{
  "schema": "ferrofinder.endpoint_parent_recovery.v4_variable_cell",
  "status": "complete",
  "input_atom_count": 64,
  "input_formula": "C8B52Li4",
  "input_spacegroup": "Imm2",
  "input_pointgroup": "mm2",
  "input_is_polar_point_group": true,
  "input_energy_eV": -425.5046727688668,
  "input_cartesian_polarization_e_A2": [
    -6.630028997264329e-18,
    -6.666308601355768e-18,
    0.0004845595493683714
  ],
  "input_reduced_polarization": [
    -5.776976248714696e-16,
    -3.043705588988287e-16,
    0.02977430685813843
  ],
  "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": [
        0.5,
        0.0,
        0.0
      ],
      "target_reduced_polarization": [
        -0.5,
        0.0,
        0.0
      ]
    },
    {
      "orbit_id": 3,
      "representative_formal_class": [
        0.0,
        0.5,
        0.0
      ],
      "target_reduced_polarization": [
        0.0,
        -0.5,
        0.0
      ]
    },
    {
      "orbit_id": 4,
      "representative_formal_class": [
        0.5,
        0.0,
        0.5
      ],
      "target_reduced_polarization": [
        -0.5,
        0.0,
        0.5
      ]
    },
    {
      "orbit_id": 5,
      "representative_formal_class": [
        0.0,
        0.5,
        0.5
      ],
      "target_reduced_polarization": [
        0.0,
        -0.5,
        0.5
      ]
    },
    {
      "orbit_id": 6,
      "representative_formal_class": [
        0.5,
        0.5,
        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": "Imma",
      "spacegroup_number": 74,
      "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": 2.862162988967259e-15,
      "parent_symmetrization_rmsd_A": 0.037490613244395087,
      "parent_cell_rmsd_A": 0.0,
      "energy_eV": -425.50496506279705,
      "reduced_polarization": [
        3.821309823324384e-16,
        -1.4558524417223977e-15,
        -2.4344294107011136e-15
      ],
      "cartesian_polarization_e_A2": [
        4.38558059535185e-18,
        -3.188600661532696e-17,
        -3.961892459289965e-17
      ],
      "ranking_score": 0.03749061324440081
    },
    {
      "candidate_id": "symmetry_projection_00",
      "source": "spglib_refine_cell_from_polar_endpoint",
      "spacegroup": "Imma",
      "spacegroup_number": 74,
      "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": 2.4951727569527457e-15,
      "parent_symmetrization_rmsd_A": 2.7852640001725275,
      "parent_cell_rmsd_A": 1.6817620414219087e-15,
      "energy_eV": -424.9938006317798,
      "reduced_polarization": [
        -1.999472489831127e-15,
        3.0757445951881646e-16,
        -1.4606145286486048e-15
      ],
      "cartesian_polarization_e_A2": [
        -2.2947230551211102e-17,
        6.7364802708437246e-18,
        -2.3770653039044913e-17
      ],
      "ranking_score": 2.785264000172533
    },
    {
      "candidate_id": "bec_projection_00",
      "source": "MACEField_BEC_backprojection",
      "spacegroup": "Imm2",
      "spacegroup_number": 44,
      "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": 1.5564885228037627e-05,
      "parent_symmetrization_rmsd_A": 0.008386596041860858,
      "parent_cell_rmsd_A": 0.0011738587229901893,
      "energy_eV": -425.4879145815479,
      "reduced_polarization": [
        2.092420712006361e-15,
        1.300999837422333e-16,
        1.5564885228037627e-05
      ],
      "cartesian_polarization_e_A2": [
        2.4007308370727792e-17,
        2.848237232297976e-18,
        2.5329562684304055e-07
      ],
      "ranking_score": 0.5087111904930645
    },
    {
      "candidate_id": "inversion_parent_bec_00_00",
      "source": "same_species_inversion_center_projection_after_BEC",
      "spacegroup": "Imma",
      "spacegroup_number": 74,
      "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": 3.627991642927658e-15,
      "parent_symmetrization_rmsd_A": 0.03749071581658569,
      "parent_cell_rmsd_A": 0.0011738587229901893,
      "energy_eV": -425.5059200003457,
      "reduced_polarization": [
        -1.895423983488803e-15,
        -5.574453186272851e-16,
        3.042851623183242e-15
      ],
      "cartesian_polarization_e_A2": [
        -2.1747395345249696e-17,
        -1.2206730995562753e-17,
        4.951793720240212e-17
      ],
      "ranking_score": 0.037784180497340496
    },
    {
      "candidate_id": "symmetry_parent_00_00",
      "source": "spglib_refine_cell_after_MACEField_BEC_backprojection",
      "spacegroup": "Imma",
      "spacegroup_number": 74,
      "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": 1.5003724524159655e-15,
      "parent_symmetrization_rmsd_A": 2.784691134709798,
      "parent_cell_rmsd_A": 0.0011738587229884103,
      "energy_eV": -425.18361713382257,
      "reduced_polarization": [
        2.1431728118791253e-17,
        -1.491646783637159e-15,
        1.6015008543069728e-16
      ],
      "cartesian_polarization_e_A2": [
        2.458997397898075e-19,
        -3.266352845709208e-17,
        2.6062072211790604e-18
      ],
      "ranking_score": 2.7849845993905484
    },
    {
      "candidate_id": "bec_projection_01",
      "source": "MACEField_BEC_backprojection",
      "spacegroup": "Imm2",
      "spacegroup_number": 44,
      "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": 6.75632138694704e-05,
      "parent_symmetrization_rmsd_A": 0.13539780886226666,
      "parent_cell_rmsd_A": 0.01887175731978011,
      "energy_eV": -421.48213791059305,
      "reduced_polarization": [
        -3.571579287438885e-15,
        1.4633248119362654e-15,
        0.5000675632138695
      ],
      "cartesian_polarization_e_A2": [
        1.428333782196202e-16,
        3.647317829666685e-16,
        0.008145481478977888
      ],
      "ranking_score": 0.6402508746199507
    },
    {
      "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": [
        -0.5,
        0.0,
        0.0
      ],
      "formal_class": [
        0.5,
        0.0,
        0.0
      ],
      "target_residual": 0.0009828824438923686,
      "parent_symmetrization_rmsd_A": 0.06089691926398505,
      "parent_cell_rmsd_A": 0.002958125256469574,
      "energy_eV": -421.6727529060997,
      "reduced_polarization": [
        -0.5001696121734127,
        1.1964236032450837e-14,
        0.0009681371850838343
      ],
      "cartesian_polarization_e_A2": [
        -0.005738753981039202,
        1.403774064489702e-16,
        1.2697180618806323e-05
      ],
      "ranking_score": 0.5636022154658872
    },
    {
      "candidate_id": "symmetry_parent_02_00",
      "source": "spglib_refine_cell_after_MACEField_BEC_backprojection",
      "spacegroup": "Imma",
      "spacegroup_number": 74,
      "pointgroup": "mmm",
      "has_inversion": true,
      "is_polar_point_group": false,
      "nonpolar_parent_hypothesis": true,
      "symmetry_tolerance_A": null,
      "target_reduced_polarization": [
        -0.5,
        0.0,
        0.0
      ],
      "formal_class": [
        0.5,
        0.0,
        0.0
      ],
      "target_residual": 0.4999999999999994,
      "parent_symmetrization_rmsd_A": 2.9717097550637726,
      "parent_cell_rmsd_A": 0.001175129412967664,
      "energy_eV": -423.9965050388342,
      "reduced_polarization": [
        -6.042593744024073e-16,
        2.6911153313041777e-16,
        1.0406519421399052e-15
      ],
      "cartesian_polarization_e_A2": [
        -6.93304711294293e-18,
        5.8929012730587866e-18,
        1.693507580138561e-17
      ],
      "ranking_score": 3.972003537417013
    },
    {
      "candidate_id": "bec_projection_03",
      "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": 7.107056867668472e-05,
      "parent_symmetrization_rmsd_A": 0.12301799877097268,
      "parent_cell_rmsd_A": 0.029016980741932673,
      "energy_eV": -405.0474841383041,
      "reduced_polarization": [
        -4.8944553327423214e-15,
        -0.5000703298181981,
        -1.0234373661807283e-05
      ],
      "cartesian_polarization_e_A2": [
        -5.284784440101938e-18,
        -0.0109501688871746,
        -3.280534959155647e-05
      ],
      "ranking_score": 0.6304143850938092
    },
    {
      "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": [
        -0.5,
        0.0,
        0.5
      ],
      "formal_class": [
        0.5,
        0.0,
        0.5
      ],
      "target_residual": 7.566221851362749e-06,
      "parent_symmetrization_rmsd_A": 0.14962898571189706,
      "parent_cell_rmsd_A": 0.019602522353812178,
      "energy_eV": -417.159856797959,
      "reduced_polarization": [
        -0.49999920798438374,
        -9.018855202171452e-16,
        0.5000075246544351
      ],
      "cartesian_polarization_e_A2": [
        -0.005758989913948406,
        6.896357675858914e-17,
        0.00814163870458554
      ],
      "ranking_score": 0.6545447487440528
    },
    {
      "candidate_id": "bec_projection_05",
      "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": 0.00022374566602363004,
      "parent_symmetrization_rmsd_A": 0.19855752991878287,
      "parent_cell_rmsd_A": 0.037198784884481584,
      "energy_eV": -400.9779355303244,
      "reduced_polarization": [
        4.4031400858892284e-15,
        -0.5001394484332118,
        0.5001749750197575
      ],
      "cartesian_polarization_e_A2": [
        -3.7038819847217834e-16,
        -0.010968785102271299,
        0.008114036962713653
      ],
      "ranking_score": 0.7083047174719506
    },
    {
      "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": 8.801982950462341e-05,
      "parent_symmetrization_rmsd_A": 0.14385834710739007,
      "parent_cell_rmsd_A": 0.030399539839450283,
      "energy_eV": -400.84672942252195,
      "reduced_polarization": [
        -0.5000691535007469,
        -0.5000538423637119,
        -8.14147347806053e-06
      ],
      "cartesian_polarization_e_A2": [
        -0.005737406071518615,
        -0.010949743323149885,
        -3.7627434640759904e-05
      ],
      "ranking_score": 0.6516342717262619
    },
    {
      "candidate_id": "bec_projection_07",
      "source": "MACEField_BEC_backprojection",
      "spacegroup": "P1",
      "spacegroup_number": 1,
      "pointgroup": "1",
      "has_inversion": false,
      "is_polar_point_group": true,
      "nonpolar_parent_hypothesis": false,
      "symmetry_tolerance_A": null,
      "target_reduced_polarization": [
        -0.5,
        -0.5,
        0.5
      ],
      "formal_class": [
        0.5,
        0.5,
        0.5
      ],
      "target_residual": 0.0003080092875762862,
      "parent_symmetrization_rmsd_A": 0.21438356771362402,
      "parent_cell_rmsd_A": 0.03872459504976483,
      "energy_eV": -395.88897046692756,
      "reduced_polarization": [
        -0.5001070067356932,
        -0.5001730543995194,
        0.5002312389555341
      ],
      "cartesian_polarization_e_A2": [
        -0.005763263355978843,
        -0.010969254588157768,
        0.008110057894750578
      ],
      "ranking_score": 0.7246807350512178
    }
  ],
  "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": [
              -5.776976248714696e-16,
              -3.043705588988287e-16,
              0.02977430685813843
            ],
            "branch_aligned_reduced_polarization": [
              -5.776976248714696e-16,
              -3.043705588988287e-16,
              0.02977430685813843
            ],
            "target_residual": 0.02977430685813843,
            "energy_eV": -425.5046727688668,
            "max_atomic_step_A": 0.007468112390766066,
            "max_log_strain_component": 0.00020252565097105219,
            "step_scale": 1.0,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 0.17306773967256842,
            "cell_principal_stretches": [
              1.0002025461606752,
              1.0000598969072851,
              0.9999947399652053
            ],
            "cell_volume_ratio": 1.0002571937845306,
            "cell_rmsd_from_input_A": 0.0011738587229901893
          },
          {
            "iteration": 1,
            "reduced_polarization": [
              2.092420712006361e-15,
              1.300999837422333e-16,
              1.5564885228037627e-05
            ],
            "branch_aligned_reduced_polarization": [
              2.092420712006361e-15,
              1.300999837422333e-16,
              1.5564885228037627e-05
            ],
            "target_residual": 1.5564885228037627e-05,
            "energy_eV": -425.4879145815479
          }
        ],
        "iterations": 1
      },
      "parent": {
        "candidate_id": "inversion_parent_endpoint_00",
        "source": "same_species_inversion_center_projection_from_endpoint",
        "spacegroup": "Imma",
        "spacegroup_number": 74,
        "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": 2.862162988967259e-15,
        "parent_symmetrization_rmsd_A": 0.037490613244395087,
        "parent_cell_rmsd_A": 0.0,
        "energy_eV": -425.50496506279705,
        "reduced_polarization": [
          3.821309823324384e-16,
          -1.4558524417223977e-15,
          -2.4344294107011136e-15
        ],
        "cartesian_polarization_e_A2": [
          4.38558059535185e-18,
          -3.188600661532696e-17,
          -3.961892459289965e-17
        ],
        "ranking_score": 0.03749061324440081
      },
      "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": [
          -425.5046727688669,
          -425.50474154636737,
          -425.50480095806125,
          -425.50485113532477,
          -425.5048921532466,
          -425.504924048038,
          -425.5049468318424,
          -425.5049605046138,
          -425.50496506279717
        ],
        "cartesian_polarizations_e_A2": [
          [
            -2.7979849995003475e-17,
            9.571415718157124e-18,
            0.0004845595493683717
          ],
          [
            1.801372277012951e-17,
            -1.2939655853578986e-17,
            0.00042421679319020703
          ],
          [
            -6.113441064280668e-18,
            -6.357553255608764e-18,
            0.0003637831580893281
          ],
          [
            2.115184194044557e-17,
            -2.7451157103688175e-17,
            0.00030327162912539667
          ],
          [
            1.184823888002238e-17,
            -2.2539140239531293e-17,
            0.00024269519083673486
          ],
          [
            1.52109309658286e-17,
            -4.8586863953460356e-17,
            0.00018206682673017506
          ],
          [
            1.256987696125752e-17,
            1.4750084926368237e-17,
            0.00012139951925362292
          ],
          [
            -5.09420956723977e-18,
            2.4082916968266313e-17,
            6.070625000131812e-05
          ],
          [
            -1.1269950660668753e-18,
            -2.802656479348941e-17,
            -4.50502118112674e-18
          ]
        ],
        "raw_reduced_polarization": [
          [
            -2.4379822310042726e-15,
            4.3701204456631825e-16,
            0.02977430685813845
          ],
          [
            1.569598694619712e-15,
            -5.907992743257265e-16,
            0.026066478292059266
          ],
          [
            -5.326855107396821e-16,
            -2.90273396170883e-16,
            0.02235306556829429
          ],
          [
            1.843033998146023e-15,
            -1.2533659225391768e-15,
            0.018634866568448455
          ],
          [
            1.0323785103689559e-15,
            -1.0290928791400398e-15,
            0.014912679142092412
          ],
          [
            1.325381637798097e-15,
            -2.2183807892794633e-15,
            0.01118730107541575
          ],
          [
            1.0952573613842926e-15,
            6.734599103214084e-16,
            0.007459530089541123
          ],
          [
            -4.438763041317364e-16,
            1.0995786927797686e-15,
            0.0037301638531367105
          ],
          [
            -9.819902343976762e-17,
            -1.2796379076230755e-15,
            -2.768160966472042e-16
          ]
        ],
        "unwrapped_reduced_polarization": [
          [
            -2.4379822310042726e-15,
            4.3701204456631825e-16,
            0.02977430685813845
          ],
          [
            1.5695986946197118e-15,
            -5.907992743257265e-16,
            0.026066478292059266
          ],
          [
            -5.326855107396821e-16,
            -2.90273396170883e-16,
            0.02235306556829429
          ],
          [
            1.843033998146023e-15,
            -1.2533659225391768e-15,
            0.018634866568448455
          ],
          [
            1.0323785103689559e-15,
            -1.0290928791400398e-15,
            0.014912679142092412
          ],
          [
            1.325381637798097e-15,
            -2.2183807892794633e-15,
            0.01118730107541575
          ],
          [
            1.0952573613842926e-15,
            6.734599103214085e-16,
            0.007459530089541123
          ],
          [
            -4.438763041317364e-16,
            1.0995786927797686e-15,
            0.0037301638531367105
          ],
          [
            -9.819902343976761e-17,
            -1.2796379076230757e-15,
            -2.7668839441830073e-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": [
          [
            -2.4424906541753444e-15,
            4.440892098500626e-16,
            0.029774306858138422
          ],
          [
            1.5543122344752192e-15,
            -6.106226635438361e-16,
            0.026066478292059214
          ],
          [
            -5.551115123125783e-16,
            -2.7755575615628914e-16,
            0.022353065568294306
          ],
          [
            1.887379141862766e-15,
            -1.27675647831893e-15,
            0.018634866568448483
          ],
          [
            9.992007221626409e-16,
            -1.0547118733938987e-15,
            0.014912679142092378
          ],
          [
            1.3322676295501878e-15,
            -2.220446049250313e-15,
            0.011187301075415768
          ],
          [
            1.1102230246251565e-15,
            6.661338147750939e-16,
            0.007459530089541144
          ],
          [
            -4.440892098500626e-16,
            1.1102230246251565e-15,
            0.0037301638531367365
          ],
          [
            -1.1102230246251565e-16,
            -1.27675647831893e-15,
            -2.7755575615628914e-16
          ]
        ]
      },
      "reflected": {
        "reached": true,
        "construction": "reflect_displacements_about_reconstructed_parent",
        "energies_eV": [
          -425.50496506279717,
          -425.50496050461385,
          -425.5049468318424,
          -425.5049240480379,
          -425.5048921532467,
          -425.50485113532466,
          -425.50480095806165,
          -425.50474154636765,
          -425.5046727688668
        ],
        "cartesian_polarizations_e_A2": [
          [
            -1.1269950660668753e-18,
            -2.802656479348941e-17,
            -4.50502118112674e-18
          ],
          [
            1.0100137723676302e-17,
            -6.733673404064205e-17,
            -6.070625000128749e-05
          ],
          [
            -2.0716566413400028e-17,
            3.648926813373684e-19,
            -0.00012139951925376587
          ],
          [
            1.1579605410574334e-17,
            -5.1674417410930396e-17,
            -0.00018206682673020696
          ],
          [
            1.0832288126102455e-18,
            -4.490986847229149e-19,
            -0.00024269519083683987
          ],
          [
            -1.0532924811042784e-17,
            1.1143261114687326e-17,
            -0.00030327162912544616
          ],
          [
            2.6888284061024922e-18,
            -8.277450132799225e-17,
            -0.0003637831580894034
          ],
          [
            -1.329131959374088e-17,
            4.556948216547827e-17,
            -0.00042421679319025007
          ],
          [
            4.846996185108693e-18,
            -3.5198109415158455e-17,
            -0.00048455954936846047
          ]
        ],
        "raw_reduced_polarization": [
          [
            -9.819902343976762e-17,
            -1.2796379076230755e-15,
            -2.768160966472042e-16
          ],
          [
            8.800603400452829e-16,
            -3.0744630349401686e-15,
            -0.0037301638531348283
          ],
          [
            -1.805106918454118e-15,
            1.6660283223935888e-17,
            -0.007459530089549906
          ],
          [
            1.0089715362327715e-15,
            -2.3593524165589204e-15,
            -0.01118730107541771
          ],
          [
            9.438551663883956e-17,
            -2.0504963967921094e-17,
            -0.014912679142098864
          ],
          [
            -9.177705932809506e-16,
            5.087794184540421e-16,
            -0.018634866568451494
          ],
          [
            2.3428702718091903e-16,
            -3.779321171337456e-15,
            -0.022353065568298913
          ],
          [
            -1.1581191822660153e-15,
            2.080613062619993e-15,
            -0.02606647829206191
          ],
          [
            4.2233573715193973e-16,
            -1.6070765509858155e-15,
            -0.029774306858143904
          ]
        ],
        "unwrapped_reduced_polarization": [
          [
            -9.819902343976762e-17,
            -1.2796379076230755e-15,
            -2.768160966472042e-16
          ],
          [
            8.80060340045283e-16,
            -3.074463034940168e-15,
            -0.0037301638531348283
          ],
          [
            -1.805106918454118e-15,
            1.6660283223935786e-17,
            -0.007459530089549906
          ],
          [
            1.0089715362327715e-15,
            -2.3593524165589204e-15,
            -0.01118730107541771
          ],
          [
            9.438551663883956e-17,
            -2.050496396792118e-17,
            -0.014912679142098864
          ],
          [
            -9.177705932809506e-16,
            5.087794184540421e-16,
            -0.018634866568451494
          ],
          [
            2.3428702718091903e-16,
            -3.779321171337456e-15,
            -0.022353065568298913
          ],
          [
            -1.1581191822660153e-15,
            2.080613062619993e-15,
            -0.02606647829206191
          ],
          [
            4.2233573715193963e-16,
            -1.6070765509858157e-15,
            -0.029774306858143904
          ]
        ],
        "gauge_integer_shift": [
          0,
          0,
          0
        ],
        "expected_opposite_endpoint_reduced_polarization": [
          2.2415841841247372e-15,
          -2.9962878598124692e-15,
          -0.029774306858139005
        ],
        "actual_opposite_endpoint_branch_residual": 5.4072537776952645e-15
      },
      "pnp_branch": {
        "construction": "incoming_path_concatenated_with_parent_reflection",
        "reduced_polarization": [
          [
            -2.4379822310042726e-15,
            4.3701204456631825e-16,
            0.02977430685813845
          ],
          [
            1.569598694619712e-15,
            -5.907992743257265e-16,
            0.026066478292059266
          ],
          [
            -5.326855107396821e-16,
            -2.90273396170883e-16,
            0.02235306556829429
          ],
          [
            1.843033998146023e-15,
            -1.2533659225391768e-15,
            0.018634866568448455
          ],
          [
            1.0323785103689559e-15,
            -1.0290928791400398e-15,
            0.014912679142092412
          ],
          [
            1.325381637798097e-15,
            -2.2183807892794633e-15,
            0.01118730107541575
          ],
          [
            1.0952573613842926e-15,
            6.734599103214084e-16,
            0.007459530089541123
          ],
          [
            -4.438763041317364e-16,
            1.0995786927797686e-15,
            0.0037301638531367105
          ],
          [
            -9.819902343976762e-17,
            -1.2796379076230755e-15,
            -2.768160966472042e-16
          ],
          [
            8.800603400452829e-16,
            -3.0744630349401686e-15,
            -0.0037301638531348283
          ],
          [
            -1.805106918454118e-15,
            1.6660283223935888e-17,
            -0.007459530089549906
          ],
          [
            1.0089715362327715e-15,
            -2.3593524165589204e-15,
            -0.01118730107541771
          ],
          [
            9.438551663883956e-17,
            -2.0504963967921094e-17,
            -0.014912679142098864
          ],
          [
            -9.177705932809506e-16,
            5.087794184540421e-16,
            -0.018634866568451494
          ],
          [
            2.3428702718091903e-16,
            -3.779321171337456e-15,
            -0.022353065568298913
          ],
          [
            -1.1581191822660153e-15,
            2.080613062619993e-15,
            -0.02606647829206191
          ],
          [
            4.2233573715193973e-16,
            -1.6070765509858155e-15,
            -0.029774306858143904
          ]
        ],
        "unwrapped_reduced_polarization": [
          [
            -2.4379822310042726e-15,
            4.3701204456631825e-16,
            0.02977430685813845
          ],
          [
            1.5695986946197118e-15,
            -5.907992743257265e-16,
            0.026066478292059266
          ],
          [
            -5.326855107396821e-16,
            -2.90273396170883e-16,
            0.02235306556829429
          ],
          [
            1.843033998146023e-15,
            -1.2533659225391768e-15,
            0.018634866568448455
          ],
          [
            1.0323785103689559e-15,
            -1.0290928791400398e-15,
            0.014912679142092412
          ],
          [
            1.325381637798097e-15,
            -2.2183807892794633e-15,
            0.01118730107541575
          ],
          [
            1.0952573613842926e-15,
            6.734599103214085e-16,
            0.007459530089541123
          ],
          [
            -4.438763041317364e-16,
            1.0995786927797686e-15,
            0.0037301638531367105
          ],
          [
            -9.819902343976761e-17,
            -1.2796379076230757e-15,
            -2.7668839441830073e-16
          ],
          [
            8.80060340045283e-16,
            -3.0744630349401686e-15,
            -0.0037301638531348283
          ],
          [
            -1.805106918454118e-15,
            1.6660283223935786e-17,
            -0.007459530089549906
          ],
          [
            1.0089715362327715e-15,
            -2.3593524165589204e-15,
            -0.01118730107541771
          ],
          [
            9.438551663883956e-17,
            -2.050496396792118e-17,
            -0.014912679142098864
          ],
          [
            -9.177705932809506e-16,
            5.087794184540421e-16,
            -0.018634866568451494
          ],
          [
            2.3428702718091903e-16,
            -3.779321171337456e-15,
            -0.022353065568298913
          ],
          [
            -1.1581191822660153e-15,
            2.080613062619993e-15,
            -0.02606647829206191
          ],
          [
            4.2233573715193963e-16,
            -1.6070765509858157e-15,
            -0.029774306858143904
          ]
        ],
        "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": [
          [
            -2.4424906541753444e-15,
            4.440892098500626e-16,
            0.029774306858138422
          ],
          [
            1.5543122344752192e-15,
            -6.106226635438361e-16,
            0.026066478292059214
          ],
          [
            -5.551115123125783e-16,
            -2.7755575615628914e-16,
            0.022353065568294306
          ],
          [
            1.887379141862766e-15,
            -1.27675647831893e-15,
            0.018634866568448483
          ],
          [
            9.992007221626409e-16,
            -1.0547118733938987e-15,
            0.014912679142092378
          ],
          [
            1.3322676295501878e-15,
            -2.220446049250313e-15,
            0.011187301075415768
          ],
          [
            1.1102230246251565e-15,
            6.661338147750939e-16,
            0.007459530089541144
          ],
          [
            -4.440892098500626e-16,
            1.1102230246251565e-15,
            0.0037301638531367365
          ],
          [
            -1.1102230246251565e-16,
            -1.27675647831893e-15,
            -2.7755575615628914e-16
          ],
          [
            8.881784197001252e-16,
            -3.0531133177191805e-15,
            -0.003730163853134849
          ],
          [
            -1.8318679906315083e-15,
            0.0,
            -0.007459530089549915
          ],
          [
            9.992007221626409e-16,
            -2.3869795029440866e-15,
            -0.01118730107541771
          ],
          [
            1.1102230246251565e-16,
            0.0,
            -0.014912679142098872
          ],
          [
            -9.43689570931383e-16,
            5.551115123125783e-16,
            -0.01863486656845148
          ],
          [
            2.220446049250313e-16,
            -3.774758283725532e-15,
            -0.022353065568298913
          ],
          [
            -1.1657341758564144e-15,
            2.1094237467877974e-15,
            -0.026066478292061934
          ],
          [
            4.440892098500626e-16,
            -1.609823385706477e-15,
            -0.029774306858143917
          ]
        ]
      },
      "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": [
              -5.776976248714696e-16,
              -3.043705588988287e-16,
              0.02977430685813843
            ],
            "branch_aligned_reduced_polarization": [
              -5.776976248714696e-16,
              -3.043705588988287e-16,
              0.029774306858138422
            ],
            "target_residual": 0.4702256931418616,
            "energy_eV": -425.5046727688668,
            "max_atomic_step_A": 0.1179439152736958,
            "max_log_strain_component": 0.003198488047450182,
            "step_scale": 1.0,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 0.17306773967256842,
            "cell_principal_stretches": [
              1.000083075410038,
              0.9990545235860441,
              0.9968066216662071
            ],
            "cell_volume_ratio": 0.9959468963399559,
            "cell_rmsd_from_input_A": 0.018485726596595878
          },
          {
            "iteration": 1,
            "reduced_polarization": [
              -2.0066144422535172e-14,
              -2.9013717762020747e-14,
              0.49122013800968195
            ],
            "branch_aligned_reduced_polarization": [
              -2.0066144422535172e-14,
              -2.9013717762020747e-14,
              0.49122013800968195
            ],
            "target_residual": 0.00877986199031805,
            "energy_eV": -421.6514702688421,
            "max_atomic_step_A": 0.0024837752194793146,
            "max_log_strain_component": 6.697689831583913e-05,
            "step_scale": 1.0,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 0.17306773967256842,
            "cell_principal_stretches": [
              1.0000848150974035,
              0.9990347347032309,
              0.9967398608862069
            ],
            "cell_volume_ratio": 0.9958621994748085,
            "cell_rmsd_from_input_A": 0.01887175731978011
          },
          {
            "iteration": 2,
            "reduced_polarization": [
              -3.571579287438885e-15,
              1.4633248119362654e-15,
              0.5000675632138695
            ],
            "branch_aligned_reduced_polarization": [
              -3.571579287438885e-15,
              1.4633248119362654e-15,
              0.5000675632138695
            ],
            "target_residual": 6.75632138694704e-05,
            "energy_eV": -421.48213791059305
          }
        ],
        "iterations": 2
      },
      "parent": {
        "candidate_id": "bec_projection_01",
        "source": "MACEField_BEC_backprojection",
        "spacegroup": "Imm2",
        "spacegroup_number": 44,
        "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": 6.75632138694704e-05,
        "parent_symmetrization_rmsd_A": 0.13539780886226666,
        "parent_cell_rmsd_A": 0.01887175731978011,
        "energy_eV": -421.48213791059305,
        "reduced_polarization": [
          -3.571579287438885e-15,
          1.4633248119362654e-15,
          0.5000675632138695
        ],
        "cartesian_polarization_e_A2": [
          1.428333782196202e-16,
          3.647317829666685e-16,
          0.008145481478977888
        ],
        "ranking_score": 0.6402508746199507
      },
      "branch_status": "awaiting_branch_sampling"
    },
    {
      "orbit_id": 2,
      "formal_class": [
        0.5,
        0.0,
        0.0
      ],
      "formal_classes_in_orbit": [
        [
          0.5,
          0.0,
          0.0
        ]
      ],
      "target_reduced_polarization": [
        -0.5,
        0.0,
        0.0
      ],
      "bec_backprojection": {
        "converged_to_target": true,
        "history": [
          {
            "iteration": 0,
            "reduced_polarization": [
              -5.776976248714696e-16,
              -3.043705588988287e-16,
              0.02977430685813843
            ],
            "branch_aligned_reduced_polarization": [
              -5.551115123125783e-16,
              -3.043705588988287e-16,
              0.02977430685813843
            ],
            "target_residual": 0.5008857248403892,
            "energy_eV": -425.5046727688668,
            "max_atomic_step_A": 0.10258416157709005,
            "max_log_strain_component": 0.0005327827788431059,
            "step_scale": 1.0,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 0.17306773967256842,
            "cell_principal_stretches": [
              1.0006416564203993,
              1.0000598969072754,
              0.9995559135909972
            ],
            "cell_volume_ratio": 1.000257193784541,
            "cell_rmsd_from_input_A": 0.002958125256469574
          },
          {
            "iteration": 1,
            "reduced_polarization": [
              -0.5001696121734127,
              1.1964236032450837e-14,
              0.0009681371850838343
            ],
            "branch_aligned_reduced_polarization": [
              -0.5001696121734127,
              1.1964236032450837e-14,
              0.0009681371850838343
            ],
            "target_residual": 0.0009828824438923686,
            "energy_eV": -421.6727529060997
          }
        ],
        "iterations": 1
      },
      "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": [
          -0.5,
          0.0,
          0.0
        ],
        "formal_class": [
          0.5,
          0.0,
          0.0
        ],
        "target_residual": 0.0009828824438923686,
        "parent_symmetrization_rmsd_A": 0.06089691926398505,
        "parent_cell_rmsd_A": 0.002958125256469574,
        "energy_eV": -421.6727529060997,
        "reduced_polarization": [
          -0.5001696121734127,
          1.1964236032450837e-14,
          0.0009681371850838343
        ],
        "cartesian_polarization_e_A2": [
          -0.005738753981039202,
          1.403774064489702e-16,
          1.2697180618806323e-05
        ],
        "ranking_score": 0.5636022154658872
      },
      "branch_status": "awaiting_branch_sampling"
    },
    {
      "orbit_id": 3,
      "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": [
              -5.776976248714696e-16,
              -3.043705588988287e-16,
              0.02977430685813843
            ],
            "branch_aligned_reduced_polarization": [
              -5.776976248714696e-16,
              -2.7755575615628914e-16,
              0.02977430685813843
            ],
            "target_residual": 0.5008857248403894,
            "energy_eV": -425.5046727688668,
            "max_atomic_step_A": 0.11999999999999998,
            "max_log_strain_component": 0.001749139169849907,
            "step_scale": 0.5753699290668015,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 0.17306773967256842,
            "cell_principal_stretches": [
              1.0018267814358819,
              0.9999969735308046,
              0.9983272746837722
            ],
            "cell_volume_ratio": 1.0001479734899057,
            "cell_rmsd_from_input_A": 0.01702215153388756
          },
          {
            "iteration": 1,
            "reduced_polarization": [
              1.1903401571806448e-15,
              -0.2815208899124217,
              0.013061026459329638
            ],
            "branch_aligned_reduced_polarization": [
              1.1903401571806448e-15,
              -0.2815208899124217,
              0.013061026459329638
            ],
            "target_residual": 0.21886916629994155,
            "energy_eV": -419.8217846810501,
            "max_atomic_step_A": 0.08661061794225824,
            "max_log_strain_component": 0.0013122873859401148,
            "step_scale": 1.0,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 0.17306773967256842,
            "cell_principal_stretches": [
              1.003211285023595,
              0.9999942385970397,
              0.9970855492924693
            ],
            "cell_volume_ratio": 1.0002817121249348,
            "cell_rmsd_from_input_A": 0.02980327246730672
          },
          {
            "iteration": 2,
            "reduced_polarization": [
              1.043163873724748e-15,
              -0.5184687630390709,
              0.0004125027545732083
            ],
            "branch_aligned_reduced_polarization": [
              1.043163873724748e-15,
              -0.5184687630390709,
              0.0004125027545732083
            ],
            "target_residual": 0.018473369121951747,
            "energy_eV": -403.25822023094537,
            "max_atomic_step_A": 0.00630810404981202,
            "max_log_strain_component": 8.10071641730971e-05,
            "step_scale": 1.0,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 0.17306773967256842,
            "cell_principal_stretches": [
              1.0031318470767805,
              0.9999941677222586,
              0.997168034335508
            ],
            "cell_volume_ratio": 1.0002851781538955,
            "cell_rmsd_from_input_A": 0.029016980741932673
          },
          {
            "iteration": 3,
            "reduced_polarization": [
              -4.8944553327423214e-15,
              -0.5000703298181981,
              -1.0234373661807283e-05
            ],
            "branch_aligned_reduced_polarization": [
              -4.8944553327423214e-15,
              -0.5000703298181981,
              -1.0234373661807283e-05
            ],
            "target_residual": 7.107056867668472e-05,
            "energy_eV": -405.0474841383041
          }
        ],
        "iterations": 3
      },
      "parent": {
        "candidate_id": "bec_projection_03",
        "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": 7.107056867668472e-05,
        "parent_symmetrization_rmsd_A": 0.12301799877097268,
        "parent_cell_rmsd_A": 0.029016980741932673,
        "energy_eV": -405.0474841383041,
        "reduced_polarization": [
          -4.8944553327423214e-15,
          -0.5000703298181981,
          -1.0234373661807283e-05
        ],
        "cartesian_polarization_e_A2": [
          -5.284784440101938e-18,
          -0.0109501688871746,
          -3.280534959155647e-05
        ],
        "ranking_score": 0.6304143850938092
      },
      "branch_status": "awaiting_branch_sampling"
    },
    {
      "orbit_id": 4,
      "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": [
              -5.776976248714696e-16,
              -3.043705588988287e-16,
              0.02977430685813843
            ],
            "branch_aligned_reduced_polarization": [
              -5.551115123125783e-16,
              -3.043705588988287e-16,
              0.029774306858138422
            ],
            "target_residual": 0.6863761377632118,
            "energy_eV": -425.5046727688668,
            "max_atomic_step_A": 0.12,
            "max_log_strain_component": 0.0025008973202097374,
            "step_scale": 0.7818998486526353,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 0.17306773967256842,
            "cell_principal_stretches": [
              1.0001309028499246,
              0.9992606558840617,
              0.9974364538603394
            ],
            "cell_volume_ratio": 0.996829475827439,
            "cell_rmsd_from_input_A": 0.014615836853684451
          },
          {
            "iteration": 1,
            "reduced_polarization": [
              -0.39094384386384307,
              -5.860964511927658e-15,
              0.3894576547312444
            ],
            "branch_aligned_reduced_polarization": [
              -0.39094384386384307,
              -5.860964511927658e-15,
              0.3894576547312444
            ],
            "target_residual": 0.15528314553972242,
            "energy_eV": -420.82004877484553,
            "max_atomic_step_A": 0.035277719911506196,
            "max_log_strain_component": 0.0008515442284396996,
            "step_scale": 1.0,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 0.17306773967256842,
            "cell_principal_stretches": [
              1.000168376176163,
              0.9990090373260179,
              0.9965721554481306
            ],
            "cell_volume_ratio": 0.9957522223664024,
            "cell_rmsd_from_input_A": 0.019561262179503058
          },
          {
            "iteration": 2,
            "reduced_polarization": [
              -0.5008642219702044,
              -2.2176766867348605e-15,
              0.499043817980307
            ],
            "branch_aligned_reduced_polarization": [
              -0.5008642219702044,
              -2.2176766867348605e-15,
              0.499043817980307
            ],
            "target_residual": 0.0012888613845438075,
            "energy_eV": -417.16498362245073,
            "max_atomic_step_A": 0.00032257325962635345,
            "max_log_strain_component": 7.329041496706141e-06,
            "step_scale": 1.0,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 0.17306773967256842,
            "cell_principal_stretches": [
              1.0001681587809472,
              0.999006871979117,
              0.9965652578661556
            ],
            "cell_volume_ratio": 0.9957429557532431,
            "cell_rmsd_from_input_A": 0.019602522353812178
          },
          {
            "iteration": 3,
            "reduced_polarization": [
              -0.49999920798438374,
              -9.018855202171452e-16,
              0.5000075246544351
            ],
            "branch_aligned_reduced_polarization": [
              -0.49999920798438374,
              -9.018855202171452e-16,
              0.5000075246544351
            ],
            "target_residual": 7.566221851362749e-06,
            "energy_eV": -417.159856797959
          }
        ],
        "iterations": 3
      },
      "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": [
          -0.5,
          0.0,
          0.5
        ],
        "formal_class": [
          0.5,
          0.0,
          0.5
        ],
        "target_residual": 7.566221851362749e-06,
        "parent_symmetrization_rmsd_A": 0.14962898571189706,
        "parent_cell_rmsd_A": 0.019602522353812178,
        "energy_eV": -417.159856797959,
        "reduced_polarization": [
          -0.49999920798438374,
          -9.018855202171452e-16,
          0.5000075246544351
        ],
        "cartesian_polarization_e_A2": [
          -0.005758989913948406,
          6.896357675858914e-17,
          0.00814163870458554
        ],
        "ranking_score": 0.6545447487440528
      },
      "branch_status": "awaiting_branch_sampling"
    },
    {
      "orbit_id": 5,
      "formal_class": [
        0.0,
        0.5,
        0.5
      ],
      "formal_classes_in_orbit": [
        [
          0.0,
          0.5,
          0.5
        ]
      ],
      "target_reduced_polarization": [
        0.0,
        -0.5,
        0.5
      ],
      "bec_backprojection": {
        "converged_to_target": true,
        "history": [
          {
            "iteration": 0,
            "reduced_polarization": [
              -5.776976248714696e-16,
              -3.043705588988287e-16,
              0.02977430685813843
            ],
            "branch_aligned_reduced_polarization": [
              -5.776976248714696e-16,
              -2.7755575615628914e-16,
              0.029774306858138422
            ],
            "target_residual": 0.6863761377632122,
            "energy_eV": -425.5046727688668,
            "max_atomic_step_A": 0.12,
            "max_log_strain_component": 0.0018381376952487038,
            "step_scale": 0.5746895620635328,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 0.17306773967256842,
            "cell_principal_stretches": [
              1.0006724680530168,
              1.0000477417276374,
              0.9969506664943342
            ],
            "cell_volume_ratio": 0.9976687121220617,
            "cell_rmsd_from_input_A": 0.019991577605237915
          },
          {
            "iteration": 1,
            "reduced_polarization": [
              4.939358024496201e-15,
              -0.2817782641748198,
              0.2857943007143208
            ],
            "branch_aligned_reduced_polarization": [
              4.939358024496201e-15,
              -0.2817782641748198,
              0.2857943007143208
            ],
            "target_residual": 0.30578555818256287,
            "energy_eV": -418.6863006134913,
            "max_atomic_step_A": 0.09403795040308575,
            "max_log_strain_component": 0.001777867123661943,
            "step_scale": 1.0,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 0.17306773967256842,
            "cell_principal_stretches": [
              1.0010822624732303,
              1.0000939202234114,
              0.9942495151952521
            ],
            "cell_volume_ratio": 0.9954190353329864,
            "cell_rmsd_from_input_A": 0.0371339982190725
          },
          {
            "iteration": 2,
            "reduced_polarization": [
              -8.210910771564014e-16,
              -0.5153921913018944,
              0.4805975237370378
            ],
            "branch_aligned_reduced_polarization": [
              -8.210910771564014e-16,
              -0.5153921913018944,
              0.4805975237370378
            ],
            "target_residual": 0.024766421586675084,
            "energy_eV": -399.8506853204466,
            "max_atomic_step_A": 0.006364934814750415,
            "max_log_strain_component": 0.00014644945776821366,
            "step_scale": 1.0,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 0.17306773967256842,
            "cell_principal_stretches": [
              1.0009587280362833,
              1.0000977242111062,
              0.9941835468908344
            ],
            "cell_volume_ratio": 0.9952339474792571,
            "cell_rmsd_from_input_A": 0.037198784884481584
          },
          {
            "iteration": 3,
            "reduced_polarization": [
              4.4031400858892284e-15,
              -0.5001394484332118,
              0.5001749750197575
            ],
            "branch_aligned_reduced_polarization": [
              4.4031400858892284e-15,
              -0.5001394484332118,
              0.5001749750197575
            ],
            "target_residual": 0.00022374566602363004,
            "energy_eV": -400.9779355303244
          }
        ],
        "iterations": 3
      },
      "parent": {
        "candidate_id": "bec_projection_05",
        "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": 0.00022374566602363004,
        "parent_symmetrization_rmsd_A": 0.19855752991878287,
        "parent_cell_rmsd_A": 0.037198784884481584,
        "energy_eV": -400.9779355303244,
        "reduced_polarization": [
          4.4031400858892284e-15,
          -0.5001394484332118,
          0.5001749750197575
        ],
        "cartesian_polarization_e_A2": [
          -3.7038819847217834e-16,
          -0.010968785102271299,
          0.008114036962713653
        ],
        "ranking_score": 0.7083047174719506
      },
      "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": [
              -5.776976248714696e-16,
              -3.043705588988287e-16,
              0.02977430685813843
            ],
            "branch_aligned_reduced_polarization": [
              -5.551115123125783e-16,
              -2.7755575615628914e-16,
              0.02977430685813843
            ],
            "target_residual": 0.707733360347583,
            "energy_eV": -425.5046727688668,
            "max_atomic_step_A": 0.12,
            "max_log_strain_component": 0.0017236870064006532,
            "step_scale": 0.5669975766914584,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 0.17306773967256842,
            "cell_principal_stretches": [
              1.0018259590728777,
              0.9999981199465182,
              0.9983248002379991
            ],
            "cell_volume_ratio": 1.0001458201335056,
            "cell_rmsd_from_input_A": 0.016844881978037136
          },
          {
            "iteration": 1,
            "reduced_polarization": [
              -0.27047777618603003,
              -0.2757387668518515,
              0.013524867505016736
            ],
            "branch_aligned_reduced_polarization": [
              -0.27047777618603003,
              -0.2757387668518515,
              0.013524867505016736
            ],
            "target_residual": 0.3211798156152821,
            "energy_eV": -418.895501349217,
            "max_atomic_step_A": 0.08944696342731294,
            "max_log_strain_component": 0.0014446255530012827,
            "step_scale": 1.0,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 0.17306773967256842,
            "cell_principal_stretches": [
              1.003374602698185,
              0.9999965757203044,
              0.9969259435354848
            ],
            "cell_volume_ratio": 1.000286747241103,
            "cell_rmsd_from_input_A": 0.030989485654335024
          },
          {
            "iteration": 2,
            "reduced_polarization": [
              -0.48383494798787086,
              -0.5155101968337673,
              0.0007824918149792566
            ],
            "branch_aligned_reduced_polarization": [
              -0.48383494798787086,
              -0.5155101968337673,
              0.0007824918149792566
            ],
            "target_residual": 0.022416230856626085,
            "energy_eV": -399.58564635902223,
            "max_atomic_step_A": 0.005967548119834267,
            "max_log_strain_component": 6.203654791588824e-05,
            "step_scale": 1.0,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 0.17306773967256842,
            "cell_principal_stretches": [
              1.0033201019351177,
              0.9999967260326638,
              0.9969871219187353
            ],
            "cell_volume_ratio": 1.0002939458510776,
            "cell_rmsd_from_input_A": 0.030399539839450283
          },
          {
            "iteration": 3,
            "reduced_polarization": [
              -0.5000691535007469,
              -0.5000538423637119,
              -8.14147347806053e-06
            ],
            "branch_aligned_reduced_polarization": [
              -0.5000691535007469,
              -0.5000538423637119,
              -8.14147347806053e-06
            ],
            "target_residual": 8.801982950462341e-05,
            "energy_eV": -400.84672942252195
          }
        ],
        "iterations": 3
      },
      "parent": {
        "candidate_id": "bec_projection_06",
        "source": "MACEField_BEC_backprojection",
        "spacegroup": "P1",
        "spacegroup_number": 1,
        "pointgroup": "1",
        "has_inversion": false,
        "is_polar_point_group": true,
        "nonpolar_parent_hypothesis": false,
        "symmetry_tolerance_A": null,
        "target_reduced_polarization": [
          -0.5,
          -0.5,
          0.0
        ],
        "formal_class": [
          0.5,
          0.5,
          0.0
        ],
        "target_residual": 8.801982950462341e-05,
        "parent_symmetrization_rmsd_A": 0.14385834710739007,
        "parent_cell_rmsd_A": 0.030399539839450283,
        "energy_eV": -400.84672942252195,
        "reduced_polarization": [
          -0.5000691535007469,
          -0.5000538423637119,
          -8.14147347806053e-06
        ],
        "cartesian_polarization_e_A2": [
          -0.005737406071518615,
          -0.010949743323149885,
          -3.7627434640759904e-05
        ],
        "ranking_score": 0.6516342717262619
      },
      "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": [
              -5.776976248714696e-16,
              -3.043705588988287e-16,
              0.02977430685813843
            ],
            "branch_aligned_reduced_polarization": [
              -5.551115123125783e-16,
              -2.7755575615628914e-16,
              0.029774306858138422
            ],
            "target_residual": 0.8491832561295255,
            "energy_eV": -425.5046727688668,
            "max_atomic_step_A": 0.12,
            "max_log_strain_component": 0.0018114523408692307,
            "step_scale": 0.5663464468236802,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 0.17306773967256842,
            "cell_principal_stretches": [
              1.0007087931508656,
              1.0000209771825372,
              0.9969749403683233
            ],
            "cell_volume_ratio": 0.9977025179264558,
            "cell_rmsd_from_input_A": 0.019761614691904367
          },
          {
            "iteration": 1,
            "reduced_polarization": [
              -0.2701957257286465,
              -0.2758618522825051,
              0.2812648356738994
            ],
            "branch_aligned_reduced_polarization": [
              -0.2701957257286465,
              -0.2758618522825051,
              0.2812648356738994
            ],
            "target_residual": 0.3884494636994358,
            "energy_eV": -417.76792866641796,
            "max_atomic_step_A": 0.09722719429618308,
            "max_log_strain_component": 0.0018431353543291401,
            "step_scale": 1.0,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 0.17306773967256842,
            "cell_principal_stretches": [
              1.0012650797249114,
              1.000036233889072,
              0.9940766186251869
            ],
            "cell_volume_ratio": 0.9953702696295842,
            "cell_rmsd_from_input_A": 0.0382704635370663
          },
          {
            "iteration": 2,
            "reduced_polarization": [
              -0.48485393080325884,
              -0.5110274360647261,
              0.4773048352291086
            ],
            "branch_aligned_reduced_polarization": [
              -0.48485393080325884,
              -0.5110274360647261,
              0.4773048352291086
            ],
            "target_residual": 0.029429207638874744,
            "energy_eV": -395.5474735645444,
            "max_atomic_step_A": 0.0068289364267326265,
            "max_log_strain_component": 0.00019140310896158448,
            "step_scale": 1.0,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 0.17306773967256842,
            "cell_principal_stretches": [
              1.0011602427573822,
              1.000029759452499,
              0.9939455548359788
            ],
            "cell_volume_ratio": 0.9951283865618759,
            "cell_rmsd_from_input_A": 0.03872459504976483
          },
          {
            "iteration": 3,
            "reduced_polarization": [
              -0.5001070067356932,
              -0.5001730543995194,
              0.5002312389555341
            ],
            "branch_aligned_reduced_polarization": [
              -0.5001070067356932,
              -0.5001730543995194,
              0.5002312389555341
            ],
            "target_residual": 0.0003080092875762862,
            "energy_eV": -395.88897046692756
          }
        ],
        "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": 0.0003080092875762862,
        "parent_symmetrization_rmsd_A": 0.21438356771362402,
        "parent_cell_rmsd_A": 0.03872459504976483,
        "energy_eV": -395.88897046692756,
        "reduced_polarization": [
          -0.5001070067356932,
          -0.5001730543995194,
          0.5002312389555341
        ],
        "cartesian_polarization_e_A2": [
          -0.005763263355978843,
          -0.010969254588157768,
          0.008110057894750578
        ],
        "ranking_score": 0.7246807350512178
      },
      "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,
          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
        ],
        "endpoint_rmsd_A": 0.037490613244395087,
        "minimum_distance_A_by_image": [
          1.4160888246889154,
          1.4161727220211286,
          1.416256953852128,
          1.4163415201222338,
          1.4164264207715438,
          1.416511655739934,
          1.4165972249670569,
          1.4166831283923442,
          1.4167693659550058
        ],
        "minimum_distance_A": 1.4160888246889154,
        "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": [
          494.422745998529,
          494.422745998529,
          494.422745998529,
          494.422745998529,
          494.422745998529,
          494.422745998529,
          494.422745998529,
          494.422745998529,
          494.422745998529
        ],
        "cell_deformation_log_strain_norm": 0.0
      },
      "parent_reduced_polarization": [
        -9.819902343976762e-17,
        -1.2796379076230755e-15,
        -2.768160966472042e-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": [
          -425.5046727688669,
          -425.50474154636737,
          -425.50480095806125,
          -425.50485113532477,
          -425.5048921532466,
          -425.504924048038,
          -425.5049468318424,
          -425.5049605046138,
          -425.50496506279717
        ],
        "cartesian_polarizations_e_A2": [
          [
            -2.7979849995003475e-17,
            9.571415718157124e-18,
            0.0004845595493683717
          ],
          [
            1.801372277012951e-17,
            -1.2939655853578986e-17,
            0.00042421679319020703
          ],
          [
            -6.113441064280668e-18,
            -6.357553255608764e-18,
            0.0003637831580893281
          ],
          [
            2.115184194044557e-17,
            -2.7451157103688175e-17,
            0.00030327162912539667
          ],
          [
            1.184823888002238e-17,
            -2.2539140239531293e-17,
            0.00024269519083673486
          ],
          [
            1.52109309658286e-17,
            -4.8586863953460356e-17,
            0.00018206682673017506
          ],
          [
            1.256987696125752e-17,
            1.4750084926368237e-17,
            0.00012139951925362292
          ],
          [
            -5.09420956723977e-18,
            2.4082916968266313e-17,
            6.070625000131812e-05
          ],
          [
            -1.1269950660668753e-18,
            -2.802656479348941e-17,
            -4.50502118112674e-18
          ]
        ],
        "raw_reduced_polarization": [
          [
            -2.4379822310042726e-15,
            4.3701204456631825e-16,
            0.02977430685813845
          ],
          [
            1.569598694619712e-15,
            -5.907992743257265e-16,
            0.026066478292059266
          ],
          [
            -5.326855107396821e-16,
            -2.90273396170883e-16,
            0.02235306556829429
          ],
          [
            1.843033998146023e-15,
            -1.2533659225391768e-15,
            0.018634866568448455
          ],
          [
            1.0323785103689559e-15,
            -1.0290928791400398e-15,
            0.014912679142092412
          ],
          [
            1.325381637798097e-15,
            -2.2183807892794633e-15,
            0.01118730107541575
          ],
          [
            1.0952573613842926e-15,
            6.734599103214084e-16,
            0.007459530089541123
          ],
          [
            -4.438763041317364e-16,
            1.0995786927797686e-15,
            0.0037301638531367105
          ],
          [
            -9.819902343976762e-17,
            -1.2796379076230755e-15,
            -2.768160966472042e-16
          ]
        ],
        "unwrapped_reduced_polarization": [
          [
            -2.4379822310042726e-15,
            4.3701204456631825e-16,
            0.02977430685813845
          ],
          [
            1.5695986946197118e-15,
            -5.907992743257265e-16,
            0.026066478292059266
          ],
          [
            -5.326855107396821e-16,
            -2.90273396170883e-16,
            0.02235306556829429
          ],
          [
            1.843033998146023e-15,
            -1.2533659225391768e-15,
            0.018634866568448455
          ],
          [
            1.0323785103689559e-15,
            -1.0290928791400398e-15,
            0.014912679142092412
          ],
          [
            1.325381637798097e-15,
            -2.2183807892794633e-15,
            0.01118730107541575
          ],
          [
            1.0952573613842926e-15,
            6.734599103214085e-16,
            0.007459530089541123
          ],
          [
            -4.438763041317364e-16,
            1.0995786927797686e-15,
            0.0037301638531367105
          ],
          [
            -9.819902343976761e-17,
            -1.2796379076230757e-15,
            -2.7668839441830073e-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": [
          [
            -2.4424906541753444e-15,
            4.440892098500626e-16,
            0.029774306858138422
          ],
          [
            1.5543122344752192e-15,
            -6.106226635438361e-16,
            0.026066478292059214
          ],
          [
            -5.551115123125783e-16,
            -2.7755575615628914e-16,
            0.022353065568294306
          ],
          [
            1.887379141862766e-15,
            -1.27675647831893e-15,
            0.018634866568448483
          ],
          [
            9.992007221626409e-16,
            -1.0547118733938987e-15,
            0.014912679142092378
          ],
          [
            1.3322676295501878e-15,
            -2.220446049250313e-15,
            0.011187301075415768
          ],
          [
            1.1102230246251565e-15,
            6.661338147750939e-16,
            0.007459530089541144
          ],
          [
            -4.440892098500626e-16,
            1.1102230246251565e-15,
            0.0037301638531367365
          ],
          [
            -1.1102230246251565e-16,
            -1.27675647831893e-15,
            -2.7755575615628914e-16
          ]
        ]
      },
      "reflected": {
        "reached": true,
        "construction": "reflect_displacements_about_reconstructed_parent",
        "energies_eV": [
          -425.50496506279717,
          -425.50496050461385,
          -425.5049468318424,
          -425.5049240480379,
          -425.5048921532467,
          -425.50485113532466,
          -425.50480095806165,
          -425.50474154636765,
          -425.5046727688668
        ],
        "cartesian_polarizations_e_A2": [
          [
            -1.1269950660668753e-18,
            -2.802656479348941e-17,
            -4.50502118112674e-18
          ],
          [
            1.0100137723676302e-17,
            -6.733673404064205e-17,
            -6.070625000128749e-05
          ],
          [
            -2.0716566413400028e-17,
            3.648926813373684e-19,
            -0.00012139951925376587
          ],
          [
            1.1579605410574334e-17,
            -5.1674417410930396e-17,
            -0.00018206682673020696
          ],
          [
            1.0832288126102455e-18,
            -4.490986847229149e-19,
            -0.00024269519083683987
          ],
          [
            -1.0532924811042784e-17,
            1.1143261114687326e-17,
            -0.00030327162912544616
          ],
          [
            2.6888284061024922e-18,
            -8.277450132799225e-17,
            -0.0003637831580894034
          ],
          [
            -1.329131959374088e-17,
            4.556948216547827e-17,
            -0.00042421679319025007
          ],
          [
            4.846996185108693e-18,
            -3.5198109415158455e-17,
            -0.00048455954936846047
          ]
        ],
        "raw_reduced_polarization": [
          [
            -9.819902343976762e-17,
            -1.2796379076230755e-15,
            -2.768160966472042e-16
          ],
          [
            8.800603400452829e-16,
            -3.0744630349401686e-15,
            -0.0037301638531348283
          ],
          [
            -1.805106918454118e-15,
            1.6660283223935888e-17,
            -0.007459530089549906
          ],
          [
            1.0089715362327715e-15,
            -2.3593524165589204e-15,
            -0.01118730107541771
          ],
          [
            9.438551663883956e-17,
            -2.0504963967921094e-17,
            -0.014912679142098864
          ],
          [
            -9.177705932809506e-16,
            5.087794184540421e-16,
            -0.018634866568451494
          ],
          [
            2.3428702718091903e-16,
            -3.779321171337456e-15,
            -0.022353065568298913
          ],
          [
            -1.1581191822660153e-15,
            2.080613062619993e-15,
            -0.02606647829206191
          ],
          [
            4.2233573715193973e-16,
            -1.6070765509858155e-15,
            -0.029774306858143904
          ]
        ],
        "unwrapped_reduced_polarization": [
          [
            -9.819902343976762e-17,
            -1.2796379076230755e-15,
            -2.768160966472042e-16
          ],
          [
            8.80060340045283e-16,
            -3.074463034940168e-15,
            -0.0037301638531348283
          ],
          [
            -1.805106918454118e-15,
            1.6660283223935786e-17,
            -0.007459530089549906
          ],
          [
            1.0089715362327715e-15,
            -2.3593524165589204e-15,
            -0.01118730107541771
          ],
          [
            9.438551663883956e-17,
            -2.050496396792118e-17,
            -0.014912679142098864
          ],
          [
            -9.177705932809506e-16,
            5.087794184540421e-16,
            -0.018634866568451494
          ],
          [
            2.3428702718091903e-16,
            -3.779321171337456e-15,
            -0.022353065568298913
          ],
          [
            -1.1581191822660153e-15,
            2.080613062619993e-15,
            -0.02606647829206191
          ],
          [
            4.2233573715193963e-16,
            -1.6070765509858157e-15,
            -0.029774306858143904
          ]
        ],
        "gauge_integer_shift": [
          0,
          0,
          0
        ],
        "expected_opposite_endpoint_reduced_polarization": [
          2.2415841841247372e-15,
          -2.9962878598124692e-15,
          -0.029774306858139005
        ],
        "actual_opposite_endpoint_branch_residual": 5.4072537776952645e-15
      },
      "pnp_branch": {
        "construction": "incoming_path_concatenated_with_parent_reflection",
        "reduced_polarization": [
          [
            -2.4379822310042726e-15,
            4.3701204456631825e-16,
            0.02977430685813845
          ],
          [
            1.569598694619712e-15,
            -5.907992743257265e-16,
            0.026066478292059266
          ],
          [
            -5.326855107396821e-16,
            -2.90273396170883e-16,
            0.02235306556829429
          ],
          [
            1.843033998146023e-15,
            -1.2533659225391768e-15,
            0.018634866568448455
          ],
          [
            1.0323785103689559e-15,
            -1.0290928791400398e-15,
            0.014912679142092412
          ],
          [
            1.325381637798097e-15,
            -2.2183807892794633e-15,
            0.01118730107541575
          ],
          [
            1.0952573613842926e-15,
            6.734599103214084e-16,
            0.007459530089541123
          ],
          [
            -4.438763041317364e-16,
            1.0995786927797686e-15,
            0.0037301638531367105
          ],
          [
            -9.819902343976762e-17,
            -1.2796379076230755e-15,
            -2.768160966472042e-16
          ],
          [
            8.800603400452829e-16,
            -3.0744630349401686e-15,
            -0.0037301638531348283
          ],
          [
            -1.805106918454118e-15,
            1.6660283223935888e-17,
            -0.007459530089549906
          ],
          [
            1.0089715362327715e-15,
            -2.3593524165589204e-15,
            -0.01118730107541771
          ],
          [
            9.438551663883956e-17,
            -2.0504963967921094e-17,
            -0.014912679142098864
          ],
          [
            -9.177705932809506e-16,
            5.087794184540421e-16,
            -0.018634866568451494
          ],
          [
            2.3428702718091903e-16,
            -3.779321171337456e-15,
            -0.022353065568298913
          ],
          [
            -1.1581191822660153e-15,
            2.080613062619993e-15,
            -0.02606647829206191
          ],
          [
            4.2233573715193973e-16,
            -1.6070765509858155e-15,
            -0.029774306858143904
          ]
        ],
        "unwrapped_reduced_polarization": [
          [
            -2.4379822310042726e-15,
            4.3701204456631825e-16,
            0.02977430685813845
          ],
          [
            1.5695986946197118e-15,
            -5.907992743257265e-16,
            0.026066478292059266
          ],
          [
            -5.326855107396821e-16,
            -2.90273396170883e-16,
            0.02235306556829429
          ],
          [
            1.843033998146023e-15,
            -1.2533659225391768e-15,
            0.018634866568448455
          ],
          [
            1.0323785103689559e-15,
            -1.0290928791400398e-15,
            0.014912679142092412
          ],
          [
            1.325381637798097e-15,
            -2.2183807892794633e-15,
            0.01118730107541575
          ],
          [
            1.0952573613842926e-15,
            6.734599103214085e-16,
            0.007459530089541123
          ],
          [
            -4.438763041317364e-16,
            1.0995786927797686e-15,
            0.0037301638531367105
          ],
          [
            -9.819902343976761e-17,
            -1.2796379076230757e-15,
            -2.7668839441830073e-16
          ],
          [
            8.80060340045283e-16,
            -3.0744630349401686e-15,
            -0.0037301638531348283
          ],
          [
            -1.805106918454118e-15,
            1.6660283223935786e-17,
            -0.007459530089549906
          ],
          [
            1.0089715362327715e-15,
            -2.3593524165589204e-15,
            -0.01118730107541771
          ],
          [
            9.438551663883956e-17,
            -2.050496396792118e-17,
            -0.014912679142098864
          ],
          [
            -9.177705932809506e-16,
            5.087794184540421e-16,
            -0.018634866568451494
          ],
          [
            2.3428702718091903e-16,
            -3.779321171337456e-15,
            -0.022353065568298913
          ],
          [
            -1.1581191822660153e-15,
            2.080613062619993e-15,
            -0.02606647829206191
          ],
          [
            4.2233573715193963e-16,
            -1.6070765509858157e-15,
            -0.029774306858143904
          ]
        ],
        "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": [
          [
            -2.4424906541753444e-15,
            4.440892098500626e-16,
            0.029774306858138422
          ],
          [
            1.5543122344752192e-15,
            -6.106226635438361e-16,
            0.026066478292059214
          ],
          [
            -5.551115123125783e-16,
            -2.7755575615628914e-16,
            0.022353065568294306
          ],
          [
            1.887379141862766e-15,
            -1.27675647831893e-15,
            0.018634866568448483
          ],
          [
            9.992007221626409e-16,
            -1.0547118733938987e-15,
            0.014912679142092378
          ],
          [
            1.3322676295501878e-15,
            -2.220446049250313e-15,
            0.011187301075415768
          ],
          [
            1.1102230246251565e-15,
            6.661338147750939e-16,
            0.007459530089541144
          ],
          [
            -4.440892098500626e-16,
            1.1102230246251565e-15,
            0.0037301638531367365
          ],
          [
            -1.1102230246251565e-16,
            -1.27675647831893e-15,
            -2.7755575615628914e-16
          ],
          [
            8.881784197001252e-16,
            -3.0531133177191805e-15,
            -0.003730163853134849
          ],
          [
            -1.8318679906315083e-15,
            0.0,
            -0.007459530089549915
          ],
          [
            9.992007221626409e-16,
            -2.3869795029440866e-15,
            -0.01118730107541771
          ],
          [
            1.1102230246251565e-16,
            0.0,
            -0.014912679142098872
          ],
          [
            -9.43689570931383e-16,
            5.551115123125783e-16,
            -0.01863486656845148
          ],
          [
            2.220446049250313e-16,
            -3.774758283725532e-15,
            -0.022353065568298913
          ],
          [
            -1.1657341758564144e-15,
            2.1094237467877974e-15,
            -0.026066478292061934
          ],
          [
            4.440892098500626e-16,
            -1.609823385706477e-15,
            -0.029774306858143917
          ]
        ]
      },
      "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": "Imma",
        "spacegroup_number": 74,
        "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": 2.862162988967259e-15,
        "parent_symmetrization_rmsd_A": 0.037490613244395087,
        "parent_cell_rmsd_A": 0.0,
        "energy_eV": -425.50496506279705,
        "reduced_polarization": [
          3.821309823324384e-16,
          -1.4558524417223977e-15,
          -2.4344294107011136e-15
        ],
        "cartesian_polarization_e_A2": [
          4.38558059535185e-18,
          -3.188600661532696e-17,
          -3.961892459289965e-17
        ],
        "ranking_score": 0.03749061324440081
      }
    }
  ],
  "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": 55,
      "full_response": 20,
      "energy_polarization": 35
    },
    "model_evaluations_for_recovery_and_path_properties": {
      "total": 80,
      "full_response": 45,
      "energy_polarization": 35
    },
    "elapsed_seconds": 2927.110391441034
  }
}
