{
  "schema": "ferrofinder.endpoint_parent_recovery.v4_variable_cell",
  "status": "complete",
  "input_atom_count": 52,
  "input_formula": "I4Li24P4S20",
  "input_spacegroup": "Cc",
  "input_pointgroup": "m",
  "input_is_polar_point_group": true,
  "input_energy_eV": -208.45305892485788,
  "input_cartesian_polarization_e_A2": [
    0.0009995834256393014,
    -1.4068245529468863e-17,
    0.0016009319006622252
  ],
  "input_reduced_polarization": [
    0.09001854700462908,
    -2.0669450962520085e-15,
    0.16888187325286497
  ],
  "input_formal_targets": [
    {
      "orbit_id": 0,
      "representative_formal_class": [
        0.0,
        0.0,
        0.0
      ],
      "target_reduced_polarization": [
        0.0,
        0.0,
        0.0
      ]
    },
    {
      "orbit_id": 1,
      "representative_formal_class": [
        0.0,
        0.0,
        0.5
      ],
      "target_reduced_polarization": [
        0.0,
        0.0,
        0.5
      ]
    },
    {
      "orbit_id": 2,
      "representative_formal_class": [
        0.5,
        0.0,
        0.0
      ],
      "target_reduced_polarization": [
        0.5,
        0.0,
        0.0
      ]
    },
    {
      "orbit_id": 3,
      "representative_formal_class": [
        0.5,
        0.0,
        0.5
      ],
      "target_reduced_polarization": [
        0.5,
        0.0,
        0.5
      ]
    },
    {
      "orbit_id": 4,
      "representative_formal_class": [
        0.0,
        0.5,
        0.0
      ],
      "target_reduced_polarization": [
        0.0,
        -0.5,
        0.0
      ]
    },
    {
      "orbit_id": 5,
      "representative_formal_class": [
        0.0,
        0.5,
        0.5
      ],
      "target_reduced_polarization": [
        0.0,
        -0.5,
        0.5
      ]
    },
    {
      "orbit_id": 6,
      "representative_formal_class": [
        0.5,
        0.5,
        0.0
      ],
      "target_reduced_polarization": [
        0.5,
        -0.5,
        0.0
      ]
    },
    {
      "orbit_id": 7,
      "representative_formal_class": [
        0.5,
        0.5,
        0.5
      ],
      "target_reduced_polarization": [
        0.5,
        -0.5,
        0.5
      ]
    }
  ],
  "parent_candidates": [
    {
      "candidate_id": "inversion_parent_endpoint_00",
      "source": "same_species_inversion_center_projection_from_endpoint",
      "spacegroup": "C2/c",
      "spacegroup_number": 15,
      "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": 4.379559518350762e-15,
      "parent_symmetrization_rmsd_A": 0.8025295278427111,
      "parent_cell_rmsd_A": 0.0,
      "energy_eV": -164.46198450451624,
      "reduced_polarization": [
        -1.034239432047622e-15,
        -4.219560937569214e-15,
        -5.533496779745937e-16
      ],
      "cartesian_polarization_e_A2": [
        -1.1481682057647057e-17,
        -2.8719591731739914e-17,
        -2.3400421131603706e-18
      ],
      "ranking_score": 0.8025295278427199
    },
    {
      "candidate_id": "inversion_parent_endpoint_01",
      "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": 1.803451209924652e-15,
      "parent_symmetrization_rmsd_A": 0.8030487144560872,
      "parent_cell_rmsd_A": 0.0,
      "energy_eV": -161.96443070226644,
      "reduced_polarization": [
        -1.6635704330604676e-15,
        1.849572641480118e-16,
        -6.713869906876218e-16
      ],
      "cartesian_polarization_e_A2": [
        -1.846781677899833e-17,
        1.2588743693343909e-18,
        -1.2329181967707951e-18
      ],
      "ranking_score": 0.8030487144560907
    },
    {
      "candidate_id": "inversion_parent_endpoint_02",
      "source": "same_species_inversion_center_projection_from_endpoint",
      "spacegroup": "P-1",
      "spacegroup_number": 2,
      "pointgroup": "-1",
      "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": 1.2848495707618062e-15,
      "parent_symmetrization_rmsd_A": 0.8259696741242083,
      "parent_cell_rmsd_A": 0.0,
      "energy_eV": -149.28299588846883,
      "reduced_polarization": [
        -4.839581905511317e-16,
        1.1288113440785874e-15,
        -3.7736963148187326e-16
      ],
      "cartesian_polarization_e_A2": [
        -5.372927720664307e-18,
        7.683027078824323e-18,
        -2.4658363935415903e-18
      ],
      "ranking_score": 0.8259696741242109
    },
    {
      "candidate_id": "bec_projection_00",
      "source": "MACEField_BEC_backprojection",
      "spacegroup": "Cc",
      "spacegroup_number": 9,
      "pointgroup": "m",
      "has_inversion": false,
      "is_polar_point_group": true,
      "nonpolar_parent_hypothesis": false,
      "symmetry_tolerance_A": null,
      "target_reduced_polarization": [
        0.0,
        0.0,
        0.0
      ],
      "formal_class": [
        0.0,
        0.0,
        0.0
      ],
      "target_residual": 0.0001465258799995141,
      "parent_symmetrization_rmsd_A": 0.02154620852829739,
      "parent_cell_rmsd_A": 0.22722909908371824,
      "energy_eV": -208.0108251406361,
      "reduced_polarization": [
        9.960703647012359e-05,
        2.1637689066741745e-15,
        0.00010746288566417466
      ],
      "cartesian_polarization_e_A2": [
        1.0923376261036815e-06,
        1.4799653553835237e-17,
        8.291001147104604e-07
      ],
      "ranking_score": 0.578646535059226
    },
    {
      "candidate_id": "inversion_parent_bec_00_00",
      "source": "same_species_inversion_center_projection_after_BEC",
      "spacegroup": "C2/c",
      "spacegroup_number": 15,
      "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": 2.377647001715334e-15,
      "parent_symmetrization_rmsd_A": 0.8025325349027789,
      "parent_cell_rmsd_A": 0.22722909908371824,
      "energy_eV": -167.09012994212327,
      "reduced_polarization": [
        -7.183647207513287e-16,
        2.009236699965002e-15,
        1.0488685695832113e-15
      ],
      "cartesian_polarization_e_A2": [
        -8.239752757250728e-18,
        1.3739718453572168e-17,
        1.5029153124668693e-17
      ],
      "ranking_score": 0.8593398096737132
    },
    {
      "candidate_id": "inversion_parent_bec_00_01",
      "source": "same_species_inversion_center_projection_after_BEC",
      "spacegroup": "P2/c",
      "spacegroup_number": 13,
      "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": 1.1716923899970967e-15,
      "parent_symmetrization_rmsd_A": 0.8030521932794644,
      "parent_cell_rmsd_A": 0.22722909908371824,
      "energy_eV": -164.86721712395806,
      "reduced_polarization": [
        1.6971810548865326e-17,
        2.0123607206739707e-16,
        1.1541572933195402e-15
      ],
      "cartesian_polarization_e_A2": [
        -3.921096744397383e-20,
        1.3761081374618728e-18,
        1.3224609156557465e-17
      ],
      "ranking_score": 0.8598594680503963
    },
    {
      "candidate_id": "bec_projection_01",
      "source": "MACEField_BEC_backprojection",
      "spacegroup": "Cc",
      "spacegroup_number": 9,
      "pointgroup": "m",
      "has_inversion": false,
      "is_polar_point_group": true,
      "nonpolar_parent_hypothesis": false,
      "symmetry_tolerance_A": null,
      "target_reduced_polarization": [
        0.0,
        0.0,
        0.5
      ],
      "formal_class": [
        0.0,
        0.0,
        0.5
      ],
      "target_residual": 0.00043955250309894923,
      "parent_symmetrization_rmsd_A": 0.05663121135302419,
      "parent_cell_rmsd_A": 0.364404261632327,
      "energy_eV": -206.64388381360615,
      "reduced_polarization": [
        -0.000310440819659184,
        7.337187557748329e-16,
        0.49968882014771215
      ],
      "cartesian_polarization_e_A2": [
        0.0001651208935672017,
        2.2305356758402297e-17,
        0.005801835854170266
      ],
      "ranking_score": 0.6486113817673038
    },
    {
      "candidate_id": "bec_projection_02",
      "source": "MACEField_BEC_backprojection",
      "spacegroup": "Cc",
      "spacegroup_number": 9,
      "pointgroup": "m",
      "has_inversion": false,
      "is_polar_point_group": true,
      "nonpolar_parent_hypothesis": false,
      "symmetry_tolerance_A": null,
      "target_reduced_polarization": [
        0.5,
        0.0,
        0.0
      ],
      "formal_class": [
        0.5,
        0.0,
        0.0
      ],
      "target_residual": 0.00016406377615467226,
      "parent_symmetrization_rmsd_A": 0.07791398473534254,
      "parent_cell_rmsd_A": 0.3557541337442422,
      "energy_eV": -204.4913610922098,
      "reduced_polarization": [
        0.49983801937348227,
        8.70915180946859e-15,
        2.606145197515349e-05
      ],
      "cartesian_polarization_e_A2": [
        0.005319550135023253,
        8.620975602284592e-17,
        -0.002000692203106753
      ],
      "ranking_score": 0.6671806457237124
    },
    {
      "candidate_id": "bec_projection_03",
      "source": "MACEField_BEC_backprojection",
      "spacegroup": "Cc",
      "spacegroup_number": 9,
      "pointgroup": "m",
      "has_inversion": false,
      "is_polar_point_group": true,
      "nonpolar_parent_hypothesis": false,
      "symmetry_tolerance_A": null,
      "target_reduced_polarization": [
        0.5,
        0.0,
        0.5
      ],
      "formal_class": [
        0.5,
        0.0,
        0.5
      ],
      "target_residual": 4.6244638933304736e-07,
      "parent_symmetrization_rmsd_A": 0.060937698882627206,
      "parent_cell_rmsd_A": 0.6895583404273292,
      "energy_eV": -205.5274961418287,
      "reduced_polarization": [
        0.4999997682082607,
        -5.629559486298621e-16,
        0.49999959983846687
      ],
      "cartesian_polarization_e_A2": [
        0.005619585387153882,
        -7.799894681339357e-17,
        0.004166079406599387
      ],
      "ranking_score": 0.7333282088822382
    },
    {
      "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,
        0.0
      ],
      "formal_class": [
        0.0,
        0.5,
        0.0
      ],
      "target_residual": 8.687753327478475e-05,
      "parent_symmetrization_rmsd_A": 0.04655421337767346,
      "parent_cell_rmsd_A": 0.4122936445979621,
      "energy_eV": -206.51447437015176,
      "reduced_polarization": [
        -3.432392465448565e-05,
        -0.4999216228938244,
        1.5053345533977956e-05
      ],
      "cartesian_polarization_e_A2": [
        4.622129156854513e-05,
        -0.0034259884604211453,
        -0.00011895033999632578
      ],
      "ranking_score": 0.6498013795937135
    },
    {
      "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": [
        0.0,
        -0.5,
        0.5
      ],
      "formal_class": [
        0.0,
        0.5,
        0.5
      ],
      "target_residual": 0.0006758441539011124,
      "parent_symmetrization_rmsd_A": 0.07028172366700497,
      "parent_cell_rmsd_A": 0.4506999007812909,
      "energy_eV": -204.42435501157462,
      "reduced_polarization": [
        -0.0004512179430463165,
        -0.5000217107829849,
        0.49949731090111527
      ],
      "cartesian_polarization_e_A2": [
        0.00019998709480116398,
        -0.003153498483288393,
        0.00569997987628608
      ],
      "ranking_score": 0.6843083871701299
    },
    {
      "candidate_id": "bec_projection_06",
      "source": "MACEField_BEC_backprojection",
      "spacegroup": "P1",
      "spacegroup_number": 1,
      "pointgroup": "1",
      "has_inversion": false,
      "is_polar_point_group": true,
      "nonpolar_parent_hypothesis": false,
      "symmetry_tolerance_A": null,
      "target_reduced_polarization": [
        0.5,
        -0.5,
        0.0
      ],
      "formal_class": [
        0.5,
        0.5,
        0.0
      ],
      "target_residual": 7.917249756236604e-06,
      "parent_symmetrization_rmsd_A": 0.09317059903043508,
      "parent_cell_rmsd_A": 0.5868940173761698,
      "energy_eV": -202.54773478009912,
      "reduced_polarization": [
        0.4999987894502158,
        -0.4999928019315523,
        3.066793691327126e-06
      ],
      "cartesian_polarization_e_A2": [
        0.00536730020636403,
        -0.0037057646091640875,
        -0.0021753529410136804
      ],
      "ranking_score": 0.73990993787399
    },
    {
      "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": 0.0009775433433335324,
      "parent_symmetrization_rmsd_A": 0.07334212495454653,
      "parent_cell_rmsd_A": 0.742616627256711,
      "energy_eV": -203.9609096571158,
      "reduced_polarization": [
        0.4996120504314482,
        -0.500213090616774,
        0.499128404618301
      ],
      "cartesian_polarization_e_A2": [
        0.005643724777785034,
        -0.0033497198717974378,
        0.004037594921771555
      ],
      "ranking_score": 0.7609513684553912
    }
  ],
  "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": [
              0.09001854700462908,
              -2.0669450962520085e-15,
              0.16888187325286497
            ],
            "branch_aligned_reduced_polarization": [
              0.09001854700462908,
              -2.0669450962520085e-15,
              0.16888187325286497
            ],
            "target_residual": 0.19137509220956986,
            "energy_eV": -208.45305892485788,
            "max_atomic_step_A": 0.03230222092304012,
            "max_log_strain_component": 0.01787893332757411,
            "step_scale": 1.0,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 6.6242856995056325,
            "cell_principal_stretches": [
              1.015901249080307,
              1.0044297473314856,
              0.9796851117835473
            ],
            "cell_volume_ratio": 0.9996720938410135,
            "cell_rmsd_from_input_A": 0.23466105228276998
          },
          {
            "iteration": 1,
            "reduced_polarization": [
              -0.003919360412632998,
              -6.583057389534767e-14,
              -0.004864490376083021
            ],
            "branch_aligned_reduced_polarization": [
              -0.003919360412632998,
              -6.583057389534767e-14,
              -0.004864490376083021
            ],
            "target_residual": 0.00624697147929451,
            "energy_eV": -207.985290056876,
            "max_atomic_step_A": 0.0009861937024080968,
            "max_log_strain_component": 0.0005344152071896638,
            "step_scale": 1.0,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 6.6242856995056325,
            "cell_principal_stretches": [
              1.015367814209908,
              1.0043837833993166,
              0.9802590818041702
            ],
            "cell_volume_ratio": 0.999686803980321,
            "cell_rmsd_from_input_A": 0.22722909908371824
          },
          {
            "iteration": 2,
            "reduced_polarization": [
              9.960703647012359e-05,
              2.1637689066741745e-15,
              0.00010746288566417466
            ],
            "branch_aligned_reduced_polarization": [
              9.960703647012359e-05,
              2.1637689066741745e-15,
              0.00010746288566417466
            ],
            "target_residual": 0.0001465258799995141,
            "energy_eV": -208.0108251406361
          }
        ],
        "iterations": 2
      },
      "parent": {
        "candidate_id": "bec_projection_00",
        "source": "MACEField_BEC_backprojection",
        "spacegroup": "Cc",
        "spacegroup_number": 9,
        "pointgroup": "m",
        "has_inversion": false,
        "is_polar_point_group": true,
        "nonpolar_parent_hypothesis": false,
        "symmetry_tolerance_A": null,
        "target_reduced_polarization": [
          0.0,
          0.0,
          0.0
        ],
        "formal_class": [
          0.0,
          0.0,
          0.0
        ],
        "target_residual": 0.0001465258799995141,
        "parent_symmetrization_rmsd_A": 0.02154620852829739,
        "parent_cell_rmsd_A": 0.22722909908371824,
        "energy_eV": -208.0108251406361,
        "reduced_polarization": [
          9.960703647012359e-05,
          2.1637689066741745e-15,
          0.00010746288566417466
        ],
        "cartesian_polarization_e_A2": [
          1.0923376261036815e-06,
          1.4799653553835237e-17,
          8.291001147104604e-07
        ],
        "ranking_score": 0.578646535059226
      },
      "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": [
          -208.45305892485788,
          -208.4394850856173,
          -208.4146461533415,
          -208.37823786452984,
          -208.32993836534905,
          -208.2694085728975,
          -208.1962936031834,
          -208.11022515646442,
          -208.01082514063611
        ],
        "cartesian_polarizations_e_A2": [
          [
            0.0009995834256393244,
            4.93167278708318e-19,
            0.0016009319006622354
          ],
          [
            0.0008744707810806685,
            1.3238166346088351e-17,
            0.0014006249472237864
          ],
          [
            0.0007493989514672366,
            -1.2356105724703235e-17,
            0.001200219744291214
          ],
          [
            0.0006243909300433702,
            -1.3446876858158256e-17,
            0.000999811879296444
          ],
          [
            0.0004994665167511981,
            7.684230508263769e-18,
            0.0007994934910050277
          ],
          [
            0.00037464586445602873,
            4.361490791799571e-17,
            0.0005993528516927487
          ],
          [
            0.0002499535296780795,
            1.0047398978546643e-17,
            0.00039947427306665303
          ],
          [
            0.00012542208477740068,
            -2.2847693309320497e-17,
            0.0001999386884899907
          ],
          [
            1.092337626066254e-06,
            1.617576169129711e-17,
            8.291001146868849e-07
          ]
        ],
        "raw_reduced_polarization": [
          [
            0.09001854700463115,
            7.245748492396339e-17,
            0.16888187325286655
          ],
          [
            0.07901603410936962,
            1.852685326890472e-15,
            0.14807958595969534
          ],
          [
            0.06794190582254211,
            -1.9696170166437968e-15,
            0.12717655226903016
          ],
          [
            0.0567980100470221,
            -2.1676886374458654e-15,
            0.10618139398176331
          ],
          [
            0.0455859776624696,
            9.177460539057731e-16,
            0.08510239544947484
          ],
          [
            0.03430753835631774,
            6.193657288565693e-15,
            0.06394757440829005
          ],
          [
            0.022964881560594324,
            1.3144355308808994e-15,
            0.04272480060374283
          ],
          [
            0.011560978528158086,
            -3.4346065192056536e-15,
            0.021441963849652912
          ],
          [
            9.960703646671819e-05,
            2.3650049787415928e-15,
            0.0001074628856609148
          ]
        ],
        "unwrapped_reduced_polarization": [
          [
            0.09001854700463115,
            7.245748492396339e-17,
            0.16888187325286655
          ],
          [
            0.07901603410936962,
            1.852685326890472e-15,
            0.14807958595969534
          ],
          [
            0.06794190582254211,
            -1.969617016643797e-15,
            0.12717655226903016
          ],
          [
            0.0567980100470221,
            -2.1676886374458654e-15,
            0.10618139398176331
          ],
          [
            0.0455859776624696,
            9.17746053905773e-16,
            0.08510239544947484
          ],
          [
            0.03430753835631774,
            6.193657288565693e-15,
            0.06394757440829005
          ],
          [
            0.022964881560594324,
            1.314435530880899e-15,
            0.04272480060374283
          ],
          [
            0.011560978528158086,
            -3.434606519205654e-15,
            0.021441963849652912
          ],
          [
            9.960703646671835e-05,
            2.3650049787415928e-15,
            0.00010746288566091527
          ]
        ],
        "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": [
          [
            0.09001854700463119,
            1.1102230246251565e-16,
            0.16888187325286652
          ],
          [
            0.07901603410936964,
            1.887379141862766e-15,
            0.14807958595969528
          ],
          [
            0.06794190582254211,
            -1.942890293094024e-15,
            0.12717655226903013
          ],
          [
            0.05679801004702212,
            -2.1649348980190553e-15,
            0.1061813939817633
          ],
          [
            0.045585977662469634,
            8.881784197001252e-16,
            0.08510239544947484
          ],
          [
            0.034307538356317724,
            6.217248937900877e-15,
            0.06394757440829002
          ],
          [
            0.022964881560594286,
            1.3322676295501878e-15,
            0.04272480060374284
          ],
          [
            0.011560978528158072,
            -3.4416913763379853e-15,
            0.021441963849652912
          ],
          [
            9.960703646672009e-05,
            2.3314683517128287e-15,
            0.00010746288566088058
          ]
        ]
      },
      "reflected": {
        "reached": true,
        "construction": "reflect_displacements_about_reconstructed_parent",
        "energies_eV": [
          -208.01082514063611,
          -208.00647559598417,
          -207.99674694687093,
          -207.98157327652694,
          -207.9608889223423,
          -207.93462819522674,
          -207.9027223461619,
          -207.86510365086892,
          -207.82170744048045
        ],
        "cartesian_polarizations_e_A2": [
          [
            1.0923376260760166e-06,
            1.5007367989678537e-17,
            8.291001146920648e-07
          ],
          [
            -1.9246164402318177e-05,
            2.944236842360164e-17,
            -6.025478144892073e-05
          ],
          [
            -4.060983794249365e-05,
            7.739353063319777e-17,
            -0.00012224845096644457
          ],
          [
            -6.299513558227298e-05,
            8.844999480750679e-17,
            -0.00018515486324202057
          ],
          [
            -8.639945794975891e-05,
            1.343701929418016e-16,
            -0.00024897339615867074
          ],
          [
            -0.00011081934658395962,
            1.6351713770181248e-16,
            -0.0003137007198468366
          ],
          [
            -0.0001362473387873908,
            1.472089822789749e-16,
            -0.00037933075482738754
          ],
          [
            -0.00016267558366657277,
            2.0332266076256872e-16,
            -0.00044585594763776415
          ],
          [
            -0.00019009765243711014,
            2.1219171070739474e-16,
            -0.0005132683398986998
          ]
        ],
        "raw_reduced_polarization": [
          [
            9.960703646760495e-05,
            2.1941441628353024e-15,
            0.0001074628856616804
          ],
          [
            -0.0018140973726294691,
            4.335208143963564e-15,
            -0.005870469010629297
          ],
          [
            -0.003797520090864033,
            1.1378206958751197e-14,
            -0.011937556436953019
          ],
          [
            -0.005849880102474409,
            1.3016924133649552e-14,
            -0.018093143007311196
          ],
          [
            -0.00797047961113792,
            1.9759954328908762e-14,
            -0.0243362961888423
          ],
          [
            -0.010158545217354518,
            2.4042788372704287e-14,
            -0.030665827820446086
          ],
          [
            -0.012412947234665472,
            2.1651856022142813e-14,
            -0.0370801955377857
          ],
          [
            -0.014732528079001155,
            2.9883920220231924e-14,
            -0.04357772970646028
          ],
          [
            -0.017116266697377366,
            3.1175786276494776e-14,
            -0.05015678233337402
          ]
        ],
        "unwrapped_reduced_polarization": [
          [
            9.960703646760495e-05,
            2.1941441628353024e-15,
            0.0001074628856616804
          ],
          [
            -0.0018140973726294691,
            4.335208143963564e-15,
            -0.005870469010629297
          ],
          [
            -0.003797520090864033,
            1.1378206958751197e-14,
            -0.011937556436953019
          ],
          [
            -0.005849880102474409,
            1.3016924133649552e-14,
            -0.018093143007311196
          ],
          [
            -0.00797047961113792,
            1.9759954328908762e-14,
            -0.0243362961888423
          ],
          [
            -0.010158545217354518,
            2.4042788372704287e-14,
            -0.030665827820446086
          ],
          [
            -0.012412947234665472,
            2.1651856022142813e-14,
            -0.0370801955377857
          ],
          [
            -0.014732528079001155,
            2.9883920220231924e-14,
            -0.04357772970646028
          ],
          [
            -0.017116266697377366,
            3.1175786276494776e-14,
            -0.05015678233337402
          ]
        ],
        "gauge_integer_shift": [
          0,
          0,
          0
        ],
        "expected_opposite_endpoint_reduced_polarization": [
          -0.08982177572717369,
          4.680716780613603e-15,
          -0.16867179560433684
        ],
        "actual_opposite_endpoint_branch_residual": 0.1390392009970508
      },
      "pnp_branch": {
        "construction": "incoming_path_concatenated_with_parent_reflection",
        "reduced_polarization": [
          [
            0.09001854700463115,
            7.245748492396339e-17,
            0.16888187325286655
          ],
          [
            0.07901603410936962,
            1.852685326890472e-15,
            0.14807958595969534
          ],
          [
            0.06794190582254211,
            -1.9696170166437968e-15,
            0.12717655226903016
          ],
          [
            0.0567980100470221,
            -2.1676886374458654e-15,
            0.10618139398176331
          ],
          [
            0.0455859776624696,
            9.177460539057731e-16,
            0.08510239544947484
          ],
          [
            0.03430753835631774,
            6.193657288565693e-15,
            0.06394757440829005
          ],
          [
            0.022964881560594324,
            1.3144355308808994e-15,
            0.04272480060374283
          ],
          [
            0.011560978528158086,
            -3.4346065192056536e-15,
            0.021441963849652912
          ],
          [
            9.960703646671819e-05,
            2.3650049787415928e-15,
            0.0001074628856609148
          ],
          [
            -0.0018140973726294691,
            4.335208143963564e-15,
            -0.005870469010629297
          ],
          [
            -0.003797520090864033,
            1.1378206958751197e-14,
            -0.011937556436953019
          ],
          [
            -0.005849880102474409,
            1.3016924133649552e-14,
            -0.018093143007311196
          ],
          [
            -0.00797047961113792,
            1.9759954328908762e-14,
            -0.0243362961888423
          ],
          [
            -0.010158545217354518,
            2.4042788372704287e-14,
            -0.030665827820446086
          ],
          [
            -0.012412947234665472,
            2.1651856022142813e-14,
            -0.0370801955377857
          ],
          [
            -0.014732528079001155,
            2.9883920220231924e-14,
            -0.04357772970646028
          ],
          [
            -0.017116266697377366,
            3.1175786276494776e-14,
            -0.05015678233337402
          ]
        ],
        "unwrapped_reduced_polarization": [
          [
            0.09001854700463115,
            7.245748492396339e-17,
            0.16888187325286655
          ],
          [
            0.07901603410936962,
            1.852685326890472e-15,
            0.14807958595969534
          ],
          [
            0.06794190582254211,
            -1.969617016643797e-15,
            0.12717655226903016
          ],
          [
            0.0567980100470221,
            -2.1676886374458654e-15,
            0.10618139398176331
          ],
          [
            0.0455859776624696,
            9.17746053905773e-16,
            0.08510239544947484
          ],
          [
            0.03430753835631774,
            6.193657288565693e-15,
            0.06394757440829005
          ],
          [
            0.022964881560594324,
            1.314435530880899e-15,
            0.04272480060374283
          ],
          [
            0.011560978528158086,
            -3.434606519205654e-15,
            0.021441963849652912
          ],
          [
            9.960703646671835e-05,
            2.3650049787415928e-15,
            0.00010746288566091527
          ],
          [
            -0.0018140973726294691,
            4.335208143963564e-15,
            -0.005870469010629297
          ],
          [
            -0.003797520090864033,
            1.1378206958751197e-14,
            -0.011937556436953019
          ],
          [
            -0.005849880102474409,
            1.3016924133649552e-14,
            -0.018093143007311196
          ],
          [
            -0.00797047961113792,
            1.9759954328908762e-14,
            -0.0243362961888423
          ],
          [
            -0.010158545217354518,
            2.4042788372704287e-14,
            -0.030665827820446086
          ],
          [
            -0.012412947234665472,
            2.1651856022142813e-14,
            -0.0370801955377857
          ],
          [
            -0.014732528079001155,
            2.9883920220231924e-14,
            -0.04357772970646028
          ],
          [
            -0.017116266697377366,
            3.1175786276494776e-14,
            -0.05015678233337402
          ]
        ],
        "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": [
          [
            0.09001854700463119,
            1.1102230246251565e-16,
            0.16888187325286652
          ],
          [
            0.07901603410936964,
            1.887379141862766e-15,
            0.14807958595969528
          ],
          [
            0.06794190582254211,
            -1.942890293094024e-15,
            0.12717655226903013
          ],
          [
            0.05679801004702212,
            -2.1649348980190553e-15,
            0.1061813939817633
          ],
          [
            0.045585977662469634,
            8.881784197001252e-16,
            0.08510239544947484
          ],
          [
            0.034307538356317724,
            6.217248937900877e-15,
            0.06394757440829002
          ],
          [
            0.022964881560594286,
            1.3322676295501878e-15,
            0.04272480060374284
          ],
          [
            0.011560978528158072,
            -3.4416913763379853e-15,
            0.021441963849652912
          ],
          [
            9.960703646672009e-05,
            2.3314683517128287e-15,
            0.00010746288566088058
          ],
          [
            -0.0018140973726294418,
            4.3298697960381105e-15,
            -0.00587046901062932
          ],
          [
            -0.003797520090864037,
            1.1324274851176597e-14,
            -0.011937556436953045
          ],
          [
            -0.005849880102474392,
            1.2989609388114332e-14,
            -0.018093143007311185
          ],
          [
            -0.007970479611137948,
            1.9761969838327786e-14,
            -0.02433629618884231
          ],
          [
            -0.010158545217354542,
            2.4091839634365897e-14,
            -0.03066582782044608
          ],
          [
            -0.012412947234665461,
            2.1649348980190553e-14,
            -0.03708019553778569
          ],
          [
            -0.014732528079001161,
            2.986499936241671e-14,
            -0.04357772970646029
          ],
          [
            -0.01711626669737737,
            3.11972669919669e-14,
            -0.050156782333374006
          ]
        ]
      },
      "incoming_structure_ids": [
        "incoming_00_000",
        "incoming_00_001",
        "incoming_00_002",
        "incoming_00_003",
        "incoming_00_004",
        "incoming_00_005",
        "incoming_00_006",
        "incoming_00_007",
        "incoming_00_008"
      ],
      "reflected_structure_ids": [
        "reflected_00_001",
        "reflected_00_002",
        "reflected_00_003",
        "reflected_00_004",
        "reflected_00_005",
        "reflected_00_006",
        "reflected_00_007",
        "reflected_00_008"
      ]
    },
    {
      "orbit_id": 1,
      "formal_class": [
        0.0,
        0.0,
        0.5
      ],
      "formal_classes_in_orbit": [
        [
          0.0,
          0.0,
          0.5
        ]
      ],
      "target_reduced_polarization": [
        0.0,
        0.0,
        0.5
      ],
      "bec_backprojection": {
        "converged_to_target": true,
        "history": [
          {
            "iteration": 0,
            "reduced_polarization": [
              0.09001854700462908,
              -2.0669450962520085e-15,
              0.16888187325286497
            ],
            "branch_aligned_reduced_polarization": [
              0.09001854700462908,
              -2.0669450962520085e-15,
              0.16888187325286497
            ],
            "target_residual": 0.34313634704787016,
            "energy_eV": -208.45305892485788,
            "max_atomic_step_A": 0.06393470475051356,
            "max_log_strain_component": 0.02,
            "step_scale": 0.7551257831457033,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 6.6242856995056325,
            "cell_principal_stretches": [
              1.0305234618622543,
              0.9872968907797518,
              0.9825170935844431
            ],
            "cell_volume_ratio": 0.9996449306714065,
            "cell_rmsd_from_input_A": 0.2571556148494092
          },
          {
            "iteration": 1,
            "reduced_polarization": [
              0.014171906742680462,
              3.678383873473182e-14,
              0.41227067701847775
            ],
            "branch_aligned_reduced_polarization": [
              0.014171906742680462,
              3.678383873473182e-14,
              0.41227067701847775
            ],
            "target_residual": 0.08886662507105511,
            "energy_eV": -207.4897371706689,
            "max_atomic_step_A": 0.021161696524989903,
            "max_log_strain_component": 0.008105209239442407,
            "step_scale": 1.0,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 6.6242856995056325,
            "cell_principal_stretches": [
              1.0420632859402483,
              0.9819665823510144,
              0.9768458353405602
            ],
            "cell_volume_ratio": 0.9995783307728846,
            "cell_rmsd_from_input_A": 0.35852256040845204
          },
          {
            "iteration": 2,
            "reduced_polarization": [
              -0.004068391060033984,
              1.962990900434429e-14,
              0.49611102355856107
            ],
            "branch_aligned_reduced_polarization": [
              -0.004068391060033984,
              1.962990900434429e-14,
              0.49611102355856107
            ],
            "target_residual": 0.0056281385536810875,
            "energy_eV": -206.65905080480084,
            "max_atomic_step_A": 0.0009191397081525454,
            "max_log_strain_component": 0.0005622820107989087,
            "step_scale": 1.0,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 6.6242856995056325,
            "cell_principal_stretches": [
              1.0425588848985807,
              0.9815215389564129,
              0.9768417536164568
            ],
            "cell_volume_ratio": 0.9995963065567102,
            "cell_rmsd_from_input_A": 0.364404261632327
          },
          {
            "iteration": 3,
            "reduced_polarization": [
              -0.000310440819659184,
              7.337187557748329e-16,
              0.49968882014771215
            ],
            "branch_aligned_reduced_polarization": [
              -0.000310440819659184,
              7.337187557748329e-16,
              0.49968882014771215
            ],
            "target_residual": 0.00043955250309894923,
            "energy_eV": -206.64388381360615
          }
        ],
        "iterations": 3
      },
      "parent": {
        "candidate_id": "bec_projection_01",
        "source": "MACEField_BEC_backprojection",
        "spacegroup": "Cc",
        "spacegroup_number": 9,
        "pointgroup": "m",
        "has_inversion": false,
        "is_polar_point_group": true,
        "nonpolar_parent_hypothesis": false,
        "symmetry_tolerance_A": null,
        "target_reduced_polarization": [
          0.0,
          0.0,
          0.5
        ],
        "formal_class": [
          0.0,
          0.0,
          0.5
        ],
        "target_residual": 0.00043955250309894923,
        "parent_symmetrization_rmsd_A": 0.05663121135302419,
        "parent_cell_rmsd_A": 0.364404261632327,
        "energy_eV": -206.64388381360615,
        "reduced_polarization": [
          -0.000310440819659184,
          7.337187557748329e-16,
          0.49968882014771215
        ],
        "cartesian_polarization_e_A2": [
          0.0001651208935672017,
          2.2305356758402297e-17,
          0.005801835854170266
        ],
        "ranking_score": 0.6486113817673038
      },
      "branch_status": "awaiting_branch_sampling"
    },
    {
      "orbit_id": 2,
      "formal_class": [
        0.5,
        0.0,
        0.0
      ],
      "formal_classes_in_orbit": [
        [
          0.5,
          0.0,
          0.0
        ]
      ],
      "target_reduced_polarization": [
        0.5,
        0.0,
        0.0
      ],
      "bec_backprojection": {
        "converged_to_target": true,
        "history": [
          {
            "iteration": 0,
            "reduced_polarization": [
              0.09001854700462908,
              -2.0669450962520085e-15,
              0.16888187325286497
            ],
            "branch_aligned_reduced_polarization": [
              0.09001854700462908,
              -2.0669450962520085e-15,
              0.16888187325286497
            ],
            "target_residual": 0.4434026149151494,
            "energy_eV": -208.45305892485788,
            "max_atomic_step_A": 0.05557974367325208,
            "max_log_strain_component": 0.02,
            "step_scale": 0.4697546004507922,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 6.6242856995056325,
            "cell_principal_stretches": [
              1.0151369211046972,
              1.005848414571657,
              0.9801714394976233
            ],
            "cell_volume_ratio": 1.000827437803038,
            "cell_rmsd_from_input_A": 0.1757765329132823
          },
          {
            "iteration": 1,
            "reduced_polarization": [
              0.28701831724092636,
              4.89540646012499e-14,
              0.09135712618059483
            ],
            "branch_aligned_reduced_polarization": [
              0.28701831724092636,
              4.89540646012499e-14,
              0.09135712618059483
            ],
            "target_residual": 0.23174840170940514,
            "energy_eV": -207.5999777257674,
            "max_atomic_step_A": 0.05561844635228173,
            "max_log_strain_component": 0.02,
            "step_scale": 0.9226766794974693,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 6.6242856995056325,
            "cell_principal_stretches": [
              1.030785095720421,
              1.0115223966677902,
              0.9606555415873921
            ],
            "cell_volume_ratio": 1.0016392304942228,
            "cell_rmsd_from_input_A": 0.3434894110320456
          },
          {
            "iteration": 2,
            "reduced_polarization": [
              0.48581305930396956,
              4.128134191563154e-14,
              0.009163945608330237
            ],
            "branch_aligned_reduced_polarization": [
              0.48581305930396956,
              4.128134191563154e-14,
              0.009163945608330237
            ],
            "target_residual": 0.016889262429872997,
            "energy_eV": -204.80708333006098,
            "max_atomic_step_A": 0.004378343134462832,
            "max_log_strain_component": 0.0015801875895907556,
            "step_scale": 1.0,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 6.6242856995056325,
            "cell_principal_stretches": [
              1.0321158462697628,
              1.0119185240515756,
              0.9590981330739551
            ],
            "cell_volume_ratio": 1.0016985327762453,
            "cell_rmsd_from_input_A": 0.3557541337442422
          },
          {
            "iteration": 3,
            "reduced_polarization": [
              0.49983801937348227,
              8.70915180946859e-15,
              2.606145197515349e-05
            ],
            "branch_aligned_reduced_polarization": [
              0.49983801937348227,
              8.70915180946859e-15,
              2.606145197515349e-05
            ],
            "target_residual": 0.00016406377615467226,
            "energy_eV": -204.4913610922098
          }
        ],
        "iterations": 3
      },
      "parent": {
        "candidate_id": "bec_projection_02",
        "source": "MACEField_BEC_backprojection",
        "spacegroup": "Cc",
        "spacegroup_number": 9,
        "pointgroup": "m",
        "has_inversion": false,
        "is_polar_point_group": true,
        "nonpolar_parent_hypothesis": false,
        "symmetry_tolerance_A": null,
        "target_reduced_polarization": [
          0.5,
          0.0,
          0.0
        ],
        "formal_class": [
          0.5,
          0.0,
          0.0
        ],
        "target_residual": 0.00016406377615467226,
        "parent_symmetrization_rmsd_A": 0.07791398473534254,
        "parent_cell_rmsd_A": 0.3557541337442422,
        "energy_eV": -204.4913610922098,
        "reduced_polarization": [
          0.49983801937348227,
          8.70915180946859e-15,
          2.606145197515349e-05
        ],
        "cartesian_polarization_e_A2": [
          0.005319550135023253,
          8.620975602284592e-17,
          -0.002000692203106753
        ],
        "ranking_score": 0.6671806457237124
      },
      "branch_status": "awaiting_branch_sampling"
    },
    {
      "orbit_id": 3,
      "formal_class": [
        0.5,
        0.0,
        0.5
      ],
      "formal_classes_in_orbit": [
        [
          0.5,
          0.0,
          0.5
        ]
      ],
      "target_reduced_polarization": [
        0.5,
        0.0,
        0.5
      ],
      "bec_backprojection": {
        "converged_to_target": true,
        "history": [
          {
            "iteration": 0,
            "reduced_polarization": [
              0.09001854700462908,
              -2.0669450962520085e-15,
              0.16888187325286497
            ],
            "branch_aligned_reduced_polarization": [
              0.09001854700462908,
              -2.0669450962520085e-15,
              0.16888187325286497
            ],
            "target_residual": 0.5269952615163891,
            "energy_eV": -208.45305892485788,
            "max_atomic_step_A": 0.04100874515111249,
            "max_log_strain_component": 0.02,
            "step_scale": 0.46991220294939334,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 6.6242856995056325,
            "cell_principal_stretches": [
              1.021808223146256,
              1.001977719680207,
              0.9774686059659884
            ],
            "cell_volume_ratio": 1.0007607771028002,
            "cell_rmsd_from_input_A": 0.29773262907558673
          },
          {
            "iteration": 1,
            "reduced_polarization": [
              0.2817312892899305,
              1.0439805879028709e-13,
              0.3166151821525695
            ],
            "branch_aligned_reduced_polarization": [
              0.2817312892899305,
              1.0439805879028709e-13,
              0.3166151821525695
            ],
            "target_residual": 0.2850810788038576,
            "energy_eV": -207.92832848147535,
            "max_atomic_step_A": 0.038023384119993925,
            "max_log_strain_component": 0.02,
            "step_scale": 0.8105231222560705,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 6.6242856995056325,
            "cell_principal_stretches": [
              1.0442123253034339,
              1.0027914364643715,
              0.956384140675475
            ],
            "cell_volume_ratio": 1.001455825988916,
            "cell_rmsd_from_input_A": 0.5817287464058625
          },
          {
            "iteration": 2,
            "reduced_polarization": [
              0.45213593614479164,
              1.3143946017791799e-13,
              0.44802386734279487
            ],
            "branch_aligned_reduced_polarization": [
              0.45213593614479164,
              1.3143946017791799e-13,
              0.44802386734279487
            ],
            "target_residual": 0.07065753303601004,
            "energy_eV": -206.32225284991324,
            "max_atomic_step_A": 0.011563817555216642,
            "max_log_strain_component": 0.007164910624442442,
            "step_scale": 1.0,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 6.6242856995056325,
            "cell_principal_stretches": [
              1.0524746177288336,
              1.0021380270561835,
              0.9496801436326573
            ],
            "cell_volume_ratio": 1.0016512346357211,
            "cell_rmsd_from_input_A": 0.6767480037844041
          },
          {
            "iteration": 3,
            "reduced_polarization": [
              0.4964938248662458,
              3.034957571005398e-14,
              0.492667476842928
            ],
            "branch_aligned_reduced_polarization": [
              0.4964938248662458,
              3.034957571005398e-14,
              0.492667476842928
            ],
            "target_residual": 0.008127678630307259,
            "energy_eV": -205.61285185508876,
            "max_atomic_step_A": 0.0014643188624217647,
            "max_log_strain_component": 0.0009402778975786307,
            "step_scale": 1.0,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 6.6242856995056325,
            "cell_principal_stretches": [
              1.0535883010749165,
              1.0018733333816645,
              0.94894158970246
            ],
            "cell_volume_ratio": 1.0016667043343015,
            "cell_rmsd_from_input_A": 0.6881710619177771
          },
          {
            "iteration": 4,
            "reduced_polarization": [
              0.4994762762822659,
              5.531984030890228e-15,
              0.49908032913509776
            ],
            "branch_aligned_reduced_polarization": [
              0.4994762762822659,
              5.531984030890228e-15,
              0.49908032913509776
            ],
            "target_residual": 0.0010583388078811515,
            "energy_eV": -205.53877620778601,
            "max_atomic_step_A": 0.00023724030162152398,
            "max_log_strain_component": 0.00011233391420578133,
            "step_scale": 1.0,
            "strain_jacobian_refreshed": true,
            "strain_jacobian_frobenius_norm": 6.4968737355282,
            "cell_principal_stretches": [
              1.0537136591981797,
              1.0018417631779812,
              0.9488480470355043
            ],
            "cell_volume_ratio": 1.0016555685468216,
            "cell_rmsd_from_input_A": 0.6895583404273292
          },
          {
            "iteration": 5,
            "reduced_polarization": [
              0.4999997682082607,
              -5.629559486298621e-16,
              0.49999959983846687
            ],
            "branch_aligned_reduced_polarization": [
              0.4999997682082607,
              -5.629559486298621e-16,
              0.49999959983846687
            ],
            "target_residual": 4.6244638933304736e-07,
            "energy_eV": -205.5274961418287
          }
        ],
        "iterations": 5
      },
      "parent": {
        "candidate_id": "bec_projection_03",
        "source": "MACEField_BEC_backprojection",
        "spacegroup": "Cc",
        "spacegroup_number": 9,
        "pointgroup": "m",
        "has_inversion": false,
        "is_polar_point_group": true,
        "nonpolar_parent_hypothesis": false,
        "symmetry_tolerance_A": null,
        "target_reduced_polarization": [
          0.5,
          0.0,
          0.5
        ],
        "formal_class": [
          0.5,
          0.0,
          0.5
        ],
        "target_residual": 4.6244638933304736e-07,
        "parent_symmetrization_rmsd_A": 0.060937698882627206,
        "parent_cell_rmsd_A": 0.6895583404273292,
        "energy_eV": -205.5274961418287,
        "reduced_polarization": [
          0.4999997682082607,
          -5.629559486298621e-16,
          0.49999959983846687
        ],
        "cartesian_polarization_e_A2": [
          0.005619585387153882,
          -7.799894681339357e-17,
          0.004166079406599387
        ],
        "ranking_score": 0.7333282088822382
      },
      "branch_status": "awaiting_branch_sampling"
    },
    {
      "orbit_id": 4,
      "formal_class": [
        0.0,
        0.5,
        0.0
      ],
      "formal_classes_in_orbit": [
        [
          0.0,
          0.5,
          0.0
        ]
      ],
      "target_reduced_polarization": [
        0.0,
        -0.5,
        0.0
      ],
      "bec_backprojection": {
        "converged_to_target": true,
        "history": [
          {
            "iteration": 0,
            "reduced_polarization": [
              0.09001854700462908,
              -2.0669450962520085e-15,
              0.16888187325286497
            ],
            "branch_aligned_reduced_polarization": [
              0.09001854700462908,
              -2.0539125955565396e-15,
              0.16888187325286497
            ],
            "target_residual": 0.535373165108431,
            "energy_eV": -208.45305892485788,
            "max_atomic_step_A": 0.04249126318983181,
            "max_log_strain_component": 0.02,
            "step_scale": 0.6093727672046024,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 6.6242856995056325,
            "cell_principal_stretches": [
              1.0267394207311378,
              0.9945883582497201,
              0.9790606550135575
            ],
            "cell_volume_ratio": 0.9998001701173779,
            "cell_rmsd_from_input_A": 0.24001631005959712
          },
          {
            "iteration": 1,
            "reduced_polarization": [
              0.029725726450226423,
              -0.29771485007576765,
              0.06750161010556305
            ],
            "branch_aligned_reduced_polarization": [
              0.029725726450226423,
              -0.29771485007576765,
              0.06750161010556305
            ],
            "target_residual": 0.2153122571051316,
            "energy_eV": -207.7663733462891,
            "max_atomic_step_A": 0.028195226031481304,
            "max_log_strain_component": 0.01394919307841344,
            "step_scale": 1.0,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 6.6242856995056325,
            "cell_principal_stretches": [
              1.045818586044205,
              0.9901960113086502,
              0.9653861646013241
            ],
            "cell_volume_ratio": 0.9997205024144757,
            "cell_rmsd_from_input_A": 0.40595111293106995
          },
          {
            "iteration": 2,
            "reduced_polarization": [
              -0.00678207153032728,
              -0.48897152773190805,
              0.0013597004053217585
            ],
            "branch_aligned_reduced_polarization": [
              -0.00678207153032728,
              -0.48897152773190805,
              0.0013597004053217585
            ],
            "target_residual": 0.013018159624262607,
            "energy_eV": -206.58539494530646,
            "max_atomic_step_A": 0.0022857564664850835,
            "max_log_strain_component": 0.000880048962910367,
            "step_scale": 1.0,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 6.6242856995056325,
            "cell_principal_stretches": [
              1.0469425734596898,
              0.989577614333336,
              0.9649837808536847
            ],
            "cell_volume_ratio": 0.9997530479543464,
            "cell_rmsd_from_input_A": 0.41164669179712443
          },
          {
            "iteration": 3,
            "reduced_polarization": [
              -0.0003554139055917591,
              -0.4990624795618774,
              0.0002429881227522377
            ],
            "branch_aligned_reduced_polarization": [
              -0.0003554139055917591,
              -0.4990624795618774,
              0.0002429881227522377
            ],
            "target_residual": 0.0010316524821781176,
            "energy_eV": -206.52084617531386,
            "max_atomic_step_A": 0.00017046460912465704,
            "max_log_strain_component": 7.419929633032962e-05,
            "step_scale": 1.0,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 6.6242856995056325,
            "cell_principal_stretches": [
              1.047044049707599,
              0.989530397074385,
              0.9649380998337863
            ],
            "cell_volume_ratio": 0.9997549136196751,
            "cell_rmsd_from_input_A": 0.4122936445979621
          },
          {
            "iteration": 4,
            "reduced_polarization": [
              -3.432392465448565e-05,
              -0.4999216228938244,
              1.5053345533977956e-05
            ],
            "branch_aligned_reduced_polarization": [
              -3.432392465448565e-05,
              -0.4999216228938244,
              1.5053345533977956e-05
            ],
            "target_residual": 8.687753327478475e-05,
            "energy_eV": -206.51447437015176
          }
        ],
        "iterations": 4
      },
      "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,
          0.0
        ],
        "formal_class": [
          0.0,
          0.5,
          0.0
        ],
        "target_residual": 8.687753327478475e-05,
        "parent_symmetrization_rmsd_A": 0.04655421337767346,
        "parent_cell_rmsd_A": 0.4122936445979621,
        "energy_eV": -206.51447437015176,
        "reduced_polarization": [
          -3.432392465448565e-05,
          -0.4999216228938244,
          1.5053345533977956e-05
        ],
        "cartesian_polarization_e_A2": [
          4.622129156854513e-05,
          -0.0034259884604211453,
          -0.00011895033999632578
        ],
        "ranking_score": 0.6498013795937135
      },
      "branch_status": "awaiting_branch_sampling"
    },
    {
      "orbit_id": 5,
      "formal_class": [
        0.0,
        0.5,
        0.5
      ],
      "formal_classes_in_orbit": [
        [
          0.0,
          0.5,
          0.5
        ]
      ],
      "target_reduced_polarization": [
        0.0,
        -0.5,
        0.5
      ],
      "bec_backprojection": {
        "converged_to_target": true,
        "history": [
          {
            "iteration": 0,
            "reduced_polarization": [
              0.09001854700462908,
              -2.0669450962520085e-15,
              0.16888187325286497
            ],
            "branch_aligned_reduced_polarization": [
              0.09001854700462908,
              -2.0539125955565396e-15,
              0.16888187325286497
            ],
            "target_residual": 0.6064178037173334,
            "energy_eV": -208.45305892485788,
            "max_atomic_step_A": 0.06370506879245037,
            "max_log_strain_component": 0.02,
            "step_scale": 0.6093727672047411,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 6.6242856995056325,
            "cell_principal_stretches": [
              1.0255051199974123,
              1.0079903768252116,
              0.967122124488348
            ],
            "cell_volume_ratio": 0.9997134556922602,
            "cell_rmsd_from_input_A": 0.2746373532285194
          },
          {
            "iteration": 1,
            "reduced_polarization": [
              0.028130664350273664,
              -0.31990646543076495,
              0.3682571847890848
            ],
            "branch_aligned_reduced_polarization": [
              0.028130664350273664,
              -0.31990646543076495,
              0.3682571847890848
            ],
            "target_residual": 0.22490261187928737,
            "energy_eV": -207.07857046470141,
            "max_atomic_step_A": 0.0381555190160094,
            "max_log_strain_component": 0.011467278181199208,
            "step_scale": 1.0,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 6.6242856995056325,
            "cell_principal_stretches": [
              1.042883854575906,
              1.0106966491895863,
              0.9483325192083738
            ],
            "cell_volume_ratio": 0.9995796662996068,
            "cell_rmsd_from_input_A": 0.44431706125604165
          },
          {
            "iteration": 2,
            "reduced_polarization": [
              -0.005571004875181778,
              -0.5030031125706027,
              0.49335615634945074
            ],
            "branch_aligned_reduced_polarization": [
              -0.005571004875181778,
              -0.5030031125706027,
              0.49335615634945074
            ],
            "target_residual": 0.009175807260614998,
            "energy_eV": -204.43439000975653,
            "max_atomic_step_A": 0.0014341929420997222,
            "max_log_strain_component": 0.0009097783687966333,
            "step_scale": 1.0,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 6.6242856995056325,
            "cell_principal_stretches": [
              1.0437826153029595,
              1.0099457722094616,
              0.94824370954888
            ],
            "cell_volume_ratio": 0.999604229574303,
            "cell_rmsd_from_input_A": 0.4506999007812909
          },
          {
            "iteration": 3,
            "reduced_polarization": [
              -0.0004512179430463165,
              -0.5000217107829849,
              0.49949731090111527
            ],
            "branch_aligned_reduced_polarization": [
              -0.0004512179430463165,
              -0.5000217107829849,
              0.49949731090111527
            ],
            "target_residual": 0.0006758441539011124,
            "energy_eV": -204.42435501157462
          }
        ],
        "iterations": 3
      },
      "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": [
          0.0,
          -0.5,
          0.5
        ],
        "formal_class": [
          0.0,
          0.5,
          0.5
        ],
        "target_residual": 0.0006758441539011124,
        "parent_symmetrization_rmsd_A": 0.07028172366700497,
        "parent_cell_rmsd_A": 0.4506999007812909,
        "energy_eV": -204.42435501157462,
        "reduced_polarization": [
          -0.0004512179430463165,
          -0.5000217107829849,
          0.49949731090111527
        ],
        "cartesian_polarization_e_A2": [
          0.00019998709480116398,
          -0.003153498483288393,
          0.00569997987628608
        ],
        "ranking_score": 0.6843083871701299
      },
      "branch_status": "awaiting_branch_sampling"
    },
    {
      "orbit_id": 6,
      "formal_class": [
        0.5,
        0.5,
        0.0
      ],
      "formal_classes_in_orbit": [
        [
          0.5,
          0.5,
          0.0
        ]
      ],
      "target_reduced_polarization": [
        0.5,
        -0.5,
        0.0
      ],
      "bec_backprojection": {
        "converged_to_target": true,
        "history": [
          {
            "iteration": 0,
            "reduced_polarization": [
              0.09001854700462908,
              -2.0669450962520085e-15,
              0.16888187325286497
            ],
            "branch_aligned_reduced_polarization": [
              0.09001854700462908,
              -2.0539125955565396e-15,
              0.16888187325286497
            ],
            "target_residual": 0.6682857763813249,
            "energy_eV": -208.45305892485788,
            "max_atomic_step_A": 0.06324270266185796,
            "max_log_strain_component": 0.02,
            "step_scale": 0.4697546004506117,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 6.6242856995056325,
            "cell_principal_stretches": [
              1.0274632345170311,
              0.9948518106585039,
              0.9791168347489467
            ],
            "cell_volume_ratio": 1.0008274378030388,
            "cell_rmsd_from_input_A": 0.23011876278831686
          },
          {
            "iteration": 1,
            "reduced_polarization": [
              0.28452128029849916,
              -0.21563272166662198,
              0.0941283124260374
            ],
            "branch_aligned_reduced_polarization": [
              0.28452128029849916,
              -0.21563272166662195,
              0.0941283124260374
            ],
            "target_residual": 0.36899317992492026,
            "energy_eV": -207.3678985337134,
            "max_atomic_step_A": 0.06339359531901326,
            "max_log_strain_component": 0.02,
            "step_scale": 0.8755363419516661,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 6.6242856995056325,
            "cell_principal_stretches": [
              1.0605958014924548,
              0.9856330500430014,
              0.9581680468717262
            ],
            "cell_volume_ratio": 1.0016288963388165,
            "cell_rmsd_from_input_A": 0.48688886798361675
          },
          {
            "iteration": 2,
            "reduced_polarization": [
              0.469529713213723,
              -0.4164210676046912,
              0.023055392529120616
            ],
            "branch_aligned_reduced_polarization": [
              0.469529713213723,
              -0.4164210676046912,
              0.023055392529120616
            ],
            "target_residual": 0.09189900675115804,
            "energy_eV": -203.9808364792588,
            "max_atomic_step_A": 0.015155201945031957,
            "max_log_strain_component": 0.007727500842281345,
            "step_scale": 1.0,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 6.6242856995056325,
            "cell_principal_stretches": [
              1.0719445546548234,
              0.980309916457418,
              0.9533122537070141
            ],
            "cell_volume_ratio": 1.001776624632592,
            "cell_rmsd_from_input_A": 0.5670450089228648
          },
          {
            "iteration": 3,
            "reduced_polarization": [
              0.4957372305964917,
              -0.482366469231214,
              0.004510133646583053
            ],
            "branch_aligned_reduced_polarization": [
              0.4957372305964917,
              -0.482366469231214,
              0.004510133646583053
            ],
            "target_residual": 0.018693686524365625,
            "energy_eV": -202.82843668811785,
            "max_atomic_step_A": 0.002870747004972896,
            "max_log_strain_component": 0.0016783005090684777,
            "step_scale": 1.0,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 6.6242856995056325,
            "cell_principal_stretches": [
              1.074335213025944,
              0.9790773834388226,
              0.9524110294861287
            ],
            "cell_volume_ratio": 1.0018005028282855,
            "cell_rmsd_from_input_A": 0.5837994216919663
          },
          {
            "iteration": 4,
            "reduced_polarization": [
              0.4989486419069339,
              -0.4961349013180281,
              0.0010166307128711136
            ],
            "branch_aligned_reduced_polarization": [
              0.4989486419069339,
              -0.4961349013180281,
              0.0010166307128711136
            ],
            "target_residual": 0.004132539130799514,
            "energy_eV": -202.60215924723613,
            "max_atomic_step_A": 0.0009678912502477709,
            "max_log_strain_component": 0.00032530579701640195,
            "step_scale": 1.0,
            "strain_jacobian_refreshed": true,
            "strain_jacobian_frobenius_norm": 5.937726322343752,
            "cell_principal_stretches": [
              1.0747428126557903,
              0.9788193777570314,
              0.952238566412193
            ],
            "cell_volume_ratio": 1.0017350616356921,
            "cell_rmsd_from_input_A": 0.5868940173761698
          },
          {
            "iteration": 5,
            "reduced_polarization": [
              0.4999987894502158,
              -0.4999928019315523,
              3.066793691327126e-06
            ],
            "branch_aligned_reduced_polarization": [
              0.4999987894502158,
              -0.4999928019315523,
              3.066793691327126e-06
            ],
            "target_residual": 7.917249756236604e-06,
            "energy_eV": -202.54773478009912
          }
        ],
        "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,
          -0.5,
          0.0
        ],
        "formal_class": [
          0.5,
          0.5,
          0.0
        ],
        "target_residual": 7.917249756236604e-06,
        "parent_symmetrization_rmsd_A": 0.09317059903043508,
        "parent_cell_rmsd_A": 0.5868940173761698,
        "energy_eV": -202.54773478009912,
        "reduced_polarization": [
          0.4999987894502158,
          -0.4999928019315523,
          3.066793691327126e-06
        ],
        "cartesian_polarization_e_A2": [
          0.00536730020636403,
          -0.0037057646091640875,
          -0.0021753529410136804
        ],
        "ranking_score": 0.73990993787399
      },
      "branch_status": "awaiting_branch_sampling"
    },
    {
      "orbit_id": 7,
      "formal_class": [
        0.5,
        0.5,
        0.5
      ],
      "formal_classes_in_orbit": [
        [
          0.5,
          0.5,
          0.5
        ]
      ],
      "target_reduced_polarization": [
        0.5,
        -0.5,
        0.5
      ],
      "bec_backprojection": {
        "converged_to_target": true,
        "history": [
          {
            "iteration": 0,
            "reduced_polarization": [
              0.09001854700462908,
              -2.0669450962520085e-15,
              0.16888187325286497
            ],
            "branch_aligned_reduced_polarization": [
              0.09001854700462908,
              -2.0539125955565396e-15,
              0.16888187325286497
            ],
            "target_residual": 0.7264461478050009,
            "energy_eV": -208.45305892485788,
            "max_atomic_step_A": 0.05104647199578406,
            "max_log_strain_component": 0.02,
            "step_scale": 0.4699122029492716,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 6.6242856995056325,
            "cell_principal_stretches": [
              1.0266466876621578,
              1.0033088363047211,
              0.9715711900606144
            ],
            "cell_volume_ratio": 1.0007607771028006,
            "cell_rmsd_from_input_A": 0.32956110597924815
          },
          {
            "iteration": 1,
            "reduced_polarization": [
              0.2796925717919384,
              -0.2337914513548463,
              0.3185522873242061
            ],
            "branch_aligned_reduced_polarization": [
              0.2796925717919384,
              -0.2337914513548463,
              0.3185522873242061
            ],
            "target_residual": 0.3902891578441385,
            "energy_eV": -207.61317054459033,
            "max_atomic_step_A": 0.04855004330211082,
            "max_log_strain_component": 0.02,
            "step_scale": 0.8296785326162561,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 6.6242856995056325,
            "cell_principal_stretches": [
              1.053554078044196,
              1.0064513983120382,
              0.944490062680352
            ],
            "cell_volume_ratio": 1.0014909588833598,
            "cell_rmsd_from_input_A": 0.6451413768599261
          },
          {
            "iteration": 2,
            "reduced_polarization": [
              0.4532578163092851,
              -0.4527736265959152,
              0.4542123141320446
            ],
            "branch_aligned_reduced_polarization": [
              0.4532578163092851,
              -0.4527736265959152,
              0.4542123141320446
            ],
            "target_residual": 0.08069494567952287,
            "energy_eV": -205.01574563316487,
            "max_atomic_step_A": 0.012303235501044252,
            "max_log_strain_component": 0.006284750562782578,
            "step_scale": 1.0,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 6.6242856995056325,
            "cell_principal_stretches": [
              1.0611404461414624,
              1.007074224099191,
              0.9373386949703915
            ],
            "cell_volume_ratio": 1.001684363825187,
            "cell_rmsd_from_input_A": 0.7337639658986962
          },
          {
            "iteration": 3,
            "reduced_polarization": [
              0.4965130855797165,
              -0.5002527829828308,
              0.4937157552170259
            ],
            "branch_aligned_reduced_polarization": [
              0.4965130855797165,
              -0.5002527829828308,
              0.4937157552170259
            ],
            "target_residual": 0.007191258853853562,
            "energy_eV": -204.03208967929638,
            "max_atomic_step_A": 0.0012471051075425667,
            "max_log_strain_component": 0.0008273906427991129,
            "step_scale": 1.0,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 6.6242856995056325,
            "cell_principal_stretches": [
              1.0618357387789008,
              1.0070237673146167,
              0.9367857204546032
            ],
            "cell_volume_ratio": 1.0016991871056424,
            "cell_rmsd_from_input_A": 0.742616627256711
          },
          {
            "iteration": 4,
            "reduced_polarization": [
              0.4996120504314482,
              -0.500213090616774,
              0.499128404618301
            ],
            "branch_aligned_reduced_polarization": [
              0.4996120504314482,
              -0.500213090616774,
              0.499128404618301
            ],
            "target_residual": 0.0009775433433335324,
            "energy_eV": -203.9609096571158
          }
        ],
        "iterations": 4
      },
      "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": 0.0009775433433335324,
        "parent_symmetrization_rmsd_A": 0.07334212495454653,
        "parent_cell_rmsd_A": 0.742616627256711,
        "energy_eV": -203.9609096571158,
        "reduced_polarization": [
          0.4996120504314482,
          -0.500213090616774,
          0.499128404618301
        ],
        "cartesian_polarization_e_A2": [
          0.005643724777785034,
          -0.0033497198717974378,
          0.004037594921771555
        ],
        "ranking_score": 0.7609513684553912
      },
      "branch_status": "awaiting_branch_sampling"
    }
  ],
  "sampled_polarization_branches": [
    {
      "orbit_id": 0,
      "candidate_id": "bec_projection_00",
      "formal_class": [
        0.0,
        0.0,
        0.0
      ],
      "construction": "MACEField-BEC-parent plus variable-cell P-N-P path and symmetric log-strain continuation beyond both polar endpoints",
      "geometry_diagnostics": {
        "collision_aware": false,
        "permutations_tested": 1,
        "selected_order": [
          0,
          1,
          2,
          3,
          4,
          5,
          6,
          7,
          8,
          9,
          10,
          11,
          12,
          13,
          14,
          15,
          16,
          17,
          18,
          19,
          20,
          21,
          22,
          23,
          24,
          25,
          26,
          27,
          28,
          29,
          30,
          31,
          32,
          33,
          34,
          35,
          36,
          37,
          38,
          39,
          40,
          41,
          42,
          43,
          44,
          45,
          46,
          47,
          48,
          49,
          50,
          51
        ],
        "endpoint_rmsd_A": 0.02154620852829739,
        "minimum_distance_A_by_image": [
          2.056811588682404,
          2.048996741754774,
          2.0381387753773765,
          2.0273303010983517,
          2.0165711765644985,
          2.0058612599328844,
          1.995200409868403,
          1.9845884855412408,
          1.9740252797160007
        ],
        "minimum_distance_A": 1.9740252797160007,
        "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": [
          1069.3246682508561,
          1069.282798984725,
          1069.2409313579813,
          1069.1990653705573,
          1069.157201022391,
          1069.115338313418,
          1069.073477243574,
          1069.0316178127935,
          1068.9897600210145
        ],
        "cell_deformation_log_strain_norm": 0.025480641556634882
      },
      "parent_reduced_polarization": [
        9.960703646671819e-05,
        2.3650049787415928e-15,
        0.0001074628856609148
      ],
      "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": [
          -208.45305892485788,
          -208.4394850856173,
          -208.4146461533415,
          -208.37823786452984,
          -208.32993836534905,
          -208.2694085728975,
          -208.1962936031834,
          -208.11022515646442,
          -208.01082514063611
        ],
        "cartesian_polarizations_e_A2": [
          [
            0.0009995834256393244,
            4.93167278708318e-19,
            0.0016009319006622354
          ],
          [
            0.0008744707810806685,
            1.3238166346088351e-17,
            0.0014006249472237864
          ],
          [
            0.0007493989514672366,
            -1.2356105724703235e-17,
            0.001200219744291214
          ],
          [
            0.0006243909300433702,
            -1.3446876858158256e-17,
            0.000999811879296444
          ],
          [
            0.0004994665167511981,
            7.684230508263769e-18,
            0.0007994934910050277
          ],
          [
            0.00037464586445602873,
            4.361490791799571e-17,
            0.0005993528516927487
          ],
          [
            0.0002499535296780795,
            1.0047398978546643e-17,
            0.00039947427306665303
          ],
          [
            0.00012542208477740068,
            -2.2847693309320497e-17,
            0.0001999386884899907
          ],
          [
            1.092337626066254e-06,
            1.617576169129711e-17,
            8.291001146868849e-07
          ]
        ],
        "raw_reduced_polarization": [
          [
            0.09001854700463115,
            7.245748492396339e-17,
            0.16888187325286655
          ],
          [
            0.07901603410936962,
            1.852685326890472e-15,
            0.14807958595969534
          ],
          [
            0.06794190582254211,
            -1.9696170166437968e-15,
            0.12717655226903016
          ],
          [
            0.0567980100470221,
            -2.1676886374458654e-15,
            0.10618139398176331
          ],
          [
            0.0455859776624696,
            9.177460539057731e-16,
            0.08510239544947484
          ],
          [
            0.03430753835631774,
            6.193657288565693e-15,
            0.06394757440829005
          ],
          [
            0.022964881560594324,
            1.3144355308808994e-15,
            0.04272480060374283
          ],
          [
            0.011560978528158086,
            -3.4346065192056536e-15,
            0.021441963849652912
          ],
          [
            9.960703646671819e-05,
            2.3650049787415928e-15,
            0.0001074628856609148
          ]
        ],
        "unwrapped_reduced_polarization": [
          [
            0.09001854700463115,
            7.245748492396339e-17,
            0.16888187325286655
          ],
          [
            0.07901603410936962,
            1.852685326890472e-15,
            0.14807958595969534
          ],
          [
            0.06794190582254211,
            -1.969617016643797e-15,
            0.12717655226903016
          ],
          [
            0.0567980100470221,
            -2.1676886374458654e-15,
            0.10618139398176331
          ],
          [
            0.0455859776624696,
            9.17746053905773e-16,
            0.08510239544947484
          ],
          [
            0.03430753835631774,
            6.193657288565693e-15,
            0.06394757440829005
          ],
          [
            0.022964881560594324,
            1.314435530880899e-15,
            0.04272480060374283
          ],
          [
            0.011560978528158086,
            -3.434606519205654e-15,
            0.021441963849652912
          ],
          [
            9.960703646671835e-05,
            2.3650049787415928e-15,
            0.00010746288566091527
          ]
        ],
        "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": [
          [
            0.09001854700463119,
            1.1102230246251565e-16,
            0.16888187325286652
          ],
          [
            0.07901603410936964,
            1.887379141862766e-15,
            0.14807958595969528
          ],
          [
            0.06794190582254211,
            -1.942890293094024e-15,
            0.12717655226903013
          ],
          [
            0.05679801004702212,
            -2.1649348980190553e-15,
            0.1061813939817633
          ],
          [
            0.045585977662469634,
            8.881784197001252e-16,
            0.08510239544947484
          ],
          [
            0.034307538356317724,
            6.217248937900877e-15,
            0.06394757440829002
          ],
          [
            0.022964881560594286,
            1.3322676295501878e-15,
            0.04272480060374284
          ],
          [
            0.011560978528158072,
            -3.4416913763379853e-15,
            0.021441963849652912
          ],
          [
            9.960703646672009e-05,
            2.3314683517128287e-15,
            0.00010746288566088058
          ]
        ]
      },
      "reflected": {
        "reached": true,
        "construction": "reflect_displacements_about_reconstructed_parent",
        "energies_eV": [
          -208.01082514063611,
          -208.00647559598417,
          -207.99674694687093,
          -207.98157327652694,
          -207.9608889223423,
          -207.93462819522674,
          -207.9027223461619,
          -207.86510365086892,
          -207.82170744048045
        ],
        "cartesian_polarizations_e_A2": [
          [
            1.0923376260760166e-06,
            1.5007367989678537e-17,
            8.291001146920648e-07
          ],
          [
            -1.9246164402318177e-05,
            2.944236842360164e-17,
            -6.025478144892073e-05
          ],
          [
            -4.060983794249365e-05,
            7.739353063319777e-17,
            -0.00012224845096644457
          ],
          [
            -6.299513558227298e-05,
            8.844999480750679e-17,
            -0.00018515486324202057
          ],
          [
            -8.639945794975891e-05,
            1.343701929418016e-16,
            -0.00024897339615867074
          ],
          [
            -0.00011081934658395962,
            1.6351713770181248e-16,
            -0.0003137007198468366
          ],
          [
            -0.0001362473387873908,
            1.472089822789749e-16,
            -0.00037933075482738754
          ],
          [
            -0.00016267558366657277,
            2.0332266076256872e-16,
            -0.00044585594763776415
          ],
          [
            -0.00019009765243711014,
            2.1219171070739474e-16,
            -0.0005132683398986998
          ]
        ],
        "raw_reduced_polarization": [
          [
            9.960703646760495e-05,
            2.1941441628353024e-15,
            0.0001074628856616804
          ],
          [
            -0.0018140973726294691,
            4.335208143963564e-15,
            -0.005870469010629297
          ],
          [
            -0.003797520090864033,
            1.1378206958751197e-14,
            -0.011937556436953019
          ],
          [
            -0.005849880102474409,
            1.3016924133649552e-14,
            -0.018093143007311196
          ],
          [
            -0.00797047961113792,
            1.9759954328908762e-14,
            -0.0243362961888423
          ],
          [
            -0.010158545217354518,
            2.4042788372704287e-14,
            -0.030665827820446086
          ],
          [
            -0.012412947234665472,
            2.1651856022142813e-14,
            -0.0370801955377857
          ],
          [
            -0.014732528079001155,
            2.9883920220231924e-14,
            -0.04357772970646028
          ],
          [
            -0.017116266697377366,
            3.1175786276494776e-14,
            -0.05015678233337402
          ]
        ],
        "unwrapped_reduced_polarization": [
          [
            9.960703646760495e-05,
            2.1941441628353024e-15,
            0.0001074628856616804
          ],
          [
            -0.0018140973726294691,
            4.335208143963564e-15,
            -0.005870469010629297
          ],
          [
            -0.003797520090864033,
            1.1378206958751197e-14,
            -0.011937556436953019
          ],
          [
            -0.005849880102474409,
            1.3016924133649552e-14,
            -0.018093143007311196
          ],
          [
            -0.00797047961113792,
            1.9759954328908762e-14,
            -0.0243362961888423
          ],
          [
            -0.010158545217354518,
            2.4042788372704287e-14,
            -0.030665827820446086
          ],
          [
            -0.012412947234665472,
            2.1651856022142813e-14,
            -0.0370801955377857
          ],
          [
            -0.014732528079001155,
            2.9883920220231924e-14,
            -0.04357772970646028
          ],
          [
            -0.017116266697377366,
            3.1175786276494776e-14,
            -0.05015678233337402
          ]
        ],
        "gauge_integer_shift": [
          0,
          0,
          0
        ],
        "expected_opposite_endpoint_reduced_polarization": [
          -0.08982177572717369,
          4.680716780613603e-15,
          -0.16867179560433684
        ],
        "actual_opposite_endpoint_branch_residual": 0.1390392009970508
      },
      "pnp_branch": {
        "construction": "incoming_path_concatenated_with_parent_reflection",
        "reduced_polarization": [
          [
            0.09001854700463115,
            7.245748492396339e-17,
            0.16888187325286655
          ],
          [
            0.07901603410936962,
            1.852685326890472e-15,
            0.14807958595969534
          ],
          [
            0.06794190582254211,
            -1.9696170166437968e-15,
            0.12717655226903016
          ],
          [
            0.0567980100470221,
            -2.1676886374458654e-15,
            0.10618139398176331
          ],
          [
            0.0455859776624696,
            9.177460539057731e-16,
            0.08510239544947484
          ],
          [
            0.03430753835631774,
            6.193657288565693e-15,
            0.06394757440829005
          ],
          [
            0.022964881560594324,
            1.3144355308808994e-15,
            0.04272480060374283
          ],
          [
            0.011560978528158086,
            -3.4346065192056536e-15,
            0.021441963849652912
          ],
          [
            9.960703646671819e-05,
            2.3650049787415928e-15,
            0.0001074628856609148
          ],
          [
            -0.0018140973726294691,
            4.335208143963564e-15,
            -0.005870469010629297
          ],
          [
            -0.003797520090864033,
            1.1378206958751197e-14,
            -0.011937556436953019
          ],
          [
            -0.005849880102474409,
            1.3016924133649552e-14,
            -0.018093143007311196
          ],
          [
            -0.00797047961113792,
            1.9759954328908762e-14,
            -0.0243362961888423
          ],
          [
            -0.010158545217354518,
            2.4042788372704287e-14,
            -0.030665827820446086
          ],
          [
            -0.012412947234665472,
            2.1651856022142813e-14,
            -0.0370801955377857
          ],
          [
            -0.014732528079001155,
            2.9883920220231924e-14,
            -0.04357772970646028
          ],
          [
            -0.017116266697377366,
            3.1175786276494776e-14,
            -0.05015678233337402
          ]
        ],
        "unwrapped_reduced_polarization": [
          [
            0.09001854700463115,
            7.245748492396339e-17,
            0.16888187325286655
          ],
          [
            0.07901603410936962,
            1.852685326890472e-15,
            0.14807958595969534
          ],
          [
            0.06794190582254211,
            -1.969617016643797e-15,
            0.12717655226903016
          ],
          [
            0.0567980100470221,
            -2.1676886374458654e-15,
            0.10618139398176331
          ],
          [
            0.0455859776624696,
            9.17746053905773e-16,
            0.08510239544947484
          ],
          [
            0.03430753835631774,
            6.193657288565693e-15,
            0.06394757440829005
          ],
          [
            0.022964881560594324,
            1.314435530880899e-15,
            0.04272480060374283
          ],
          [
            0.011560978528158086,
            -3.434606519205654e-15,
            0.021441963849652912
          ],
          [
            9.960703646671835e-05,
            2.3650049787415928e-15,
            0.00010746288566091527
          ],
          [
            -0.0018140973726294691,
            4.335208143963564e-15,
            -0.005870469010629297
          ],
          [
            -0.003797520090864033,
            1.1378206958751197e-14,
            -0.011937556436953019
          ],
          [
            -0.005849880102474409,
            1.3016924133649552e-14,
            -0.018093143007311196
          ],
          [
            -0.00797047961113792,
            1.9759954328908762e-14,
            -0.0243362961888423
          ],
          [
            -0.010158545217354518,
            2.4042788372704287e-14,
            -0.030665827820446086
          ],
          [
            -0.012412947234665472,
            2.1651856022142813e-14,
            -0.0370801955377857
          ],
          [
            -0.014732528079001155,
            2.9883920220231924e-14,
            -0.04357772970646028
          ],
          [
            -0.017116266697377366,
            3.1175786276494776e-14,
            -0.05015678233337402
          ]
        ],
        "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": [
          [
            0.09001854700463119,
            1.1102230246251565e-16,
            0.16888187325286652
          ],
          [
            0.07901603410936964,
            1.887379141862766e-15,
            0.14807958595969528
          ],
          [
            0.06794190582254211,
            -1.942890293094024e-15,
            0.12717655226903013
          ],
          [
            0.05679801004702212,
            -2.1649348980190553e-15,
            0.1061813939817633
          ],
          [
            0.045585977662469634,
            8.881784197001252e-16,
            0.08510239544947484
          ],
          [
            0.034307538356317724,
            6.217248937900877e-15,
            0.06394757440829002
          ],
          [
            0.022964881560594286,
            1.3322676295501878e-15,
            0.04272480060374284
          ],
          [
            0.011560978528158072,
            -3.4416913763379853e-15,
            0.021441963849652912
          ],
          [
            9.960703646672009e-05,
            2.3314683517128287e-15,
            0.00010746288566088058
          ],
          [
            -0.0018140973726294418,
            4.3298697960381105e-15,
            -0.00587046901062932
          ],
          [
            -0.003797520090864037,
            1.1324274851176597e-14,
            -0.011937556436953045
          ],
          [
            -0.005849880102474392,
            1.2989609388114332e-14,
            -0.018093143007311185
          ],
          [
            -0.007970479611137948,
            1.9761969838327786e-14,
            -0.02433629618884231
          ],
          [
            -0.010158545217354542,
            2.4091839634365897e-14,
            -0.03066582782044608
          ],
          [
            -0.012412947234665461,
            2.1649348980190553e-14,
            -0.03708019553778569
          ],
          [
            -0.014732528079001161,
            2.986499936241671e-14,
            -0.04357772970646029
          ],
          [
            -0.01711626669737737,
            3.11972669919669e-14,
            -0.050156782333374006
          ]
        ]
      },
      "incoming_structure_ids": [
        "incoming_00_000",
        "incoming_00_001",
        "incoming_00_002",
        "incoming_00_003",
        "incoming_00_004",
        "incoming_00_005",
        "incoming_00_006",
        "incoming_00_007",
        "incoming_00_008"
      ],
      "reflected_structure_ids": [
        "reflected_00_001",
        "reflected_00_002",
        "reflected_00_003",
        "reflected_00_004",
        "reflected_00_005",
        "reflected_00_006",
        "reflected_00_007",
        "reflected_00_008"
      ],
      "positive_extension_structure_ids": [
        "extension_plus_00_000",
        "extension_plus_00_001",
        "extension_plus_00_002",
        "extension_plus_00_003"
      ],
      "negative_extension_structure_ids": [
        "extension_minus_00_000",
        "extension_minus_00_001",
        "extension_minus_00_002",
        "extension_minus_00_003"
      ],
      "extension": {
        "enabled": true,
        "fraction_beyond_polar_endpoint": 0.35,
        "images_per_side": 4,
        "construction": "continue fractional atomic displacements and symmetric log strain beyond +P; reflect these structures about N for the -P side",
        "positive_path_coordinates": [
          1.35,
          1.2625,
          1.175,
          1.0875
        ],
        "negative_path_coordinates": [
          -1.0875,
          -1.175,
          -1.2625,
          -1.35
        ]
      },
      "branch_coordinates": [
        1.35,
        1.2625,
        1.175,
        1.0875,
        1.0,
        0.875,
        0.75,
        0.625,
        0.5,
        0.375,
        0.25,
        0.125,
        0.0,
        -0.125,
        -0.25,
        -0.375,
        -0.5,
        -0.625,
        -0.75,
        -0.875,
        -1.0,
        -1.0875,
        -1.175,
        -1.2625,
        -1.35
      ],
      "parent": {
        "candidate_id": "bec_projection_00",
        "source": "MACEField_BEC_backprojection",
        "spacegroup": "Cc",
        "spacegroup_number": 9,
        "pointgroup": "m",
        "has_inversion": false,
        "is_polar_point_group": true,
        "nonpolar_parent_hypothesis": false,
        "symmetry_tolerance_A": null,
        "target_reduced_polarization": [
          0.0,
          0.0,
          0.0
        ],
        "formal_class": [
          0.0,
          0.0,
          0.0
        ],
        "target_residual": 0.0001465258799995141,
        "parent_symmetrization_rmsd_A": 0.02154620852829739,
        "parent_cell_rmsd_A": 0.22722909908371824,
        "energy_eV": -208.0108251406361,
        "reduced_polarization": [
          9.960703647012359e-05,
          2.1637689066741745e-15,
          0.00010746288566417466
        ],
        "cartesian_polarization_e_A2": [
          1.0923376261036815e-06,
          1.4799653553835237e-17,
          8.291001147104604e-07
        ],
        "ranking_score": 0.578646535059226
      }
    }
  ],
  "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": 89,
      "full_response": 30,
      "energy_polarization": 59
    },
    "model_evaluations_for_recovery_and_path_properties": {
      "total": 114,
      "full_response": 55,
      "energy_polarization": 59
    },
    "elapsed_seconds": 885.596830303024
  }
}