e-16,
            0.27580162829680144
          ],
          [
            2.4424906541753444e-15,
            -1.8318679906315083e-15,
            1.9984014443252818e-15
          ],
          [
            1.887379141862766e-15,
            -6.661338147750939e-16,
            -0.2758016282967892
          ],
          [
            1.4432899320127035e-15,
            -9.992007221626409e-16,
            0.2891643447887082
          ],
          [
            3.3306690738754696e-16,
            -3.774758283725532e-15,
            -0.4130012162059167
          ],
          [
            -1.6653345369377348e-16,
            -2.4980018054066022e-15,
            -0.42166536246392106
          ],
          [
            4.440892098500626e-15,
            -1.2212453270876722e-15,
            0.31835378162817296
          ],
          [
            3.6637359812630166e-15,
            -3.3306690738754696e-15,
            -0.09199063054445933
          ],
          [
            1.6653345369377348e-15,
            -8.326672684688674e-16,
            0.43286648699838626
          ],
          [
            4.773959005888173e-15,
            -7.216449660063518e-16,
            -0.06492632512263263
          ]
        ]
      },
      "incoming_structure_ids": [
        "incoming_00_000",
        "incoming_00_001",
        "incoming_00_002",
        "incoming_00_003",
        "incoming_00_004",
        "incoming_00_005",
        "incoming_00_006",
        "incoming_00_007",
        "incoming_00_008"
      ],
      "reflected_structure_ids": [
        "reflected_00_001",
        "reflected_00_002",
        "reflected_00_003",
        "reflected_00_004",
        "reflected_00_005",
        "reflected_00_006",
        "reflected_00_007",
        "reflected_00_008"
      ],
      "positive_extension_structure_ids": [
        "extension_plus_00_000",
        "extension_plus_00_001",
        "extension_plus_00_002",
        "extension_plus_00_003"
      ],
      "negative_extension_structure_ids": [
        "extension_minus_00_000",
        "extension_minus_00_001",
        "extension_minus_00_002",
        "extension_minus_00_003"
      ],
      "extension": {
        "enabled": true,
        "fraction_beyond_polar_endpoint": 0.35,
        "images_per_side": 4,
        "construction": "continue fractional atomic displacements and symmetric log strain beyond +P; reflect these structures about N for the -P side",
        "positive_path_coordinates": [
          1.35,
          1.2625,
          1.175,
          1.0875
        ],
        "negative_path_coordinates": [
          -1.0875,
          -1.175,
          -1.2625,
          -1.35
        ]
      },
      "branch_coordinates": [
        1.35,
        1.2625,
        1.175,
        1.0875,
        1.0,
        0.875,
        0.75,
        0.625,
        0.5,
        0.375,
        0.25,
        0.125,
        0.0,
        -0.125,
        -0.25,
        -0.375,
        -0.5,
        -0.625,
        -0.75,
        -0.875,
        -1.0,
        -1.0875,
        -1.175,
        -1.2625,
        -1.35
      ],
      "parent": {
        "candidate_id": "inversion_parent_endpoint_00",
        "source": "same_species_inversion_center_projection_from_endpoint",
        "spacegroup": "Cmcm",
        "spacegroup_number": 63,
        "pointgroup": "mmm",
        "has_inversion": true,
        "is_polar_point_group": false,
        "nonpolar_parent_hypothesis": true,
        "symmetry_tolerance_A": null,
        "target_reduced_polarization": [
          0.0,
          0.0,
          0.0
        ],
        "formal_class": [
          0.0,
          0.0,
          0.0
        ],
        "target_residual": 9.927371598046309e-15,
        "parent_symmetrization_rmsd_A": 0.4409445565951117,
        "parent_cell_rmsd_A": 0.0,
        "energy_eV": -129.8316506253975,
        "reduced_polarization": [
          -1.7311010643618293e-15,
          -2.3071522804440123e-15,
          9.499107553107495e-15
        ],
        "cartesian_polarization_e_A2": [
          -5.39796849158916e-17,
          -4.2902237639027887e-17,
          1.559780629879988e-16
        ],
        "ranking_score": 0.4409445565951316
      }
    }
  ],
  "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": 51,
      "full_response": 17,
      "energy_polarization": 34
    },
    "model_evaluations_for_recovery_and_path_properties": {
      "total": 76,
      "full_response": 42,
      "energy_polarization": 34
    },
    "elapsed_seconds": 546.1233664129977
  }
}