{
  "schema": "ferrofinder.endpoint_parent_recovery.v4_variable_cell",
  "status": "complete",
  "input_atom_count": 28,
  "input_formula": "H8O16U4",
  "input_spacegroup": "Cmc2_1",
  "input_pointgroup": "mm2",
  "input_is_polar_point_group": true,
  "input_energy_eV": -204.2736162324927,
  "input_cartesian_polarization_e_A2": [
    -8.457201079453956e-20,
    8.486482708912715e-17,
    0.0017984789654613557
  ],
  "input_reduced_polarization": [
    -6.286468763157711e-18,
    2.5154067906601663e-15,
    0.07739812206320316
  ],
  "input_formal_targets": [
    {
      "orbit_id": 0,
      "representative_formal_class": [
        0.0,
        0.0,
        0.0
      ],
      "target_reduced_polarization": [
        0.0,
        0.0,
        0.0
      ]
    },
    {
      "orbit_id": 1,
      "representative_formal_class": [
        0.0,
        0.0,
        0.5
      ],
      "target_reduced_polarization": [
        0.0,
        0.0,
        0.5
      ]
    },
    {
      "orbit_id": 2,
      "representative_formal_class": [
        0.0,
        0.5,
        0.0
      ],
      "target_reduced_polarization": [
        0.0,
        0.5,
        0.0
      ]
    },
    {
      "orbit_id": 3,
      "representative_formal_class": [
        0.5,
        0.0,
        0.0
      ],
      "target_reduced_polarization": [
        0.5,
        0.0,
        0.0
      ]
    },
    {
      "orbit_id": 4,
      "representative_formal_class": [
        0.0,
        0.5,
        0.5
      ],
      "target_reduced_polarization": [
        0.0,
        0.5,
        0.5
      ]
    },
    {
      "orbit_id": 5,
      "representative_formal_class": [
        0.5,
        0.0,
        0.5
      ],
      "target_reduced_polarization": [
        0.5,
        0.0,
        0.5
      ]
    },
    {
      "orbit_id": 6,
      "representative_formal_class": [
        0.5,
        0.5,
        0.0
      ],
      "target_reduced_polarization": [
        0.5,
        0.5,
        0.0
      ]
    },
    {
      "orbit_id": 7,
      "representative_formal_class": [
        0.5,
        0.5,
        0.5
      ],
      "target_reduced_polarization": [
        0.5,
        0.5,
        0.5
      ]
    }
  ],
  "parent_candidates": [
    {
      "candidate_id": "inversion_parent_endpoint_00",
      "source": "same_species_inversion_center_projection_from_endpoint",
      "spacegroup": "Cmce",
      "spacegroup_number": 64,
      "pointgroup": "mmm",
      "has_inversion": true,
      "is_polar_point_group": false,
      "nonpolar_parent_hypothesis": true,
      "symmetry_tolerance_A": null,
      "target_reduced_polarization": [
        0.0,
        0.0,
        0.0
      ],
      "formal_class": [
        0.0,
        0.0,
        0.0
      ],
      "target_residual": 3.257378057398563e-15,
      "parent_symmetrization_rmsd_A": 0.07688723416342665,
      "parent_cell_rmsd_A": 0.0,
      "energy_eV": -204.3131740883924,
      "reduced_polarization": [
        -1.873979424491821e-18,
        3.2474529517232412e-15,
        -2.5408192255011483e-16
      ],
      "cartesian_polarization_e_A2": [
        -2.5210688876032725e-20,
        1.0956261001256935e-16,
        -5.904032049217024e-18
      ],
      "ranking_score": 0.07688723416343315
    },
    {
      "candidate_id": "symmetry_projection_00",
      "source": "spglib_refine_cell_from_polar_endpoint",
      "spacegroup": "Cmce",
      "spacegroup_number": 64,
      "pointgroup": "mmm",
      "has_inversion": true,
      "is_polar_point_group": false,
      "nonpolar_parent_hypothesis": true,
      "symmetry_tolerance_A": null,
      "target_reduced_polarization": [
        0.0,
        0.0,
        0.0
      ],
      "formal_class": [
        0.0,
        0.0,
        0.0
      ],
      "target_residual": 3.5076500434076713e-15,
      "parent_symmetrization_rmsd_A": 2.7516228932215308,
      "parent_cell_rmsd_A": 1.879431752032075e-15,
      "energy_eV": -203.0486404529531,
      "reduced_polarization": [
        3.299815330582249e-18,
        -6.09147900446647e-16,
        3.4543504126851497e-15
      ],
      "cartesian_polarization_e_A2": [
        4.439249255377043e-20,
        -2.0551439804908118e-17,
        8.026779450118719e-17
      ],
      "ranking_score": 2.7516228932215383
    },
    {
      "candidate_id": "bec_projection_00",
      "source": "MACEField_BEC_backprojection",
      "spacegroup": "Cmc2_1",
      "spacegroup_number": 36,
      "pointgroup": "mm2",
      "has_inversion": false,
      "is_polar_point_group": true,
      "nonpolar_parent_hypothesis": false,
      "symmetry_tolerance_A": null,
      "target_reduced_polarization": [
        0.0,
        0.0,
        0.0
      ],
      "formal_class": [
        0.0,
        0.0,
        0.0
      ],
      "target_residual": 0.00023203629512978416,
      "parent_symmetrization_rmsd_A": 0.022478653232133338,
      "parent_cell_rmsd_A": 0.007003482812573579,
      "energy_eV": -204.2130419574364,
      "reduced_polarization": [
        -2.1174029856048215e-15,
        1.4486386926236348e-16,
        0.00023203629512978416
      ],
      "cartesian_polarization_e_A2": [
        -2.848538476461485e-17,
        4.90747347261998e-18,
        5.393555885314704e-06
      ],
      "ranking_score": 0.5246935965255363
    },
    {
      "candidate_id": "inversion_parent_bec_00_00",
      "source": "same_species_inversion_center_projection_after_BEC",
      "spacegroup": "Cmce",
      "spacegroup_number": 64,
      "pointgroup": "mmm",
      "has_inversion": true,
      "is_polar_point_group": false,
      "nonpolar_parent_hypothesis": true,
      "symmetry_tolerance_A": null,
      "target_reduced_polarization": [
        0.0,
        0.0,
        0.0
      ],
      "formal_class": [
        0.0,
        0.0,
        0.0
      ],
      "target_residual": 1.930676938983879e-15,
      "parent_symmetrization_rmsd_A": 0.07688942802574121,
      "parent_cell_rmsd_A": 0.007003482812573579,
      "energy_eV": -204.30911014668683,
      "reduced_polarization": [
        1.3484172290593461e-15,
        -1.2828965392379679e-15,
        -5.132844130804296e-16
      ],
      "cartesian_polarization_e_A2": [
        1.8122429134326583e-17,
        -4.322178471298331e-17,
        -1.1931013488479768e-17
      ],
      "ranking_score": 0.07864029872888846
    },
    {
      "candidate_id": "symmetry_parent_00_00",
      "source": "spglib_refine_cell_after_MACEField_BEC_backprojection",
      "spacegroup": "Cmce",
      "spacegroup_number": 64,
      "pointgroup": "mmm",
      "has_inversion": true,
      "is_polar_point_group": false,
      "nonpolar_parent_hypothesis": true,
      "symmetry_tolerance_A": null,
      "target_reduced_polarization": [
        0.0,
        0.0,
        0.0
      ],
      "formal_class": [
        0.0,
        0.0,
        0.0
      ],
      "target_residual": 2.1572002431098808e-16,
      "parent_symmetrization_rmsd_A": 2.7529084504937225,
      "parent_cell_rmsd_A": 0.0070034828125739735,
      "energy_eV": -203.37991840862807,
      "reduced_polarization": [
        3.907075258741514e-18,
        1.296260044855031e-16,
        1.723860859024885e-16
      ],
      "cartesian_polarization_e_A2": [
        5.2510226785234773e-20,
        4.36720116370769e-18,
        4.007019624432829e-18
      ],
      "ranking_score": 2.754659321196866
    },
    {
      "candidate_id": "bec_projection_01",
      "source": "MACEField_BEC_backprojection",
      "spacegroup": "Cmc2_1",
      "spacegroup_number": 36,
      "pointgroup": "mm2",
      "has_inversion": false,
      "is_polar_point_group": true,
      "nonpolar_parent_hypothesis": false,
      "symmetry_tolerance_A": null,
      "target_reduced_polarization": [
        0.0,
        0.0,
        0.5
      ],
      "formal_class": [
        0.0,
        0.0,
        0.5
      ],
      "target_residual": 0.00012637053873892912,
      "parent_symmetrization_rmsd_A": 0.1295182811080003,
      "parent_cell_rmsd_A": 0.04105128853744488,
      "energy_eV": -203.24895355069862,
      "reduced_polarization": [
        -2.646141057820117e-14,
        -3.742496180425475e-15,
        0.49987362946126107
      ],
      "cartesian_polarization_e_A2": [
        -6.151751888116819e-18,
        -4.717007558392981e-16,
        0.011592679870087785
      ],
      "ranking_score": 0.6400338443198393
    },
    {
      "candidate_id": "bec_projection_02",
      "source": "MACEField_BEC_backprojection",
      "spacegroup": "Cm",
      "spacegroup_number": 8,
      "pointgroup": "m",
      "has_inversion": false,
      "is_polar_point_group": true,
      "nonpolar_parent_hypothesis": false,
      "symmetry_tolerance_A": null,
      "target_reduced_polarization": [
        0.0,
        0.5,
        0.0
      ],
      "formal_class": [
        0.0,
        0.5,
        0.0
      ],
      "target_residual": 6.063154358874999e-06,
      "parent_symmetrization_rmsd_A": 0.13766703234880118,
      "parent_cell_rmsd_A": 0.09456536064073756,
      "energy_eV": -192.73146071286976,
      "reduced_polarization": [
        -3.774399741578073e-15,
        0.4999939500561249,
        4.000248588765682e-07
      ],
      "cartesian_polarization_e_A2": [
        -3.377612935993313e-16,
        0.016845752029654933,
        0.00017374446317892854
      ],
      "ranking_score": 0.6613204988177033
    },
    {
      "candidate_id": "bec_projection_03",
      "source": "MACEField_BEC_backprojection",
      "spacegroup": "Cc",
      "spacegroup_number": 9,
      "pointgroup": "m",
      "has_inversion": false,
      "is_polar_point_group": true,
      "nonpolar_parent_hypothesis": false,
      "symmetry_tolerance_A": null,
      "target_reduced_polarization": [
        0.5,
        0.0,
        0.0
      ],
      "formal_class": [
        0.5,
        0.0,
        0.0
      ],
      "target_residual": 3.840625327194839e-05,
      "parent_symmetrization_rmsd_A": 0.08267164853016777,
      "parent_cell_rmsd_A": 0.009435527329660262,
      "energy_eV": -204.08152065888936,
      "reduced_polarization": [
        0.49998434590590574,
        -5.40401443557804e-15,
        3.507120797002829e-05
      ],
      "cartesian_polarization_e_A2": [
        0.006719490119258119,
        -2.0883138342048179e-16,
        -1.0367301076229016e-05
      ],
      "ranking_score": 0.5851073428691267
    },
    {
      "candidate_id": "symmetry_parent_03_00",
      "source": "spglib_refine_cell_after_MACEField_BEC_backprojection",
      "spacegroup": "Cmce",
      "spacegroup_number": 64,
      "pointgroup": "mmm",
      "has_inversion": true,
      "is_polar_point_group": false,
      "nonpolar_parent_hypothesis": true,
      "symmetry_tolerance_A": null,
      "target_reduced_polarization": [
        0.5,
        0.0,
        0.0
      ],
      "formal_class": [
        0.5,
        0.0,
        0.0
      ],
      "target_residual": 0.5,
      "parent_symmetrization_rmsd_A": 2.7529173239110083,
      "parent_cell_rmsd_A": 0.007222612873991566,
      "energy_eV": -203.38832948448692,
      "reduced_polarization": [
        -3.559593181484445e-18,
        6.775372714117224e-16,
        -1.4526290222366532e-17
      ],
      "cartesian_polarization_e_A2": [
        -4.783861143993996e-20,
        2.2825681951770785e-17,
        -3.376580170380294e-19
      ],
      "ranking_score": 3.7547229771295063
    },
    {
      "candidate_id": "bec_projection_04",
      "source": "MACEField_BEC_backprojection",
      "spacegroup": "Cm",
      "spacegroup_number": 8,
      "pointgroup": "m",
      "has_inversion": false,
      "is_polar_point_group": true,
      "nonpolar_parent_hypothesis": false,
      "symmetry_tolerance_A": null,
      "target_reduced_polarization": [
        0.0,
        0.5,
        0.5
      ],
      "formal_class": [
        0.0,
        0.5,
        0.5
      ],
      "target_residual": 4.932065536320558e-05,
      "parent_symmetrization_rmsd_A": 0.1726530755302123,
      "parent_cell_rmsd_A": 0.0948773825327382,
      "energy_eV": -194.69325116086893,
      "reduced_polarization": [
        -3.829981527420098e-15,
        0.4999899890120246,
        0.5000482939661367
      ],
      "cartesian_polarization_e_A2": [
        -1.7445997683047031e-16,
        0.017118973186408277,
        0.011756330909503197
      ],
      "ranking_score": 0.6964710624741233
    },
    {
      "candidate_id": "bec_projection_05",
      "source": "MACEField_BEC_backprojection",
      "spacegroup": "Cc",
      "spacegroup_number": 9,
      "pointgroup": "m",
      "has_inversion": false,
      "is_polar_point_group": true,
      "nonpolar_parent_hypothesis": false,
      "symmetry_tolerance_A": null,
      "target_reduced_polarization": [
        0.5,
        0.0,
        0.5
      ],
      "formal_class": [
        0.5,
        0.0,
        0.5
      ],
      "target_residual": 0.00019018611959373496,
      "parent_symmetrization_rmsd_A": 0.1569926461922749,
      "parent_cell_rmsd_A": 0.043548634603073,
      "energy_eV": -202.99475401114682,
      "reduced_polarization": [
        0.5000179001811157,
        7.552193206449483e-16,
        0.5001893418696489
      ],
      "cartesian_polarization_e_A2": [
        0.006745952619746531,
        -5.357684926938001e-16,
        0.011586236979464681
      ],
      "ranking_score": 0.6682601770822306
    },
    {
      "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": 1.0932647417397724e-05,
      "parent_symmetrization_rmsd_A": 0.15848610640629002,
      "parent_cell_rmsd_A": 0.09477689234562918,
      "energy_eV": -192.71694245217301,
      "reduced_polarization": [
        0.5000022539987264,
        0.4999918348529223,
        6.911775639736533e-06
      ],
      "cartesian_polarization_e_A2": [
        0.00671947153127189,
        0.016844934811169335,
        0.0001624770430914419
      ],
      "ranking_score": 0.6822021947875321
    },
    {
      "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": 0.000258376641237587,
      "parent_symmetrization_rmsd_A": 0.19307374646497225,
      "parent_cell_rmsd_A": 0.09571484602217213,
      "energy_eV": -194.55684619567495,
      "reduced_polarization": [
        0.5000020290367999,
        0.5000499423650303,
        0.5002534958222971
      ],
      "cartesian_polarization_e_A2": [
        0.006745250129416258,
        0.017126640878956503,
        0.011747287411854315
      ],
      "ranking_score": 0.7175192112529905
    }
  ],
  "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": [
              -6.286468763157711e-18,
              2.5154067906601663e-15,
              0.07739812206320316
            ],
            "branch_aligned_reduced_polarization": [
              -6.286468763157711e-18,
              2.5154067906601663e-15,
              0.07739812206320316
            ],
            "target_residual": 0.07739812206320316,
            "energy_eV": -204.2736162324927,
            "max_atomic_step_A": 0.029397884152197684,
            "max_log_strain_component": 0.0013591445225714645,
            "step_scale": 1.0,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 0.9162524725127975,
            "cell_principal_stretches": [
              1.0013600685780821,
              1.0000418399726365,
              0.9996259193909764
            ],
            "cell_volume_ratio": 1.0010273603988358,
            "cell_rmsd_from_input_A": 0.007003482812573579
          },
          {
            "iteration": 1,
            "reduced_polarization": [
              -2.1174029856048215e-15,
              1.4486386926236348e-16,
              0.00023203629512978416
            ],
            "branch_aligned_reduced_polarization": [
              -2.1174029856048215e-15,
              1.4486386926236348e-16,
              0.00023203629512978416
            ],
            "target_residual": 0.00023203629512978416,
            "energy_eV": -204.2130419574364
          }
        ],
        "iterations": 1
      },
      "parent": {
        "candidate_id": "inversion_parent_endpoint_00",
        "source": "same_species_inversion_center_projection_from_endpoint",
        "spacegroup": "Cmce",
        "spacegroup_number": 64,
        "pointgroup": "mmm",
        "has_inversion": true,
        "is_polar_point_group": false,
        "nonpolar_parent_hypothesis": true,
        "symmetry_tolerance_A": null,
        "target_reduced_polarization": [
          0.0,
          0.0,
          0.0
        ],
        "formal_class": [
          0.0,
          0.0,
          0.0
        ],
        "target_residual": 3.257378057398563e-15,
        "parent_symmetrization_rmsd_A": 0.07688723416342665,
        "parent_cell_rmsd_A": 0.0,
        "energy_eV": -204.3131740883924,
        "reduced_polarization": [
          -1.873979424491821e-18,
          3.2474529517232412e-15,
          -2.5408192255011483e-16
        ],
        "cartesian_polarization_e_A2": [
          -2.5210688876032725e-20,
          1.0956261001256935e-16,
          -5.904032049217024e-18
        ],
        "ranking_score": 0.07688723416343315
      },
      "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": [
          -204.27361623249269,
          -204.28274149418564,
          -204.29072748910193,
          -204.29753847644616,
          -204.30314557166434,
          -204.30752533506865,
          -204.31066165924773,
          -204.3125457702565,
          -204.31317408839234
        ],
        "cartesian_polarizations_e_A2": [
          [
            1.478718388944043e-17,
            5.687701103902202e-17,
            0.0017984789654612804
          ],
          [
            2.345753327006909e-17,
            8.143958712164246e-17,
            0.0015794950846072576
          ],
          [
            9.288556772864989e-18,
            1.1267236735146992e-17,
            0.001358134003572728
          ],
          [
            1.304441079212029e-18,
            1.374602881687933e-17,
            0.0011347417385894163
          ],
          [
            1.3005224593259505e-17,
            3.5694605976945674e-17,
            0.0009096951630035448
          ],
          [
            -2.164519574620539e-17,
            2.244433557641281e-17,
            0.000683361310476972
          ],
          [
            2.1224586924801587e-17,
            -2.041623296408635e-17,
            0.0004560861297154003
          ],
          [
            1.0918408729136104e-17,
            -1.0780492108188643e-16,
            0.00022819525641887134
          ],
          [
            1.1925821007972093e-17,
            5.54348047369232e-18,
            1.6360027739433432e-17
          ]
        ],
        "raw_reduced_polarization": [
          [
            1.0991718033271378e-15,
            1.6858435314992723e-15,
            0.07739812206319993
          ],
          [
            1.7436625755685977e-15,
            2.413882140585725e-15,
            0.06797408015572855
          ],
          [
            6.904438177459401e-16,
            3.3396266471855624e-16,
            0.058447734672139255
          ],
          [
            9.69626714654822e-17,
            4.0743445095663864e-16,
            0.04883397653251129
          ],
          [
            9.66713897367272e-16,
            1.0579937218283863e-15,
            0.03914902460279386
          ],
          [
            -1.6089465728978494e-15,
            6.652536281193641e-16,
            0.02940867429494751
          ],
          [
            1.5776815693532689e-15,
            -6.05140348470024e-16,
            0.01962781362304733
          ],
          [
            8.115951693031553e-16,
            -3.195354776027147e-15,
            0.009820456424421415
          ],
          [
            8.864788780269506e-16,
            1.6430963104152967e-16,
            7.040590678297074e-16
          ]
        ],
        "unwrapped_reduced_polarization": [
          [
            1.0991718033271378e-15,
            1.6858435314992723e-15,
            0.07739812206319993
          ],
          [
            1.7436625755685977e-15,
            2.413882140585725e-15,
            0.06797408015572855
          ],
          [
            6.904438177459401e-16,
            3.3396266471855604e-16,
            0.058447734672139255
          ],
          [
            9.69626714654822e-17,
            4.0743445095663864e-16,
            0.04883397653251129
          ],
          [
            9.66713897367272e-16,
            1.0579937218283863e-15,
            0.03914902460279386
          ],
          [
            -1.6089465728978496e-15,
            6.652536281193641e-16,
            0.02940867429494751
          ],
          [
            1.5776815693532689e-15,
            -6.051403484700239e-16,
            0.01962781362304733
          ],
          [
            8.115951693031553e-16,
            -3.1953547760271475e-15,
            0.009820456424421415
          ],
          [
            8.864788780269506e-16,
            1.6430963104152967e-16,
            7.042977312465837e-16
          ]
        ],
        "berry_integer_shifts": [
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ]
        ],
        "folded_reduced_polarization": [
          [
            1.1102230246251565e-15,
            1.6653345369377348e-15,
            0.07739812206319996
          ],
          [
            1.7763568394002505e-15,
            2.4424906541753444e-15,
            0.06797408015572859
          ],
          [
            6.661338147750939e-16,
            3.3306690738754696e-16,
            0.05844773467213926
          ],
          [
            1.1102230246251565e-16,
            4.440892098500626e-16,
            0.048833976532511314
          ],
          [
            9.992007221626409e-16,
            1.1102230246251565e-15,
            0.0391490246027939
          ],
          [
            -1.609823385706477e-15,
            6.661338147750939e-16,
            0.029408674294947534
          ],
          [
            1.5543122344752192e-15,
            -6.106226635438361e-16,
            0.01962781362304733
          ],
          [
            7.771561172376096e-16,
            -3.219646771412954e-15,
            0.00982045642442142
          ],
          [
            8.881784197001252e-16,
            1.1102230246251565e-16,
            6.661338147750939e-16
          ]
        ]
      },
      "reflected": {
        "reached": true,
        "construction": "reflect_displacements_about_reconstructed_parent",
        "energies_eV": [
          -204.31317408839237,
          -204.31254577025646,
          -204.3106616592477,
          -204.30752533506865,
          -204.30314557166437,
          -204.29753847644616,
          -204.29072748910195,
          -204.2827414941856,
          -204.27361623249266
        ],
        "cartesian_polarizations_e_A2": [
          [
            -2.057475228193399e-18,
            1.3069994612770512e-18,
            2.487805871120456e-17
          ],
          [
            3.832297737690501e-19,
            2.5824506596956907e-17,
            -0.0002281952564188417
          ],
          [
            -9.037761279067052e-18,
            4.222960328333093e-17,
            -0.00045608612971533984
          ],
          [
            -4.250955614027248e-18,
            -6.165431941472435e-17,
            -0.0006833613104770321
          ],
          [
            1.2522615350510522e-17,
            -3.772270858927213e-17,
            -0.0009096951630035464
          ],
          [
            2.350391755178532e-19,
            5.836428628806142e-17,
            -0.0011347417385893772
          ],
          [
            1.8355357380191884e-17,
            -1.0352337112253057e-16,
            -0.0013581340035726595
          ],
          [
            -1.3371394440397395e-17,
            -5.687701103902202e-17,
            -0.0015794950846071659
          ],
          [
            1.7850491647325755e-17,
            -8.558593024017655e-17,
            -0.0017984789654612414
          ]
        ],
        "raw_reduced_polarization": [
          [
            -1.5293775838475978e-16,
            3.873966910735253e-17,
            1.0706352766997202e-15
          ],
          [
            2.848651674800522e-17,
            7.654424275349311e-16,
            -0.009820456424420138
          ],
          [
            -6.718015030736343e-16,
            1.251692067365149e-15,
            -0.019627813623044728
          ],
          [
            -3.159851519443549e-16,
            -1.8274437013399403e-15,
            -0.02940867429495009
          ],
          [
            9.308402330089383e-16,
            -1.1181070014777263e-15,
            -0.03914902460279392
          ],
          [
            1.747110446032728e-17,
            1.7299266032421216e-15,
            -0.04883397653250961
          ],
          [
            1.3644038934761015e-15,
            -3.068448963434095e-15,
            -0.058447734672136306
          ],
          [
            -9.93932303130792e-16,
            -1.6858435314992723e-15,
            -0.06797408015572459
          ],
          [
            1.3268758433631368e-15,
            -2.5367804012021535e-15,
            -0.07739812206319824
          ]
        ],
        "unwrapped_reduced_polarization": [
          [
            -1.5293775838475978e-16,
            3.873966910735253e-17,
            1.0706352766997202e-15
          ],
          [
            2.8486516748005234e-17,
            7.654424275349311e-16,
            -0.009820456424420138
          ],
          [
            -6.718015030736343e-16,
            1.251692067365149e-15,
            -0.019627813623044728
          ],
          [
            -3.159851519443549e-16,
            -1.8274437013399403e-15,
            -0.02940867429495009
          ],
          [
            9.308402330089383e-16,
            -1.1181070014777263e-15,
            -0.03914902460279392
          ],
          [
            1.7471104460327302e-17,
            1.7299266032421216e-15,
            -0.04883397653250961
          ],
          [
            1.3644038934761015e-15,
            -3.0684489634340947e-15,
            -0.058447734672136306
          ],
          [
            -9.939323031307919e-16,
            -1.6858435314992723e-15,
            -0.06797408015572459
          ],
          [
            1.3268758433631366e-15,
            -2.5367804012021535e-15,
            -0.07739812206319824
          ]
        ],
        "gauge_integer_shift": [
          0,
          0,
          0
        ],
        "expected_opposite_endpoint_reduced_polarization": [
          6.737859527267633e-16,
          -1.3572242694162126e-15,
          -0.07739812206319853
        ],
        "actual_opposite_endpoint_branch_residual": 1.3794247293102729e-15
      },
      "pnp_branch": {
        "construction": "incoming_path_concatenated_with_parent_reflection",
        "reduced_polarization": [
          [
            1.0991718033271378e-15,
            1.6858435314992723e-15,
            0.07739812206319993
          ],
          [
            1.7436625755685977e-15,
            2.413882140585725e-15,
            0.06797408015572855
          ],
          [
            6.904438177459401e-16,
            3.3396266471855624e-16,
            0.058447734672139255
          ],
          [
            9.69626714654822e-17,
            4.0743445095663864e-16,
            0.04883397653251129
          ],
          [
            9.66713897367272e-16,
            1.0579937218283863e-15,
            0.03914902460279386
          ],
          [
            -1.6089465728978494e-15,
            6.652536281193641e-16,
            0.02940867429494751
          ],
          [
            1.5776815693532689e-15,
            -6.05140348470024e-16,
            0.01962781362304733
          ],
          [
            8.115951693031553e-16,
            -3.195354776027147e-15,
            0.009820456424421415
          ],
          [
            8.864788780269506e-16,
            1.6430963104152967e-16,
            7.040590678297074e-16
          ],
          [
            2.848651674800522e-17,
            7.654424275349311e-16,
            -0.009820456424420138
          ],
          [
            -6.718015030736343e-16,
            1.251692067365149e-15,
            -0.019627813623044728
          ],
          [
            -3.159851519443549e-16,
            -1.8274437013399403e-15,
            -0.02940867429495009
          ],
          [
            9.308402330089383e-16,
            -1.1181070014777263e-15,
            -0.03914902460279392
          ],
          [
            1.747110446032728e-17,
            1.7299266032421216e-15,
            -0.04883397653250961
          ],
          [
            1.3644038934761015e-15,
            -3.068448963434095e-15,
            -0.058447734672136306
          ],
          [
            -9.93932303130792e-16,
            -1.6858435314992723e-15,
            -0.06797408015572459
          ],
          [
            1.3268758433631368e-15,
            -2.5367804012021535e-15,
            -0.07739812206319824
          ]
        ],
        "unwrapped_reduced_polarization": [
          [
            1.0991718033271378e-15,
            1.6858435314992723e-15,
            0.07739812206319993
          ],
          [
            1.7436625755685977e-15,
            2.413882140585725e-15,
            0.06797408015572855
          ],
          [
            6.904438177459401e-16,
            3.3396266471855604e-16,
            0.058447734672139255
          ],
          [
            9.69626714654822e-17,
            4.0743445095663864e-16,
            0.04883397653251129
          ],
          [
            9.66713897367272e-16,
            1.0579937218283863e-15,
            0.03914902460279386
          ],
          [
            -1.6089465728978496e-15,
            6.652536281193641e-16,
            0.02940867429494751
          ],
          [
            1.5776815693532689e-15,
            -6.051403484700239e-16,
            0.01962781362304733
          ],
          [
            8.115951693031553e-16,
            -3.1953547760271475e-15,
            0.009820456424421415
          ],
          [
            8.864788780269506e-16,
            1.6430963104152967e-16,
            7.042977312465837e-16
          ],
          [
            2.848651674800526e-17,
            7.654424275349311e-16,
            -0.009820456424420138
          ],
          [
            -6.718015030736343e-16,
            1.251692067365149e-15,
            -0.019627813623044728
          ],
          [
            -3.159851519443549e-16,
            -1.8274437013399403e-15,
            -0.02940867429495009
          ],
          [
            9.308402330089383e-16,
            -1.1181070014777263e-15,
            -0.03914902460279392
          ],
          [
            1.7471104460327302e-17,
            1.7299266032421216e-15,
            -0.04883397653250961
          ],
          [
            1.3644038934761015e-15,
            -3.0684489634340947e-15,
            -0.058447734672136306
          ],
          [
            -9.939323031307919e-16,
            -1.6858435314992723e-15,
            -0.06797408015572459
          ],
          [
            1.3268758433631366e-15,
            -2.5367804012021535e-15,
            -0.07739812206319824
          ]
        ],
        "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": [
          [
            1.1102230246251565e-15,
            1.6653345369377348e-15,
            0.07739812206319996
          ],
          [
            1.7763568394002505e-15,
            2.4424906541753444e-15,
            0.06797408015572859
          ],
          [
            6.661338147750939e-16,
            3.3306690738754696e-16,
            0.05844773467213926
          ],
          [
            1.1102230246251565e-16,
            4.440892098500626e-16,
            0.048833976532511314
          ],
          [
            9.992007221626409e-16,
            1.1102230246251565e-15,
            0.0391490246027939
          ],
          [
            -1.609823385706477e-15,
            6.661338147750939e-16,
            0.029408674294947534
          ],
          [
            1.5543122344752192e-15,
            -6.106226635438361e-16,
            0.01962781362304733
          ],
          [
            7.771561172376096e-16,
            -3.219646771412954e-15,
            0.00982045642442142
          ],
          [
            8.881784197001252e-16,
            1.1102230246251565e-16,
            6.661338147750939e-16
          ],
          [
            0.0,
            7.771561172376096e-16,
            -0.009820456424420143
          ],
          [
            -6.661338147750939e-16,
            1.2212453270876722e-15,
            -0.01962781362304472
          ],
          [
            -3.3306690738754696e-16,
            -1.8318679906315083e-15,
            -0.029408674294950088
          ],
          [
            8.881784197001252e-16,
            -1.1102230246251565e-15,
            -0.0391490246027939
          ],
          [
            0.0,
            1.7763568394002505e-15,
            -0.04883397653250959
          ],
          [
            1.3322676295501878e-15,
            -3.0531133177191805e-15,
            -0.05844773467213632
          ],
          [
            -9.992007221626409e-16,
            -1.6653345369377348e-15,
            -0.06797408015572459
          ],
          [
            1.3322676295501878e-15,
            -2.55351295663786e-15,
            -0.07739812206319824
          ]
        ]
      },
      "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": [
              -6.286468763157711e-18,
              2.5154067906601663e-15,
              0.07739812206320316
            ],
            "branch_aligned_reduced_polarization": [
              -6.286468763157711e-18,
              2.5154067906601663e-15,
              0.07739812206320318
            ],
            "target_residual": 0.4226018779367968,
            "energy_eV": -204.2736162324927,
            "max_atomic_step_A": 0.12,
            "max_log_strain_component": 0.005547927934683878,
            "step_scale": 0.7475911863347676,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 0.9162524725127975,
            "cell_principal_stretches": [
              1.001528422045276,
              0.9998292304658549,
              0.9944674333965187
            ],
            "cell_volume_ratio": 0.9958173150408305,
            "cell_rmsd_from_input_A": 0.028454365615849353
          },
          {
            "iteration": 1,
            "reduced_polarization": [
              -6.212048286069967e-14,
              -1.2557823888857902e-14,
              0.3842745140354866
            ],
            "branch_aligned_reduced_polarization": [
              -6.212048286069967e-14,
              -1.2557823888857902e-14,
              0.3842745140354866
            ],
            "target_residual": 0.11572548596451337,
            "energy_eV": -203.7305883286343,
            "max_atomic_step_A": 0.04485672794676619,
            "max_log_strain_component": 0.0024694102787438015,
            "step_scale": 1.0,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 0.9162524725127975,
            "cell_principal_stretches": [
              1.0022094813853153,
              0.9997532294772539,
              0.9920147149251024
            ],
            "cell_volume_ratio": 0.9939612121008939,
            "cell_rmsd_from_input_A": 0.04105128853744488
          },
          {
            "iteration": 2,
            "reduced_polarization": [
              -2.646141057820117e-14,
              -3.742496180425475e-15,
              0.49987362946126107
            ],
            "branch_aligned_reduced_polarization": [
              -2.646141057820117e-14,
              -3.742496180425475e-15,
              0.49987362946126107
            ],
            "target_residual": 0.00012637053873892912,
            "energy_eV": -203.24895355069862
          }
        ],
        "iterations": 2
      },
      "parent": {
        "candidate_id": "bec_projection_01",
        "source": "MACEField_BEC_backprojection",
        "spacegroup": "Cmc2_1",
        "spacegroup_number": 36,
        "pointgroup": "mm2",
        "has_inversion": false,
        "is_polar_point_group": true,
        "nonpolar_parent_hypothesis": false,
        "symmetry_tolerance_A": null,
        "target_reduced_polarization": [
          0.0,
          0.0,
          0.5
        ],
        "formal_class": [
          0.0,
          0.0,
          0.5
        ],
        "target_residual": 0.00012637053873892912,
        "parent_symmetrization_rmsd_A": 0.1295182811080003,
        "parent_cell_rmsd_A": 0.04105128853744488,
        "energy_eV": -203.24895355069862,
        "reduced_polarization": [
          -2.646141057820117e-14,
          -3.742496180425475e-15,
          0.49987362946126107
        ],
        "cartesian_polarization_e_A2": [
          -6.151751888116819e-18,
          -4.717007558392981e-16,
          0.011592679870087785
        ],
        "ranking_score": 0.6400338443198393
      },
      "branch_status": "awaiting_branch_sampling"
    },
    {
      "orbit_id": 2,
      "formal_class": [
        0.0,
        0.5,
        0.0
      ],
      "formal_classes_in_orbit": [
        [
          0.0,
          0.5,
          0.0
        ]
      ],
      "target_reduced_polarization": [
        0.0,
        0.5,
        0.0
      ],
      "bec_backprojection": {
        "converged_to_target": true,
        "history": [
          {
            "iteration": 0,
            "reduced_polarization": [
              -6.286468763157711e-18,
              2.5154067906601663e-15,
              0.07739812206320316
            ],
            "branch_aligned_reduced_polarization": [
              -6.286468763157711e-18,
              2.4980018054066022e-15,
              0.07739812206320316
            ],
            "target_residual": 0.5059550071882953,
            "energy_eV": -204.2736162324927,
            "max_atomic_step_A": 0.12,
            "max_log_strain_component": 0.008939079515926509,
            "step_scale": 0.7454776126063786,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 0.9162524725127975,
            "cell_principal_stretches": [
              1.0093731974176539,
              1.000031190596823,
              0.9914415828948491
            ],
            "cell_volume_ratio": 1.0007657740875997,
            "cell_rmsd_from_input_A": 0.08195538759581467
          },
          {
            "iteration": 1,
            "reduced_polarization": [
              1.3020791689615495e-14,
              0.3935682772623693,
              0.016689672583457982
            ],
            "branch_aligned_reduced_polarization": [
              1.3020791689615495e-14,
              0.3935682772623693,
              0.016689672583457982
            ],
            "target_residual": 0.10773233857966197,
            "energy_eV": -195.2438981210871,
            "max_atomic_step_A": 0.03859261555469345,
            "max_log_strain_component": 0.0013511787110828874,
            "step_scale": 1.0,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 0.9162524725127975,
            "cell_principal_stretches": [
              1.0108822400625719,
              1.0000421558446233,
              0.9902171419779597
            ],
            "cell_volume_ratio": 1.001035120333153,
            "cell_rmsd_from_input_A": 0.09444153795512941
          },
          {
            "iteration": 2,
            "reduced_polarization": [
              -3.2452393539509033e-15,
              0.49902945611621646,
              0.0004454397051001189
            ],
            "branch_aligned_reduced_polarization": [
              -3.2452393539509033e-15,
              0.49902945611621646,
              0.0004454397051001189
            ],
            "target_residual": 0.0010678819978018695,
            "energy_eV": -192.76046786714363,
            "max_atomic_step_A": 0.00035567026333210394,
            "max_log_strain_component": 1.3136626415162931e-05,
            "step_scale": 1.0,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 0.9162524725127975,
            "cell_principal_stretches": [
              1.0108991215776841,
              1.000042422750954,
              0.9902068276454186
            ],
            "cell_volume_ratio": 1.001041677387265,
            "cell_rmsd_from_input_A": 0.09456536064073756
          },
          {
            "iteration": 3,
            "reduced_polarization": [
              -3.774399741578073e-15,
              0.4999939500561249,
              4.000248588765682e-07
            ],
            "branch_aligned_reduced_polarization": [
              -3.774399741578073e-15,
              0.4999939500561249,
              4.000248588765682e-07
            ],
            "target_residual": 6.063154358874999e-06,
            "energy_eV": -192.73146071286976
          }
        ],
        "iterations": 3
      },
      "parent": {
        "candidate_id": "bec_projection_02",
        "source": "MACEField_BEC_backprojection",
        "spacegroup": "Cm",
        "spacegroup_number": 8,
        "pointgroup": "m",
        "has_inversion": false,
        "is_polar_point_group": true,
        "nonpolar_parent_hypothesis": false,
        "symmetry_tolerance_A": null,
        "target_reduced_polarization": [
          0.0,
          0.5,
          0.0
        ],
        "formal_class": [
          0.0,
          0.5,
          0.0
        ],
        "target_residual": 6.063154358874999e-06,
        "parent_symmetrization_rmsd_A": 0.13766703234880118,
        "parent_cell_rmsd_A": 0.09456536064073756,
        "energy_eV": -192.73146071286976,
        "reduced_polarization": [
          -3.774399741578073e-15,
          0.4999939500561249,
          4.000248588765682e-07
        ],
        "cartesian_polarization_e_A2": [
          -3.377612935993313e-16,
          0.016845752029654933,
          0.00017374446317892854
        ],
        "ranking_score": 0.6613204988177033
      },
      "branch_status": "awaiting_branch_sampling"
    },
    {
      "orbit_id": 3,
      "formal_class": [
        0.5,
        0.0,
        0.0
      ],
      "formal_classes_in_orbit": [
        [
          0.5,
          0.0,
          0.0
        ]
      ],
      "target_reduced_polarization": [
        0.5,
        0.0,
        0.0
      ],
      "bec_backprojection": {
        "converged_to_target": true,
        "history": [
          {
            "iteration": 0,
            "reduced_polarization": [
              -6.286468763157711e-18,
              2.5154067906601663e-15,
              0.07739812206320316
            ],
            "branch_aligned_reduced_polarization": [
              0.0,
              2.5154067906601663e-15,
              0.07739812206320316
            ],
            "target_residual": 0.5059550071882978,
            "energy_eV": -204.2736162324927,
            "max_atomic_step_A": 0.07612109475081413,
            "max_log_strain_component": 0.001626422783592032,
            "step_scale": 1.0,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 0.9162524725127975,
            "cell_principal_stretches": [
              1.0024582375051687,
              0.9996259193909763,
              0.9989463181510216
            ],
            "cell_volume_ratio": 1.0010273603988356,
            "cell_rmsd_from_input_A": 0.009189469817536754
          },
          {
            "iteration": 1,
            "reduced_polarization": [
              0.4899522987629167,
              4.516361142362214e-15,
              0.0020792966434706314
            ],
            "branch_aligned_reduced_polarization": [
              0.4899522987629167,
              4.516361142362214e-15,
              0.0020792966434706314
            ],
            "target_residual": 0.010260593290898625,
            "energy_eV": -204.08937767952312,
            "max_atomic_step_A": 0.001683479385163743,
            "max_log_strain_component": 4.0407820563651886e-05,
            "step_scale": 1.0,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 0.9162524725127975,
            "cell_principal_stretches": [
              1.0025205291493453,
              0.9996147999918201,
              0.9989258546949789
            ],
            "cell_volume_ratio": 1.0010579203174201,
            "cell_rmsd_from_input_A": 0.009435527329660262
          },
          {
            "iteration": 2,
            "reduced_polarization": [
              0.49998434590590574,
              -5.40401443557804e-15,
              3.507120797002829e-05
            ],
            "branch_aligned_reduced_polarization": [
              0.49998434590590574,
              -5.40401443557804e-15,
              3.507120797002829e-05
            ],
            "target_residual": 3.840625327194839e-05,
            "energy_eV": -204.08152065888936
          }
        ],
        "iterations": 2
      },
      "parent": {
        "candidate_id": "bec_projection_03",
        "source": "MACEField_BEC_backprojection",
        "spacegroup": "Cc",
        "spacegroup_number": 9,
        "pointgroup": "m",
        "has_inversion": false,
        "is_polar_point_group": true,
        "nonpolar_parent_hypothesis": false,
        "symmetry_tolerance_A": null,
        "target_reduced_polarization": [
          0.5,
          0.0,
          0.0
        ],
        "formal_class": [
          0.5,
          0.0,
          0.0
        ],
        "target_residual": 3.840625327194839e-05,
        "parent_symmetrization_rmsd_A": 0.08267164853016777,
        "parent_cell_rmsd_A": 0.009435527329660262,
        "energy_eV": -204.08152065888936,
        "reduced_polarization": [
          0.49998434590590574,
          -5.40401443557804e-15,
          3.507120797002829e-05
        ],
        "cartesian_polarization_e_A2": [
          0.006719490119258119,
          -2.0883138342048179e-16,
          -1.0367301076229016e-05
        ],
        "ranking_score": 0.5851073428691267
      },
      "branch_status": "awaiting_branch_sampling"
    },
    {
      "orbit_id": 4,
      "formal_class": [
        0.0,
        0.5,
        0.5
      ],
      "formal_classes_in_orbit": [
        [
          0.0,
          0.5,
          0.5
        ]
      ],
      "target_reduced_polarization": [
        0.0,
        0.5,
        0.5
      ],
      "bec_backprojection": {
        "converged_to_target": true,
        "history": [
          {
            "iteration": 0,
            "reduced_polarization": [
              -6.286468763157711e-18,
              2.5154067906601663e-15,
              0.07739812206320316
            ],
            "branch_aligned_reduced_polarization": [
              -6.286468763157711e-18,
              2.4980018054066022e-15,
              0.07739812206320318
            ],
            "target_residual": 0.6546696474067702,
            "energy_eV": -204.2736162324927,
            "max_atomic_step_A": 0.12,
            "max_log_strain_component": 0.006022697181693343,
            "step_scale": 0.5022649041741726,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 0.9162524725127975,
            "cell_principal_stretches": [
              1.0051372092876316,
              0.9998852662407811,
              0.9922052130950906
            ],
            "cell_volume_ratio": 0.9971879546800265,
            "cell_rmsd_from_input_A": 0.058166897902144216
          },
          {
            "iteration": 1,
            "reduced_polarization": [
              -4.491033094151135e-14,
              0.2623981855637556,
              0.2820719947781339
            ],
            "branch_aligned_reduced_polarization": [
              -4.491033094151135e-14,
              0.2623981855637556,
              0.2820719947781339
            ],
            "target_residual": 0.32240849505460806,
            "energy_eV": -200.3408470106142,
            "max_atomic_step_A": 0.10243779304764042,
            "max_log_strain_component": 0.0042523080818893475,
            "step_scale": 1.0,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 0.9162524725127975,
            "cell_principal_stretches": [
              1.007859051769727,
              0.9997543893003619,
              0.986480902407275
            ],
            "cell_volume_ratio": 0.9939895124527877,
            "cell_rmsd_from_input_A": 0.09504587016889618
          },
          {
            "iteration": 2,
            "reduced_polarization": [
              -5.983405057172149e-14,
              0.501844842634101,
              0.4985572765671231
            ],
            "branch_aligned_reduced_polarization": [
              -5.983405057172149e-14,
              0.501844842634101,
              0.4985572765671231
            ],
            "target_residual": 0.002341985321979792,
            "energy_eV": -194.63633420420496,
            "max_atomic_step_A": 0.0008341730149787294,
            "max_log_strain_component": 2.7573951417846e-05,
            "step_scale": 1.0,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 0.9162524725127975,
            "cell_principal_stretches": [
              1.0078330055897164,
              0.9997535588321554,
              0.9864871047900974
            ],
            "cell_volume_ratio": 0.993969248471844,
            "cell_rmsd_from_input_A": 0.0948773825327382
          },
          {
            "iteration": 3,
            "reduced_polarization": [
              -3.829981527420098e-15,
              0.4999899890120246,
              0.5000482939661367
            ],
            "branch_aligned_reduced_polarization": [
              -3.829981527420098e-15,
              0.4999899890120246,
              0.5000482939661367
            ],
            "target_residual": 4.932065536320558e-05,
            "energy_eV": -194.69325116086893
          }
        ],
        "iterations": 3
      },
      "parent": {
        "candidate_id": "bec_projection_04",
        "source": "MACEField_BEC_backprojection",
        "spacegroup": "Cm",
        "spacegroup_number": 8,
        "pointgroup": "m",
        "has_inversion": false,
        "is_polar_point_group": true,
        "nonpolar_parent_hypothesis": false,
        "symmetry_tolerance_A": null,
        "target_reduced_polarization": [
          0.0,
          0.5,
          0.5
        ],
        "formal_class": [
          0.0,
          0.5,
          0.5
        ],
        "target_residual": 4.932065536320558e-05,
        "parent_symmetrization_rmsd_A": 0.1726530755302123,
        "parent_cell_rmsd_A": 0.0948773825327382,
        "energy_eV": -194.69325116086893,
        "reduced_polarization": [
          -3.829981527420098e-15,
          0.4999899890120246,
          0.5000482939661367
        ],
        "cartesian_polarization_e_A2": [
          -1.7445997683047031e-16,
          0.017118973186408277,
          0.011756330909503197
        ],
        "ranking_score": 0.6964710624741233
      },
      "branch_status": "awaiting_branch_sampling"
    },
    {
      "orbit_id": 5,
      "formal_class": [
        0.5,
        0.0,
        0.5
      ],
      "formal_classes_in_orbit": [
        [
          0.5,
          0.0,
          0.5
        ]
      ],
      "target_reduced_polarization": [
        0.5,
        0.0,
        0.5
      ],
      "bec_backprojection": {
        "converged_to_target": true,
        "history": [
          {
            "iteration": 0,
            "reduced_polarization": [
              -6.286468763157711e-18,
              2.5154067906601663e-15,
              0.07739812206320316
            ],
            "branch_aligned_reduced_polarization": [
              0.0,
              2.5154067906601663e-15,
              0.07739812206320318
            ],
            "target_residual": 0.6546696474067721,
            "energy_eV": -204.2736162324927,
            "max_atomic_step_A": 0.12,
            "max_log_strain_component": 0.00508289425626642,
            "step_scale": 0.6849272362210027,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 0.9162524725127975,
            "cell_principal_stretches": [
              1.0014002183074941,
              1.0000837219124314,
              0.994691061032404
            ],
            "cell_volume_ratio": 0.9961672397108636,
            "cell_rmsd_from_input_A": 0.026383828928098214
          },
          {
            "iteration": 1,
            "reduced_polarization": [
              0.3329131573446628,
              -6.332139750936895e-15,
              0.3552087911664926
            ],
            "branch_aligned_reduced_polarization": [
              0.3329131573446628,
              -6.332139750936895e-15,
              0.3552087911664926
            ],
            "target_residual": 0.22109388762242557,
            "energy_eV": -203.7581021597693,
            "max_atomic_step_A": 0.06298693236101248,
            "max_log_strain_component": 0.00320282724391853,
            "step_scale": 1.0,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 0.9162524725127975,
            "cell_principal_stretches": [
              1.0022835289565257,
              1.0001487056281244,
              0.9913481656052936
            ],
            "cell_volume_ratio": 0.9937596935347819,
            "cell_rmsd_from_input_A": 0.0429262861045268
          },
          {
            "iteration": 2,
            "reduced_polarization": [
              0.4935608266832555,
              -7.759092012433286e-15,
              0.4957623413591923
            ],
            "branch_aligned_reduced_polarization": [
              0.4935608266832555,
              -7.759092012433286e-15,
              0.4957623413591923
            ],
            "target_residual": 0.00770848258473005,
            "energy_eV": -203.02274636616295,
            "max_atomic_step_A": 0.0020372284032167502,
            "max_log_strain_component": 0.00011982577731974848,
            "step_scale": 1.0,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 0.9162524725127975,
            "cell_principal_stretches": [
              1.0023165909329461,
              1.0001548941843286,
              0.9912195940642664
            ],
            "cell_volume_ratio": 0.9936697342147683,
            "cell_rmsd_from_input_A": 0.043548634603073
          },
          {
            "iteration": 3,
            "reduced_polarization": [
              0.5000179001811157,
              7.552193206449483e-16,
              0.5001893418696489
            ],
            "branch_aligned_reduced_polarization": [
              0.5000179001811157,
              7.552193206449483e-16,
              0.5001893418696489
            ],
            "target_residual": 0.00019018611959373496,
            "energy_eV": -202.99475401114682
          }
        ],
        "iterations": 3
      },
      "parent": {
        "candidate_id": "bec_projection_05",
        "source": "MACEField_BEC_backprojection",
        "spacegroup": "Cc",
        "spacegroup_number": 9,
        "pointgroup": "m",
        "has_inversion": false,
        "is_polar_point_group": true,
        "nonpolar_parent_hypothesis": false,
        "symmetry_tolerance_A": null,
        "target_reduced_polarization": [
          0.5,
          0.0,
          0.5
        ],
        "formal_class": [
          0.5,
          0.0,
          0.5
        ],
        "target_residual": 0.00019018611959373496,
        "parent_symmetrization_rmsd_A": 0.1569926461922749,
        "parent_cell_rmsd_A": 0.043548634603073,
        "energy_eV": -202.99475401114682,
        "reduced_polarization": [
          0.5000179001811157,
          7.552193206449483e-16,
          0.5001893418696489
        ],
        "cartesian_polarization_e_A2": [
          0.006745952619746531,
          -5.357684926938001e-16,
          0.011586236979464681
        ],
        "ranking_score": 0.6682601770822306
      },
      "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": [
              -6.286468763157711e-18,
              2.5154067906601663e-15,
              0.07739812206320316
            ],
            "branch_aligned_reduced_polarization": [
              0.0,
              2.4980018054066022e-15,
              0.07739812206320316
            ],
            "target_residual": 0.711330070571256,
            "energy_eV": -204.2736162324927,
            "max_atomic_step_A": 0.12,
            "max_log_strain_component": 0.008919838620450557,
            "step_scale": 0.7438730115064216,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 0.9162524725127975,
            "cell_principal_stretches": [
              1.0094378639132968,
              1.0000255538481448,
              0.9913820238219012
            ],
            "cell_volume_ratio": 1.0007641251698227,
            "cell_rmsd_from_input_A": 0.08189842528648107
          },
          {
            "iteration": 1,
            "reduced_polarization": [
              0.3644399008908229,
              0.3921084035634922,
              0.01753227850315527
            ],
            "branch_aligned_reduced_polarization": [
              0.3644399008908229,
              0.3921084035634922,
              0.01753227850315527
            ],
            "target_residual": 0.17413936327441992,
            "energy_eV": -195.27544171918592,
            "max_atomic_step_A": 0.039223089545174505,
            "max_log_strain_component": 0.0013760002110982013,
            "step_scale": 1.0,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 0.9162524725127975,
            "cell_principal_stretches": [
              1.0110458120240846,
              1.0000319638962185,
              0.9900915042178234
            ],
            "cell_volume_ratio": 1.0010598656109688,
            "cell_rmsd_from_input_A": 0.09470963292132957
          },
          {
            "iteration": 2,
            "reduced_polarization": [
              0.4985212844963004,
              0.49954367878333444,
              0.0008348913198625871
            ],
            "branch_aligned_reduced_polarization": [
              0.4985212844963004,
              0.49954367878333444,
              0.0008348913198625871
            ],
            "target_residual": 0.0017583720054762564,
            "energy_eV": -192.73205152291627,
            "max_atomic_step_A": 0.00038915443017648797,
            "max_log_strain_component": 1.6124528598194323e-05,
            "step_scale": 1.0,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 0.9162524725127975,
            "cell_principal_stretches": [
              1.0110599828637077,
              1.0000322748110753,
              0.9900893807169652
            ],
            "cell_volume_ratio": 1.0010720606701182,
            "cell_rmsd_from_input_A": 0.09477689234562918
          },
          {
            "iteration": 3,
            "reduced_polarization": [
              0.5000022539987264,
              0.4999918348529223,
              6.911775639736533e-06
            ],
            "branch_aligned_reduced_polarization": [
              0.5000022539987264,
              0.4999918348529223,
              6.911775639736533e-06
            ],
            "target_residual": 1.0932647417397724e-05,
            "energy_eV": -192.71694245217301
          }
        ],
        "iterations": 3
      },
      "parent": {
        "candidate_id": "bec_projection_06",
        "source": "MACEField_BEC_backprojection",
        "spacegroup": "P1",
        "spacegroup_number": 1,
        "pointgroup": "1",
        "has_inversion": false,
        "is_polar_point_group": true,
        "nonpolar_parent_hypothesis": false,
        "symmetry_tolerance_A": null,
        "target_reduced_polarization": [
          0.5,
          0.5,
          0.0
        ],
        "formal_class": [
          0.5,
          0.5,
          0.0
        ],
        "target_residual": 1.0932647417397724e-05,
        "parent_symmetrization_rmsd_A": 0.15848610640629002,
        "parent_cell_rmsd_A": 0.09477689234562918,
        "energy_eV": -192.71694245217301,
        "reduced_polarization": [
          0.5000022539987264,
          0.4999918348529223,
          6.911775639736533e-06
        ],
        "cartesian_polarization_e_A2": [
          0.00671947153127189,
          0.016844934811169335,
          0.0001624770430914419
        ],
        "ranking_score": 0.6822021947875321
      },
      "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": [
              -6.286468763157711e-18,
              2.5154067906601663e-15,
              0.07739812206320316
            ],
            "branch_aligned_reduced_polarization": [
              0.0,
              2.4980018054066022e-15,
              0.07739812206320318
            ],
            "target_residual": 0.8237671680977003,
            "energy_eV": -204.2736162324927,
            "max_atomic_step_A": 0.12,
            "max_log_strain_component": 0.005778325545617142,
            "step_scale": 0.4818854474832742,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 0.9162524725127975,
            "cell_principal_stretches": [
              1.004967082000463,
              0.9999077274739081,
              0.9924642802727823
            ],
            "cell_volume_ratio": 0.9973018996778377,
            "cell_rmsd_from_input_A": 0.05588401756987117
          },
          {
            "iteration": 1,
            "reduced_polarization": [
              0.23609831439610487,
              0.2509854784611676,
              0.2724808020097852
            ],
            "branch_aligned_reduced_polarization": [
              0.23609831439610485,
              0.2509854784611676,
              0.2724808020097852
            ],
            "target_residual": 0.4282724799189195,
            "energy_eV": -200.64642060557168,
            "max_atomic_step_A": 0.10779189776022563,
            "max_log_strain_component": 0.004562633779955225,
            "step_scale": 1.0,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 0.9162524725127975,
            "cell_principal_stretches": [
              1.007962239640815,
              0.9998224017305867,
              0.9861942767082894
            ],
            "cell_volume_ratio": 0.9938700509174083,
            "cell_rmsd_from_input_A": 0.09566794220462187
          },
          {
            "iteration": 2,
            "reduced_polarization": [
              0.48635373735241194,
              0.5038464310448392,
              0.4915963531394621
            ],
            "branch_aligned_reduced_polarization": [
              0.48635373735241194,
              0.5038464310448392,
              0.4915963531394621
            ],
            "target_residual": 0.016481407603305253,
            "energy_eV": -194.4759201850742,
            "max_atomic_step_A": 0.004689612411519559,
            "max_log_strain_component": 0.00019688766022691426,
            "step_scale": 1.0,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 0.9162524725127975,
            "cell_principal_stretches": [
              1.0079151828468444,
              0.9998238406659465,
              0.9860922093488689
            ],
            "cell_volume_ratio": 0.993722225201557,
            "cell_rmsd_from_input_A": 0.09571484602217213
          },
          {
            "iteration": 3,
            "reduced_polarization": [
              0.5000020290367999,
              0.5000499423650303,
              0.5002534958222971
            ],
            "branch_aligned_reduced_polarization": [
              0.5000020290367999,
              0.5000499423650303,
              0.5002534958222971
            ],
            "target_residual": 0.000258376641237587,
            "energy_eV": -194.55684619567495
          }
        ],
        "iterations": 3
      },
      "parent": {
        "candidate_id": "bec_projection_07",
        "source": "MACEField_BEC_backprojection",
        "spacegroup": "P1",
        "spacegroup_number": 1,
        "pointgroup": "1",
        "has_inversion": false,
        "is_polar_point_group": true,
        "nonpolar_parent_hypothesis": false,
        "symmetry_tolerance_A": null,
        "target_reduced_polarization": [
          0.5,
          0.5,
          0.5
        ],
        "formal_class": [
          0.5,
          0.5,
          0.5
        ],
        "target_residual": 0.000258376641237587,
        "parent_symmetrization_rmsd_A": 0.19307374646497225,
        "parent_cell_rmsd_A": 0.09571484602217213,
        "energy_eV": -194.55684619567495,
        "reduced_polarization": [
          0.5000020290367999,
          0.5000499423650303,
          0.5002534958222971
        ],
        "cartesian_polarization_e_A2": [
          0.006745250129416258,
          0.017126640878956503,
          0.011747287411854315
        ],
        "ranking_score": 0.7175192112529905
      },
      "branch_status": "awaiting_branch_sampling"
    }
  ],
  "sampled_polarization_branches": [
    {
      "orbit_id": 0,
      "candidate_id": "inversion_parent_endpoint_00",
      "formal_class": [
        0.0,
        0.0,
        0.0
      ],
      "construction": "MACEField-BEC-parent plus variable-cell P-N-P path and symmetric log-strain continuation beyond both polar endpoints",
      "geometry_diagnostics": {
        "collision_aware": false,
        "permutations_tested": 1,
        "selected_order": [
          0,
          1,
          2,
          3,
          4,
          5,
          6,
          7,
          8,
          9,
          10,
          11,
          12,
          13,
          14,
          15,
          16,
          17,
          18,
          19,
          20,
          21,
          22,
          23,
          24,
          25,
          26,
          27
        ],
        "endpoint_rmsd_A": 0.07688723416342665,
        "minimum_distance_A_by_image": [
          0.9925574964518878,
          0.9926912059374089,
          0.992828871686512,
          0.9929704920537071,
          0.9931160653471791,
          0.993265589828904,
          0.9934190637147446,
          0.993576485174552,
          0.9937378523322777
        ],
        "minimum_distance_A": 0.9925574964518878,
        "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": [
          307.923498325994,
          307.923498325994,
          307.923498325994,
          307.923498325994,
          307.923498325994,
          307.923498325994,
          307.923498325994,
          307.923498325994,
          307.923498325994
        ],
        "cell_deformation_log_strain_norm": 0.0
      },
      "parent_reduced_polarization": [
        8.864788780269506e-16,
        1.6430963104152967e-16,
        7.040590678297074e-16
      ],
      "incoming": {
        "reached": true,
        "construction": "variable_cell_linear_interpolation",
        "continuation_fractions": [
          0.0,
          0.125,
          0.25,
          0.375,
          0.5,
          0.625,
          0.75,
          0.875,
          1.0
        ],
        "energies_eV": [
          -204.27361623249269,
          -204.28274149418564,
          -204.29072748910193,
          -204.29753847644616,
          -204.30314557166434,
          -204.30752533506865,
          -204.31066165924773,
          -204.3125457702565,
          -204.31317408839234
        ],
        "cartesian_polarizations_e_A2": [
          [
            1.478718388944043e-17,
            5.687701103902202e-17,
            0.0017984789654612804
          ],
          [
            2.345753327006909e-17,
            8.143958712164246e-17,
            0.0015794950846072576
          ],
          [
            9.288556772864989e-18,
            1.1267236735146992e-17,
            0.001358134003572728
          ],
          [
            1.304441079212029e-18,
            1.374602881687933e-17,
            0.0011347417385894163
          ],
          [
            1.3005224593259505e-17,
            3.5694605976945674e-17,
            0.0009096951630035448
          ],
          [
            -2.164519574620539e-17,
            2.244433557641281e-17,
            0.000683361310476972
          ],
          [
            2.1224586924801587e-17,
            -2.041623296408635e-17,
            0.0004560861297154003
          ],
          [
            1.0918408729136104e-17,
            -1.0780492108188643e-16,
            0.00022819525641887134
          ],
          [
            1.1925821007972093e-17,
            5.54348047369232e-18,
            1.6360027739433432e-17
          ]
        ],
        "raw_reduced_polarization": [
          [
            1.0991718033271378e-15,
            1.6858435314992723e-15,
            0.07739812206319993
          ],
          [
            1.7436625755685977e-15,
            2.413882140585725e-15,
            0.06797408015572855
          ],
          [
            6.904438177459401e-16,
            3.3396266471855624e-16,
            0.058447734672139255
          ],
          [
            9.69626714654822e-17,
            4.0743445095663864e-16,
            0.04883397653251129
          ],
          [
            9.66713897367272e-16,
            1.0579937218283863e-15,
            0.03914902460279386
          ],
          [
            -1.6089465728978494e-15,
            6.652536281193641e-16,
            0.02940867429494751
          ],
          [
            1.5776815693532689e-15,
            -6.05140348470024e-16,
            0.01962781362304733
          ],
          [
            8.115951693031553e-16,
            -3.195354776027147e-15,
            0.009820456424421415
          ],
          [
            8.864788780269506e-16,
            1.6430963104152967e-16,
            7.040590678297074e-16
          ]
        ],
        "unwrapped_reduced_polarization": [
          [
            1.0991718033271378e-15,
            1.6858435314992723e-15,
            0.07739812206319993
          ],
          [
            1.7436625755685977e-15,
            2.413882140585725e-15,
            0.06797408015572855
          ],
          [
            6.904438177459401e-16,
            3.3396266471855604e-16,
            0.058447734672139255
          ],
          [
            9.69626714654822e-17,
            4.0743445095663864e-16,
            0.04883397653251129
          ],
          [
            9.66713897367272e-16,
            1.0579937218283863e-15,
            0.03914902460279386
          ],
          [
            -1.6089465728978496e-15,
            6.652536281193641e-16,
            0.02940867429494751
          ],
          [
            1.5776815693532689e-15,
            -6.051403484700239e-16,
            0.01962781362304733
          ],
          [
            8.115951693031553e-16,
            -3.1953547760271475e-15,
            0.009820456424421415
          ],
          [
            8.864788780269506e-16,
            1.6430963104152967e-16,
            7.042977312465837e-16
          ]
        ],
        "berry_integer_shifts": [
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ]
        ],
        "folded_reduced_polarization": [
          [
            1.1102230246251565e-15,
            1.6653345369377348e-15,
            0.07739812206319996
          ],
          [
            1.7763568394002505e-15,
            2.4424906541753444e-15,
            0.06797408015572859
          ],
          [
            6.661338147750939e-16,
            3.3306690738754696e-16,
            0.05844773467213926
          ],
          [
            1.1102230246251565e-16,
            4.440892098500626e-16,
            0.048833976532511314
          ],
          [
            9.992007221626409e-16,
            1.1102230246251565e-15,
            0.0391490246027939
          ],
          [
            -1.609823385706477e-15,
            6.661338147750939e-16,
            0.029408674294947534
          ],
          [
            1.5543122344752192e-15,
            -6.106226635438361e-16,
            0.01962781362304733
          ],
          [
            7.771561172376096e-16,
            -3.219646771412954e-15,
            0.00982045642442142
          ],
          [
            8.881784197001252e-16,
            1.1102230246251565e-16,
            6.661338147750939e-16
          ]
        ]
      },
      "reflected": {
        "reached": true,
        "construction": "reflect_displacements_about_reconstructed_parent",
        "energies_eV": [
          -204.31317408839237,
          -204.31254577025646,
          -204.3106616592477,
          -204.30752533506865,
          -204.30314557166437,
          -204.29753847644616,
          -204.29072748910195,
          -204.2827414941856,
          -204.27361623249266
        ],
        "cartesian_polarizations_e_A2": [
          [
            -2.057475228193399e-18,
            1.3069994612770512e-18,
            2.487805871120456e-17
          ],
          [
            3.832297737690501e-19,
            2.5824506596956907e-17,
            -0.0002281952564188417
          ],
          [
            -9.037761279067052e-18,
            4.222960328333093e-17,
            -0.00045608612971533984
          ],
          [
            -4.250955614027248e-18,
            -6.165431941472435e-17,
            -0.0006833613104770321
          ],
          [
            1.2522615350510522e-17,
            -3.772270858927213e-17,
            -0.0009096951630035464
          ],
          [
            2.350391755178532e-19,
            5.836428628806142e-17,
            -0.0011347417385893772
          ],
          [
            1.8355357380191884e-17,
            -1.0352337112253057e-16,
            -0.0013581340035726595
          ],
          [
            -1.3371394440397395e-17,
            -5.687701103902202e-17,
            -0.0015794950846071659
          ],
          [
            1.7850491647325755e-17,
            -8.558593024017655e-17,
            -0.0017984789654612414
          ]
        ],
        "raw_reduced_polarization": [
          [
            -1.5293775838475978e-16,
            3.873966910735253e-17,
            1.0706352766997202e-15
          ],
          [
            2.848651674800522e-17,
            7.654424275349311e-16,
            -0.009820456424420138
          ],
          [
            -6.718015030736343e-16,
            1.251692067365149e-15,
            -0.019627813623044728
          ],
          [
            -3.159851519443549e-16,
            -1.8274437013399403e-15,
            -0.02940867429495009
          ],
          [
            9.308402330089383e-16,
            -1.1181070014777263e-15,
            -0.03914902460279392
          ],
          [
            1.747110446032728e-17,
            1.7299266032421216e-15,
            -0.04883397653250961
          ],
          [
            1.3644038934761015e-15,
            -3.068448963434095e-15,
            -0.058447734672136306
          ],
          [
            -9.93932303130792e-16,
            -1.6858435314992723e-15,
            -0.06797408015572459
          ],
          [
            1.3268758433631368e-15,
            -2.5367804012021535e-15,
            -0.07739812206319824
          ]
        ],
        "unwrapped_reduced_polarization": [
          [
            -1.5293775838475978e-16,
            3.873966910735253e-17,
            1.0706352766997202e-15
          ],
          [
            2.8486516748005234e-17,
            7.654424275349311e-16,
            -0.009820456424420138
          ],
          [
            -6.718015030736343e-16,
            1.251692067365149e-15,
            -0.019627813623044728
          ],
          [
            -3.159851519443549e-16,
            -1.8274437013399403e-15,
            -0.02940867429495009
          ],
          [
            9.308402330089383e-16,
            -1.1181070014777263e-15,
            -0.03914902460279392
          ],
          [
            1.7471104460327302e-17,
            1.7299266032421216e-15,
            -0.04883397653250961
          ],
          [
            1.3644038934761015e-15,
            -3.0684489634340947e-15,
            -0.058447734672136306
          ],
          [
            -9.939323031307919e-16,
            -1.6858435314992723e-15,
            -0.06797408015572459
          ],
          [
            1.3268758433631366e-15,
            -2.5367804012021535e-15,
            -0.07739812206319824
          ]
        ],
        "gauge_integer_shift": [
          0,
          0,
          0
        ],
        "expected_opposite_endpoint_reduced_polarization": [
          6.737859527267633e-16,
          -1.3572242694162126e-15,
          -0.07739812206319853
        ],
        "actual_opposite_endpoint_branch_residual": 1.3794247293102729e-15
      },
      "pnp_branch": {
        "construction": "incoming_path_concatenated_with_parent_reflection",
        "reduced_polarization": [
          [
            1.0991718033271378e-15,
            1.6858435314992723e-15,
            0.07739812206319993
          ],
          [
            1.7436625755685977e-15,
            2.413882140585725e-15,
            0.06797408015572855
          ],
          [
            6.904438177459401e-16,
            3.3396266471855624e-16,
            0.058447734672139255
          ],
          [
            9.69626714654822e-17,
            4.0743445095663864e-16,
            0.04883397653251129
          ],
          [
            9.66713897367272e-16,
            1.0579937218283863e-15,
            0.03914902460279386
          ],
          [
            -1.6089465728978494e-15,
            6.652536281193641e-16,
            0.02940867429494751
          ],
          [
            1.5776815693532689e-15,
            -6.05140348470024e-16,
            0.01962781362304733
          ],
          [
            8.115951693031553e-16,
            -3.195354776027147e-15,
            0.009820456424421415
          ],
          [
            8.864788780269506e-16,
            1.6430963104152967e-16,
            7.040590678297074e-16
          ],
          [
            2.848651674800522e-17,
            7.654424275349311e-16,
            -0.009820456424420138
          ],
          [
            -6.718015030736343e-16,
            1.251692067365149e-15,
            -0.019627813623044728
          ],
          [
            -3.159851519443549e-16,
            -1.8274437013399403e-15,
            -0.02940867429495009
          ],
          [
            9.308402330089383e-16,
            -1.1181070014777263e-15,
            -0.03914902460279392
          ],
          [
            1.747110446032728e-17,
            1.7299266032421216e-15,
            -0.04883397653250961
          ],
          [
            1.3644038934761015e-15,
            -3.068448963434095e-15,
            -0.058447734672136306
          ],
          [
            -9.93932303130792e-16,
            -1.6858435314992723e-15,
            -0.06797408015572459
          ],
          [
            1.3268758433631368e-15,
            -2.5367804012021535e-15,
            -0.07739812206319824
          ]
        ],
        "unwrapped_reduced_polarization": [
          [
            1.0991718033271378e-15,
            1.6858435314992723e-15,
            0.07739812206319993
          ],
          [
            1.7436625755685977e-15,
            2.413882140585725e-15,
            0.06797408015572855
          ],
          [
            6.904438177459401e-16,
            3.3396266471855604e-16,
            0.058447734672139255
          ],
          [
            9.69626714654822e-17,
            4.0743445095663864e-16,
            0.04883397653251129
          ],
          [
            9.66713897367272e-16,
            1.0579937218283863e-15,
            0.03914902460279386
          ],
          [
            -1.6089465728978496e-15,
            6.652536281193641e-16,
            0.02940867429494751
          ],
          [
            1.5776815693532689e-15,
            -6.051403484700239e-16,
            0.01962781362304733
          ],
          [
            8.115951693031553e-16,
            -3.1953547760271475e-15,
            0.009820456424421415
          ],
          [
            8.864788780269506e-16,
            1.6430963104152967e-16,
            7.042977312465837e-16
          ],
          [
            2.848651674800526e-17,
            7.654424275349311e-16,
            -0.009820456424420138
          ],
          [
            -6.718015030736343e-16,
            1.251692067365149e-15,
            -0.019627813623044728
          ],
          [
            -3.159851519443549e-16,
            -1.8274437013399403e-15,
            -0.02940867429495009
          ],
          [
            9.308402330089383e-16,
            -1.1181070014777263e-15,
            -0.03914902460279392
          ],
          [
            1.7471104460327302e-17,
            1.7299266032421216e-15,
            -0.04883397653250961
          ],
          [
            1.3644038934761015e-15,
            -3.0684489634340947e-15,
            -0.058447734672136306
          ],
          [
            -9.939323031307919e-16,
            -1.6858435314992723e-15,
            -0.06797408015572459
          ],
          [
            1.3268758433631366e-15,
            -2.5367804012021535e-15,
            -0.07739812206319824
          ]
        ],
        "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": [
          [
            1.1102230246251565e-15,
            1.6653345369377348e-15,
            0.07739812206319996
          ],
          [
            1.7763568394002505e-15,
            2.4424906541753444e-15,
            0.06797408015572859
          ],
          [
            6.661338147750939e-16,
            3.3306690738754696e-16,
            0.05844773467213926
          ],
          [
            1.1102230246251565e-16,
            4.440892098500626e-16,
            0.048833976532511314
          ],
          [
            9.992007221626409e-16,
            1.1102230246251565e-15,
            0.0391490246027939
          ],
          [
            -1.609823385706477e-15,
            6.661338147750939e-16,
            0.029408674294947534
          ],
          [
            1.5543122344752192e-15,
            -6.106226635438361e-16,
            0.01962781362304733
          ],
          [
            7.771561172376096e-16,
            -3.219646771412954e-15,
            0.00982045642442142
          ],
          [
            8.881784197001252e-16,
            1.1102230246251565e-16,
            6.661338147750939e-16
          ],
          [
            0.0,
            7.771561172376096e-16,
            -0.009820456424420143
          ],
          [
            -6.661338147750939e-16,
            1.2212453270876722e-15,
            -0.01962781362304472
          ],
          [
            -3.3306690738754696e-16,
            -1.8318679906315083e-15,
            -0.029408674294950088
          ],
          [
            8.881784197001252e-16,
            -1.1102230246251565e-15,
            -0.0391490246027939
          ],
          [
            0.0,
            1.7763568394002505e-15,
            -0.04883397653250959
          ],
          [
            1.3322676295501878e-15,
            -3.0531133177191805e-15,
            -0.05844773467213632
          ],
          [
            -9.992007221626409e-16,
            -1.6653345369377348e-15,
            -0.06797408015572459
          ],
          [
            1.3322676295501878e-15,
            -2.55351295663786e-15,
            -0.07739812206319824
          ]
        ]
      },
      "incoming_structure_ids": [
        "incoming_00_000",
        "incoming_00_001",
        "incoming_00_002",
        "incoming_00_003",
        "incoming_00_004",
        "incoming_00_005",
        "incoming_00_006",
        "incoming_00_007",
        "incoming_00_008"
      ],
      "reflected_structure_ids": [
        "reflected_00_001",
        "reflected_00_002",
        "reflected_00_003",
        "reflected_00_004",
        "reflected_00_005",
        "reflected_00_006",
        "reflected_00_007",
        "reflected_00_008"
      ],
      "positive_extension_structure_ids": [
        "extension_plus_00_000",
        "extension_plus_00_001",
        "extension_plus_00_002",
        "extension_plus_00_003"
      ],
      "negative_extension_structure_ids": [
        "extension_minus_00_000",
        "extension_minus_00_001",
        "extension_minus_00_002",
        "extension_minus_00_003"
      ],
      "extension": {
        "enabled": true,
        "fraction_beyond_polar_endpoint": 0.35,
        "images_per_side": 4,
        "construction": "continue fractional atomic displacements and symmetric log strain beyond +P; reflect these structures about N for the -P side",
        "positive_path_coordinates": [
          1.35,
          1.2625,
          1.175,
          1.0875
        ],
        "negative_path_coordinates": [
          -1.0875,
          -1.175,
          -1.2625,
          -1.35
        ]
      },
      "branch_coordinates": [
        1.35,
        1.2625,
        1.175,
        1.0875,
        1.0,
        0.875,
        0.75,
        0.625,
        0.5,
        0.375,
        0.25,
        0.125,
        0.0,
        -0.125,
        -0.25,
        -0.375,
        -0.5,
        -0.625,
        -0.75,
        -0.875,
        -1.0,
        -1.0875,
        -1.175,
        -1.2625,
        -1.35
      ],
      "parent": {
        "candidate_id": "inversion_parent_endpoint_00",
        "source": "same_species_inversion_center_projection_from_endpoint",
        "spacegroup": "Cmce",
        "spacegroup_number": 64,
        "pointgroup": "mmm",
        "has_inversion": true,
        "is_polar_point_group": false,
        "nonpolar_parent_hypothesis": true,
        "symmetry_tolerance_A": null,
        "target_reduced_polarization": [
          0.0,
          0.0,
          0.0
        ],
        "formal_class": [
          0.0,
          0.0,
          0.0
        ],
        "target_residual": 3.257378057398563e-15,
        "parent_symmetrization_rmsd_A": 0.07688723416342665,
        "parent_cell_rmsd_A": 0.0,
        "energy_eV": -204.3131740883924,
        "reduced_polarization": [
          -1.873979424491821e-18,
          3.2474529517232412e-15,
          -2.5408192255011483e-16
        ],
        "cartesian_polarization_e_A2": [
          -2.5210688876032725e-20,
          1.0956261001256935e-16,
          -5.904032049217024e-18
        ],
        "ranking_score": 0.07688723416343315
      }
    }
  ],
  "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": 56,
      "full_response": 21,
      "energy_polarization": 35
    },
    "model_evaluations_for_recovery_and_path_properties": {
      "total": 81,
      "full_response": 46,
      "energy_polarization": 35
    },
    "elapsed_seconds": 872.7802496430231
  }
}
