{
  "schema": "ferrofinder.endpoint_parent_recovery.v4_variable_cell",
  "status": "complete",
  "input_atom_count": 116,
  "input_formula": "Ag4Al44O68",
  "input_spacegroup": "Ama2",
  "input_pointgroup": "mm2",
  "input_is_polar_point_group": true,
  "input_energy_eV": -812.8027880005689,
  "input_cartesian_polarization_e_A2": [
    -1.0074779871992175e-07,
    -4.212728462001122e-09,
    0.0014789230598400436
  ],
  "input_reduced_polarization": [
    -5.581459754033081e-06,
    -5.437950341829949e-07,
    0.3303460789987775
  ],
  "input_formal_targets": [
    {
      "orbit_id": 0,
      "representative_formal_class": [
        0.0,
        0.0,
        0.5
      ],
      "target_reduced_polarization": [
        0.0,
        0.0,
        0.5
      ]
    },
    {
      "orbit_id": 1,
      "representative_formal_class": [
        0.0,
        0.0,
        0.0
      ],
      "target_reduced_polarization": [
        0.0,
        0.0,
        0.0
      ]
    },
    {
      "orbit_id": 2,
      "representative_formal_class": [
        0.5,
        0.0,
        0.5
      ],
      "target_reduced_polarization": [
        -0.5,
        0.0,
        0.5
      ]
    },
    {
      "orbit_id": 3,
      "representative_formal_class": [
        0.0,
        0.5,
        0.5
      ],
      "target_reduced_polarization": [
        0.0,
        -0.5,
        0.5
      ]
    },
    {
      "orbit_id": 4,
      "representative_formal_class": [
        0.5,
        0.0,
        0.0
      ],
      "target_reduced_polarization": [
        -0.5,
        0.0,
        0.0
      ]
    },
    {
      "orbit_id": 5,
      "representative_formal_class": [
        0.0,
        0.5,
        0.0
      ],
      "target_reduced_polarization": [
        0.0,
        -0.5,
        0.0
      ]
    },
    {
      "orbit_id": 6,
      "representative_formal_class": [
        0.5,
        0.5,
        0.5
      ],
      "target_reduced_polarization": [
        -0.5,
        -0.5,
        0.5
      ]
    },
    {
      "orbit_id": 7,
      "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": "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": 6.8340852005413154e-15,
      "parent_symmetrization_rmsd_A": 0.061283688002926044,
      "parent_cell_rmsd_A": 0.0,
      "energy_eV": -812.8023804749596,
      "reduced_polarization": [
        3.8961216579154386e-15,
        -5.0092202843039964e-15,
        2.5362706279688437e-15
      ],
      "cartesian_polarization_e_A2": [
        7.032670625213398e-17,
        -3.880595359945768e-17,
        1.1354604628777786e-17
      ],
      "ranking_score": 0.061283688002939714
    },
    {
      "candidate_id": "inversion_parent_endpoint_01",
      "source": "same_species_inversion_center_projection_from_endpoint",
      "spacegroup": "Pmmn",
      "spacegroup_number": 59,
      "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": 7.32205099738144e-15,
      "parent_symmetrization_rmsd_A": 0.5271792423272293,
      "parent_cell_rmsd_A": 0.0,
      "energy_eV": -743.4809683314127,
      "reduced_polarization": [
        1.039534270228928e-15,
        -3.3421968465713083e-15,
        -6.431292214480924e-15
      ],
      "cartesian_polarization_e_A2": [
        1.8764049914327136e-17,
        -2.5891681416905517e-17,
        -2.879218784552541e-17
      ],
      "ranking_score": 0.527179242327244
    },
    {
      "candidate_id": "inversion_parent_endpoint_02",
      "source": "same_species_inversion_center_projection_from_endpoint",
      "spacegroup": "P2_1/m",
      "spacegroup_number": 11,
      "pointgroup": "2/m",
      "has_inversion": true,
      "is_polar_point_group": false,
      "nonpolar_parent_hypothesis": true,
      "symmetry_tolerance_A": null,
      "target_reduced_polarization": [
        0.0,
        0.0,
        0.0
      ],
      "formal_class": [
        0.0,
        0.0,
        0.0
      ],
      "target_residual": 7.826476215236031e-15,
      "parent_symmetrization_rmsd_A": 0.5383961857379195,
      "parent_cell_rmsd_A": 0.0,
      "energy_eV": -749.665924946886,
      "reduced_polarization": [
        4.747819755279623e-16,
        -1.428725369526666e-15,
        -7.680303108721685e-15
      ],
      "cartesian_polarization_e_A2": [
        8.570023078957858e-18,
        -1.1068199689669533e-17,
        -3.4383872236278933e-17
      ],
      "ranking_score": 0.5383961857379351
    },
    {
      "candidate_id": "bec_projection_00",
      "source": "MACEField_BEC_backprojection",
      "spacegroup": "Ama2",
      "spacegroup_number": 40,
      "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": 3.4371487587907976e-05,
      "parent_symmetrization_rmsd_A": 0.0052432852690628366,
      "parent_cell_rmsd_A": 0.0025185610443496293,
      "energy_eV": -812.7931821646598,
      "reduced_polarization": [
        2.0381974652687498e-09,
        -4.3526968272508e-10,
        0.5000343714875247
      ],
      "cartesian_polarization_e_A2": [
        -5.662478624975869e-12,
        1.2343007105284224e-11,
        0.002239214437001474
      ],
      "ranking_score": 0.5059416685053261
    },
    {
      "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,
        0.5
      ],
      "formal_class": [
        0.0,
        0.0,
        0.5
      ],
      "target_residual": 0.4999999999999969,
      "parent_symmetrization_rmsd_A": 0.06128374237448081,
      "parent_cell_rmsd_A": 0.0025185610443496293,
      "energy_eV": -812.8049552802373,
      "reduced_polarization": [
        -1.8428562707604895e-16,
        -1.7093108312783396e-15,
        -3.0935772009696893e-15
      ],
      "cartesian_polarization_e_A2": [
        -3.32771526341194e-18,
        -1.3245993428499157e-17,
        -1.3853413165807033e-17
      ],
      "ranking_score": 1.061913382635562
    },
    {
      "candidate_id": "inversion_parent_bec_00_01",
      "source": "same_species_inversion_center_projection_after_BEC",
      "spacegroup": "P2_1/m",
      "spacegroup_number": 11,
      "pointgroup": "2/m",
      "has_inversion": true,
      "is_polar_point_group": false,
      "nonpolar_parent_hypothesis": true,
      "symmetry_tolerance_A": null,
      "target_reduced_polarization": [
        0.0,
        0.0,
        0.5
      ],
      "formal_class": [
        0.0,
        0.0,
        0.5
      ],
      "target_residual": 0.4999999999999982,
      "parent_symmetrization_rmsd_A": 0.5383962170427486,
      "parent_cell_rmsd_A": 0.0025185610443496293,
      "energy_eV": -749.5912166158754,
      "reduced_polarization": [
        3.1930551403512675e-15,
        7.921732536076135e-15,
        -1.7212873618263494e-15
      ],
      "cartesian_polarization_e_A2": [
        5.765820899728312e-17,
        6.138802511171743e-17,
        -7.708133804191194e-18
      ],
      "ranking_score": 1.5390258573038325
    },
    {
      "candidate_id": "bec_projection_01",
      "source": "MACEField_BEC_backprojection",
      "spacegroup": "Ama2",
      "spacegroup_number": 40,
      "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": 0.0001751731546318666,
      "parent_symmetrization_rmsd_A": 0.010203270825232027,
      "parent_cell_rmsd_A": 0.004905660205582144,
      "energy_eV": -812.7430734741471,
      "reduced_polarization": [
        -6.716828218592767e-09,
        -2.4871810649794493e-09,
        0.00017517315448543474
      ],
      "cartesian_polarization_e_A2": [
        -1.2118650603944386e-10,
        -1.9267431434487343e-11,
        7.838112198585984e-07
      ],
      "ranking_score": 0.5117800321858913
    },
    {
      "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,
        0.5
      ],
      "formal_class": [
        0.5,
        0.0,
        0.5
      ],
      "target_residual": 8.976361537906771e-06,
      "parent_symmetrization_rmsd_A": 0.060519519835805655,
      "parent_cell_rmsd_A": 0.020864468942439686,
      "energy_eV": -810.3351080488129,
      "reduced_polarization": [
        -0.4999989381978065,
        2.6854609724668666e-11,
        0.5000089133407071
      ],
      "cartesian_polarization_e_A2": [
        -0.009022962691909846,
        -1.183359696689911e-10,
        0.002216462270056563
      ],
      "ranking_score": 0.5657535897944914
    },
    {
      "candidate_id": "bec_projection_03",
      "source": "MACEField_BEC_backprojection",
      "spacegroup": "Pm",
      "spacegroup_number": 6,
      "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": 0.0001744724335011622,
      "parent_symmetrization_rmsd_A": 0.027206847029202886,
      "parent_cell_rmsd_A": 0.0025961557603501008,
      "energy_eV": -812.4396286754145,
      "reduced_polarization": [
        -1.3055750152999092e-08,
        -0.4998292355135401,
        0.49996422123471324
      ],
      "cartesian_polarization_e_A2": [
        -1.0656041091809612e-10,
        -0.0038729383714456666,
        0.002238212592763346
      ],
      "ranking_score": 0.5282048308362928
    },
    {
      "candidate_id": "bec_projection_04",
      "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": 1.6800694951031436e-05,
      "parent_symmetrization_rmsd_A": 0.06119930040989421,
      "parent_cell_rmsd_A": 0.021421030860329603,
      "energy_eV": -810.2936592641263,
      "reduced_polarization": [
        -0.499997686112162,
        -1.104184554852382e-11,
        1.6640591152679664e-05
      ],
      "cartesian_polarization_e_A2": [
        -0.009018281446879191,
        -1.298014318804569e-10,
        -2.2558664860739363e-05
      ],
      "ranking_score": 0.5665881595148787
    },
    {
      "candidate_id": "bec_projection_05",
      "source": "MACEField_BEC_backprojection",
      "spacegroup": "Pm",
      "spacegroup_number": 6,
      "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": 0.0007219732685995607,
      "parent_symmetrization_rmsd_A": 0.028562291062890762,
      "parent_cell_rmsd_A": 0.004946258425514057,
      "energy_eV": -812.391814853509,
      "reduced_polarization": [
        -2.2087827113993575e-08,
        -0.49940537359925113,
        0.0004094689776001484
      ],
      "cartesian_polarization_e_A2": [
        -2.3006280421003752e-10,
        -0.0038665003269601,
        1.1457260391088238e-06
      ],
      "ranking_score": 0.5312428022064684
    },
    {
      "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,
        0.5
      ],
      "formal_class": [
        0.5,
        0.5,
        0.5
      ],
      "target_residual": 1.4001157257927363e-05,
      "parent_symmetrization_rmsd_A": 0.06625542893612493,
      "parent_cell_rmsd_A": 0.020898112195414566,
      "energy_eV": -809.9679554457375,
      "reduced_polarization": [
        -0.49999885837581287,
        -0.4999992886109702,
        0.5000139363920878
      ],
      "cartesian_polarization_e_A2": [
        -0.009022956613562514,
        -0.003874213139934695,
        0.002215767704167692
      ],
      "ranking_score": 0.5715079592994944
    },
    {
      "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,
        0.0
      ],
      "formal_class": [
        0.5,
        0.5,
        0.0
      ],
      "target_residual": 2.233837937931401e-05,
      "parent_symmetrization_rmsd_A": 0.06687986850054524,
      "parent_cell_rmsd_A": 0.021455266760776522,
      "energy_eV": -809.9281810021344,
      "reduced_polarization": [
        -0.4999972835730917,
        -0.4999986878662531,
        2.2133741734653176e-05
      ],
      "cartesian_polarization_e_A2": [
        -0.009018269433387396,
        -0.0038710346806137504,
        -2.325148916743649e-05
      ],
      "ranking_score": 0.5722883619494981
    }
  ],
  "formal_branches": [
    {
      "orbit_id": 0,
      "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": [
              -5.581459754033081e-06,
              -5.437950341829949e-07,
              0.3303460789987775
            ],
            "branch_aligned_reduced_polarization": [
              -5.581459754033081e-06,
              -5.437950341829949e-07,
              0.3303460789987775
            ],
            "target_residual": 0.1696539210939065,
            "energy_eV": -812.8027880005689,
            "max_atomic_step_A": 0.0043108695958438475,
            "max_log_strain_component": 0.00021047369996129764,
            "step_scale": 1.0,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 1.0025154814562427,
            "cell_principal_stretches": [
              0.9998990357952989,
              0.9998260483404949,
              0.9997895484434415
            ],
            "cell_volume_ratio": 0.9995147079949023,
            "cell_rmsd_from_input_A": 0.0025185610443496293
          },
          {
            "iteration": 1,
            "reduced_polarization": [
              2.0381974652687498e-09,
              -4.3526968272508e-10,
              0.5000343714875247
            ],
            "branch_aligned_reduced_polarization": [
              2.0381974652687498e-09,
              -4.3526968272508e-10,
              0.5000343714875247
            ],
            "target_residual": 3.4371487587907976e-05,
            "energy_eV": -812.7931821646598
          }
        ],
        "iterations": 1
      },
      "parent": {
        "candidate_id": "bec_projection_00",
        "source": "MACEField_BEC_backprojection",
        "spacegroup": "Ama2",
        "spacegroup_number": 40,
        "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": 3.4371487587907976e-05,
        "parent_symmetrization_rmsd_A": 0.0052432852690628366,
        "parent_cell_rmsd_A": 0.0025185610443496293,
        "energy_eV": -812.7931821646598,
        "reduced_polarization": [
          2.0381974652687498e-09,
          -4.3526968272508e-10,
          0.5000343714875247
        ],
        "cartesian_polarization_e_A2": [
          -5.662478624975869e-12,
          1.2343007105284224e-11,
          0.002239214437001474
        ],
        "ranking_score": 0.5059416685053261
      },
      "branch_status": "awaiting_branch_sampling"
    },
    {
      "orbit_id": 1,
      "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": [
              -5.581459754033081e-06,
              -5.437950341829949e-07,
              0.3303460789987775
            ],
            "branch_aligned_reduced_polarization": [
              -5.581459754033081e-06,
              -5.437950341829949e-07,
              0.3303460789987775
            ],
            "target_residual": 0.3303460790463767,
            "energy_eV": -812.8027880005689,
            "max_atomic_step_A": 0.008393976423296956,
            "max_log_strain_component": 0.000409829381939294,
            "step_scale": 1.0,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 1.0025154814562427,
            "cell_principal_stretches": [
              1.0004099133859699,
              1.0003388013758567,
              1.0001966243482843
            ],
            "cell_volume_ratio": 1.0009456252321893,
            "cell_rmsd_from_input_A": 0.004905660205582144
          },
          {
            "iteration": 1,
            "reduced_polarization": [
              -6.716828218592767e-09,
              -2.4871810649794493e-09,
              0.00017517315448543474
            ],
            "branch_aligned_reduced_polarization": [
              -6.716828218592767e-09,
              -2.4871810649794493e-09,
              0.00017517315448543474
            ],
            "target_residual": 0.0001751731546318666,
            "energy_eV": -812.7430734741471
          }
        ],
        "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": 6.8340852005413154e-15,
        "parent_symmetrization_rmsd_A": 0.061283688002926044,
        "parent_cell_rmsd_A": 0.0,
        "energy_eV": -812.8023804749596,
        "reduced_polarization": [
          3.8961216579154386e-15,
          -5.0092202843039964e-15,
          2.5362706279688437e-15
        ],
        "cartesian_polarization_e_A2": [
          7.032670625213398e-17,
          -3.880595359945768e-17,
          1.1354604628777786e-17
        ],
        "ranking_score": 0.061283688002939714
      },
      "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": [
          -812.8027880005689,
          -812.8030805837753,
          -812.8031649608167,
          -812.8031593601161,
          -812.8030688511624,
          -812.8028830998145,
          -812.8026480851474,
          -812.802454540929,
          -812.8023804749596
        ],
        "cartesian_polarizations_e_A2": [
          [
            -1.0074779873390036e-07,
            -4.212728470101881e-09,
            0.0014789230598400598
          ],
          [
            -8.811612771390523e-08,
            -3.745511852658549e-09,
            0.0013069129368959787
          ],
          [
            -7.549535379313206e-08,
            -3.265728569904672e-09,
            0.001129572965736717
          ],
          [
            -6.288582832850821e-08,
            -2.7678682947863924e-09,
            0.0009477532764926205
          ],
          [
            -5.028864604695433e-08,
            -2.248794222119357e-09,
            0.0007623300777440624
          ],
          [
            -3.770376233791896e-08,
            -1.7085422039970604e-09,
            0.0005741358170946907
          ],
          [
            -2.5129467629155966e-08,
            -1.15007237767687e-09,
            0.0003839058294156306
          ],
          [
            -1.2562771530151224e-08,
            -5.784565458858471e-10,
            0.00019230443701251918
          ],
          [
            1.6833660173434208e-17,
            -3.540753315902839e-17,
            -2.8449558913008034e-18
          ]
        ],
        "raw_reduced_polarization": [
          [
            -5.5814597548075e-06,
            -5.437950352286716e-07,
            0.3303460789987811
          ],
          [
            -4.881661205160901e-06,
            -4.834849348400101e-07,
            0.29192429005945614
          ],
          [
            -4.182466358240472e-06,
            -4.2155268143252594e-07,
            0.2523119764016012
          ],
          [
            -3.483894679330564e-06,
            -3.572869810038549e-07,
            0.21169903103779047
          ],
          [
            -2.7860068166470847e-06,
            -2.9028292279418014e-07,
            0.17028117210696667
          ],
          [
            -2.088800298751444e-06,
            -2.2054513472827372e-07,
            0.12824434288725192
          ],
          [
            -1.3921804148032116e-06,
            -1.4845572259709178e-07,
            0.08575279464906296
          ],
          [
            -6.959814962268399e-07,
            -7.466937401276246e-08,
            0.04295491663239331
          ],
          [
            9.32590071097144e-16,
            -4.570539230863021e-15,
            -6.354759413362186e-16
          ]
        ],
        "unwrapped_reduced_polarization": [
          [
            -5.5814597548075e-06,
            -5.437950352286716e-07,
            0.3303460789987811
          ],
          [
            -4.881661205160901e-06,
            -4.834849348400101e-07,
            0.29192429005945614
          ],
          [
            -4.182466358240472e-06,
            -4.2155268143252594e-07,
            0.2523119764016012
          ],
          [
            -3.483894679330564e-06,
            -3.572869810038549e-07,
            0.21169903103779047
          ],
          [
            -2.7860068166470847e-06,
            -2.9028292279418014e-07,
            0.17028117210696667
          ],
          [
            -2.088800298751444e-06,
            -2.2054513472827372e-07,
            0.12824434288725192
          ],
          [
            -1.3921804148032116e-06,
            -1.4845572259709178e-07,
            0.08575279464906296
          ],
          [
            -6.959814962268399e-07,
            -7.466937401276246e-08,
            0.04295491663239331
          ],
          [
            9.325900511905627e-16,
            -4.570539226105165e-15,
            -6.38378239159465e-16
          ]
        ],
        "berry_integer_shifts": [
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ]
        ],
        "folded_reduced_polarization": [
          [
            -5.581459754822049e-06,
            -5.437950352238374e-07,
            0.3303460789987811
          ],
          [
            -4.881661205158316e-06,
            -4.834849348656078e-07,
            0.2919242900594561
          ],
          [
            -4.182466358249037e-06,
            -4.215526814288495e-07,
            0.2523119764016012
          ],
          [
            -3.483894679356947e-06,
            -3.5728698100090384e-07,
            0.21169903103779042
          ],
          [
            -2.7860068166352114e-06,
            -2.902829228101922e-07,
            0.1702811721069667
          ],
          [
            -2.088800298727378e-06,
            -2.205451347103704e-07,
            0.12824434288725195
          ],
          [
            -1.3921804147831729e-06,
            -1.4845572260391293e-07,
            0.08575279464906294
          ],
          [
            -6.959814962126387e-07,
            -7.466937401723328e-08,
            0.04295491663239326
          ],
          [
            8.881784197001252e-16,
            -4.551914400963142e-15,
            -6.661338147750939e-16
          ]
        ]
      },
      "reflected": {
        "reached": true,
        "construction": "reflect_displacements_about_reconstructed_parent",
        "energies_eV": [
          -812.8023804749596,
          -812.8024545409288,
          -812.8026480851477,
          -812.8028830998147,
          -812.8030688511627,
          -812.8031593601157,
          -812.8031649608167,
          -812.8030805837748,
          -812.802788000569
        ],
        "cartesian_polarizations_e_A2": [
          [
            1.9503744644904716e-17,
            -3.115401743007429e-17,
            2.9982891725337437e-19
          ],
          [
            1.2562771631210623e-08,
            5.78456453306341e-10,
            -0.00019230443701260958
          ],
          [
            2.5129467658752445e-08,
            1.1500723336744626e-09,
            -0.00038390582941563863
          ],
          [
            3.7703762379477565e-08,
            1.7085422006713847e-09,
            -0.00057413581709468
          ],
          [
            5.0288646124021235e-08,
            2.2487941393658977e-09,
            -0.0007623300777440847
          ],
          [
            6.288582837774151e-08,
            2.7678682927577713e-09,
            -0.0009477532764925916
          ],
          [
            7.549535386369403e-08,
            3.2657285538733514e-09,
            -0.0011295729657367698
          ],
          [
            8.811612782331591e-08,
            3.745511812915148e-09,
            -0.0013069129368959874
          ],
          [
            1.0074779874463448e-07,
            4.212728405479735e-09,
            -0.0014789230598400485
          ]
        ],
        "raw_reduced_polarization": [
          [
            1.0805135910820468e-15,
            -4.021479220922156e-15,
            6.69725896327655e-17
          ],
          [
            6.959815018255624e-07,
            7.466936206224723e-08,
            -0.04295491663241349
          ],
          [
            1.392180416442866e-06,
            1.4845571691709344e-07,
            -0.08575279464906474
          ],
          [
            2.088800301053804e-06,
            2.2054513429898283e-07,
            -0.12824434288724956
          ],
          [
            2.786006820916615e-06,
            2.902829121120485e-07,
            -0.17028117210697166
          ],
          [
            3.4838946820581045e-06,
            3.572869807419928e-07,
            -0.21169903103778398
          ],
          [
            4.182466362149628e-06,
            4.2155267936314207e-07,
            -0.25231197640161296
          ],
          [
            4.881661211222286e-06,
            4.834849297097804e-07,
            -0.2919242900594581
          ],
          [
            5.581459755402174e-06,
            5.43795026886999e-07,
            -0.33034607899877855
          ]
        ],
        "unwrapped_reduced_polarization": [
          [
            1.0805135910820468e-15,
            -4.021479220922156e-15,
            6.69725896327655e-17
          ],
          [
            6.959815018255624e-07,
            7.466936206224723e-08,
            -0.04295491663241349
          ],
          [
            1.392180416442866e-06,
            1.4845571691709344e-07,
            -0.08575279464906474
          ],
          [
            2.088800301053804e-06,
            2.2054513429898283e-07,
            -0.12824434288724956
          ],
          [
            2.786006820916615e-06,
            2.902829121120485e-07,
            -0.17028117210697166
          ],
          [
            3.4838946820581045e-06,
            3.572869807419928e-07,
            -0.21169903103778398
          ],
          [
            4.182466362149628e-06,
            4.2155267936314207e-07,
            -0.25231197640161296
          ],
          [
            4.881661211222286e-06,
            4.834849297097804e-07,
            -0.2919242900594581
          ],
          [
            5.581459755402174e-06,
            5.43795026886999e-07,
            -0.33034607899877855
          ]
        ],
        "gauge_integer_shift": [
          0,
          0,
          0
        ],
        "expected_opposite_endpoint_reduced_polarization": [
          5.581459756672681e-06,
          5.437950260875932e-07,
          -0.3303460789987824
        ],
        "actual_opposite_endpoint_branch_residual": 4.113903467213528e-15
      },
      "pnp_branch": {
        "construction": "incoming_path_concatenated_with_parent_reflection",
        "reduced_polarization": [
          [
            -5.5814597548075e-06,
            -5.437950352286716e-07,
            0.3303460789987811
          ],
          [
            -4.881661205160901e-06,
            -4.834849348400101e-07,
            0.29192429005945614
          ],
          [
            -4.182466358240472e-06,
            -4.2155268143252594e-07,
            0.2523119764016012
          ],
          [
            -3.483894679330564e-06,
            -3.572869810038549e-07,
            0.21169903103779047
          ],
          [
            -2.7860068166470847e-06,
            -2.9028292279418014e-07,
            0.17028117210696667
          ],
          [
            -2.088800298751444e-06,
            -2.2054513472827372e-07,
            0.12824434288725192
          ],
          [
            -1.3921804148032116e-06,
            -1.4845572259709178e-07,
            0.08575279464906296
          ],
          [
            -6.959814962268399e-07,
            -7.466937401276246e-08,
            0.04295491663239331
          ],
          [
            9.32590071097144e-16,
            -4.570539230863021e-15,
            -6.354759413362186e-16
          ],
          [
            6.959815018255624e-07,
            7.466936206224723e-08,
            -0.04295491663241349
          ],
          [
            1.392180416442866e-06,
            1.4845571691709344e-07,
            -0.08575279464906474
          ],
          [
            2.088800301053804e-06,
            2.2054513429898283e-07,
            -0.12824434288724956
          ],
          [
            2.786006820916615e-06,
            2.902829121120485e-07,
            -0.17028117210697166
          ],
          [
            3.4838946820581045e-06,
            3.572869807419928e-07,
            -0.21169903103778398
          ],
          [
            4.182466362149628e-06,
            4.2155267936314207e-07,
            -0.25231197640161296
          ],
          [
            4.881661211222286e-06,
            4.834849297097804e-07,
            -0.2919242900594581
          ],
          [
            5.581459755402174e-06,
            5.43795026886999e-07,
            -0.33034607899877855
          ]
        ],
        "unwrapped_reduced_polarization": [
          [
            -5.5814597548075e-06,
            -5.437950352286716e-07,
            0.3303460789987811
          ],
          [
            -4.881661205160901e-06,
            -4.834849348400101e-07,
            0.29192429005945614
          ],
          [
            -4.182466358240472e-06,
            -4.2155268143252594e-07,
            0.2523119764016012
          ],
          [
            -3.483894679330564e-06,
            -3.572869810038549e-07,
            0.21169903103779047
          ],
          [
            -2.7860068166470847e-06,
            -2.9028292279418014e-07,
            0.17028117210696667
          ],
          [
            -2.088800298751444e-06,
            -2.2054513472827372e-07,
            0.12824434288725192
          ],
          [
            -1.3921804148032116e-06,
            -1.4845572259709178e-07,
            0.08575279464906296
          ],
          [
            -6.959814962268399e-07,
            -7.466937401276246e-08,
            0.04295491663239331
          ],
          [
            9.325900511905627e-16,
            -4.570539226105165e-15,
            -6.38378239159465e-16
          ],
          [
            6.959815018255624e-07,
            7.466936206224723e-08,
            -0.04295491663241349
          ],
          [
            1.392180416442866e-06,
            1.4845571691709344e-07,
            -0.08575279464906474
          ],
          [
            2.088800301053804e-06,
            2.2054513429898283e-07,
            -0.12824434288724956
          ],
          [
            2.786006820916615e-06,
            2.902829121120485e-07,
            -0.17028117210697166
          ],
          [
            3.4838946820581045e-06,
            3.572869807419928e-07,
            -0.21169903103778398
          ],
          [
            4.182466362149628e-06,
            4.2155267936314207e-07,
            -0.25231197640161296
          ],
          [
            4.881661211222286e-06,
            4.834849297097804e-07,
            -0.2919242900594581
          ],
          [
            5.581459755402174e-06,
            5.43795026886999e-07,
            -0.33034607899877855
          ]
        ],
        "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": [
          [
            -5.581459754822049e-06,
            -5.437950352238374e-07,
            0.3303460789987811
          ],
          [
            -4.881661205158316e-06,
            -4.834849348656078e-07,
            0.2919242900594561
          ],
          [
            -4.182466358249037e-06,
            -4.215526814288495e-07,
            0.2523119764016012
          ],
          [
            -3.483894679356947e-06,
            -3.5728698100090384e-07,
            0.21169903103779042
          ],
          [
            -2.7860068166352114e-06,
            -2.902829228101922e-07,
            0.1702811721069667
          ],
          [
            -2.088800298727378e-06,
            -2.205451347103704e-07,
            0.12824434288725195
          ],
          [
            -1.3921804147831729e-06,
            -1.4845572260391293e-07,
            0.08575279464906294
          ],
          [
            -6.959814962126387e-07,
            -7.466937401723328e-08,
            0.04295491663239326
          ],
          [
            8.881784197001252e-16,
            -4.551914400963142e-15,
            -6.661338147750939e-16
          ],
          [
            6.959815018747761e-07,
            7.466936202682461e-08,
            -0.042954916632413465
          ],
          [
            1.3921804163929963e-06,
            1.484557169417755e-07,
            -0.08575279464906471
          ],
          [
            2.0888003010588463e-06,
            2.205451342662812e-07,
            -0.12824434288724956
          ],
          [
            2.78600682090957e-06,
            2.9028291215205115e-07,
            -0.1702811721069717
          ],
          [
            3.4838946820769934e-06,
            3.5728698077885923e-07,
            -0.21169903103778398
          ],
          [
            4.182466362134818e-06,
            4.2155267931942575e-07,
            -0.25231197640161296
          ],
          [
            4.881661211264543e-06,
            4.834849297585819e-07,
            -0.2919242900594581
          ],
          [
            5.5814597553771605e-06,
            5.437950268971647e-07,
            -0.33034607899877855
          ]
        ]
      },
      "incoming_structure_ids": [
        "incoming_01_000",
        "incoming_01_001",
        "incoming_01_002",
        "incoming_01_003",
        "incoming_01_004",
        "incoming_01_005",
        "incoming_01_006",
        "incoming_01_007",
        "incoming_01_008"
      ],
      "reflected_structure_ids": [
        "reflected_01_001",
        "reflected_01_002",
        "reflected_01_003",
        "reflected_01_004",
        "reflected_01_005",
        "reflected_01_006",
        "reflected_01_007",
        "reflected_01_008"
      ]
    },
    {
      "orbit_id": 2,
      "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": [
              -5.581459754033081e-06,
              -5.437950341829949e-07,
              0.3303460789987775
            ],
            "branch_aligned_reduced_polarization": [
              -5.581459754044893e-06,
              -5.437950341829949e-07,
              0.3303460789987775
            ],
            "target_residual": 0.5279932494670584,
            "energy_eV": -812.8027880005689,
            "max_atomic_step_A": 0.058809972515392446,
            "max_log_strain_component": 0.0025004814762269473,
            "step_scale": 1.0,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 1.0025154814562427,
            "cell_principal_stretches": [
              1.0023480944949967,
              0.9998260687231451,
              0.9973467068612434
            ],
            "cell_volume_ratio": 0.9995146940635861,
            "cell_rmsd_from_input_A": 0.020830357494642418
          },
          {
            "iteration": 1,
            "reduced_polarization": [
              -0.4989484694949481,
              6.077748394739961e-08,
              0.5060578901663403
            ],
            "branch_aligned_reduced_polarization": [
              -0.4989484694949481,
              6.077748394739961e-08,
              0.5060578901663403
            ],
            "target_residual": 0.006148475394290113,
            "energy_eV": -810.3446333568553,
            "max_atomic_step_A": 0.00019177949497408125,
            "max_log_strain_component": 7.587803140934992e-06,
            "step_scale": 1.0,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 1.0025154814562427,
            "cell_principal_stretches": [
              1.0023590535222304,
              0.9998323394034057,
              0.9973470005984099
            ],
            "cell_volume_ratio": 0.9995321852889198,
            "cell_rmsd_from_input_A": 0.020864468942439686
          },
          {
            "iteration": 2,
            "reduced_polarization": [
              -0.4999989381978065,
              2.6854609724668666e-11,
              0.5000089133407071
            ],
            "branch_aligned_reduced_polarization": [
              -0.4999989381978065,
              2.6854609724668666e-11,
              0.5000089133407071
            ],
            "target_residual": 8.976361537906771e-06,
            "energy_eV": -810.3351080488129
          }
        ],
        "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,
          0.5
        ],
        "formal_class": [
          0.5,
          0.0,
          0.5
        ],
        "target_residual": 8.976361537906771e-06,
        "parent_symmetrization_rmsd_A": 0.060519519835805655,
        "parent_cell_rmsd_A": 0.020864468942439686,
        "energy_eV": -810.3351080488129,
        "reduced_polarization": [
          -0.4999989381978065,
          2.6854609724668666e-11,
          0.5000089133407071
        ],
        "cartesian_polarization_e_A2": [
          -0.009022962691909846,
          -1.183359696689911e-10,
          0.002216462270056563
        ],
        "ranking_score": 0.5657535897944914
      },
      "branch_status": "awaiting_branch_sampling"
    },
    {
      "orbit_id": 3,
      "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": [
              -5.581459754033081e-06,
              -5.437950341829949e-07,
              0.3303460789987775
            ],
            "branch_aligned_reduced_polarization": [
              -5.581459754033081e-06,
              -5.437950341691256e-07,
              0.3303460789987775
            ],
            "target_residual": 0.5279980200223323,
            "energy_eV": -812.8027880005689,
            "max_atomic_step_A": 0.02256382385004237,
            "max_log_strain_component": 0.0002105044381202586,
            "step_scale": 1.0,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 1.0025154814562427,
            "cell_principal_stretches": [
              0.9999862593988402,
              0.9998990400539691,
              0.9996293513112838
            ],
            "cell_volume_ratio": 0.9995146946644372,
            "cell_rmsd_from_input_A": 0.0025961557603501008
          },
          {
            "iteration": 1,
            "reduced_polarization": [
              -1.3055750152999092e-08,
              -0.4998292355135401,
              0.49996422123471324
            ],
            "branch_aligned_reduced_polarization": [
              -1.3055750152999092e-08,
              -0.4998292355135401,
              0.49996422123471324
            ],
            "target_residual": 0.0001744724335011622,
            "energy_eV": -812.4396286754145
          }
        ],
        "iterations": 1
      },
      "parent": {
        "candidate_id": "bec_projection_03",
        "source": "MACEField_BEC_backprojection",
        "spacegroup": "Pm",
        "spacegroup_number": 6,
        "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": 0.0001744724335011622,
        "parent_symmetrization_rmsd_A": 0.027206847029202886,
        "parent_cell_rmsd_A": 0.0025961557603501008,
        "energy_eV": -812.4396286754145,
        "reduced_polarization": [
          -1.3055750152999092e-08,
          -0.4998292355135401,
          0.49996422123471324
        ],
        "cartesian_polarization_e_A2": [
          -1.0656041091809612e-10,
          -0.0038729383714456666,
          0.002238212592763346
        ],
        "ranking_score": 0.5282048308362928
      },
      "branch_status": "awaiting_branch_sampling"
    },
    {
      "orbit_id": 4,
      "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": [
              -5.581459754033081e-06,
              -5.437950341829949e-07,
              0.3303460789987775
            ],
            "branch_aligned_reduced_polarization": [
              -5.581459754044893e-06,
              -5.437950341829949e-07,
              0.3303460789987775
            ],
            "target_residual": 0.5992686797101622,
            "energy_eV": -812.8027880005689,
            "max_atomic_step_A": 0.05909799564141729,
            "max_log_strain_component": 0.0025004551025438527,
            "step_scale": 1.0,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 1.0025154814562427,
            "cell_principal_stretches": [
              1.0028098675315384,
              1.0003388217733957,
              0.9978028900400738
            ],
            "cell_volume_ratio": 1.0009456112809292,
            "cell_rmsd_from_input_A": 0.02131868436742933
          },
          {
            "iteration": 1,
            "reduced_polarization": [
              -0.4982517959238663,
              5.693453241834878e-08,
              0.008232100014386297
            ],
            "branch_aligned_reduced_polarization": [
              -0.4982517959238663,
              5.693453241834878e-08,
              0.008232100014386297
            ],
            "target_residual": 0.008415681086038778,
            "energy_eV": -810.3137484363899,
            "max_atomic_step_A": 0.00029002667856818214,
            "max_log_strain_component": 1.0375736854513976e-05,
            "step_scale": 1.0,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 1.0025154814562427,
            "cell_principal_stretches": [
              1.0028266627000593,
              1.0003474008721354,
              0.9978014982954962
            ],
            "cell_volume_ratio": 1.000969563509708,
            "cell_rmsd_from_input_A": 0.021421030860329603
          },
          {
            "iteration": 2,
            "reduced_polarization": [
              -0.499997686112162,
              -1.104184554852382e-11,
              1.6640591152679664e-05
            ],
            "branch_aligned_reduced_polarization": [
              -0.499997686112162,
              -1.104184554852382e-11,
              1.6640591152679664e-05
            ],
            "target_residual": 1.6800694951031436e-05,
            "energy_eV": -810.2936592641263
          }
        ],
        "iterations": 2
      },
      "parent": {
        "candidate_id": "bec_projection_04",
        "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": 1.6800694951031436e-05,
        "parent_symmetrization_rmsd_A": 0.06119930040989421,
        "parent_cell_rmsd_A": 0.021421030860329603,
        "energy_eV": -810.2936592641263,
        "reduced_polarization": [
          -0.499997686112162,
          -1.104184554852382e-11,
          1.6640591152679664e-05
        ],
        "cartesian_polarization_e_A2": [
          -0.009018281446879191,
          -1.298014318804569e-10,
          -2.2558664860739363e-05
        ],
        "ranking_score": 0.5665881595148787
      },
      "branch_status": "awaiting_branch_sampling"
    },
    {
      "orbit_id": 5,
      "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": [
              -5.581459754033081e-06,
              -5.437950341829949e-07,
              0.3303460789987775
            ],
            "branch_aligned_reduced_polarization": [
              -5.581459754033081e-06,
              -5.437950341691256e-07,
              0.3303460789987775
            ],
            "target_residual": 0.5992728828724697,
            "energy_eV": -812.8027880005689,
            "max_atomic_step_A": 0.02366169390232659,
            "max_log_strain_component": 0.00040979864378033303,
            "step_scale": 1.0,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 1.0025154814562427,
            "cell_principal_stretches": [
              1.0005554798272334,
              1.0001966286404012,
              1.0001932488265768
            ],
            "cell_volume_ratio": 1.0009456118826408,
            "cell_rmsd_from_input_A": 0.004946258425514057
          },
          {
            "iteration": 1,
            "reduced_polarization": [
              -2.2087827113993575e-08,
              -0.49940537359925113,
              0.0004094689776001484
            ],
            "branch_aligned_reduced_polarization": [
              -2.2087827113993575e-08,
              -0.49940537359925113,
              0.0004094689776001484
            ],
            "target_residual": 0.0007219732685995607,
            "energy_eV": -812.391814853509
          }
        ],
        "iterations": 1
      },
      "parent": {
        "candidate_id": "bec_projection_05",
        "source": "MACEField_BEC_backprojection",
        "spacegroup": "Pm",
        "spacegroup_number": 6,
        "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": 0.0007219732685995607,
        "parent_symmetrization_rmsd_A": 0.028562291062890762,
        "parent_cell_rmsd_A": 0.004946258425514057,
        "energy_eV": -812.391814853509,
        "reduced_polarization": [
          -2.2087827113993575e-08,
          -0.49940537359925113,
          0.0004094689776001484
        ],
        "cartesian_polarization_e_A2": [
          -2.3006280421003752e-10,
          -0.0038665003269601,
          1.1457260391088238e-06
        ],
        "ranking_score": 0.5312428022064684
      },
      "branch_status": "awaiting_branch_sampling"
    },
    {
      "orbit_id": 6,
      "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": [
              -5.581459754033081e-06,
              -5.437950341829949e-07,
              0.3303460789987775
            ],
            "branch_aligned_reduced_polarization": [
              -5.581459754044893e-06,
              -5.437950341691256e-07,
              0.3303460789987775
            ],
            "target_residual": 0.72717008167811,
            "energy_eV": -812.8027880005689,
            "max_atomic_step_A": 0.061800745492049496,
            "max_log_strain_component": 0.0025004815012084265,
            "step_scale": 1.0,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 1.0025154814562427,
            "cell_principal_stretches": [
              1.0023542061449937,
              0.9998264518297789,
              0.9973402302878535
            ],
            "cell_volume_ratio": 0.9995146807331216,
            "cell_rmsd_from_input_A": 0.0208398828361737
          },
          {
            "iteration": 1,
            "reduced_polarization": [
              -0.4983838669422733,
              -0.4978869804109865,
              0.5059952545570542
            ],
            "branch_aligned_reduced_polarization": [
              -0.4983838669422733,
              -0.4978869804109865,
              0.5059952545570542
            ],
            "target_residual": 0.006558949233506137,
            "energy_eV": -809.9862868671318,
            "max_atomic_step_A": 0.00025970527407988676,
            "max_log_strain_component": 8.282934287682645e-06,
            "step_scale": 1.0,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 1.0025154814562427,
            "cell_principal_stretches": [
              1.0023680872747214,
              0.9998326608855473,
              0.9973375406532745
            ],
            "cell_volume_ratio": 0.9995320341924694,
            "cell_rmsd_from_input_A": 0.020898112195414566
          },
          {
            "iteration": 2,
            "reduced_polarization": [
              -0.49999885837581287,
              -0.4999992886109702,
              0.5000139363920878
            ],
            "branch_aligned_reduced_polarization": [
              -0.49999885837581287,
              -0.4999992886109702,
              0.5000139363920878
            ],
            "target_residual": 1.4001157257927363e-05,
            "energy_eV": -809.9679554457375
          }
        ],
        "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,
          0.5
        ],
        "formal_class": [
          0.5,
          0.5,
          0.5
        ],
        "target_residual": 1.4001157257927363e-05,
        "parent_symmetrization_rmsd_A": 0.06625542893612493,
        "parent_cell_rmsd_A": 0.020898112195414566,
        "energy_eV": -809.9679554457375,
        "reduced_polarization": [
          -0.49999885837581287,
          -0.4999992886109702,
          0.5000139363920878
        ],
        "cartesian_polarization_e_A2": [
          -0.009022956613562514,
          -0.003874213139934695,
          0.002215767704167692
        ],
        "ranking_score": 0.5715079592994944
      },
      "branch_status": "awaiting_branch_sampling"
    },
    {
      "orbit_id": 7,
      "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": [
              -5.581459754033081e-06,
              -5.437950341829949e-07,
              0.3303460789987775
            ],
            "branch_aligned_reduced_polarization": [
              -5.581459754044893e-06,
              -5.437950341691256e-07,
              0.3303460789987775
            ],
            "target_residual": 0.7804629438266283,
            "energy_eV": -812.8027880005689,
            "max_atomic_step_A": 0.06218939026837001,
            "max_log_strain_component": 0.002500455127525332,
            "step_scale": 1.0,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 1.0025154814562427,
            "cell_principal_stretches": [
              1.0028165192946872,
              1.0003381268607996,
              0.997796951372004
            ],
            "cell_volume_ratio": 1.0009455979313808,
            "cell_rmsd_from_input_A": 0.02132806418840214
          },
          {
            "iteration": 1,
            "reduced_polarization": [
              -0.4976850534037529,
              -0.4974707260315711,
              0.008472412386701956
            ],
            "branch_aligned_reduced_polarization": [
              -0.4976850534037529,
              -0.4974707260315711,
              0.008472412386701956
            ],
            "target_residual": 0.009139911170311708,
            "energy_eV": -809.9577699302158,
            "max_atomic_step_A": 0.0003654404464929322,
            "max_log_strain_component": 1.1915054191289865e-05,
            "step_scale": 1.0,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 1.0025154814562427,
            "cell_principal_stretches": [
              1.002836576229092,
              1.0003469714185298,
              0.9977928415110633
            ],
            "cell_volume_ratio": 1.0009703446030382,
            "cell_rmsd_from_input_A": 0.021455266760776522
          },
          {
            "iteration": 2,
            "reduced_polarization": [
              -0.4999972835730917,
              -0.4999986878662531,
              2.2133741734653176e-05
            ],
            "branch_aligned_reduced_polarization": [
              -0.4999972835730917,
              -0.4999986878662531,
              2.2133741734653176e-05
            ],
            "target_residual": 2.233837937931401e-05,
            "energy_eV": -809.9281810021344
          }
        ],
        "iterations": 2
      },
      "parent": {
        "candidate_id": "bec_projection_07",
        "source": "MACEField_BEC_backprojection",
        "spacegroup": "P1",
        "spacegroup_number": 1,
        "pointgroup": "1",
        "has_inversion": false,
        "is_polar_point_group": true,
        "nonpolar_parent_hypothesis": false,
        "symmetry_tolerance_A": null,
        "target_reduced_polarization": [
          -0.5,
          -0.5,
          0.0
        ],
        "formal_class": [
          0.5,
          0.5,
          0.0
        ],
        "target_residual": 2.233837937931401e-05,
        "parent_symmetrization_rmsd_A": 0.06687986850054524,
        "parent_cell_rmsd_A": 0.021455266760776522,
        "energy_eV": -809.9281810021344,
        "reduced_polarization": [
          -0.4999972835730917,
          -0.4999986878662531,
          2.2133741734653176e-05
        ],
        "cartesian_polarization_e_A2": [
          -0.009018269433387396,
          -0.0038710346806137504,
          -2.325148916743649e-05
        ],
        "ranking_score": 0.5722883619494981
      },
      "branch_status": "awaiting_branch_sampling"
    }
  ],
  "sampled_polarization_branches": [
    {
      "orbit_id": 1,
      "candidate_id": "inversion_parent_endpoint_00",
      "formal_class": [
        0.0,
        0.0,
        0.0
      ],
      "construction": "MACEField-BEC-parent plus variable-cell P-N-P path and symmetric log-strain continuation beyond both polar endpoints",
      "geometry_diagnostics": {
        "collision_aware": false,
        "permutations_tested": 1,
        "selected_order": [
          0,
          1,
          2,
          3,
          4,
          5,
          6,
          7,
          8,
          9,
          10,
          11,
          12,
          13,
          14,
          15,
          16,
          17,
          18,
          19,
          20,
          21,
          22,
          23,
          24,
          25,
          26,
          27,
          28,
          29,
          30,
          31,
          32,
          33,
          34,
          35,
          36,
          37,
          38,
          39,
          40,
          41,
          42,
          43,
          44,
          45,
          46,
          47,
          48,
          49,
          50,
          51,
          52,
          53,
          54,
          55,
          56,
          57,
          58,
          59,
          60,
          61,
          62,
          63,
          64,
          65,
          66,
          67,
          68,
          69,
          70,
          71,
          72,
          73,
          74,
          75,
          76,
          77,
          78,
          79,
          80,
          81,
          82,
          83,
          84,
          85,
          86,
          87,
          88,
          89,
          90,
          91,
          92,
          93,
          94,
          95,
          96,
          97,
          98,
          99,
          100,
          101,
          102,
          103,
          104,
          105,
          106,
          107,
          108,
          109,
          110,
          111,
          112,
          113,
          114,
          115
        ],
        "endpoint_rmsd_A": 0.061283688002926044,
        "minimum_distance_A_by_image": [
          1.696591616851958,
          1.6964943497614413,
          1.6964100471051526,
          1.6963387108159662,
          1.6962803425297548,
          1.6962349435852355,
          1.6962025150237798,
          1.6961830575893124,
          1.6961765717282262
        ],
        "minimum_distance_A": 1.6961765717282262,
        "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": [
          1263.8740267157796,
          1263.8740267157796,
          1263.8740267157796,
          1263.8740267157796,
          1263.8740267157796,
          1263.8740267157796,
          1263.8740267157796,
          1263.8740267157796,
          1263.8740267157796
        ],
        "cell_deformation_log_strain_norm": 0.0
      },
      "parent_reduced_polarization": [
        9.32590071097144e-16,
        -4.570539230863021e-15,
        -6.354759413362186e-16
      ],
      "incoming": {
        "reached": true,
        "construction": "variable_cell_linear_interpolation",
        "continuation_fractions": [
          0.0,
          0.125,
          0.25,
          0.375,
          0.5,
          0.625,
          0.75,
          0.875,
          1.0
        ],
        "energies_eV": [
          -812.8027880005689,
          -812.8030805837753,
          -812.8031649608167,
          -812.8031593601161,
          -812.8030688511624,
          -812.8028830998145,
          -812.8026480851474,
          -812.802454540929,
          -812.8023804749596
        ],
        "cartesian_polarizations_e_A2": [
          [
            -1.0074779873390036e-07,
            -4.212728470101881e-09,
            0.0014789230598400598
          ],
          [
            -8.811612771390523e-08,
            -3.745511852658549e-09,
            0.0013069129368959787
          ],
          [
            -7.549535379313206e-08,
            -3.265728569904672e-09,
            0.001129572965736717
          ],
          [
            -6.288582832850821e-08,
            -2.7678682947863924e-09,
            0.0009477532764926205
          ],
          [
            -5.028864604695433e-08,
            -2.248794222119357e-09,
            0.0007623300777440624
          ],
          [
            -3.770376233791896e-08,
            -1.7085422039970604e-09,
            0.0005741358170946907
          ],
          [
            -2.5129467629155966e-08,
            -1.15007237767687e-09,
            0.0003839058294156306
          ],
          [
            -1.2562771530151224e-08,
            -5.784565458858471e-10,
            0.00019230443701251918
          ],
          [
            1.6833660173434208e-17,
            -3.540753315902839e-17,
            -2.8449558913008034e-18
          ]
        ],
        "raw_reduced_polarization": [
          [
            -5.5814597548075e-06,
            -5.437950352286716e-07,
            0.3303460789987811
          ],
          [
            -4.881661205160901e-06,
            -4.834849348400101e-07,
            0.29192429005945614
          ],
          [
            -4.182466358240472e-06,
            -4.2155268143252594e-07,
            0.2523119764016012
          ],
          [
            -3.483894679330564e-06,
            -3.572869810038549e-07,
            0.21169903103779047
          ],
          [
            -2.7860068166470847e-06,
            -2.9028292279418014e-07,
            0.17028117210696667
          ],
          [
            -2.088800298751444e-06,
            -2.2054513472827372e-07,
            0.12824434288725192
          ],
          [
            -1.3921804148032116e-06,
            -1.4845572259709178e-07,
            0.08575279464906296
          ],
          [
            -6.959814962268399e-07,
            -7.466937401276246e-08,
            0.04295491663239331
          ],
          [
            9.32590071097144e-16,
            -4.570539230863021e-15,
            -6.354759413362186e-16
          ]
        ],
        "unwrapped_reduced_polarization": [
          [
            -5.5814597548075e-06,
            -5.437950352286716e-07,
            0.3303460789987811
          ],
          [
            -4.881661205160901e-06,
            -4.834849348400101e-07,
            0.29192429005945614
          ],
          [
            -4.182466358240472e-06,
            -4.2155268143252594e-07,
            0.2523119764016012
          ],
          [
            -3.483894679330564e-06,
            -3.572869810038549e-07,
            0.21169903103779047
          ],
          [
            -2.7860068166470847e-06,
            -2.9028292279418014e-07,
            0.17028117210696667
          ],
          [
            -2.088800298751444e-06,
            -2.2054513472827372e-07,
            0.12824434288725192
          ],
          [
            -1.3921804148032116e-06,
            -1.4845572259709178e-07,
            0.08575279464906296
          ],
          [
            -6.959814962268399e-07,
            -7.466937401276246e-08,
            0.04295491663239331
          ],
          [
            9.325900511905627e-16,
            -4.570539226105165e-15,
            -6.38378239159465e-16
          ]
        ],
        "berry_integer_shifts": [
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ]
        ],
        "folded_reduced_polarization": [
          [
            -5.581459754822049e-06,
            -5.437950352238374e-07,
            0.3303460789987811
          ],
          [
            -4.881661205158316e-06,
            -4.834849348656078e-07,
            0.2919242900594561
          ],
          [
            -4.182466358249037e-06,
            -4.215526814288495e-07,
            0.2523119764016012
          ],
          [
            -3.483894679356947e-06,
            -3.5728698100090384e-07,
            0.21169903103779042
          ],
          [
            -2.7860068166352114e-06,
            -2.902829228101922e-07,
            0.1702811721069667
          ],
          [
            -2.088800298727378e-06,
            -2.205451347103704e-07,
            0.12824434288725195
          ],
          [
            -1.3921804147831729e-06,
            -1.4845572260391293e-07,
            0.08575279464906294
          ],
          [
            -6.959814962126387e-07,
            -7.466937401723328e-08,
            0.04295491663239326
          ],
          [
            8.881784197001252e-16,
            -4.551914400963142e-15,
            -6.661338147750939e-16
          ]
        ]
      },
      "reflected": {
        "reached": true,
        "construction": "reflect_displacements_about_reconstructed_parent",
        "energies_eV": [
          -812.8023804749596,
          -812.8024545409288,
          -812.8026480851477,
          -812.8028830998147,
          -812.8030688511627,
          -812.8031593601157,
          -812.8031649608167,
          -812.8030805837748,
          -812.802788000569
        ],
        "cartesian_polarizations_e_A2": [
          [
            1.9503744644904716e-17,
            -3.115401743007429e-17,
            2.9982891725337437e-19
          ],
          [
            1.2562771631210623e-08,
            5.78456453306341e-10,
            -0.00019230443701260958
          ],
          [
            2.5129467658752445e-08,
            1.1500723336744626e-09,
            -0.00038390582941563863
          ],
          [
            3.7703762379477565e-08,
            1.7085422006713847e-09,
            -0.00057413581709468
          ],
          [
            5.0288646124021235e-08,
            2.2487941393658977e-09,
            -0.0007623300777440847
          ],
          [
            6.288582837774151e-08,
            2.7678682927577713e-09,
            -0.0009477532764925916
          ],
          [
            7.549535386369403e-08,
            3.2657285538733514e-09,
            -0.0011295729657367698
          ],
          [
            8.811612782331591e-08,
            3.745511812915148e-09,
            -0.0013069129368959874
          ],
          [
            1.0074779874463448e-07,
            4.212728405479735e-09,
            -0.0014789230598400485
          ]
        ],
        "raw_reduced_polarization": [
          [
            1.0805135910820468e-15,
            -4.021479220922156e-15,
            6.69725896327655e-17
          ],
          [
            6.959815018255624e-07,
            7.466936206224723e-08,
            -0.04295491663241349
          ],
          [
            1.392180416442866e-06,
            1.4845571691709344e-07,
            -0.08575279464906474
          ],
          [
            2.088800301053804e-06,
            2.2054513429898283e-07,
            -0.12824434288724956
          ],
          [
            2.786006820916615e-06,
            2.902829121120485e-07,
            -0.17028117210697166
          ],
          [
            3.4838946820581045e-06,
            3.572869807419928e-07,
            -0.21169903103778398
          ],
          [
            4.182466362149628e-06,
            4.2155267936314207e-07,
            -0.25231197640161296
          ],
          [
            4.881661211222286e-06,
            4.834849297097804e-07,
            -0.2919242900594581
          ],
          [
            5.581459755402174e-06,
            5.43795026886999e-07,
            -0.33034607899877855
          ]
        ],
        "unwrapped_reduced_polarization": [
          [
            1.0805135910820468e-15,
            -4.021479220922156e-15,
            6.69725896327655e-17
          ],
          [
            6.959815018255624e-07,
            7.466936206224723e-08,
            -0.04295491663241349
          ],
          [
            1.392180416442866e-06,
            1.4845571691709344e-07,
            -0.08575279464906474
          ],
          [
            2.088800301053804e-06,
            2.2054513429898283e-07,
            -0.12824434288724956
          ],
          [
            2.786006820916615e-06,
            2.902829121120485e-07,
            -0.17028117210697166
          ],
          [
            3.4838946820581045e-06,
            3.572869807419928e-07,
            -0.21169903103778398
          ],
          [
            4.182466362149628e-06,
            4.2155267936314207e-07,
            -0.25231197640161296
          ],
          [
            4.881661211222286e-06,
            4.834849297097804e-07,
            -0.2919242900594581
          ],
          [
            5.581459755402174e-06,
            5.43795026886999e-07,
            -0.33034607899877855
          ]
        ],
        "gauge_integer_shift": [
          0,
          0,
          0
        ],
        "expected_opposite_endpoint_reduced_polarization": [
          5.581459756672681e-06,
          5.437950260875932e-07,
          -0.3303460789987824
        ],
        "actual_opposite_endpoint_branch_residual": 4.113903467213528e-15
      },
      "pnp_branch": {
        "construction": "incoming_path_concatenated_with_parent_reflection",
        "reduced_polarization": [
          [
            -5.5814597548075e-06,
            -5.437950352286716e-07,
            0.3303460789987811
          ],
          [
            -4.881661205160901e-06,
            -4.834849348400101e-07,
            0.29192429005945614
          ],
          [
            -4.182466358240472e-06,
            -4.2155268143252594e-07,
            0.2523119764016012
          ],
          [
            -3.483894679330564e-06,
            -3.572869810038549e-07,
            0.21169903103779047
          ],
          [
            -2.7860068166470847e-06,
            -2.9028292279418014e-07,
            0.17028117210696667
          ],
          [
            -2.088800298751444e-06,
            -2.2054513472827372e-07,
            0.12824434288725192
          ],
          [
            -1.3921804148032116e-06,
            -1.4845572259709178e-07,
            0.08575279464906296
          ],
          [
            -6.959814962268399e-07,
            -7.466937401276246e-08,
            0.04295491663239331
          ],
          [
            9.32590071097144e-16,
            -4.570539230863021e-15,
            -6.354759413362186e-16
          ],
          [
            6.959815018255624e-07,
            7.466936206224723e-08,
            -0.04295491663241349
          ],
          [
            1.392180416442866e-06,
            1.4845571691709344e-07,
            -0.08575279464906474
          ],
          [
            2.088800301053804e-06,
            2.2054513429898283e-07,
            -0.12824434288724956
          ],
          [
            2.786006820916615e-06,
            2.902829121120485e-07,
            -0.17028117210697166
          ],
          [
            3.4838946820581045e-06,
            3.572869807419928e-07,
            -0.21169903103778398
          ],
          [
            4.182466362149628e-06,
            4.2155267936314207e-07,
            -0.25231197640161296
          ],
          [
            4.881661211222286e-06,
            4.834849297097804e-07,
            -0.2919242900594581
          ],
          [
            5.581459755402174e-06,
            5.43795026886999e-07,
            -0.33034607899877855
          ]
        ],
        "unwrapped_reduced_polarization": [
          [
            -5.5814597548075e-06,
            -5.437950352286716e-07,
            0.3303460789987811
          ],
          [
            -4.881661205160901e-06,
            -4.834849348400101e-07,
            0.29192429005945614
          ],
          [
            -4.182466358240472e-06,
            -4.2155268143252594e-07,
            0.2523119764016012
          ],
          [
            -3.483894679330564e-06,
            -3.572869810038549e-07,
            0.21169903103779047
          ],
          [
            -2.7860068166470847e-06,
            -2.9028292279418014e-07,
            0.17028117210696667
          ],
          [
            -2.088800298751444e-06,
            -2.2054513472827372e-07,
            0.12824434288725192
          ],
          [
            -1.3921804148032116e-06,
            -1.4845572259709178e-07,
            0.08575279464906296
          ],
          [
            -6.959814962268399e-07,
            -7.466937401276246e-08,
            0.04295491663239331
          ],
          [
            9.325900511905627e-16,
            -4.570539226105165e-15,
            -6.38378239159465e-16
          ],
          [
            6.959815018255624e-07,
            7.466936206224723e-08,
            -0.04295491663241349
          ],
          [
            1.392180416442866e-06,
            1.4845571691709344e-07,
            -0.08575279464906474
          ],
          [
            2.088800301053804e-06,
            2.2054513429898283e-07,
            -0.12824434288724956
          ],
          [
            2.786006820916615e-06,
            2.902829121120485e-07,
            -0.17028117210697166
          ],
          [
            3.4838946820581045e-06,
            3.572869807419928e-07,
            -0.21169903103778398
          ],
          [
            4.182466362149628e-06,
            4.2155267936314207e-07,
            -0.25231197640161296
          ],
          [
            4.881661211222286e-06,
            4.834849297097804e-07,
            -0.2919242900594581
          ],
          [
            5.581459755402174e-06,
            5.43795026886999e-07,
            -0.33034607899877855
          ]
        ],
        "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": [
          [
            -5.581459754822049e-06,
            -5.437950352238374e-07,
            0.3303460789987811
          ],
          [
            -4.881661205158316e-06,
            -4.834849348656078e-07,
            0.2919242900594561
          ],
          [
            -4.182466358249037e-06,
            -4.215526814288495e-07,
            0.2523119764016012
          ],
          [
            -3.483894679356947e-06,
            -3.5728698100090384e-07,
            0.21169903103779042
          ],
          [
            -2.7860068166352114e-06,
            -2.902829228101922e-07,
            0.1702811721069667
          ],
          [
            -2.088800298727378e-06,
            -2.205451347103704e-07,
            0.12824434288725195
          ],
          [
            -1.3921804147831729e-06,
            -1.4845572260391293e-07,
            0.08575279464906294
          ],
          [
            -6.959814962126387e-07,
            -7.466937401723328e-08,
            0.04295491663239326
          ],
          [
            8.881784197001252e-16,
            -4.551914400963142e-15,
            -6.661338147750939e-16
          ],
          [
            6.959815018747761e-07,
            7.466936202682461e-08,
            -0.042954916632413465
          ],
          [
            1.3921804163929963e-06,
            1.484557169417755e-07,
            -0.08575279464906471
          ],
          [
            2.0888003010588463e-06,
            2.205451342662812e-07,
            -0.12824434288724956
          ],
          [
            2.78600682090957e-06,
            2.9028291215205115e-07,
            -0.1702811721069717
          ],
          [
            3.4838946820769934e-06,
            3.5728698077885923e-07,
            -0.21169903103778398
          ],
          [
            4.182466362134818e-06,
            4.2155267931942575e-07,
            -0.25231197640161296
          ],
          [
            4.881661211264543e-06,
            4.834849297585819e-07,
            -0.2919242900594581
          ],
          [
            5.5814597553771605e-06,
            5.437950268971647e-07,
            -0.33034607899877855
          ]
        ]
      },
      "incoming_structure_ids": [
        "incoming_01_000",
        "incoming_01_001",
        "incoming_01_002",
        "incoming_01_003",
        "incoming_01_004",
        "incoming_01_005",
        "incoming_01_006",
        "incoming_01_007",
        "incoming_01_008"
      ],
      "reflected_structure_ids": [
        "reflected_01_001",
        "reflected_01_002",
        "reflected_01_003",
        "reflected_01_004",
        "reflected_01_005",
        "reflected_01_006",
        "reflected_01_007",
        "reflected_01_008"
      ],
      "positive_extension_structure_ids": [
        "extension_plus_01_000",
        "extension_plus_01_001",
        "extension_plus_01_002",
        "extension_plus_01_003"
      ],
      "negative_extension_structure_ids": [
        "extension_minus_01_000",
        "extension_minus_01_001",
        "extension_minus_01_002",
        "extension_minus_01_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": 6.8340852005413154e-15,
        "parent_symmetrization_rmsd_A": 0.061283688002926044,
        "parent_cell_rmsd_A": 0.0,
        "energy_eV": -812.8023804749596,
        "reduced_polarization": [
          3.8961216579154386e-15,
          -5.0092202843039964e-15,
          2.5362706279688437e-15
        ],
        "cartesian_polarization_e_A2": [
          7.032670625213398e-17,
          -3.880595359945768e-17,
          1.1354604628777786e-17
        ],
        "ranking_score": 0.061283688002939714
      }
    }
  ],
  "path_sampling": {
    "num_images": 17,
    "images_per_leg_including_parent": 9,
    "extension_fraction_beyond_polar_endpoint": 0.35,
    "extension_images_per_side": 4,
    "total_images_per_sampled_branch": 25,
    "construction": "linear polar-to-parent interpolation plus parent-reflected second leg and symmetric log-strain continuation beyond both polar endpoints"
  },
  "branch_folding": "componentwise integer unwrap with per-image shifts, then reduced-coordinate fold [-0.5, 0.5)",
  "bec_backprojection_settings": {
    "variable_cell": true,
    "max_strain_step_log_component": 0.02,
    "strain_response_refresh_iterations": 4,
    "cell_principal_stretch_bounds": [
      0.85,
      1.15
    ],
    "cell_volume_ratio_bounds": [
      0.7,
      1.3
    ],
    "strain_jacobian": "branch-matched finite differences of reduced polarization in six symmetric log-strain coordinates at fixed fractional positions"
  },
  "model_input_contract": "one polar endpoint structure; no reference parent or path frame",
  "run": {
    "model_file": "MACEField-MH-0-omat-dielectric.model",
    "model_sha256": "f92e043aaf2cd8879919db8452503553fe7b608cb749d8d169dd96d4aa094aa2",
    "model_head": "mp-ferroelectric",
    "device": "cpu",
    "dtype": "float64",
    "num_images": 17,
    "compute_becs_for_every_image": true,
    "compute_polarizability_for_every_image": true,
    "initial_structure_relaxation": {
      "enabled": false
    },
    "model_evaluations_for_recovery": {
      "total": 48,
      "full_response": 13,
      "energy_polarization": 35
    },
    "model_evaluations_for_recovery_and_path_properties": {
      "total": 73,
      "full_response": 38,
      "energy_polarization": 35
    },
    "elapsed_seconds": 3878.68623679498
  }
}