{
  "schema": "ferrofinder.endpoint_parent_recovery.v4_variable_cell",
  "status": "complete",
  "input_atom_count": 6,
  "input_formula": "Ag4S2",
  "input_spacegroup": "P2_1",
  "input_pointgroup": "2",
  "input_is_polar_point_group": true,
  "input_energy_eV": -19.436754013242563,
  "input_cartesian_polarization_e_A2": [
    3.944392688564605e-12,
    0.0021387097855985198,
    2.944752100044303e-11
  ],
  "input_reduced_polarization": [
    3.9509728089959303e-10,
    0.05274135101015198,
    7.500229477867141e-10
  ],
  "input_formal_targets": [
    {
      "orbit_id": 0,
      "representative_formal_class": [
        0.0,
        0.0,
        0.0
      ],
      "target_reduced_polarization": [
        0.0,
        0.0,
        0.0
      ]
    },
    {
      "orbit_id": 1,
      "representative_formal_class": [
        0.0,
        0.5,
        0.0
      ],
      "target_reduced_polarization": [
        0.0,
        0.5,
        0.0
      ]
    },
    {
      "orbit_id": 2,
      "representative_formal_class": [
        0.0,
        0.0,
        0.5
      ],
      "target_reduced_polarization": [
        0.0,
        0.0,
        0.5
      ]
    },
    {
      "orbit_id": 3,
      "representative_formal_class": [
        0.5,
        0.0,
        0.0
      ],
      "target_reduced_polarization": [
        0.5,
        0.0,
        0.0
      ]
    },
    {
      "orbit_id": 4,
      "representative_formal_class": [
        0.0,
        0.5,
        0.5
      ],
      "target_reduced_polarization": [
        0.0,
        0.5,
        0.5
      ]
    },
    {
      "orbit_id": 5,
      "representative_formal_class": [
        0.5,
        0.5,
        0.0
      ],
      "target_reduced_polarization": [
        0.5,
        0.5,
        0.0
      ]
    },
    {
      "orbit_id": 6,
      "representative_formal_class": [
        0.5,
        0.0,
        0.5
      ],
      "target_reduced_polarization": [
        0.5,
        0.0,
        0.5
      ]
    },
    {
      "orbit_id": 7,
      "representative_formal_class": [
        0.5,
        0.5,
        0.5
      ],
      "target_reduced_polarization": [
        0.5,
        0.5,
        0.5
      ]
    }
  ],
  "parent_candidates": [
    {
      "candidate_id": "inversion_parent_endpoint_00",
      "source": "same_species_inversion_center_projection_from_endpoint",
      "spacegroup": "P2_1/m",
      "spacegroup_number": 11,
      "pointgroup": "2/m",
      "has_inversion": true,
      "is_polar_point_group": false,
      "nonpolar_parent_hypothesis": true,
      "symmetry_tolerance_A": null,
      "target_reduced_polarization": [
        0.0,
        0.0,
        0.0
      ],
      "formal_class": [
        0.0,
        0.0,
        0.0
      ],
      "target_residual": 1.7061930524110972e-15,
      "parent_symmetrization_rmsd_A": 0.30893029176220904,
      "parent_cell_rmsd_A": 0.0,
      "energy_eV": -19.29766717451739,
      "reduced_polarization": [
        1.690227918671534e-15,
        7.744205168984508e-17,
        2.196065656333133e-16
      ],
      "cartesian_polarization_e_A2": [
        4.8284477488950795e-17,
        3.140345679313701e-18,
        8.622228123026928e-18
      ],
      "ranking_score": 0.30893029176221243
    },
    {
      "candidate_id": "inversion_parent_endpoint_01",
      "source": "same_species_inversion_center_projection_from_endpoint",
      "spacegroup": "P2_1/m",
      "spacegroup_number": 11,
      "pointgroup": "2/m",
      "has_inversion": true,
      "is_polar_point_group": false,
      "nonpolar_parent_hypothesis": true,
      "symmetry_tolerance_A": null,
      "target_reduced_polarization": [
        0.0,
        0.0,
        0.0
      ],
      "formal_class": [
        0.0,
        0.0,
        0.0
      ],
      "target_residual": 1.9735559617828036e-15,
      "parent_symmetrization_rmsd_A": 0.5381809968619293,
      "parent_cell_rmsd_A": 0.0,
      "energy_eV": -18.547557001835848,
      "reduced_polarization": [
        1.5805382105217362e-15,
        8.239410335976167e-16,
        8.473153324018672e-16
      ],
      "cartesian_polarization_e_A2": [
        3.8404841097982445e-17,
        3.3411558816007345e-17,
        3.3267430174678897e-17
      ],
      "ranking_score": 0.5381809968619333
    },
    {
      "candidate_id": "inversion_parent_endpoint_02",
      "source": "same_species_inversion_center_projection_from_endpoint",
      "spacegroup": "P2_1/c",
      "spacegroup_number": 14,
      "pointgroup": "2/m",
      "has_inversion": true,
      "is_polar_point_group": false,
      "nonpolar_parent_hypothesis": true,
      "symmetry_tolerance_A": null,
      "target_reduced_polarization": [
        0.0,
        0.0,
        0.0
      ],
      "formal_class": [
        0.0,
        0.0,
        0.0
      ],
      "target_residual": 8.217297919012845e-16,
      "parent_symmetrization_rmsd_A": 0.6166779258310777,
      "parent_cell_rmsd_A": 0.0,
      "energy_eV": -17.22128188517937,
      "reduced_polarization": [
        8.077992712603139e-16,
        1.4473830261157054e-16,
        4.184509537037216e-17
      ],
      "cartesian_polarization_e_A2": [
        2.3739477696298502e-17,
        5.869269903357253e-18,
        1.6429288308055728e-18
      ],
      "ranking_score": 0.6166779258310794
    },
    {
      "candidate_id": "bec_projection_00",
      "source": "MACEField_BEC_backprojection",
      "spacegroup": "P2_1",
      "spacegroup_number": 4,
      "pointgroup": "2",
      "has_inversion": false,
      "is_polar_point_group": true,
      "nonpolar_parent_hypothesis": false,
      "symmetry_tolerance_A": null,
      "target_reduced_polarization": [
        0.0,
        0.0,
        0.0
      ],
      "formal_class": [
        0.0,
        0.0,
        0.0
      ],
      "target_residual": 6.969016895699335e-05,
      "parent_symmetrization_rmsd_A": 0.04494785374963185,
      "parent_cell_rmsd_A": 0.016515022055589055,
      "energy_eV": -19.341793174569318,
      "reduced_polarization": [
        1.5499083616573724e-12,
        6.969016895699333e-05,
        1.2192166977948747e-12
      ],
      "cartesian_polarization_e_A2": [
        3.335573804744816e-14,
        2.8410562848110065e-06,
        4.792469736766338e-14
      ],
      "ranking_score": 0.5492159896014431
    },
    {
      "candidate_id": "inversion_parent_bec_00_00",
      "source": "same_species_inversion_center_projection_after_BEC",
      "spacegroup": "P2_1/m",
      "spacegroup_number": 11,
      "pointgroup": "2/m",
      "has_inversion": true,
      "is_polar_point_group": false,
      "nonpolar_parent_hypothesis": true,
      "symmetry_tolerance_A": null,
      "target_reduced_polarization": [
        0.0,
        0.0,
        0.0
      ],
      "formal_class": [
        0.0,
        0.0,
        0.0
      ],
      "target_residual": 3.2861218159696074e-15,
      "parent_symmetrization_rmsd_A": 0.3089977278322626,
      "parent_cell_rmsd_A": 0.016515022055589055,
      "energy_eV": -19.29587904444821,
      "reduced_polarization": [
        1.1357372764118083e-15,
        2.5365397728128615e-15,
        -1.7534718159407507e-15
      ],
      "cartesian_polarization_e_A2": [
        5.2769686423728076e-17,
        1.0340701380094742e-16,
        -6.933243471730696e-17
      ],
      "ranking_score": 0.3131264833461664
    },
    {
      "candidate_id": "inversion_parent_bec_00_01",
      "source": "same_species_inversion_center_projection_after_BEC",
      "spacegroup": "P2_1/m",
      "spacegroup_number": 11,
      "pointgroup": "2/m",
      "has_inversion": true,
      "is_polar_point_group": false,
      "nonpolar_parent_hypothesis": true,
      "symmetry_tolerance_A": null,
      "target_reduced_polarization": [
        0.0,
        0.0,
        0.0
      ],
      "formal_class": [
        0.0,
        0.0,
        0.0
      ],
      "target_residual": 5.801851613785372e-16,
      "parent_symmetrization_rmsd_A": 0.5389674010443954,
      "parent_cell_rmsd_A": 0.016515022055589055,
      "energy_eV": -18.479506888388045,
      "reduced_polarization": [
        1.3456113237629326e-17,
        3.574795157686194e-16,
        -4.567736313604462e-16
      ],
      "cartesian_polarization_e_A2": [
        5.284190770989194e-18,
        1.4573352886825454e-17,
        -1.802522933839708e-17
      ],
      "ranking_score": 0.5430961565582938
    },
    {
      "candidate_id": "bec_projection_01",
      "source": "MACEField_BEC_backprojection",
      "spacegroup": "P2_1",
      "spacegroup_number": 4,
      "pointgroup": "2",
      "has_inversion": false,
      "is_polar_point_group": true,
      "nonpolar_parent_hypothesis": false,
      "symmetry_tolerance_A": null,
      "target_reduced_polarization": [
        0.0,
        0.5,
        0.0
      ],
      "formal_class": [
        0.0,
        0.5,
        0.0
      ],
      "target_residual": 0.024379957901249583,
      "parent_symmetrization_rmsd_A": 0.4446438981737826,
      "parent_cell_rmsd_A": 0.22808170287241672,
      "energy_eV": -7.024582930893935,
      "reduced_polarization": [
        1.5082355375957608e-10,
        0.5243799579012496,
        -8.492866965913008e-12
      ],
      "cartesian_polarization_e_A2": [
        5.635809775781925e-12,
        0.020595681439033665,
        -5.7380074168829665e-12
      ],
      "ranking_score": 1.050424239694386
    },
    {
      "candidate_id": "bec_projection_02",
      "source": "MACEField_BEC_backprojection",
      "spacegroup": "P1",
      "spacegroup_number": 1,
      "pointgroup": "1",
      "has_inversion": false,
      "is_polar_point_group": true,
      "nonpolar_parent_hypothesis": false,
      "symmetry_tolerance_A": null,
      "target_reduced_polarization": [
        0.0,
        0.0,
        0.5
      ],
      "formal_class": [
        0.0,
        0.0,
        0.5
      ],
      "target_residual": 0.0884999692512015,
      "parent_symmetrization_rmsd_A": 0.4337713844740285,
      "parent_cell_rmsd_A": 0.16218413651071018,
      "energy_eV": -8.398961795705507,
      "reduced_polarization": [
        -0.01976908552118417,
        0.010005043127438728,
        0.41431845632145853
      ],
      "cartesian_polarization_e_A2": [
        -0.0048550990529735326,
        0.00074302538149839,
        0.016484421794735384
      ],
      "ranking_score": 1.151317357104109
    },
    {
      "candidate_id": "bec_projection_03",
      "source": "MACEField_BEC_backprojection",
      "spacegroup": "P1",
      "spacegroup_number": 1,
      "pointgroup": "1",
      "has_inversion": false,
      "is_polar_point_group": true,
      "nonpolar_parent_hypothesis": false,
      "symmetry_tolerance_A": null,
      "target_reduced_polarization": [
        0.5,
        0.0,
        0.0
      ],
      "formal_class": [
        0.5,
        0.0,
        0.0
      ],
      "target_residual": 0.10568229913932835,
      "parent_symmetrization_rmsd_A": 0.33151671845873554,
      "parent_cell_rmsd_A": 0.25636157703125134,
      "energy_eV": -15.747053692671946,
      "reduced_polarization": [
        0.3954449323930281,
        -0.005789592340319642,
        0.014264179247644266
      ],
      "cartesian_polarization_e_A2": [
        0.011769872333535308,
        0.000439016743311167,
        0.000654246531296575
      ],
      "ranking_score": 1.106971710995205
    },
    {
      "candidate_id": "bec_projection_04",
      "source": "MACEField_BEC_backprojection",
      "spacegroup": "P1",
      "spacegroup_number": 1,
      "pointgroup": "1",
      "has_inversion": false,
      "is_polar_point_group": true,
      "nonpolar_parent_hypothesis": false,
      "symmetry_tolerance_A": null,
      "target_reduced_polarization": [
        0.0,
        0.5,
        0.5
      ],
      "formal_class": [
        0.0,
        0.5,
        0.5
      ],
      "target_residual": 0.26514731917022405,
      "parent_symmetrization_rmsd_A": 0.4106839434463461,
      "parent_cell_rmsd_A": 0.16848174923937387,
      "energy_eV": -6.536563323025386,
      "reduced_polarization": [
        -0.03796225746676964,
        0.3394161429351654,
        0.292455323553303
      ],
      "cartesian_polarization_e_A2": [
        -0.004118203160129026,
        0.013498445415227609,
        0.011065225725115474
      ],
      "ranking_score": 1.4830990190966378
    },
    {
      "candidate_id": "bec_projection_05",
      "source": "MACEField_BEC_backprojection",
      "spacegroup": "P1",
      "spacegroup_number": 1,
      "pointgroup": "1",
      "has_inversion": false,
      "is_polar_point_group": true,
      "nonpolar_parent_hypothesis": false,
      "symmetry_tolerance_A": null,
      "target_reduced_polarization": [
        0.5,
        0.5,
        0.0
      ],
      "formal_class": [
        0.5,
        0.5,
        0.0
      ],
      "target_residual": 0.34685907976039515,
      "parent_symmetrization_rmsd_A": 0.3119758319660326,
      "parent_cell_rmsd_A": 0.2089526300958643,
      "energy_eV": -16.430359344921264,
      "reduced_polarization": [
        0.22992613851912772,
        0.2823773864461063,
        -0.0034247083104100443
      ],
      "cartesian_polarization_e_A2": [
        0.007414328289177784,
        0.011655830436355208,
        0.00011434538584306422
      ],
      "ranking_score": 1.5579321490107891
    },
    {
      "candidate_id": "bec_projection_06",
      "source": "MACEField_BEC_backprojection",
      "spacegroup": "P1",
      "spacegroup_number": 1,
      "pointgroup": "1",
      "has_inversion": false,
      "is_polar_point_group": true,
      "nonpolar_parent_hypothesis": false,
      "symmetry_tolerance_A": null,
      "target_reduced_polarization": [
        0.5,
        0.0,
        0.5
      ],
      "formal_class": [
        0.5,
        0.0,
        0.5
      ],
      "target_residual": 0.09204738191724775,
      "parent_symmetrization_rmsd_A": 0.42429669227781097,
      "parent_cell_rmsd_A": 0.16738715783073624,
      "energy_eV": -9.420455803507892,
      "reduced_polarization": [
        0.4397194372714766,
        -0.0018701439704804927,
        0.4304624070269764
      ],
      "cartesian_polarization_e_A2": [
        0.00856144058966991,
        0.0003764389791826973,
        0.016895610574806725
      ],
      "ranking_score": 1.1502382455699904
    },
    {
      "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": 0.3766701982730119,
      "parent_symmetrization_rmsd_A": 0.3575020082650929,
      "parent_cell_rmsd_A": 0.16434488413931395,
      "energy_eV": -13.508352863487447,
      "reduced_polarization": [
        0.2652178079335694,
        0.3001837892476286,
        0.2835947263210166
      ],
      "cartesian_polarization_e_A2": [
        0.005520415228077318,
        0.01198891790685414,
        0.011086949574050585
      ],
      "ranking_score": 1.6519286258459451
    }
  ],
  "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": [
              3.9509728089959303e-10,
              0.05274135101015198,
              7.500229477867141e-10
            ],
            "branch_aligned_reduced_polarization": [
              3.9509728089959303e-10,
              0.05274135101015198,
              7.500229477867141e-10
            ],
            "target_residual": 0.05274135101015199,
            "energy_eV": -19.436754013242563,
            "max_atomic_step_A": 0.05582721028117025,
            "max_log_strain_component": 0.0045028362980225715,
            "step_scale": 1.0,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 1.203697092630885,
            "cell_principal_stretches": [
              1.0018968329106377,
              1.000199093154451,
              0.9924450466502057
            ],
            "cell_volume_ratio": 0.9945255128849945,
            "cell_rmsd_from_input_A": 0.017673939648930014
          },
          {
            "iteration": 1,
            "reduced_polarization": [
              -1.0717090838202923e-10,
              -0.004720616482603455,
              -3.25135097176031e-11
            ],
            "branch_aligned_reduced_polarization": [
              -1.0717090838202923e-10,
              -0.004720616482603455,
              -3.25135097176031e-11
            ],
            "target_residual": 0.004720616482603456,
            "energy_eV": -19.327218790852733,
            "max_atomic_step_A": 0.0041865952496965,
            "max_log_strain_component": 0.00029674754813076515,
            "step_scale": 1.0,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 1.203697092630885,
            "cell_principal_stretches": [
              1.0017717164715976,
              1.0001859712253385,
              0.9929411743688887
            ],
            "cell_volume_ratio": 0.9948853702522148,
            "cell_rmsd_from_input_A": 0.016515022055589055
          },
          {
            "iteration": 2,
            "reduced_polarization": [
              1.5499083616573724e-12,
              6.969016895699333e-05,
              1.2192166977948747e-12
            ],
            "branch_aligned_reduced_polarization": [
              1.5499083616573724e-12,
              6.969016895699333e-05,
              1.2192166977948747e-12
            ],
            "target_residual": 6.969016895699335e-05,
            "energy_eV": -19.341793174569318
          }
        ],
        "iterations": 2
      },
      "parent": {
        "candidate_id": "inversion_parent_endpoint_00",
        "source": "same_species_inversion_center_projection_from_endpoint",
        "spacegroup": "P2_1/m",
        "spacegroup_number": 11,
        "pointgroup": "2/m",
        "has_inversion": true,
        "is_polar_point_group": false,
        "nonpolar_parent_hypothesis": true,
        "symmetry_tolerance_A": null,
        "target_reduced_polarization": [
          0.0,
          0.0,
          0.0
        ],
        "formal_class": [
          0.0,
          0.0,
          0.0
        ],
        "target_residual": 1.7061930524110972e-15,
        "parent_symmetrization_rmsd_A": 0.30893029176220904,
        "parent_cell_rmsd_A": 0.0,
        "energy_eV": -19.29766717451739,
        "reduced_polarization": [
          1.690227918671534e-15,
          7.744205168984508e-17,
          2.196065656333133e-16
        ],
        "cartesian_polarization_e_A2": [
          4.8284477488950795e-17,
          3.140345679313701e-18,
          8.622228123026928e-18
        ],
        "ranking_score": 0.30893029176221243
      },
      "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": [
          -19.436754013242563,
          -19.456294641130228,
          -19.45489381700374,
          -19.43529298074406,
          -19.402974054878523,
          -19.36544036604803,
          -19.330797697585755,
          -19.30643548195698,
          -19.29766717451739
        ],
        "cartesian_polarizations_e_A2": [
          [
            3.944536392366656e-12,
            0.002138709785598493,
            2.944754974120344e-11
          ],
          [
            1.9189282189382423e-12,
            0.0020507565417348353,
            2.4712210751337954e-11
          ],
          [
            7.685898218032166e-13,
            0.0019211969818450864,
            2.0542992889650216e-11
          ],
          [
            9.462799562487353e-13,
            0.001739675321990905,
            1.7061841669719674e-11
          ],
          [
            1.5344668990338596e-12,
            0.0014991297596027042,
            1.38256462263187e-11
          ],
          [
            1.6833712458779793e-12,
            0.0011978271806295964,
            1.050229231931837e-11
          ],
          [
            1.4904605795344852e-12,
            0.0008392012735599862,
            7.0997696885076126e-12
          ],
          [
            9.497093037808673e-13,
            0.0004341707931177682,
            3.6081997513233437e-12
          ],
          [
            7.510918720503458e-17,
            -7.985742950724252e-17,
            -4.1578300059929855e-17
          ]
        ],
        "raw_reduced_polarization": [
          [
            3.9510233887552834e-10,
            0.05274135101015132,
            7.500236798085995e-10
          ],
          [
            2.850857363934056e-10,
            0.05057239244535171,
            6.294154660341756e-10
          ],
          [
            2.0937312917555822e-10,
            0.047377407192617293,
            5.232262533482923e-10
          ],
          [
            1.841810948023614e-10,
            0.042901017902784035,
            4.3456197156972295e-10
          ],
          [
            1.7489367352670792e-10,
            0.036969077989627404,
            3.5213666839948274e-10
          ],
          [
            1.50150963202237e-10,
            0.02953884823854522,
            2.6749145518002763e-10
          ],
          [
            1.1328068609570961e-10,
            0.020695004640195934,
            1.808298291153652e-10
          ],
          [
            6.399319979552035e-11,
            0.010706807605395632,
            9.190018452317628e-11
          ],
          [
            2.137516994954202e-15,
            -1.9693128767497897e-15,
            -1.0589916609428664e-15
          ]
        ],
        "unwrapped_reduced_polarization": [
          [
            3.9510233887552834e-10,
            0.05274135101015132,
            7.500236798085995e-10
          ],
          [
            2.850857363934056e-10,
            0.05057239244535171,
            6.294154660341756e-10
          ],
          [
            2.0937312917555822e-10,
            0.047377407192617293,
            5.232262533482923e-10
          ],
          [
            1.841810948023614e-10,
            0.042901017902784035,
            4.3456197156972295e-10
          ],
          [
            1.7489367352670792e-10,
            0.036969077989627404,
            3.5213666839948274e-10
          ],
          [
            1.50150963202237e-10,
            0.02953884823854522,
            2.6749145518002763e-10
          ],
          [
            1.1328068609570961e-10,
            0.020695004640195934,
            1.808298291153652e-10
          ],
          [
            6.399319979552035e-11,
            0.010706807605395632,
            9.190018452317628e-11
          ],
          [
            2.137516994951962e-15,
            -1.968911145233676e-15,
            -1.0589916609440764e-15
          ]
        ],
        "berry_integer_shifts": [
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ]
        ],
        "folded_reduced_polarization": [
          [
            3.951022842230145e-10,
            0.052741351010151316,
            7.500237098057028e-10
          ],
          [
            2.850857327985068e-10,
            0.05057239244535172,
            6.294155197039686e-10
          ],
          [
            2.0937307443347208e-10,
            0.047377407192617293,
            5.232262401122512e-10
          ],
          [
            1.8418111480400512e-10,
            0.042901017902784,
            4.345619419865443e-10
          ],
          [
            1.7489365511380583e-10,
            0.03696907798962745,
            3.5213665317002096e-10
          ],
          [
            1.5015100274240467e-10,
            0.029538848238545246,
            2.6749147341575963e-10
          ],
          [
            1.1328071813920815e-10,
            0.020695004640195913,
            1.8082979558187162e-10
          ],
          [
            6.399325513939402e-11,
            0.010706807605395663,
            9.190015415327935e-11
          ],
          [
            2.1094237467877974e-15,
            -1.942890293094024e-15,
            -1.0547118733938987e-15
          ]
        ]
      },
      "reflected": {
        "reached": true,
        "construction": "reflect_displacements_about_reconstructed_parent",
        "energies_eV": [
          -19.297667174517386,
          -19.306435481956985,
          -19.33079769758576,
          -19.36544036604804,
          -19.40297405487853,
          -19.43529298074405,
          -19.454893817003747,
          -19.456294641130228,
          -19.436754013242563
        ],
        "cartesian_polarizations_e_A2": [
          [
            -1.2262724441638298e-17,
            -3.028146812796933e-17,
            1.916050694005984e-18
          ],
          [
            -9.497982085330692e-13,
            -0.0004341707931177242,
            -3.6081495507951608e-12
          ],
          [
            -1.49043030593352e-12,
            -0.0008392012735599682,
            -7.099863958201757e-12
          ],
          [
            -1.6832444033220362e-12,
            -0.0011978271806296179,
            -1.0502350758864537e-11
          ],
          [
            -1.5345703657713357e-12,
            -0.001499129759602789,
            -1.3825600815917253e-11
          ],
          [
            -9.46321917758934e-13,
            -0.0017396753219908986,
            -1.7061755447438442e-11
          ],
          [
            -7.688498298823932e-13,
            -0.0019211969818453386,
            -2.054298465063223e-11
          ],
          [
            -1.9187852815564693e-12,
            -0.0020507565417348405,
            -2.471239526701979e-11
          ],
          [
            -3.944374869293151e-12,
            -0.002138709785598408,
            -2.944745872879547e-11
          ]
        ],
        "raw_reduced_polarization": [
          [
            -3.9254996496419646e-16,
            -7.467518736736947e-16,
            4.8801459029625185e-17
          ],
          [
            -6.399572110625323e-11,
            -0.010706807605394546,
            -9.18989059249497e-11
          ],
          [
            -1.1328051764968823e-10,
            -0.02069500464019549,
            -1.8083223014714945e-10
          ],
          [
            -1.501472481071236e-10,
            -0.029538848238545752,
            -2.674929436245281e-10
          ],
          [
            -1.7489672416966095e-10,
            -0.0369690779896295,
            -3.5213551180490375e-10
          ],
          [
            -1.8418172568773467e-10,
            -0.042901017902783875,
            -4.345597755040666e-10
          ],
          [
            -2.0938174206827212e-10,
            -0.04737740719262351,
            -5.232260435020184e-10
          ],
          [
            -2.850826109617739e-10,
            -0.05057239244535183,
            -6.294201656146802e-10
          ],
          [
            -3.9509612874549187e-10,
            -0.05274135101014923,
            -7.500213617392955e-10
          ]
        ],
        "unwrapped_reduced_polarization": [
          [
            -3.9254996496419646e-16,
            -7.467518736736947e-16,
            4.8801459029625185e-17
          ],
          [
            -6.399572110625323e-11,
            -0.010706807605394546,
            -9.18989059249497e-11
          ],
          [
            -1.1328051764968823e-10,
            -0.02069500464019549,
            -1.8083223014714945e-10
          ],
          [
            -1.501472481071236e-10,
            -0.029538848238545752,
            -2.674929436245281e-10
          ],
          [
            -1.7489672416966095e-10,
            -0.0369690779896295,
            -3.5213551180490375e-10
          ],
          [
            -1.8418172568773467e-10,
            -0.042901017902783875,
            -4.345597755040666e-10
          ],
          [
            -2.0938174206827212e-10,
            -0.04737740719262351,
            -5.232260435020184e-10
          ],
          [
            -2.850826109617739e-10,
            -0.05057239244535183,
            -6.294201656146802e-10
          ],
          [
            -3.9509612874549187e-10,
            -0.05274135101014923,
            -7.500213617392955e-10
          ]
        ],
        "gauge_integer_shift": [
          0,
          0,
          0
        ],
        "expected_opposite_endpoint_reduced_polarization": [
          -3.950980638415385e-10,
          -0.05274135101015526,
          -7.500257977919214e-10
        ],
        "actual_opposite_endpoint_branch_residual": 7.731936314905483e-15
      },
      "pnp_branch": {
        "construction": "incoming_path_concatenated_with_parent_reflection",
        "reduced_polarization": [
          [
            3.9510233887552834e-10,
            0.05274135101015132,
            7.500236798085995e-10
          ],
          [
            2.850857363934056e-10,
            0.05057239244535171,
            6.294154660341756e-10
          ],
          [
            2.0937312917555822e-10,
            0.047377407192617293,
            5.232262533482923e-10
          ],
          [
            1.841810948023614e-10,
            0.042901017902784035,
            4.3456197156972295e-10
          ],
          [
            1.7489367352670792e-10,
            0.036969077989627404,
            3.5213666839948274e-10
          ],
          [
            1.50150963202237e-10,
            0.02953884823854522,
            2.6749145518002763e-10
          ],
          [
            1.1328068609570961e-10,
            0.020695004640195934,
            1.808298291153652e-10
          ],
          [
            6.399319979552035e-11,
            0.010706807605395632,
            9.190018452317628e-11
          ],
          [
            2.137516994954202e-15,
            -1.9693128767497897e-15,
            -1.0589916609428664e-15
          ],
          [
            -6.399572110625323e-11,
            -0.010706807605394546,
            -9.18989059249497e-11
          ],
          [
            -1.1328051764968823e-10,
            -0.02069500464019549,
            -1.8083223014714945e-10
          ],
          [
            -1.501472481071236e-10,
            -0.029538848238545752,
            -2.674929436245281e-10
          ],
          [
            -1.7489672416966095e-10,
            -0.0369690779896295,
            -3.5213551180490375e-10
          ],
          [
            -1.8418172568773467e-10,
            -0.042901017902783875,
            -4.345597755040666e-10
          ],
          [
            -2.0938174206827212e-10,
            -0.04737740719262351,
            -5.232260435020184e-10
          ],
          [
            -2.850826109617739e-10,
            -0.05057239244535183,
            -6.294201656146802e-10
          ],
          [
            -3.9509612874549187e-10,
            -0.05274135101014923,
            -7.500213617392955e-10
          ]
        ],
        "unwrapped_reduced_polarization": [
          [
            3.9510233887552834e-10,
            0.05274135101015132,
            7.500236798085995e-10
          ],
          [
            2.850857363934056e-10,
            0.05057239244535171,
            6.294154660341756e-10
          ],
          [
            2.0937312917555822e-10,
            0.047377407192617293,
            5.232262533482923e-10
          ],
          [
            1.841810948023614e-10,
            0.042901017902784035,
            4.3456197156972295e-10
          ],
          [
            1.7489367352670792e-10,
            0.036969077989627404,
            3.5213666839948274e-10
          ],
          [
            1.50150963202237e-10,
            0.02953884823854522,
            2.6749145518002763e-10
          ],
          [
            1.1328068609570961e-10,
            0.020695004640195934,
            1.808298291153652e-10
          ],
          [
            6.399319979552035e-11,
            0.010706807605395632,
            9.190018452317628e-11
          ],
          [
            2.137516994951962e-15,
            -1.968911145233676e-15,
            -1.0589916609440764e-15
          ],
          [
            -6.399572110625323e-11,
            -0.010706807605394546,
            -9.18989059249497e-11
          ],
          [
            -1.1328051764968823e-10,
            -0.02069500464019549,
            -1.8083223014714945e-10
          ],
          [
            -1.501472481071236e-10,
            -0.029538848238545752,
            -2.674929436245281e-10
          ],
          [
            -1.7489672416966095e-10,
            -0.0369690779896295,
            -3.5213551180490375e-10
          ],
          [
            -1.8418172568773467e-10,
            -0.042901017902783875,
            -4.345597755040666e-10
          ],
          [
            -2.0938174206827212e-10,
            -0.04737740719262351,
            -5.232260435020184e-10
          ],
          [
            -2.850826109617739e-10,
            -0.05057239244535183,
            -6.294201656146802e-10
          ],
          [
            -3.9509612874549187e-10,
            -0.05274135101014923,
            -7.500213617392955e-10
          ]
        ],
        "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": [
          [
            3.951022842230145e-10,
            0.052741351010151316,
            7.500237098057028e-10
          ],
          [
            2.850857327985068e-10,
            0.05057239244535172,
            6.294155197039686e-10
          ],
          [
            2.0937307443347208e-10,
            0.047377407192617293,
            5.232262401122512e-10
          ],
          [
            1.8418111480400512e-10,
            0.042901017902784,
            4.345619419865443e-10
          ],
          [
            1.7489365511380583e-10,
            0.03696907798962745,
            3.5213665317002096e-10
          ],
          [
            1.5015100274240467e-10,
            0.029538848238545246,
            2.6749147341575963e-10
          ],
          [
            1.1328071813920815e-10,
            0.020695004640195913,
            1.8082979558187162e-10
          ],
          [
            6.399325513939402e-11,
            0.010706807605395663,
            9.190015415327935e-11
          ],
          [
            2.1094237467877974e-15,
            -1.942890293094024e-15,
            -1.0547118733938987e-15
          ],
          [
            -6.39956976300482e-11,
            -0.010706807605394553,
            -9.189893290795226e-11
          ],
          [
            -1.1328049609460322e-10,
            -0.02069500464019547,
            -1.808322380725258e-10
          ],
          [
            -1.5014722798412095e-10,
            -0.029538848238545745,
            -2.6749291670569164e-10
          ],
          [
            -1.7489670822712355e-10,
            -0.036969077989629506,
            -3.521354874358451e-10
          ],
          [
            -1.8418172542666866e-10,
            -0.04290101790278389,
            -4.345597770516463e-10
          ],
          [
            -2.0938173417306416e-10,
            -0.04737740719262351,
            -5.232260180676462e-10
          ],
          [
            -2.8508262417403785e-10,
            -0.05057239244535183,
            -6.29420182640672e-10
          ],
          [
            -3.9509612248522785e-10,
            -0.05274135101014921,
            -7.500213783373511e-10
          ]
        ]
      },
      "incoming_structure_ids": [
        "incoming_00_000",
        "incoming_00_001",
        "incoming_00_002",
        "incoming_00_003",
        "incoming_00_004",
        "incoming_00_005",
        "incoming_00_006",
        "incoming_00_007",
        "incoming_00_008"
      ],
      "reflected_structure_ids": [
        "reflected_00_001",
        "reflected_00_002",
        "reflected_00_003",
        "reflected_00_004",
        "reflected_00_005",
        "reflected_00_006",
        "reflected_00_007",
        "reflected_00_008"
      ]
    },
    {
      "orbit_id": 1,
      "formal_class": [
        0.0,
        0.5,
        0.0
      ],
      "formal_classes_in_orbit": [
        [
          0.0,
          0.5,
          0.0
        ]
      ],
      "target_reduced_polarization": [
        0.0,
        0.5,
        0.0
      ],
      "bec_backprojection": {
        "converged_to_target": false,
        "history": [
          {
            "iteration": 0,
            "reduced_polarization": [
              3.9509728089959303e-10,
              0.05274135101015198,
              7.500229477867141e-10
            ],
            "branch_aligned_reduced_polarization": [
              3.9509728089959303e-10,
              0.05274135101015198,
              7.500229477867141e-10
            ],
            "target_residual": 0.447258648989848,
            "energy_eV": -19.436754013242563,
            "max_atomic_step_A": 0.12,
            "max_log_strain_component": 0.009678799183660932,
            "step_scale": 0.2534707346721676,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 1.203697092630885,
            "cell_principal_stretches": [
              1.016434532210475,
              0.9995721854959244,
              0.9959349245434784
            ],
            "cell_volume_ratio": 1.0118695713846086,
            "cell_rmsd_from_input_A": 0.03864601599721839
          },
          {
            "iteration": 1,
            "reduced_polarization": [
              4.0042471476931226e-10,
              0.15433490560527263,
              7.757693476017912e-10
            ],
            "branch_aligned_reduced_polarization": [
              4.0042471476931226e-10,
              0.15433490560527263,
              7.757693476017912e-10
            ],
            "target_residual": 0.34566509439472737,
            "energy_eV": -19.05461165719971,
            "max_atomic_step_A": 0.12,
            "max_log_strain_component": 0.010642319573596773,
            "step_scale": 0.34717003566018173,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 1.203697092630885,
            "cell_principal_stretches": [
              1.034817048362782,
              0.9991019934970952,
              0.9914842442399243
            ],
            "cell_volume_ratio": 1.0250834401409383,
            "cell_rmsd_from_input_A": 0.08221361240621375
          },
          {
            "iteration": 2,
            "reduced_polarization": [
              2.2805880629509933e-10,
              0.28876348361726606,
              2.935807722375269e-10
            ],
            "branch_aligned_reduced_polarization": [
              2.2805880629509933e-10,
              0.28876348361726606,
              2.935807722375269e-10
            ],
            "target_residual": 0.21123651638273394,
            "energy_eV": -17.6098954606299,
            "max_atomic_step_A": 0.12000000000000001,
            "max_log_strain_component": 0.00829475655959216,
            "step_scale": 0.7248035713490399,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 1.203697092630885,
            "cell_principal_stretches": [
              1.0493748447871836,
              0.9987356733698445,
              0.9880291253325274
            ],
            "cell_volume_ratio": 1.0355020398683839,
            "cell_rmsd_from_input_A": 0.11698603814686966
          },
          {
            "iteration": 3,
            "reduced_polarization": [
              -3.659491098125881e-11,
              0.41612708439933,
              -1.5896136185099156e-11
            ],
            "branch_aligned_reduced_polarization": [
              -3.659491098125881e-11,
              0.41612708439933,
              -1.5896136185099156e-11
            ],
            "target_residual": 0.08387291560067,
            "energy_eV": -14.94419217812704,
            "max_atomic_step_A": 0.11058095104231212,
            "max_log_strain_component": 0.01263630025410672,
            "step_scale": 1.0,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 1.203697092630885,
            "cell_principal_stretches": [
              1.0719469180345316,
              0.9981778764214649,
              0.9827886974393718
            ],
            "cell_volume_ratio": 1.0515777130011759,
            "cell_rmsd_from_input_A": 0.17139840585015398
          },
          {
            "iteration": 4,
            "reduced_polarization": [
              -2.2481402466802297e-10,
              0.45931035127096426,
              8.034111100791593e-11
            ],
            "branch_aligned_reduced_polarization": [
              -2.2481402466802297e-10,
              0.45931035127096426,
              8.034111100791593e-11
            ],
            "target_residual": 0.04068964872903574,
            "energy_eV": -10.819155526131656,
            "max_atomic_step_A": 0.07617553494379552,
            "max_log_strain_component": 0.01555032267084053,
            "step_scale": 1.0,
            "strain_jacobian_refreshed": true,
            "strain_jacobian_frobenius_norm": 1.2252208440775194,
            "cell_principal_stretches": [
              1.0722087697346647,
              0.9902545027955909,
              0.9629221340005891
            ],
            "cell_volume_ratio": 1.022391783397064,
            "cell_rmsd_from_input_A": 0.22808170287241672
          },
          {
            "iteration": 5,
            "reduced_polarization": [
              1.5082355375957608e-10,
              0.5243799579012496,
              -8.492866965913008e-12
            ],
            "branch_aligned_reduced_polarization": [
              1.5082355375957608e-10,
              0.5243799579012496,
              -8.492866965913008e-12
            ],
            "target_residual": 0.024379957901249583,
            "energy_eV": -7.024582930893935
          }
        ],
        "iterations": 5
      },
      "parent": {
        "candidate_id": "bec_projection_01",
        "source": "MACEField_BEC_backprojection",
        "spacegroup": "P2_1",
        "spacegroup_number": 4,
        "pointgroup": "2",
        "has_inversion": false,
        "is_polar_point_group": true,
        "nonpolar_parent_hypothesis": false,
        "symmetry_tolerance_A": null,
        "target_reduced_polarization": [
          0.0,
          0.5,
          0.0
        ],
        "formal_class": [
          0.0,
          0.5,
          0.0
        ],
        "target_residual": 0.024379957901249583,
        "parent_symmetrization_rmsd_A": 0.4446438981737826,
        "parent_cell_rmsd_A": 0.22808170287241672,
        "energy_eV": -7.024582930893935,
        "reduced_polarization": [
          1.5082355375957608e-10,
          0.5243799579012496,
          -8.492866965913008e-12
        ],
        "cartesian_polarization_e_A2": [
          5.635809775781925e-12,
          0.020595681439033665,
          -5.7380074168829665e-12
        ],
        "ranking_score": 1.050424239694386
      },
      "branch_status": "awaiting_branch_sampling"
    },
    {
      "orbit_id": 2,
      "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": false,
        "history": [
          {
            "iteration": 0,
            "reduced_polarization": [
              3.9509728089959303e-10,
              0.05274135101015198,
              7.500229477867141e-10
            ],
            "branch_aligned_reduced_polarization": [
              3.9509728089959303e-10,
              0.05274135101015198,
              7.500229326495855e-10
            ],
            "target_residual": 0.5027739545326042,
            "energy_eV": -19.436754013242563,
            "max_atomic_step_A": 0.12,
            "max_log_strain_component": 0.0039650716081545455,
            "step_scale": 0.18284948476488136,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 1.203697092630885,
            "cell_principal_stretches": [
              1.0041369036367038,
              0.9992478061198783,
              0.9956299261367261
            ],
            "cell_volume_ratio": 0.998996746306661,
            "cell_rmsd_from_input_A": 0.0224991927463444
          },
          {
            "iteration": 1,
            "reduced_polarization": [
              0.000771012076836466,
              0.04039465503664111,
              0.09502597131740097
            ],
            "branch_aligned_reduced_polarization": [
              0.000771012076836466,
              0.04039465503664111,
              0.09502597131740098
            ],
            "target_residual": 0.40698438117766433,
            "energy_eV": -19.12446255502971,
            "max_atomic_step_A": 0.12,
            "max_log_strain_component": 0.0033909968730763376,
            "step_scale": 0.2710986526126227,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 1.203697092630885,
            "cell_principal_stretches": [
              1.0078010111302458,
              0.9992725277503911,
              0.9921056403341617
            ],
            "cell_volume_ratio": 0.9991177079362905,
            "cell_rmsd_from_input_A": 0.04232763653466507
          },
          {
            "iteration": 2,
            "reduced_polarization": [
              0.0028581929103148563,
              0.0261154083398946,
              0.20936350425197953
            ],
            "branch_aligned_reduced_polarization": [
              0.0028581929103148563,
              0.0261154083398946,
              0.20936350425197953
            ],
            "target_residual": 0.29182144623067224,
            "energy_eV": -18.083050351259573,
            "max_atomic_step_A": 0.12,
            "max_log_strain_component": 0.004487702176830557,
            "step_scale": 0.4074589020114743,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 1.203697092630885,
            "cell_principal_stretches": [
              1.0124483276108343,
              0.9993278852383792,
              0.9875142740438838
            ],
            "cell_volume_ratio": 0.9991351900862995,
            "cell_rmsd_from_input_A": 0.0665300361537602
          },
          {
            "iteration": 3,
            "reduced_polarization": [
              0.006930318345565831,
              0.02259926307060378,
              0.3130217249623891
            ],
            "branch_aligned_reduced_polarization": [
              0.006930318345565831,
              0.02259926307060378,
              0.3130217249623891
            ],
            "target_residual": 0.18846652578043058,
            "energy_eV": -15.857122092928691,
            "max_atomic_step_A": 0.12,
            "max_log_strain_component": 0.007475059326337753,
            "step_scale": 0.42551058941306075,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 1.203697092630885,
            "cell_principal_stretches": [
              1.0199625568281114,
              0.9987273340901314,
              0.9798608708323898
            ],
            "cell_volume_ratio": 0.9981494696057325,
            "cell_rmsd_from_input_A": 0.10481982880007713
          },
          {
            "iteration": 4,
            "reduced_polarization": [
              -0.004924381815186099,
              0.014901159673003345,
              0.36495513501655436
            ],
            "branch_aligned_reduced_polarization": [
              -0.004924381815186099,
              0.014901159673003345,
              0.36495513501655436
            ],
            "target_residual": 0.1359537040843652,
            "energy_eV": -11.728696455718257,
            "max_atomic_step_A": 0.12,
            "max_log_strain_component": 0.011219440495825721,
            "step_scale": 0.38677109320668435,
            "strain_jacobian_refreshed": true,
            "strain_jacobian_frobenius_norm": 1.3061326515011094,
            "cell_principal_stretches": [
              1.0149588908307787,
              1.0017606786909141,
              0.9627420176077974
            ],
            "cell_volume_ratio": 0.9788640062096706,
            "cell_rmsd_from_input_A": 0.16218413651071018
          },
          {
            "iteration": 5,
            "reduced_polarization": [
              -0.01976908552118417,
              0.010005043127438728,
              0.41431845632145853
            ],
            "branch_aligned_reduced_polarization": [
              -0.01976908552118417,
              0.010005043127438728,
              0.41431845632145853
            ],
            "target_residual": 0.0884999692512015,
            "energy_eV": -8.398961795705507
          }
        ],
        "iterations": 5
      },
      "parent": {
        "candidate_id": "bec_projection_02",
        "source": "MACEField_BEC_backprojection",
        "spacegroup": "P1",
        "spacegroup_number": 1,
        "pointgroup": "1",
        "has_inversion": false,
        "is_polar_point_group": true,
        "nonpolar_parent_hypothesis": false,
        "symmetry_tolerance_A": null,
        "target_reduced_polarization": [
          0.0,
          0.0,
          0.5
        ],
        "formal_class": [
          0.0,
          0.0,
          0.5
        ],
        "target_residual": 0.0884999692512015,
        "parent_symmetrization_rmsd_A": 0.4337713844740285,
        "parent_cell_rmsd_A": 0.16218413651071018,
        "energy_eV": -8.398961795705507,
        "reduced_polarization": [
          -0.01976908552118417,
          0.010005043127438728,
          0.41431845632145853
        ],
        "cartesian_polarization_e_A2": [
          -0.0048550990529735326,
          0.00074302538149839,
          0.016484421794735384
        ],
        "ranking_score": 1.151317357104109
      },
      "branch_status": "awaiting_branch_sampling"
    },
    {
      "orbit_id": 3,
      "formal_class": [
        0.5,
        0.0,
        0.0
      ],
      "formal_classes_in_orbit": [
        [
          0.5,
          0.0,
          0.0
        ]
      ],
      "target_reduced_polarization": [
        0.5,
        0.0,
        0.0
      ],
      "bec_backprojection": {
        "converged_to_target": false,
        "history": [
          {
            "iteration": 0,
            "reduced_polarization": [
              3.9509728089959303e-10,
              0.05274135101015198,
              7.500229477867141e-10
            ],
            "branch_aligned_reduced_polarization": [
              3.950972882194037e-10,
              0.05274135101015198,
              7.500229477867141e-10
            ],
            "target_residual": 0.5027739548855715,
            "energy_eV": -19.436754013242563,
            "max_atomic_step_A": 0.12,
            "max_log_strain_component": 0.016573906845712322,
            "step_scale": 0.23620813360378567,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 1.203697092630885,
            "cell_principal_stretches": [
              1.0163212048758592,
              1.000002527019801,
              0.982663395089809
            ],
            "cell_volume_ratio": 0.9987041694239108,
            "cell_rmsd_from_input_A": 0.07420643906864112
          },
          {
            "iteration": 1,
            "reduced_polarization": [
              0.1160472087288655,
              0.02218281951093744,
              -0.005289323892482995
            ],
            "branch_aligned_reduced_polarization": [
              0.11604720872886548,
              0.02218281951093744,
              -0.005289323892482995
            ],
            "target_residual": 0.3846294325108127,
            "energy_eV": -19.047873846357408,
            "max_atomic_step_A": 0.12,
            "max_log_strain_component": 0.012233876559199212,
            "step_scale": 0.26841643621500877,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 1.203697092630885,
            "cell_principal_stretches": [
              1.0299079900111259,
              0.9999956568654551,
              0.9714224847442094
            ],
            "cell_volume_ratio": 1.0004714335136067,
            "cell_rmsd_from_input_A": 0.1289612301980121
          },
          {
            "iteration": 2,
            "reduced_polarization": [
              0.20353753761675827,
              0.011754961506771668,
              -0.005886838535813772
            ],
            "branch_aligned_reduced_polarization": [
              0.2035375376167583,
              0.011754961506771668,
              -0.005886838535813772
            ],
            "target_residual": 0.2967538131015462,
            "energy_eV": -18.489768325279726,
            "max_atomic_step_A": 0.12,
            "max_log_strain_component": 0.01575200204665289,
            "step_scale": 0.2962828502920399,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 1.203697092630885,
            "cell_principal_stretches": [
              1.047739421314331,
              0.9999554662879335,
              0.956962243662862
            ],
            "cell_volume_ratio": 1.0026024157991873,
            "cell_rmsd_from_input_A": 0.20014732404400135
          },
          {
            "iteration": 3,
            "reduced_polarization": [
              0.2798847952861195,
              0.006198007107913486,
              0.005328035954646945
            ],
            "branch_aligned_reduced_polarization": [
              0.2798847952861195,
              0.006198007107913486,
              0.005328035954646945
            ],
            "target_residual": 0.2202668985696155,
            "energy_eV": -17.648105970266066,
            "max_atomic_step_A": 0.10151358807720627,
            "max_log_strain_component": 0.02,
            "step_scale": 0.37253188002879184,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 1.203697092630885,
            "cell_principal_stretches": [
              1.0712828238397203,
              0.9999033830222406,
              0.9392387041517039
            ],
            "cell_volume_ratio": 1.0060930761782059,
            "cell_rmsd_from_input_A": 0.2921961228376375
          },
          {
            "iteration": 4,
            "reduced_polarization": [
              0.33869581896501993,
              -0.007429132007638831,
              0.01329542963921692
            ],
            "branch_aligned_reduced_polarization": [
              0.33869581896501993,
              -0.007429132007638831,
              0.01329542963921692
            ],
            "target_residual": 0.1620216012482407,
            "energy_eV": -16.5020899895171,
            "max_atomic_step_A": 0.11055224070075398,
            "max_log_strain_component": 0.02,
            "step_scale": 0.3662499703461967,
            "strain_jacobian_refreshed": true,
            "strain_jacobian_frobenius_norm": 1.230343181062332,
            "cell_principal_stretches": [
              1.0495487312318907,
              0.9975905778819713,
              0.9347922899215689
            ],
            "cell_volume_ratio": 0.9787461535692883,
            "cell_rmsd_from_input_A": 0.25636157703125134
          },
          {
            "iteration": 5,
            "reduced_polarization": [
              0.3954449323930281,
              -0.005789592340319642,
              0.014264179247644266
            ],
            "branch_aligned_reduced_polarization": [
              0.3954449323930281,
              -0.005789592340319642,
              0.014264179247644266
            ],
            "target_residual": 0.10568229913932835,
            "energy_eV": -15.747053692671946
          }
        ],
        "iterations": 5
      },
      "parent": {
        "candidate_id": "bec_projection_03",
        "source": "MACEField_BEC_backprojection",
        "spacegroup": "P1",
        "spacegroup_number": 1,
        "pointgroup": "1",
        "has_inversion": false,
        "is_polar_point_group": true,
        "nonpolar_parent_hypothesis": false,
        "symmetry_tolerance_A": null,
        "target_reduced_polarization": [
          0.5,
          0.0,
          0.0
        ],
        "formal_class": [
          0.5,
          0.0,
          0.0
        ],
        "target_residual": 0.10568229913932835,
        "parent_symmetrization_rmsd_A": 0.33151671845873554,
        "parent_cell_rmsd_A": 0.25636157703125134,
        "energy_eV": -15.747053692671946,
        "reduced_polarization": [
          0.3954449323930281,
          -0.005789592340319642,
          0.014264179247644266
        ],
        "cartesian_polarization_e_A2": [
          0.011769872333535308,
          0.000439016743311167,
          0.000654246531296575
        ],
        "ranking_score": 1.106971710995205
      },
      "branch_status": "awaiting_branch_sampling"
    },
    {
      "orbit_id": 4,
      "formal_class": [
        0.0,
        0.5,
        0.5
      ],
      "formal_classes_in_orbit": [
        [
          0.0,
          0.5,
          0.5
        ]
      ],
      "target_reduced_polarization": [
        0.0,
        0.5,
        0.5
      ],
      "bec_backprojection": {
        "converged_to_target": false,
        "history": [
          {
            "iteration": 0,
            "reduced_polarization": [
              3.9509728089959303e-10,
              0.05274135101015198,
              7.500229477867141e-10
            ],
            "branch_aligned_reduced_polarization": [
              3.9509728089959303e-10,
              0.05274135101015198,
              7.500229326495855e-10
            ],
            "target_residual": 0.6708504291913371,
            "energy_eV": -19.436754013242563,
            "max_atomic_step_A": 0.12,
            "max_log_strain_component": 0.004779025563936924,
            "step_scale": 0.12515427512126,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 1.203697092630885,
            "cell_principal_stretches": [
              1.0084335227166563,
              1.0010931944393833,
              0.9963421860713465
            ],
            "cell_volume_ratio": 1.005843242025674,
            "cell_rmsd_from_input_A": 0.024317613592834728
          },
          {
            "iteration": 1,
            "reduced_polarization": [
              -0.006572396000078879,
              0.10859774572890829,
              0.060205470026705614
            ],
            "branch_aligned_reduced_polarization": [
              -0.006572396000078879,
              0.10859774572890829,
              0.06020547002670562
            ],
            "target_residual": 0.5887768249787902,
            "energy_eV": -19.208713105772908,
            "max_atomic_step_A": 0.12,
            "max_log_strain_component": 0.004678355759739318,
            "step_scale": 0.1710015977354528,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 1.203697092630885,
            "cell_principal_stretches": [
              1.0166969369672234,
              1.0021085675661565,
              0.9928897190641628
            ],
            "cell_volume_ratio": 1.0115964674679567,
            "cell_rmsd_from_input_A": 0.0477579578582151
          },
          {
            "iteration": 2,
            "reduced_polarization": [
              -0.001890005787455191,
              0.18662773992619777,
              0.1435058191204961
            ],
            "branch_aligned_reduced_polarization": [
              -0.001890005787455191,
              0.18662773992619774,
              0.1435058191204961
            ],
            "target_residual": 0.47465128937630396,
            "energy_eV": -18.28786565705298,
            "max_atomic_step_A": 0.12,
            "max_log_strain_component": 0.005583535799261803,
            "step_scale": 0.24184952237488358,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 1.203697092630885,
            "cell_principal_stretches": [
              1.0239410147546644,
              1.0031688234155731,
              0.9884244076395089
            ],
            "cell_volume_ratio": 1.01529542004172,
            "cell_rmsd_from_input_A": 0.07410402305370986
          },
          {
            "iteration": 3,
            "reduced_polarization": [
              0.007933489059959168,
              0.25645876813312246,
              0.22421322137987615
            ],
            "branch_aligned_reduced_polarization": [
              0.007933489059959168,
              0.25645876813312246,
              0.22421322137987615
            ],
            "target_residual": 0.3680130692374469,
            "energy_eV": -16.463502488727073,
            "max_atomic_step_A": 0.12,
            "max_log_strain_component": 0.013625543507430705,
            "step_scale": 0.24804442393827672,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 1.203697092630885,
            "cell_principal_stretches": [
              1.0394406804081522,
              1.0037472350567085,
              0.9779106270409551
            ],
            "cell_volume_ratio": 1.020289077368325,
            "cell_rmsd_from_input_A": 0.13421316411900983
          },
          {
            "iteration": 4,
            "reduced_polarization": [
              0.008182646329964254,
              0.3037849661462935,
              0.268942222127929
            ],
            "branch_aligned_reduced_polarization": [
              0.008182646329964254,
              0.3037849661462935,
              0.268942222127929
            ],
            "target_residual": 0.3032408150733535,
            "energy_eV": -12.821176302253393,
            "max_atomic_step_A": 0.12,
            "max_log_strain_component": 0.01460583772223113,
            "step_scale": 0.23804437619520102,
            "strain_jacobian_refreshed": true,
            "strain_jacobian_frobenius_norm": 1.2885645714077218,
            "cell_principal_stretches": [
              1.051002998097294,
              0.9889623040005825,
              0.9755615784079394
            ],
            "cell_volume_ratio": 1.0140009937620351,
            "cell_rmsd_from_input_A": 0.16848174923937387
          },
          {
            "iteration": 5,
            "reduced_polarization": [
              -0.03796225746676964,
              0.3394161429351654,
              0.292455323553303
            ],
            "branch_aligned_reduced_polarization": [
              -0.03796225746676964,
              0.3394161429351654,
              0.292455323553303
            ],
            "target_residual": 0.26514731917022405,
            "energy_eV": -6.536563323025386
          }
        ],
        "iterations": 5
      },
      "parent": {
        "candidate_id": "bec_projection_04",
        "source": "MACEField_BEC_backprojection",
        "spacegroup": "P1",
        "spacegroup_number": 1,
        "pointgroup": "1",
        "has_inversion": false,
        "is_polar_point_group": true,
        "nonpolar_parent_hypothesis": false,
        "symmetry_tolerance_A": null,
        "target_reduced_polarization": [
          0.0,
          0.5,
          0.5
        ],
        "formal_class": [
          0.0,
          0.5,
          0.5
        ],
        "target_residual": 0.26514731917022405,
        "parent_symmetrization_rmsd_A": 0.4106839434463461,
        "parent_cell_rmsd_A": 0.16848174923937387,
        "energy_eV": -6.536563323025386,
        "reduced_polarization": [
          -0.03796225746676964,
          0.3394161429351654,
          0.292455323553303
        ],
        "cartesian_polarization_e_A2": [
          -0.004118203160129026,
          0.013498445415227609,
          0.011065225725115474
        ],
        "ranking_score": 1.4830990190966378
      },
      "branch_status": "awaiting_branch_sampling"
    },
    {
      "orbit_id": 5,
      "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": false,
        "history": [
          {
            "iteration": 0,
            "reduced_polarization": [
              3.9509728089959303e-10,
              0.05274135101015198,
              7.500229477867141e-10
            ],
            "branch_aligned_reduced_polarization": [
              3.950972882194037e-10,
              0.05274135101015198,
              7.500229477867141e-10
            ],
            "target_residual": 0.6708504294558713,
            "energy_eV": -19.436754013242563,
            "max_atomic_step_A": 0.12,
            "max_log_strain_component": 0.01015837826665977,
            "step_scale": 0.14477525366487176,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 1.203697092630885,
            "cell_principal_stretches": [
              1.0153693652347147,
              0.9999487244404475,
              0.9915741629455629
            ],
            "cell_volume_ratio": 1.0067624034605074,
            "cell_rmsd_from_input_A": 0.050727106230153314
          },
          {
            "iteration": 1,
            "reduced_polarization": [
              0.06620341698685665,
              0.10836152625276362,
              0.0005783981691619479
            ],
            "branch_aligned_reduced_polarization": [
              0.06620341698685667,
              0.10836152625276363,
              0.0005783981691619479
            ],
            "target_residual": 0.5844317788222897,
            "energy_eV": -19.21030249208446,
            "max_atomic_step_A": 0.11999999999999998,
            "max_log_strain_component": 0.008965339069738006,
            "step_scale": 0.1478404193565535,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 1.203697092630885,
            "cell_principal_stretches": [
              1.0299733033134728,
              0.999918523032323,
              0.9842406244350148
            ],
            "cell_volume_ratio": 1.0136589706157435,
            "cell_rmsd_from_input_A": 0.09743795211308759
          },
          {
            "iteration": 2,
            "reduced_polarization": [
              0.12159224713224423,
              0.16263097284972616,
              0.0012107716867952101
            ],
            "branch_aligned_reduced_polarization": [
              0.12159224713224426,
              0.16263097284972616,
              0.0012107716867952101
            ],
            "target_residual": 0.5069632667943746,
            "energy_eV": -18.635682428768824,
            "max_atomic_step_A": 0.12,
            "max_log_strain_component": 0.012357272854204125,
            "step_scale": 0.18777240793701547,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 1.203697092630885,
            "cell_principal_stretches": [
              1.0482411978710295,
              1.0000150962243701,
              0.974037193961853
            ],
            "cell_volume_ratio": 1.0210413286058087,
            "cell_rmsd_from_input_A": 0.15947852936130968
          },
          {
            "iteration": 3,
            "reduced_polarization": [
              0.1677528456888822,
              0.2169669932646702,
              0.0026130502518641983
            ],
            "branch_aligned_reduced_polarization": [
              0.1677528456888822,
              0.21696699326467017,
              0.0026130502518641983
            ],
            "target_residual": 0.43646612982119903,
            "energy_eV": -17.61551786878689,
            "max_atomic_step_A": 0.10743756833532163,
            "max_log_strain_component": 0.02,
            "step_scale": 0.1728638493758553,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 1.203697092630885,
            "cell_principal_stretches": [
              1.0750819664559446,
              1.0000390020133147,
              0.9574285094783738
            ],
            "cell_volume_ratio": 1.029354270034191,
            "cell_rmsd_from_input_A": 0.2563615697118599
          },
          {
            "iteration": 4,
            "reduced_polarization": [
              0.19182564841098115,
              0.2469032364023962,
              0.000918074761429268
            ],
            "branch_aligned_reduced_polarization": [
              0.19182564841098115,
              0.2469032364023962,
              0.000918074761429268
            ],
            "target_residual": 0.3987859646253378,
            "energy_eV": -16.740305230000928,
            "max_atomic_step_A": 0.10274738408969962,
            "max_log_strain_component": 0.02,
            "step_scale": 0.16904679263917788,
            "strain_jacobian_refreshed": true,
            "strain_jacobian_frobenius_norm": 1.5464541802854297,
            "cell_principal_stretches": [
              1.0487653898674019,
              0.9944153608486062,
              0.9545205486739521
            ],
            "cell_volume_ratio": 0.9954775111761962,
            "cell_rmsd_from_input_A": 0.2089526300958643
          },
          {
            "iteration": 5,
            "reduced_polarization": [
              0.22992613851912772,
              0.2823773864461063,
              -0.0034247083104100443
            ],
            "branch_aligned_reduced_polarization": [
              0.2299261385191277,
              0.2823773864461063,
              -0.0034247083104100443
            ],
            "target_residual": 0.34685907976039515,
            "energy_eV": -16.430359344921264
          }
        ],
        "iterations": 5
      },
      "parent": {
        "candidate_id": "bec_projection_05",
        "source": "MACEField_BEC_backprojection",
        "spacegroup": "P1",
        "spacegroup_number": 1,
        "pointgroup": "1",
        "has_inversion": false,
        "is_polar_point_group": true,
        "nonpolar_parent_hypothesis": false,
        "symmetry_tolerance_A": null,
        "target_reduced_polarization": [
          0.5,
          0.5,
          0.0
        ],
        "formal_class": [
          0.5,
          0.5,
          0.0
        ],
        "target_residual": 0.34685907976039515,
        "parent_symmetrization_rmsd_A": 0.3119758319660326,
        "parent_cell_rmsd_A": 0.2089526300958643,
        "energy_eV": -16.430359344921264,
        "reduced_polarization": [
          0.22992613851912772,
          0.2823773864461063,
          -0.0034247083104100443
        ],
        "cartesian_polarization_e_A2": [
          0.007414328289177784,
          0.011655830436355208,
          0.00011434538584306422
        ],
        "ranking_score": 1.5579321490107891
      },
      "branch_status": "awaiting_branch_sampling"
    },
    {
      "orbit_id": 6,
      "formal_class": [
        0.5,
        0.0,
        0.5
      ],
      "formal_classes_in_orbit": [
        [
          0.5,
          0.0,
          0.5
        ]
      ],
      "target_reduced_polarization": [
        0.5,
        0.0,
        0.5
      ],
      "bec_backprojection": {
        "converged_to_target": false,
        "history": [
          {
            "iteration": 0,
            "reduced_polarization": [
              3.9509728089959303e-10,
              0.05274135101015198,
              7.500229477867141e-10
            ],
            "branch_aligned_reduced_polarization": [
              3.950972882194037e-10,
              0.05274135101015198,
              7.500229326495855e-10
            ],
            "target_residual": 0.709070975968736,
            "energy_eV": -19.436754013242563,
            "max_atomic_step_A": 0.12,
            "max_log_strain_component": 0.011066555646684146,
            "step_scale": 0.22826279700686486,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 1.203697092630885,
            "cell_principal_stretches": [
              1.0111903973047134,
              1.0002901907714037,
              0.9874084932349585
            ],
            "cell_volume_ratio": 0.9987477298696447,
            "cell_rmsd_from_input_A": 0.049742746722760446
          },
          {
            "iteration": 1,
            "reduced_polarization": [
              0.12084913309979034,
              0.03915596613731143,
              0.12143232901962737
            ],
            "branch_aligned_reduced_polarization": [
              0.12084913309979034,
              0.03915596613731143,
              0.12143232901962736
            ],
            "target_residual": 0.5372169497203438,
            "energy_eV": -18.92677247317198,
            "max_atomic_step_A": 0.12,
            "max_log_strain_component": 0.006202635027736613,
            "step_scale": 0.28357560739497495,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 1.203697092630885,
            "cell_principal_stretches": [
              1.017696179119871,
              1.0004077844126806,
              0.9805257516690313
            ],
            "cell_volume_ratio": 0.998284229815407,
            "cell_rmsd_from_input_A": 0.07765607458732023
          },
          {
            "iteration": 2,
            "reduced_polarization": [
              0.22761734329888406,
              0.0245504707112237,
              0.23336533881017574
            ],
            "branch_aligned_reduced_polarization": [
              0.22761734329888406,
              0.0245504707112237,
              0.23336533881017574
            ],
            "target_residual": 0.38195429023839095,
            "energy_eV": -17.87346710620981,
            "max_atomic_step_A": 0.11999999999999998,
            "max_log_strain_component": 0.006673521958895171,
            "step_scale": 0.3674200818930426,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 1.203697092630885,
            "cell_principal_stretches": [
              1.0249011577655034,
              1.0003905602439476,
              0.9736526500327538
            ],
            "cell_volume_ratio": 0.9982874674602118,
            "cell_rmsd_from_input_A": 0.107300072820828
          },
          {
            "iteration": 3,
            "reduced_polarization": [
              0.3141690857199197,
              0.011236155173827304,
              0.3207403945384798
            ],
            "branch_aligned_reduced_polarization": [
              0.3141690857199197,
              0.011236155173827304,
              0.3207403945384798
            ],
            "target_residual": 0.2584441642511604,
            "energy_eV": -16.397724363298938,
            "max_atomic_step_A": 0.12,
            "max_log_strain_component": 0.010103047570642697,
            "step_scale": 0.46505160665695544,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 1.203697092630885,
            "cell_principal_stretches": [
              1.0365949719054468,
              1.000117170069423,
              0.9640653306401435
            ],
            "cell_volume_ratio": 0.999462367685106,
            "cell_rmsd_from_input_A": 0.15241055637028447
          },
          {
            "iteration": 4,
            "reduced_polarization": [
              0.37543203775127754,
              -0.0002591536230343751,
              0.37934229770715466
            ],
            "branch_aligned_reduced_polarization": [
              0.37543203775127754,
              -0.0002591536230343751,
              0.37934229770715466
            ],
            "target_residual": 0.1734229670545063,
            "energy_eV": -13.887327427121015,
            "max_atomic_step_A": 0.12,
            "max_log_strain_component": 0.010300196757347807,
            "step_scale": 0.5022106716736082,
            "strain_jacobian_refreshed": true,
            "strain_jacobian_frobenius_norm": 1.3477240332381575,
            "cell_principal_stretches": [
              1.03455805720466,
              0.9970866571563335,
              0.957121082750923
            ],
            "cell_volume_ratio": 0.9873125435814176,
            "cell_rmsd_from_input_A": 0.16738715783073624
          },
          {
            "iteration": 5,
            "reduced_polarization": [
              0.4397194372714766,
              -0.0018701439704804927,
              0.4304624070269764
            ],
            "branch_aligned_reduced_polarization": [
              0.4397194372714766,
              -0.0018701439704804927,
              0.4304624070269764
            ],
            "target_residual": 0.09204738191724775,
            "energy_eV": -9.420455803507892
          }
        ],
        "iterations": 5
      },
      "parent": {
        "candidate_id": "bec_projection_06",
        "source": "MACEField_BEC_backprojection",
        "spacegroup": "P1",
        "spacegroup_number": 1,
        "pointgroup": "1",
        "has_inversion": false,
        "is_polar_point_group": true,
        "nonpolar_parent_hypothesis": false,
        "symmetry_tolerance_A": null,
        "target_reduced_polarization": [
          0.5,
          0.0,
          0.5
        ],
        "formal_class": [
          0.5,
          0.0,
          0.5
        ],
        "target_residual": 0.09204738191724775,
        "parent_symmetrization_rmsd_A": 0.42429669227781097,
        "parent_cell_rmsd_A": 0.16738715783073624,
        "energy_eV": -9.420455803507892,
        "reduced_polarization": [
          0.4397194372714766,
          -0.0018701439704804927,
          0.4304624070269764
        ],
        "cartesian_polarization_e_A2": [
          0.00856144058966991,
          0.0003764389791826973,
          0.016895610574806725
        ],
        "ranking_score": 1.1502382455699904
      },
      "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": false,
        "history": [
          {
            "iteration": 0,
            "reduced_polarization": [
              3.9509728089959303e-10,
              0.05274135101015198,
              7.500229477867141e-10
            ],
            "branch_aligned_reduced_polarization": [
              3.950972882194037e-10,
              0.05274135101015198,
              7.500229326495855e-10
            ],
            "target_residual": 0.8366841088195137,
            "energy_eV": -19.436754013242563,
            "max_atomic_step_A": 0.12,
            "max_log_strain_component": 0.007147792662274711,
            "step_scale": 0.14743296782224807,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 1.203697092630885,
            "cell_principal_stretches": [
              1.0136233460987962,
              0.9986160806453006,
              0.9947307904526157
            ],
            "cell_volume_ratio": 1.0068869708237502,
            "cell_rmsd_from_input_A": 0.039359460412906694
          },
          {
            "iteration": 1,
            "reduced_polarization": [
              0.0603606393661024,
              0.12154394074148817,
              0.07394267089927761
            ],
            "branch_aligned_reduced_polarization": [
              0.06036063936610242,
              0.12154394074148817,
              0.07394267089927764
            ],
            "target_residual": 0.7197475973481994,
            "energy_eV": -19.137568345197824,
            "max_atomic_step_A": 0.12,
            "max_log_strain_component": 0.00709434672425297,
            "step_scale": 0.1829710411666289,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 1.203697092630885,
            "cell_principal_stretches": [
              1.025351857552837,
              0.9978473363483596,
              0.9892165046777736
            ],
            "cell_volume_ratio": 1.0121115446565152,
            "cell_rmsd_from_input_A": 0.07565675858022933
          },
          {
            "iteration": 2,
            "reduced_polarization": [
              0.1378536732400195,
              0.195829217563904,
              0.15887397082489094
            ],
            "branch_aligned_reduced_polarization": [
              0.13785367324001951,
              0.19582921756390403,
              0.15887397082489096
            ],
            "target_residual": 0.5831267397867386,
            "energy_eV": -18.35648077784198,
            "max_atomic_step_A": 0.12,
            "max_log_strain_component": 0.007607066063860581,
            "step_scale": 0.2421126523164033,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 1.203697092630885,
            "cell_principal_stretches": [
              1.0378274433755812,
              0.9972155017245923,
              0.9832452189473249
            ],
            "cell_volume_ratio": 1.0175974615127035,
            "cell_rmsd_from_input_A": 0.11484431901929426
          },
          {
            "iteration": 3,
            "reduced_polarization": [
              0.19874182973117485,
              0.24729671657128094,
              0.22159760807945025
            ],
            "branch_aligned_reduced_polarization": [
              0.19874182973117482,
              0.24729671657128094,
              0.22159760807945028
            ],
            "target_residual": 0.4817917874315204,
            "energy_eV": -17.145748607508857,
            "max_atomic_step_A": 0.12,
            "max_log_strain_component": 0.012742167797448245,
            "step_scale": 0.19063341558788233,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 1.203697092630885,
            "cell_principal_stretches": [
              1.0600823837321116,
              0.996015974427036,
              0.9734376255048138
            ],
            "cell_volume_ratio": 1.0278128665417292,
            "cell_rmsd_from_input_A": 0.18362017948326692
          },
          {
            "iteration": 4,
            "reduced_polarization": [
              0.224782065439636,
              0.2685449300219049,
              0.24901860406772283
            ],
            "branch_aligned_reduced_polarization": [
              0.22478206543963597,
              0.2685449300219049,
              0.2490186040677228
            ],
            "target_residual": 0.4385293855904667,
            "energy_eV": -15.349109008786872,
            "max_atomic_step_A": 0.06723416538612186,
            "max_log_strain_component": 0.02,
            "step_scale": 0.14351974672753073,
            "strain_jacobian_refreshed": true,
            "strain_jacobian_frobenius_norm": 1.9017518222249377,
            "cell_principal_stretches": [
              1.0350092902361663,
              1.005656591409015,
              0.9660144580460898
            ],
            "cell_volume_ratio": 1.005489590647573,
            "cell_rmsd_from_input_A": 0.16434488413931395
          },
          {
            "iteration": 5,
            "reduced_polarization": [
              0.2652178079335694,
              0.3001837892476286,
              0.2835947263210166
            ],
            "branch_aligned_reduced_polarization": [
              0.2652178079335694,
              0.3001837892476286,
              0.2835947263210166
            ],
            "target_residual": 0.3766701982730119,
            "energy_eV": -13.508352863487447
          }
        ],
        "iterations": 5
      },
      "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": 0.3766701982730119,
        "parent_symmetrization_rmsd_A": 0.3575020082650929,
        "parent_cell_rmsd_A": 0.16434488413931395,
        "energy_eV": -13.508352863487447,
        "reduced_polarization": [
          0.2652178079335694,
          0.3001837892476286,
          0.2835947263210166
        ],
        "cartesian_polarization_e_A2": [
          0.005520415228077318,
          0.01198891790685414,
          0.011086949574050585
        ],
        "ranking_score": 1.6519286258459451
      },
      "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
        ],
        "endpoint_rmsd_A": 0.30893029176220904,
        "minimum_distance_A_by_image": [
          2.404986727522955,
          2.4052212488896263,
          2.4055222431604384,
          2.405889685386662,
          2.406323545128768,
          2.406823786469022,
          2.4073903680263267,
          2.4080232429732957,
          2.408722359055558
        ],
        "minimum_distance_A": 2.404986727522955,
        "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": [
          144.85825298076503,
          144.85825298076503,
          144.85825298076503,
          144.85825298076503,
          144.85825298076503,
          144.85825298076503,
          144.85825298076503,
          144.85825298076503,
          144.85825298076503
        ],
        "cell_deformation_log_strain_norm": 0.0
      },
      "parent_reduced_polarization": [
        2.137516994954202e-15,
        -1.9693128767497897e-15,
        -1.0589916609428664e-15
      ],
      "incoming": {
        "reached": true,
        "construction": "variable_cell_linear_interpolation",
        "continuation_fractions": [
          0.0,
          0.125,
          0.25,
          0.375,
          0.5,
          0.625,
          0.75,
          0.875,
          1.0
        ],
        "energies_eV": [
          -19.436754013242563,
          -19.456294641130228,
          -19.45489381700374,
          -19.43529298074406,
          -19.402974054878523,
          -19.36544036604803,
          -19.330797697585755,
          -19.30643548195698,
          -19.29766717451739
        ],
        "cartesian_polarizations_e_A2": [
          [
            3.944536392366656e-12,
            0.002138709785598493,
            2.944754974120344e-11
          ],
          [
            1.9189282189382423e-12,
            0.0020507565417348353,
            2.4712210751337954e-11
          ],
          [
            7.685898218032166e-13,
            0.0019211969818450864,
            2.0542992889650216e-11
          ],
          [
            9.462799562487353e-13,
            0.001739675321990905,
            1.7061841669719674e-11
          ],
          [
            1.5344668990338596e-12,
            0.0014991297596027042,
            1.38256462263187e-11
          ],
          [
            1.6833712458779793e-12,
            0.0011978271806295964,
            1.050229231931837e-11
          ],
          [
            1.4904605795344852e-12,
            0.0008392012735599862,
            7.0997696885076126e-12
          ],
          [
            9.497093037808673e-13,
            0.0004341707931177682,
            3.6081997513233437e-12
          ],
          [
            7.510918720503458e-17,
            -7.985742950724252e-17,
            -4.1578300059929855e-17
          ]
        ],
        "raw_reduced_polarization": [
          [
            3.9510233887552834e-10,
            0.05274135101015132,
            7.500236798085995e-10
          ],
          [
            2.850857363934056e-10,
            0.05057239244535171,
            6.294154660341756e-10
          ],
          [
            2.0937312917555822e-10,
            0.047377407192617293,
            5.232262533482923e-10
          ],
          [
            1.841810948023614e-10,
            0.042901017902784035,
            4.3456197156972295e-10
          ],
          [
            1.7489367352670792e-10,
            0.036969077989627404,
            3.5213666839948274e-10
          ],
          [
            1.50150963202237e-10,
            0.02953884823854522,
            2.6749145518002763e-10
          ],
          [
            1.1328068609570961e-10,
            0.020695004640195934,
            1.808298291153652e-10
          ],
          [
            6.399319979552035e-11,
            0.010706807605395632,
            9.190018452317628e-11
          ],
          [
            2.137516994954202e-15,
            -1.9693128767497897e-15,
            -1.0589916609428664e-15
          ]
        ],
        "unwrapped_reduced_polarization": [
          [
            3.9510233887552834e-10,
            0.05274135101015132,
            7.500236798085995e-10
          ],
          [
            2.850857363934056e-10,
            0.05057239244535171,
            6.294154660341756e-10
          ],
          [
            2.0937312917555822e-10,
            0.047377407192617293,
            5.232262533482923e-10
          ],
          [
            1.841810948023614e-10,
            0.042901017902784035,
            4.3456197156972295e-10
          ],
          [
            1.7489367352670792e-10,
            0.036969077989627404,
            3.5213666839948274e-10
          ],
          [
            1.50150963202237e-10,
            0.02953884823854522,
            2.6749145518002763e-10
          ],
          [
            1.1328068609570961e-10,
            0.020695004640195934,
            1.808298291153652e-10
          ],
          [
            6.399319979552035e-11,
            0.010706807605395632,
            9.190018452317628e-11
          ],
          [
            2.137516994951962e-15,
            -1.968911145233676e-15,
            -1.0589916609440764e-15
          ]
        ],
        "berry_integer_shifts": [
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ]
        ],
        "folded_reduced_polarization": [
          [
            3.951022842230145e-10,
            0.052741351010151316,
            7.500237098057028e-10
          ],
          [
            2.850857327985068e-10,
            0.05057239244535172,
            6.294155197039686e-10
          ],
          [
            2.0937307443347208e-10,
            0.047377407192617293,
            5.232262401122512e-10
          ],
          [
            1.8418111480400512e-10,
            0.042901017902784,
            4.345619419865443e-10
          ],
          [
            1.7489365511380583e-10,
            0.03696907798962745,
            3.5213665317002096e-10
          ],
          [
            1.5015100274240467e-10,
            0.029538848238545246,
            2.6749147341575963e-10
          ],
          [
            1.1328071813920815e-10,
            0.020695004640195913,
            1.8082979558187162e-10
          ],
          [
            6.399325513939402e-11,
            0.010706807605395663,
            9.190015415327935e-11
          ],
          [
            2.1094237467877974e-15,
            -1.942890293094024e-15,
            -1.0547118733938987e-15
          ]
        ]
      },
      "reflected": {
        "reached": true,
        "construction": "reflect_displacements_about_reconstructed_parent",
        "energies_eV": [
          -19.297667174517386,
          -19.306435481956985,
          -19.33079769758576,
          -19.36544036604804,
          -19.40297405487853,
          -19.43529298074405,
          -19.454893817003747,
          -19.456294641130228,
          -19.436754013242563
        ],
        "cartesian_polarizations_e_A2": [
          [
            -1.2262724441638298e-17,
            -3.028146812796933e-17,
            1.916050694005984e-18
          ],
          [
            -9.497982085330692e-13,
            -0.0004341707931177242,
            -3.6081495507951608e-12
          ],
          [
            -1.49043030593352e-12,
            -0.0008392012735599682,
            -7.099863958201757e-12
          ],
          [
            -1.6832444033220362e-12,
            -0.0011978271806296179,
            -1.0502350758864537e-11
          ],
          [
            -1.5345703657713357e-12,
            -0.001499129759602789,
            -1.3825600815917253e-11
          ],
          [
            -9.46321917758934e-13,
            -0.0017396753219908986,
            -1.7061755447438442e-11
          ],
          [
            -7.688498298823932e-13,
            -0.0019211969818453386,
            -2.054298465063223e-11
          ],
          [
            -1.9187852815564693e-12,
            -0.0020507565417348405,
            -2.471239526701979e-11
          ],
          [
            -3.944374869293151e-12,
            -0.002138709785598408,
            -2.944745872879547e-11
          ]
        ],
        "raw_reduced_polarization": [
          [
            -3.9254996496419646e-16,
            -7.467518736736947e-16,
            4.8801459029625185e-17
          ],
          [
            -6.399572110625323e-11,
            -0.010706807605394546,
            -9.18989059249497e-11
          ],
          [
            -1.1328051764968823e-10,
            -0.02069500464019549,
            -1.8083223014714945e-10
          ],
          [
            -1.501472481071236e-10,
            -0.029538848238545752,
            -2.674929436245281e-10
          ],
          [
            -1.7489672416966095e-10,
            -0.0369690779896295,
            -3.5213551180490375e-10
          ],
          [
            -1.8418172568773467e-10,
            -0.042901017902783875,
            -4.345597755040666e-10
          ],
          [
            -2.0938174206827212e-10,
            -0.04737740719262351,
            -5.232260435020184e-10
          ],
          [
            -2.850826109617739e-10,
            -0.05057239244535183,
            -6.294201656146802e-10
          ],
          [
            -3.9509612874549187e-10,
            -0.05274135101014923,
            -7.500213617392955e-10
          ]
        ],
        "unwrapped_reduced_polarization": [
          [
            -3.9254996496419646e-16,
            -7.467518736736947e-16,
            4.8801459029625185e-17
          ],
          [
            -6.399572110625323e-11,
            -0.010706807605394546,
            -9.18989059249497e-11
          ],
          [
            -1.1328051764968823e-10,
            -0.02069500464019549,
            -1.8083223014714945e-10
          ],
          [
            -1.501472481071236e-10,
            -0.029538848238545752,
            -2.674929436245281e-10
          ],
          [
            -1.7489672416966095e-10,
            -0.0369690779896295,
            -3.5213551180490375e-10
          ],
          [
            -1.8418172568773467e-10,
            -0.042901017902783875,
            -4.345597755040666e-10
          ],
          [
            -2.0938174206827212e-10,
            -0.04737740719262351,
            -5.232260435020184e-10
          ],
          [
            -2.850826109617739e-10,
            -0.05057239244535183,
            -6.294201656146802e-10
          ],
          [
            -3.9509612874549187e-10,
            -0.05274135101014923,
            -7.500213617392955e-10
          ]
        ],
        "gauge_integer_shift": [
          0,
          0,
          0
        ],
        "expected_opposite_endpoint_reduced_polarization": [
          -3.950980638415385e-10,
          -0.05274135101015526,
          -7.500257977919214e-10
        ],
        "actual_opposite_endpoint_branch_residual": 7.731936314905483e-15
      },
      "pnp_branch": {
        "construction": "incoming_path_concatenated_with_parent_reflection",
        "reduced_polarization": [
          [
            3.9510233887552834e-10,
            0.05274135101015132,
            7.500236798085995e-10
          ],
          [
            2.850857363934056e-10,
            0.05057239244535171,
            6.294154660341756e-10
          ],
          [
            2.0937312917555822e-10,
            0.047377407192617293,
            5.232262533482923e-10
          ],
          [
            1.841810948023614e-10,
            0.042901017902784035,
            4.3456197156972295e-10
          ],
          [
            1.7489367352670792e-10,
            0.036969077989627404,
            3.5213666839948274e-10
          ],
          [
            1.50150963202237e-10,
            0.02953884823854522,
            2.6749145518002763e-10
          ],
          [
            1.1328068609570961e-10,
            0.020695004640195934,
            1.808298291153652e-10
          ],
          [
            6.399319979552035e-11,
            0.010706807605395632,
            9.190018452317628e-11
          ],
          [
            2.137516994954202e-15,
            -1.9693128767497897e-15,
            -1.0589916609428664e-15
          ],
          [
            -6.399572110625323e-11,
            -0.010706807605394546,
            -9.18989059249497e-11
          ],
          [
            -1.1328051764968823e-10,
            -0.02069500464019549,
            -1.8083223014714945e-10
          ],
          [
            -1.501472481071236e-10,
            -0.029538848238545752,
            -2.674929436245281e-10
          ],
          [
            -1.7489672416966095e-10,
            -0.0369690779896295,
            -3.5213551180490375e-10
          ],
          [
            -1.8418172568773467e-10,
            -0.042901017902783875,
            -4.345597755040666e-10
          ],
          [
            -2.0938174206827212e-10,
            -0.04737740719262351,
            -5.232260435020184e-10
          ],
          [
            -2.850826109617739e-10,
            -0.05057239244535183,
            -6.294201656146802e-10
          ],
          [
            -3.9509612874549187e-10,
            -0.05274135101014923,
            -7.500213617392955e-10
          ]
        ],
        "unwrapped_reduced_polarization": [
          [
            3.9510233887552834e-10,
            0.05274135101015132,
            7.500236798085995e-10
          ],
          [
            2.850857363934056e-10,
            0.05057239244535171,
            6.294154660341756e-10
          ],
          [
            2.0937312917555822e-10,
            0.047377407192617293,
            5.232262533482923e-10
          ],
          [
            1.841810948023614e-10,
            0.042901017902784035,
            4.3456197156972295e-10
          ],
          [
            1.7489367352670792e-10,
            0.036969077989627404,
            3.5213666839948274e-10
          ],
          [
            1.50150963202237e-10,
            0.02953884823854522,
            2.6749145518002763e-10
          ],
          [
            1.1328068609570961e-10,
            0.020695004640195934,
            1.808298291153652e-10
          ],
          [
            6.399319979552035e-11,
            0.010706807605395632,
            9.190018452317628e-11
          ],
          [
            2.137516994951962e-15,
            -1.968911145233676e-15,
            -1.0589916609440764e-15
          ],
          [
            -6.399572110625323e-11,
            -0.010706807605394546,
            -9.18989059249497e-11
          ],
          [
            -1.1328051764968823e-10,
            -0.02069500464019549,
            -1.8083223014714945e-10
          ],
          [
            -1.501472481071236e-10,
            -0.029538848238545752,
            -2.674929436245281e-10
          ],
          [
            -1.7489672416966095e-10,
            -0.0369690779896295,
            -3.5213551180490375e-10
          ],
          [
            -1.8418172568773467e-10,
            -0.042901017902783875,
            -4.345597755040666e-10
          ],
          [
            -2.0938174206827212e-10,
            -0.04737740719262351,
            -5.232260435020184e-10
          ],
          [
            -2.850826109617739e-10,
            -0.05057239244535183,
            -6.294201656146802e-10
          ],
          [
            -3.9509612874549187e-10,
            -0.05274135101014923,
            -7.500213617392955e-10
          ]
        ],
        "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": [
          [
            3.951022842230145e-10,
            0.052741351010151316,
            7.500237098057028e-10
          ],
          [
            2.850857327985068e-10,
            0.05057239244535172,
            6.294155197039686e-10
          ],
          [
            2.0937307443347208e-10,
            0.047377407192617293,
            5.232262401122512e-10
          ],
          [
            1.8418111480400512e-10,
            0.042901017902784,
            4.345619419865443e-10
          ],
          [
            1.7489365511380583e-10,
            0.03696907798962745,
            3.5213665317002096e-10
          ],
          [
            1.5015100274240467e-10,
            0.029538848238545246,
            2.6749147341575963e-10
          ],
          [
            1.1328071813920815e-10,
            0.020695004640195913,
            1.8082979558187162e-10
          ],
          [
            6.399325513939402e-11,
            0.010706807605395663,
            9.190015415327935e-11
          ],
          [
            2.1094237467877974e-15,
            -1.942890293094024e-15,
            -1.0547118733938987e-15
          ],
          [
            -6.39956976300482e-11,
            -0.010706807605394553,
            -9.189893290795226e-11
          ],
          [
            -1.1328049609460322e-10,
            -0.02069500464019547,
            -1.808322380725258e-10
          ],
          [
            -1.5014722798412095e-10,
            -0.029538848238545745,
            -2.6749291670569164e-10
          ],
          [
            -1.7489670822712355e-10,
            -0.036969077989629506,
            -3.521354874358451e-10
          ],
          [
            -1.8418172542666866e-10,
            -0.04290101790278389,
            -4.345597770516463e-10
          ],
          [
            -2.0938173417306416e-10,
            -0.04737740719262351,
            -5.232260180676462e-10
          ],
          [
            -2.8508262417403785e-10,
            -0.05057239244535183,
            -6.29420182640672e-10
          ],
          [
            -3.9509612248522785e-10,
            -0.05274135101014921,
            -7.500213783373511e-10
          ]
        ]
      },
      "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": "P2_1/m",
        "spacegroup_number": 11,
        "pointgroup": "2/m",
        "has_inversion": true,
        "is_polar_point_group": false,
        "nonpolar_parent_hypothesis": true,
        "symmetry_tolerance_A": null,
        "target_reduced_polarization": [
          0.0,
          0.0,
          0.0
        ],
        "formal_class": [
          0.0,
          0.0,
          0.0
        ],
        "target_residual": 1.7061930524110972e-15,
        "parent_symmetrization_rmsd_A": 0.30893029176220904,
        "parent_cell_rmsd_A": 0.0,
        "energy_eV": -19.29766717451739,
        "reduced_polarization": [
          1.690227918671534e-15,
          7.744205168984508e-17,
          2.196065656333133e-16
        ],
        "cartesian_polarization_e_A2": [
          4.8284477488950795e-17,
          3.140345679313701e-18,
          8.622228123026928e-18
        ],
        "ranking_score": 0.30893029176221243
      }
    }
  ],
  "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": 157,
      "full_response": 38,
      "energy_polarization": 119
    },
    "model_evaluations_for_recovery_and_path_properties": {
      "total": 182,
      "full_response": 63,
      "energy_polarization": 119
    },
    "elapsed_seconds": 155.7938916250132
  }
}