{
  "schema": "ferrofinder.endpoint_parent_recovery.v4_variable_cell",
  "status": "complete",
  "input_atom_count": 22,
  "input_formula": "As8Ga2Na6Sr6",
  "input_spacegroup": "P6_3mc",
  "input_pointgroup": "6mm",
  "input_is_polar_point_group": true,
  "input_energy_eV": -77.72426459247508,
  "input_cartesian_polarization_e_A2": [
    2.793849723256143e-11,
    0.00201260204306983,
    -4.6693846390356987e-11
  ],
  "input_reduced_polarization": [
    6.251451213822425e-11,
    0.16373039751287446,
    -3.4401301804969566e-09
  ],
  "input_formal_targets": [
    {
      "orbit_id": 0,
      "representative_formal_class": [
        0.0,
        0.0,
        0.0
      ],
      "target_reduced_polarization": [
        0.0,
        0.0,
        0.0
      ]
    },
    {
      "orbit_id": 1,
      "representative_formal_class": [
        0.0,
        0.5,
        0.0
      ],
      "target_reduced_polarization": [
        0.0,
        0.5,
        0.0
      ]
    },
    {
      "orbit_id": 2,
      "representative_formal_class": [
        0.0,
        0.0,
        0.5
      ],
      "target_reduced_polarization": [
        0.0,
        0.0,
        -0.5
      ]
    },
    {
      "orbit_id": 3,
      "representative_formal_class": [
        0.0,
        0.5,
        0.5
      ],
      "target_reduced_polarization": [
        0.0,
        0.5,
        -0.5
      ]
    }
  ],
  "parent_candidates": [
    {
      "candidate_id": "inversion_parent_endpoint_00",
      "source": "same_species_inversion_center_projection_from_endpoint",
      "spacegroup": "P6_3/mmc",
      "spacegroup_number": 194,
      "pointgroup": "6/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": 1.5360511659152735e-15,
      "parent_symmetrization_rmsd_A": 0.7423301704637356,
      "parent_cell_rmsd_A": 0.0,
      "energy_eV": -75.28124361659812,
      "reduced_polarization": [
        -2.7194500719681184e-16,
        -2.270232915215123e-16,
        -1.4946436105229685e-15
      ],
      "cartesian_polarization_e_A2": [
        7.450614204502212e-18,
        -2.7906091189005124e-18,
        -2.0287214580933734e-17
      ],
      "ranking_score": 0.7423301704637387
    },
    {
      "candidate_id": "bec_projection_00",
      "source": "MACEField_BEC_backprojection",
      "spacegroup": "P6_3mc",
      "spacegroup_number": 186,
      "pointgroup": "6mm",
      "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": 0.0005925655756990805,
      "parent_symmetrization_rmsd_A": 0.022764896930609443,
      "parent_cell_rmsd_A": 0.009973682936103553,
      "energy_eV": -77.65435373501347,
      "reduced_polarization": [
        -3.61563857547544e-12,
        -0.0005925655756990803,
        -1.7045796533893763e-11
      ],
      "cartesian_polarization_e_A2": [
        7.674727007206441e-14,
        -7.284212871045093e-06,
        -2.3060596337087917e-13
      ],
      "ranking_score": 0.5264434488160334
    },
    {
      "candidate_id": "inversion_parent_bec_00_00",
      "source": "same_species_inversion_center_projection_after_BEC",
      "spacegroup": "P6_3/mmc",
      "spacegroup_number": 194,
      "pointgroup": "6/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": 9.234552189895655e-16,
      "parent_symmetrization_rmsd_A": 0.7423319453570781,
      "parent_cell_rmsd_A": 0.009973682936103553,
      "energy_eV": -75.26721185657982,
      "reduced_polarization": [
        -6.909515375488109e-16,
        2.3581179025441233e-16,
        5.654629199293352e-16
      ],
      "cartesian_polarization_e_A2": [
        -1.5225291760109192e-17,
        2.8987564381620287e-18,
        7.65742614993727e-18
      ],
      "ranking_score": 0.744825366091106
    },
    {
      "candidate_id": "bec_projection_01",
      "source": "MACEField_BEC_backprojection",
      "spacegroup": "P6_3mc",
      "spacegroup_number": 186,
      "pointgroup": "6mm",
      "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": 1.3763637075059343e-05,
      "parent_symmetrization_rmsd_A": 0.047675241206410555,
      "parent_cell_rmsd_A": 0.020598744890308135,
      "energy_eV": -77.72111266035839,
      "reduced_polarization": [
        -8.340721756395412e-14,
        0.5000137636370751,
        4.721786154887491e-14
      ],
      "cartesian_polarization_e_A2": [
        1.735883904956835e-13,
        0.0061457360380367445,
        1.4427627365364043e-13
      ],
      "ranking_score": 0.5528524547031377
    },
    {
      "candidate_id": "bec_projection_02",
      "source": "MACEField_BEC_backprojection",
      "spacegroup": "Cc",
      "spacegroup_number": 9,
      "pointgroup": "m",
      "has_inversion": false,
      "is_polar_point_group": true,
      "nonpolar_parent_hypothesis": false,
      "symmetry_tolerance_A": null,
      "target_reduced_polarization": [
        0.0,
        0.0,
        -0.5
      ],
      "formal_class": [
        0.0,
        0.0,
        0.5
      ],
      "target_residual": 0.00012862298915351274,
      "parent_symmetrization_rmsd_A": 0.11102819841102676,
      "parent_cell_rmsd_A": 0.022312888914772348,
      "energy_eV": -77.22265502345198,
      "reduced_polarization": [
        -5.7008988792150983e-11,
        7.884081632867417e-05,
        -0.49989837323669717
      ],
      "cartesian_polarization_e_A2": [
        0.003908125157760466,
        -1.7029047190621235e-05,
        -0.006769071790933968
      ],
      "ranking_score": 0.6168636666180268
    },
    {
      "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": [
        0.0,
        0.5,
        -0.5
      ],
      "formal_class": [
        0.0,
        0.5,
        0.5
      ],
      "target_residual": 0.00012104120710172807,
      "parent_symmetrization_rmsd_A": 0.11723590645177588,
      "parent_cell_rmsd_A": 0.028226487952931173,
      "energy_eV": -77.23349834890314,
      "reduced_polarization": [
        2.6758699001402504e-10,
        0.500120354506504,
        -0.499987124962884
      ],
      "cartesian_polarization_e_A2": [
        0.003930045252632709,
        0.00612922842339046,
        -0.006807038657481134
      ],
      "ranking_score": 0.6245346108542121
    }
  ],
  "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": [
              6.251451213822425e-11,
              0.16373039751287446,
              -3.4401301804969566e-09
            ],
            "branch_aligned_reduced_polarization": [
              6.251451213822425e-11,
              0.16373039751287446,
              -3.4401301804969566e-09
            ],
            "target_residual": 0.1637303975128745,
            "energy_eV": -77.72426459247508,
            "max_atomic_step_A": 0.03649605783286637,
            "max_log_strain_component": 0.002336891753309046,
            "step_scale": 1.0,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 1.021199267487496,
            "cell_principal_stretches": [
              1.0023396244130711,
              0.9999797212272764,
              0.9999797125971049
            ],
            "cell_volume_ratio": 1.002298963740204,
            "cell_rmsd_from_input_A": 0.009973682936103553
          },
          {
            "iteration": 1,
            "reduced_polarization": [
              -3.61563857547544e-12,
              -0.0005925655756990803,
              -1.7045796533893763e-11
            ],
            "branch_aligned_reduced_polarization": [
              -3.61563857547544e-12,
              -0.0005925655756990803,
              -1.7045796533893763e-11
            ],
            "target_residual": 0.0005925655756990805,
            "energy_eV": -77.65435373501347
          }
        ],
        "iterations": 1
      },
      "parent": {
        "candidate_id": "bec_projection_00",
        "source": "MACEField_BEC_backprojection",
        "spacegroup": "P6_3mc",
        "spacegroup_number": 186,
        "pointgroup": "6mm",
        "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": 0.0005925655756990805,
        "parent_symmetrization_rmsd_A": 0.022764896930609443,
        "parent_cell_rmsd_A": 0.009973682936103553,
        "energy_eV": -77.65435373501347,
        "reduced_polarization": [
          -3.61563857547544e-12,
          -0.0005925655756990803,
          -1.7045796533893763e-11
        ],
        "cartesian_polarization_e_A2": [
          7.674727007206441e-14,
          -7.284212871045093e-06,
          -2.3060596337087917e-13
        ],
        "ranking_score": 0.5264434488160334
      },
      "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": [
          -77.7242645924751,
          -77.71804755038377,
          -77.71111275795198,
          -77.70345914864475,
          -77.69508517034808,
          -77.68598924680113,
          -77.67616978091016,
          -77.66562515553518,
          -77.65435373501347
        ],
        "cartesian_polarizations_e_A2": [
          [
            2.7938423152809954e-11,
            0.0020126020430698273,
            -4.669384367492229e-11
          ],
          [
            2.4439430751383732e-11,
            0.0017614078770441493,
            -4.086157807076886e-11
          ],
          [
            2.0945265036248805e-11,
            0.0015098171493788124,
            -3.5036557632643765e-11
          ],
          [
            1.7455618826269e-11,
            0.0012578445038339988,
            -2.921843259558665e-11
          ],
          [
            1.3970711480729017e-11,
            0.0010055034648975318,
            -2.3407360482916334e-11
          ],
          [
            1.049043116281439e-11,
            0.0007528072786291036,
            -1.7603192454299516e-11
          ],
          [
            7.014741749783198e-12,
            0.0004997688979869328,
            -1.1805874221142464e-11
          ],
          [
            3.543507717666451e-12,
            0.0002464009637560735,
            -6.01492895356945e-12
          ],
          [
            7.671975259622151e-14,
            -7.2842128710253e-06,
            -2.3069845701832183e-13
          ]
        ],
        "raw_reduced_polarization": [
          [
            6.250988560464515e-11,
            0.16373039751287427,
            -3.4401299804395705e-09
          ],
          [
            5.4398418325006816e-11,
            0.14329437380940255,
            -3.0108105698397194e-09
          ],
          [
            4.624386386420589e-11,
            0.12282629636512062,
            -2.5819204269005784e-09
          ],
          [
            3.8039320325692925e-11,
            0.10232735695897938,
            -2.1534345059041735e-09
          ],
          [
            2.9792811955428364e-11,
            0.0817986562918975,
            -1.7253651335626262e-09
          ],
          [
            2.150252046697232e-11,
            0.06124127239219648,
            -1.2977020315845188e-09
          ],
          [
            1.3167983829649513e-11,
            0.040656259422496566,
            -8.704418728366595e-10
          ],
          [
            4.7979891484714306e-12,
            0.020044646128845312,
            -4.43550118189552e-10
          ],
          [
            -3.6208134625692604e-12,
            -0.0005925655756974701,
            -1.7052626730806193e-11
          ]
        ],
        "unwrapped_reduced_polarization": [
          [
            6.250988560464515e-11,
            0.16373039751287427,
            -3.4401299804395705e-09
          ],
          [
            5.4398418325006816e-11,
            0.14329437380940255,
            -3.0108105698397194e-09
          ],
          [
            4.624386386420589e-11,
            0.12282629636512062,
            -2.5819204269005784e-09
          ],
          [
            3.8039320325692925e-11,
            0.10232735695897938,
            -2.1534345059041735e-09
          ],
          [
            2.9792811955428364e-11,
            0.0817986562918975,
            -1.7253651335626262e-09
          ],
          [
            2.150252046697232e-11,
            0.06124127239219648,
            -1.2977020315845188e-09
          ],
          [
            1.3167983829649513e-11,
            0.040656259422496566,
            -8.704418728366595e-10
          ],
          [
            4.79798914847143e-12,
            0.020044646128845312,
            -4.43550118189552e-10
          ],
          [
            -3.6208134625692604e-12,
            -0.0005925655756974686,
            -1.7052626730806173e-11
          ]
        ],
        "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": [
          [
            6.250988615619235e-11,
            0.16373039751287433,
            -3.4401299586761525e-09
          ],
          [
            5.439837469367603e-11,
            0.14329437380940258,
            -3.0108105453230394e-09
          ],
          [
            4.624389760010672e-11,
            0.12282629636512066,
            -2.5819203997023976e-09
          ],
          [
            3.8039349448126814e-11,
            0.10232735695897932,
            -2.153434486285022e-09
          ],
          [
            2.9792834865816076e-11,
            0.08179865629189753,
            -1.7253651285464855e-09
          ],
          [
            2.1502466474032644e-11,
            0.061241272392196455,
            -1.2977020569238107e-09
          ],
          [
            1.3168022228171594e-11,
            0.04065625942249662,
            -8.704418852367724e-10
          ],
          [
            4.7979398232200765e-12,
            0.020044646128845267,
            -4.4355014106045587e-10
          ],
          [
            -3.6208258613612543e-12,
            -0.000592565575697479,
            -1.7052637080183786e-11
          ]
        ]
      },
      "reflected": {
        "reached": true,
        "construction": "reflect_displacements_about_reconstructed_parent",
        "energies_eV": [
          -77.65435373501347,
          -77.64989540937623,
          -77.64467164759762,
          -77.63866911960059,
          -77.63187483502935,
          -77.62427625435788,
          -77.61586145802353,
          -77.60661926144296,
          -77.59653931595858
        ],
        "cartesian_polarizations_e_A2": [
          [
            7.67426577042665e-14,
            -7.284212871042842e-06,
            -2.3058961857237196e-13
          ],
          [
            -3.385064578337651e-12,
            -0.0002551836646157924,
            5.5182466750608114e-12
          ],
          [
            -6.84786103056548e-12,
            -0.0005035749659619433,
            1.1266902694198694e-11
          ],
          [
            -1.0311824222466648e-11,
            -0.0007524434271641926,
            1.701529278202877e-11
          ],
          [
            -1.377746356866142e-11,
            -0.0010017748672413128,
            2.276430696869036e-11
          ],
          [
            -1.724529205066046e-11,
            -0.0012515556678968274,
            2.8514038006167745e-11
          ],
          [
            -2.0715411402214105e-11,
            -0.0015017729185967839,
            3.4264566910821024e-11
          ],
          [
            -2.4188244655011453e-11,
            -0.001752414484257818,
            4.001598968918493e-11
          ],
          [
            -2.7663997507458266e-11,
            -0.0020034690479886737,
            4.576859951795957e-11
          ]
        ],
        "raw_reduced_polarization": [
          [
            -3.6153300530412957e-12,
            -0.0005925655756988973,
            -1.704458955162935e-11
          ],
          [
            -1.3011375684294402e-11,
            -0.02075911626769935,
            4.068656101663915e-10
          ],
          [
            -2.2394129434966607e-11,
            -0.04096588350593789,
            8.306580050800768e-10
          ],
          [
            -3.177782450257933e-11,
            -0.06121167288206224,
            1.2543267770040902e-09
          ],
          [
            -4.1161904459935876e-11,
            -0.08149533135192537,
            1.6779380634478748e-09
          ],
          [
            -5.05754452927068e-11,
            -0.10181575162315457,
            2.101499119049956e-09
          ],
          [
            -6.002167621035363e-11,
            -0.12217188395864519,
            2.5250163091938438e-09
          ],
          [
            -6.952378437543917e-11,
            -0.1425627416845923,
            2.9484970818419237e-09
          ],
          [
            -7.908380775863029e-11,
            -0.1629874046692222,
            3.37196338902008e-09
          ]
        ],
        "unwrapped_reduced_polarization": [
          [
            -3.6153300530412957e-12,
            -0.0005925655756988973,
            -1.704458955162935e-11
          ],
          [
            -1.3011375684294402e-11,
            -0.02075911626769935,
            4.068656101663915e-10
          ],
          [
            -2.2394129434966607e-11,
            -0.04096588350593789,
            8.306580050800768e-10
          ],
          [
            -3.177782450257933e-11,
            -0.06121167288206224,
            1.2543267770040902e-09
          ],
          [
            -4.1161904459935876e-11,
            -0.08149533135192537,
            1.6779380634478748e-09
          ],
          [
            -5.05754452927068e-11,
            -0.10181575162315457,
            2.101499119049956e-09
          ],
          [
            -6.002167621035363e-11,
            -0.12217188395864519,
            2.5250163091938438e-09
          ],
          [
            -6.952378437543917e-11,
            -0.1425627416845923,
            2.9484970818419237e-09
          ],
          [
            -7.908380775863029e-11,
            -0.1629874046692222,
            3.37196338902008e-09
          ]
        ],
        "gauge_integer_shift": [
          0,
          0,
          0
        ],
        "expected_opposite_endpoint_reduced_polarization": [
          -6.971639281067467e-11,
          -0.16491557674197038,
          3.40613694769825e-09
        ],
        "actual_opposite_endpoint_branch_residual": 0.0019281720727481748
      },
      "pnp_branch": {
        "construction": "incoming_path_concatenated_with_parent_reflection",
        "reduced_polarization": [
          [
            6.250988560464515e-11,
            0.16373039751287427,
            -3.4401299804395705e-09
          ],
          [
            5.4398418325006816e-11,
            0.14329437380940255,
            -3.0108105698397194e-09
          ],
          [
            4.624386386420589e-11,
            0.12282629636512062,
            -2.5819204269005784e-09
          ],
          [
            3.8039320325692925e-11,
            0.10232735695897938,
            -2.1534345059041735e-09
          ],
          [
            2.9792811955428364e-11,
            0.0817986562918975,
            -1.7253651335626262e-09
          ],
          [
            2.150252046697232e-11,
            0.06124127239219648,
            -1.2977020315845188e-09
          ],
          [
            1.3167983829649513e-11,
            0.040656259422496566,
            -8.704418728366595e-10
          ],
          [
            4.7979891484714306e-12,
            0.020044646128845312,
            -4.43550118189552e-10
          ],
          [
            -3.6208134625692604e-12,
            -0.0005925655756974701,
            -1.7052626730806193e-11
          ],
          [
            -1.3011375684294402e-11,
            -0.02075911626769935,
            4.068656101663915e-10
          ],
          [
            -2.2394129434966607e-11,
            -0.04096588350593789,
            8.306580050800768e-10
          ],
          [
            -3.177782450257933e-11,
            -0.06121167288206224,
            1.2543267770040902e-09
          ],
          [
            -4.1161904459935876e-11,
            -0.08149533135192537,
            1.6779380634478748e-09
          ],
          [
            -5.05754452927068e-11,
            -0.10181575162315457,
            2.101499119049956e-09
          ],
          [
            -6.002167621035363e-11,
            -0.12217188395864519,
            2.5250163091938438e-09
          ],
          [
            -6.952378437543917e-11,
            -0.1425627416845923,
            2.9484970818419237e-09
          ],
          [
            -7.908380775863029e-11,
            -0.1629874046692222,
            3.37196338902008e-09
          ]
        ],
        "unwrapped_reduced_polarization": [
          [
            6.250988560464515e-11,
            0.16373039751287427,
            -3.4401299804395705e-09
          ],
          [
            5.4398418325006816e-11,
            0.14329437380940255,
            -3.0108105698397194e-09
          ],
          [
            4.624386386420589e-11,
            0.12282629636512062,
            -2.5819204269005784e-09
          ],
          [
            3.8039320325692925e-11,
            0.10232735695897938,
            -2.1534345059041735e-09
          ],
          [
            2.9792811955428364e-11,
            0.0817986562918975,
            -1.7253651335626262e-09
          ],
          [
            2.150252046697232e-11,
            0.06124127239219648,
            -1.2977020315845188e-09
          ],
          [
            1.3167983829649513e-11,
            0.040656259422496566,
            -8.704418728366595e-10
          ],
          [
            4.79798914847143e-12,
            0.020044646128845312,
            -4.43550118189552e-10
          ],
          [
            -3.6208134625692604e-12,
            -0.0005925655756974686,
            -1.7052626730806173e-11
          ],
          [
            -1.3011375684294402e-11,
            -0.02075911626769935,
            4.068656101663915e-10
          ],
          [
            -2.2394129434966607e-11,
            -0.04096588350593789,
            8.306580050800768e-10
          ],
          [
            -3.177782450257933e-11,
            -0.06121167288206224,
            1.2543267770040902e-09
          ],
          [
            -4.1161904459935876e-11,
            -0.08149533135192537,
            1.6779380634478748e-09
          ],
          [
            -5.05754452927068e-11,
            -0.10181575162315457,
            2.101499119049956e-09
          ],
          [
            -6.002167621035363e-11,
            -0.12217188395864519,
            2.5250163091938438e-09
          ],
          [
            -6.952378437543917e-11,
            -0.1425627416845923,
            2.9484970818419237e-09
          ],
          [
            -7.908380775863029e-11,
            -0.1629874046692222,
            3.37196338902008e-09
          ]
        ],
        "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": [
          [
            6.250988615619235e-11,
            0.16373039751287433,
            -3.4401299586761525e-09
          ],
          [
            5.439837469367603e-11,
            0.14329437380940258,
            -3.0108105453230394e-09
          ],
          [
            4.624389760010672e-11,
            0.12282629636512066,
            -2.5819203997023976e-09
          ],
          [
            3.8039349448126814e-11,
            0.10232735695897932,
            -2.153434486285022e-09
          ],
          [
            2.9792834865816076e-11,
            0.08179865629189753,
            -1.7253651285464855e-09
          ],
          [
            2.1502466474032644e-11,
            0.061241272392196455,
            -1.2977020569238107e-09
          ],
          [
            1.3168022228171594e-11,
            0.04065625942249662,
            -8.704418852367724e-10
          ],
          [
            4.7979398232200765e-12,
            0.020044646128845267,
            -4.4355014106045587e-10
          ],
          [
            -3.6208258613612543e-12,
            -0.000592565575697479,
            -1.7052637080183786e-11
          ],
          [
            -1.3011369759396985e-11,
            -0.02075911626769933,
            4.0686565228043037e-10
          ],
          [
            -2.239414209626034e-11,
            -0.04096588350593788,
            8.306579868389008e-10
          ],
          [
            -3.177780261154339e-11,
            -0.06121167288206225,
            1.2543267535747304e-09
          ],
          [
            -4.11619072160363e-11,
            -0.08149533135192538,
            1.6779380107578845e-09
          ],
          [
            -5.057543273068177e-11,
            -0.1018157516231546,
            2.1014990858603255e-09
          ],
          [
            -6.002165431340245e-11,
            -0.1221718839586452,
            2.525016307153294e-09
          ],
          [
            -6.952377562541301e-11,
            -0.14256274168459226,
            2.9484971131310544e-09
          ],
          [
            -7.908379506815777e-11,
            -0.16298740466922224,
            3.3719633751871925e-09
          ]
        ]
      },
      "incoming_structure_ids": [
        "incoming_00_000",
        "incoming_00_001",
        "incoming_00_002",
        "incoming_00_003",
        "incoming_00_004",
        "incoming_00_005",
        "incoming_00_006",
        "incoming_00_007",
        "incoming_00_008"
      ],
      "reflected_structure_ids": [
        "reflected_00_001",
        "reflected_00_002",
        "reflected_00_003",
        "reflected_00_004",
        "reflected_00_005",
        "reflected_00_006",
        "reflected_00_007",
        "reflected_00_008"
      ]
    },
    {
      "orbit_id": 1,
      "formal_class": [
        0.0,
        0.5,
        0.0
      ],
      "formal_classes_in_orbit": [
        [
          0.0,
          0.5,
          0.0
        ]
      ],
      "target_reduced_polarization": [
        0.0,
        0.5,
        0.0
      ],
      "bec_backprojection": {
        "converged_to_target": true,
        "history": [
          {
            "iteration": 0,
            "reduced_polarization": [
              6.251451213822425e-11,
              0.16373039751287446,
              -3.4401301804969566e-09
            ],
            "branch_aligned_reduced_polarization": [
              6.251451213822425e-11,
              0.16373039751287444,
              -3.4401301804969566e-09
            ],
            "target_residual": 0.3362696024871256,
            "energy_eV": -77.72426459247508,
            "max_atomic_step_A": 0.07495562855907745,
            "max_log_strain_component": 0.00479950988257317,
            "step_scale": 1.0,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 1.021199267487496,
            "cell_principal_stretches": [
              1.0000416675726782,
              1.0000416498469282,
              0.9952119893607171
            ],
            "cell_volume_ratio": 0.99529490958277,
            "cell_rmsd_from_input_A": 0.020338428005114886
          },
          {
            "iteration": 1,
            "reduced_polarization": [
              -2.1944702144080003e-11,
              0.49595953237391105,
              -1.5324795505833324e-11
            ],
            "branch_aligned_reduced_polarization": [
              -2.1944702144080003e-11,
              0.49595953237391105,
              -1.5324795505833324e-11
            ],
            "target_residual": 0.0040404676260889505,
            "energy_eV": -77.72239621965014,
            "max_atomic_step_A": 0.0009110935701865895,
            "max_log_strain_component": 6.172962667990596e-05,
            "step_scale": 1.0,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 1.021199267487496,
            "cell_principal_stretches": [
              1.0000422034978127,
              1.0000421855440709,
              0.9951505571922581
            ],
            "cell_volume_ratio": 0.9952345387660533,
            "cell_rmsd_from_input_A": 0.020598744890308135
          },
          {
            "iteration": 2,
            "reduced_polarization": [
              -8.340721756395412e-14,
              0.5000137636370751,
              4.721786154887491e-14
            ],
            "branch_aligned_reduced_polarization": [
              -8.340721756395412e-14,
              0.5000137636370751,
              4.721786154887491e-14
            ],
            "target_residual": 1.3763637075059343e-05,
            "energy_eV": -77.72111266035839
          }
        ],
        "iterations": 2
      },
      "parent": {
        "candidate_id": "bec_projection_01",
        "source": "MACEField_BEC_backprojection",
        "spacegroup": "P6_3mc",
        "spacegroup_number": 186,
        "pointgroup": "6mm",
        "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": 1.3763637075059343e-05,
        "parent_symmetrization_rmsd_A": 0.047675241206410555,
        "parent_cell_rmsd_A": 0.020598744890308135,
        "energy_eV": -77.72111266035839,
        "reduced_polarization": [
          -8.340721756395412e-14,
          0.5000137636370751,
          4.721786154887491e-14
        ],
        "cartesian_polarization_e_A2": [
          1.735883904956835e-13,
          0.0061457360380367445,
          1.4427627365364043e-13
        ],
        "ranking_score": 0.5528524547031377
      },
      "branch_status": "awaiting_branch_sampling"
    },
    {
      "orbit_id": 2,
      "formal_class": [
        0.0,
        0.0,
        0.5
      ],
      "formal_classes_in_orbit": [
        [
          0.0,
          0.0,
          0.5
        ],
        [
          0.5,
          0.0,
          0.0
        ],
        [
          0.5,
          0.0,
          0.5
        ]
      ],
      "target_reduced_polarization": [
        0.0,
        0.0,
        -0.5
      ],
      "bec_backprojection": {
        "converged_to_target": true,
        "history": [
          {
            "iteration": 0,
            "reduced_polarization": [
              6.251451213822425e-11,
              0.16373039751287446,
              -3.4401301804969566e-09
            ],
            "branch_aligned_reduced_polarization": [
              6.251451213822425e-11,
              0.16373039751287446,
              -3.4401301807207574e-09
            ],
            "target_residual": 0.5261251178470704,
            "energy_eV": -77.72426459247508,
            "max_atomic_step_A": 0.12,
            "max_log_strain_component": 0.0022478468273485672,
            "step_scale": 0.9618960178766395,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 1.021199267487496,
            "cell_principal_stretches": [
              1.0035614143106075,
              0.999980486997555,
              0.9986741314814574
            ],
            "cell_volume_ratio": 1.0022112672924335,
            "cell_rmsd_from_input_A": 0.020930650437142942
          },
          {
            "iteration": 1,
            "reduced_polarization": [
              -2.9477888625159973e-09,
              0.010550296137447627,
              -0.47203244709333253
            ],
            "branch_aligned_reduced_polarization": [
              -2.9477888625159973e-09,
              0.010550296137447627,
              -0.47203244709333253
            ],
            "target_residual": 0.029891349320080803,
            "energy_eV": -77.27718473682957,
            "max_atomic_step_A": 0.007625883715922896,
            "max_log_strain_component": 0.0001640981095126762,
            "step_scale": 1.0,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 1.021199267487496,
            "cell_principal_stretches": [
              1.003804459249503,
              0.999979062517512,
              0.9985947609175034
            ],
            "cell_volume_ratio": 1.002372886387998,
            "cell_rmsd_from_input_A": 0.022312888914772348
          },
          {
            "iteration": 2,
            "reduced_polarization": [
              -5.7008988792150983e-11,
              7.884081632867417e-05,
              -0.49989837323669717
            ],
            "branch_aligned_reduced_polarization": [
              -5.7008988792150983e-11,
              7.884081632867417e-05,
              -0.49989837323669717
            ],
            "target_residual": 0.00012862298915351274,
            "energy_eV": -77.22265502345198
          }
        ],
        "iterations": 2
      },
      "parent": {
        "candidate_id": "bec_projection_02",
        "source": "MACEField_BEC_backprojection",
        "spacegroup": "Cc",
        "spacegroup_number": 9,
        "pointgroup": "m",
        "has_inversion": false,
        "is_polar_point_group": true,
        "nonpolar_parent_hypothesis": false,
        "symmetry_tolerance_A": null,
        "target_reduced_polarization": [
          0.0,
          0.0,
          -0.5
        ],
        "formal_class": [
          0.0,
          0.0,
          0.5
        ],
        "target_residual": 0.00012862298915351274,
        "parent_symmetrization_rmsd_A": 0.11102819841102676,
        "parent_cell_rmsd_A": 0.022312888914772348,
        "energy_eV": -77.22265502345198,
        "reduced_polarization": [
          -5.7008988792150983e-11,
          7.884081632867417e-05,
          -0.49989837323669717
        ],
        "cartesian_polarization_e_A2": [
          0.003908125157760466,
          -1.7029047190621235e-05,
          -0.006769071790933968
        ],
        "ranking_score": 0.6168636666180268
      },
      "branch_status": "awaiting_branch_sampling"
    },
    {
      "orbit_id": 3,
      "formal_class": [
        0.0,
        0.5,
        0.5
      ],
      "formal_classes_in_orbit": [
        [
          0.0,
          0.5,
          0.5
        ],
        [
          0.5,
          0.5,
          0.0
        ],
        [
          0.5,
          0.5,
          0.5
        ]
      ],
      "target_reduced_polarization": [
        0.0,
        0.5,
        -0.5
      ],
      "bec_backprojection": {
        "converged_to_target": true,
        "history": [
          {
            "iteration": 0,
            "reduced_polarization": [
              6.251451213822425e-11,
              0.16373039751287446,
              -3.4401301804969566e-09
            ],
            "branch_aligned_reduced_polarization": [
              6.251451213822425e-11,
              0.16373039751287444,
              -3.4401301807207574e-09
            ],
            "target_residual": 0.6025589117395238,
            "energy_eV": -77.72426459247508,
            "max_atomic_step_A": 0.12,
            "max_log_strain_component": 0.004240399555297246,
            "step_scale": 0.8835067784611857,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 1.021199267487496,
            "cell_principal_stretches": [
              1.0008167306652187,
              1.000036810849206,
              0.994992582095934
            ],
            "cell_volume_ratio": 0.995841879485301,
            "cell_rmsd_from_input_A": 0.024710342563320734
          },
          {
            "iteration": 1,
            "reduced_polarization": [
              4.41142374647336e-09,
              0.45891431972374874,
              -0.43924684032746325
            ],
            "branch_aligned_reduced_polarization": [
              4.41142374647336e-09,
              0.45891431972374874,
              -0.43924684032746325
            ],
            "target_residual": 0.07334152666776925,
            "energy_eV": -77.36498238152069,
            "max_atomic_step_A": 0.018113824542074546,
            "max_log_strain_component": 0.0006046221803332197,
            "step_scale": 1.0,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 1.021199267487496,
            "cell_principal_stretches": [
              1.0009345929292737,
              1.0000420596762558,
              0.9942792946989553
            ],
            "cell_volume_ratio": 0.9952503992465499,
            "cell_rmsd_from_input_A": 0.028226487952931173
          },
          {
            "iteration": 2,
            "reduced_polarization": [
              2.6758699001402504e-10,
              0.500120354506504,
              -0.499987124962884
            ],
            "branch_aligned_reduced_polarization": [
              2.6758699001402504e-10,
              0.500120354506504,
              -0.499987124962884
            ],
            "target_residual": 0.00012104120710172807,
            "energy_eV": -77.23349834890314
          }
        ],
        "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": [
          0.0,
          0.5,
          -0.5
        ],
        "formal_class": [
          0.0,
          0.5,
          0.5
        ],
        "target_residual": 0.00012104120710172807,
        "parent_symmetrization_rmsd_A": 0.11723590645177588,
        "parent_cell_rmsd_A": 0.028226487952931173,
        "energy_eV": -77.23349834890314,
        "reduced_polarization": [
          2.6758699001402504e-10,
          0.500120354506504,
          -0.499987124962884
        ],
        "cartesian_polarization_e_A2": [
          0.003930045252632709,
          0.00612922842339046,
          -0.006807038657481134
        ],
        "ranking_score": 0.6245346108542121
      },
      "branch_status": "awaiting_branch_sampling"
    }
  ],
  "sampled_polarization_branches": [
    {
      "orbit_id": 0,
      "candidate_id": "bec_projection_00",
      "formal_class": [
        0.0,
        0.0,
        0.0
      ],
      "construction": "MACEField-BEC-parent plus variable-cell P-N-P path and symmetric log-strain continuation beyond both polar endpoints",
      "geometry_diagnostics": {
        "collision_aware": false,
        "permutations_tested": 1,
        "selected_order": [
          0,
          1,
          2,
          3,
          4,
          5,
          6,
          7,
          8,
          9,
          10,
          11,
          12,
          13,
          14,
          15,
          16,
          17,
          18,
          19,
          20,
          21
        ],
        "endpoint_rmsd_A": 0.022764896930609443,
        "minimum_distance_A_by_image": [
          2.5309326246092407,
          2.532555966219457,
          2.5341885640942086,
          2.535830416943725,
          2.5374815233991312,
          2.539141882012759,
          2.5408114912584883,
          2.542490349532065,
          2.5441784551514335
        ],
        "minimum_distance_A": 2.5309326246092407,
        "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": [
          618.3954001282542,
          618.5729302212152,
          618.7505112798419,
          618.9281433187678,
          619.1058263526272,
          619.2835603960601,
          619.4613454637101,
          619.6391815702245,
          619.8170687302578
        ],
        "cell_deformation_log_strain_norm": 0.0023370677976285795
      },
      "parent_reduced_polarization": [
        -3.6208134625692604e-12,
        -0.0005925655756974701,
        -1.7052626730806193e-11
      ],
      "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": [
          -77.7242645924751,
          -77.71804755038377,
          -77.71111275795198,
          -77.70345914864475,
          -77.69508517034808,
          -77.68598924680113,
          -77.67616978091016,
          -77.66562515553518,
          -77.65435373501347
        ],
        "cartesian_polarizations_e_A2": [
          [
            2.7938423152809954e-11,
            0.0020126020430698273,
            -4.669384367492229e-11
          ],
          [
            2.4439430751383732e-11,
            0.0017614078770441493,
            -4.086157807076886e-11
          ],
          [
            2.0945265036248805e-11,
            0.0015098171493788124,
            -3.5036557632643765e-11
          ],
          [
            1.7455618826269e-11,
            0.0012578445038339988,
            -2.921843259558665e-11
          ],
          [
            1.3970711480729017e-11,
            0.0010055034648975318,
            -2.3407360482916334e-11
          ],
          [
            1.049043116281439e-11,
            0.0007528072786291036,
            -1.7603192454299516e-11
          ],
          [
            7.014741749783198e-12,
            0.0004997688979869328,
            -1.1805874221142464e-11
          ],
          [
            3.543507717666451e-12,
            0.0002464009637560735,
            -6.01492895356945e-12
          ],
          [
            7.671975259622151e-14,
            -7.2842128710253e-06,
            -2.3069845701832183e-13
          ]
        ],
        "raw_reduced_polarization": [
          [
            6.250988560464515e-11,
            0.16373039751287427,
            -3.4401299804395705e-09
          ],
          [
            5.4398418325006816e-11,
            0.14329437380940255,
            -3.0108105698397194e-09
          ],
          [
            4.624386386420589e-11,
            0.12282629636512062,
            -2.5819204269005784e-09
          ],
          [
            3.8039320325692925e-11,
            0.10232735695897938,
            -2.1534345059041735e-09
          ],
          [
            2.9792811955428364e-11,
            0.0817986562918975,
            -1.7253651335626262e-09
          ],
          [
            2.150252046697232e-11,
            0.06124127239219648,
            -1.2977020315845188e-09
          ],
          [
            1.3167983829649513e-11,
            0.040656259422496566,
            -8.704418728366595e-10
          ],
          [
            4.7979891484714306e-12,
            0.020044646128845312,
            -4.43550118189552e-10
          ],
          [
            -3.6208134625692604e-12,
            -0.0005925655756974701,
            -1.7052626730806193e-11
          ]
        ],
        "unwrapped_reduced_polarization": [
          [
            6.250988560464515e-11,
            0.16373039751287427,
            -3.4401299804395705e-09
          ],
          [
            5.4398418325006816e-11,
            0.14329437380940255,
            -3.0108105698397194e-09
          ],
          [
            4.624386386420589e-11,
            0.12282629636512062,
            -2.5819204269005784e-09
          ],
          [
            3.8039320325692925e-11,
            0.10232735695897938,
            -2.1534345059041735e-09
          ],
          [
            2.9792811955428364e-11,
            0.0817986562918975,
            -1.7253651335626262e-09
          ],
          [
            2.150252046697232e-11,
            0.06124127239219648,
            -1.2977020315845188e-09
          ],
          [
            1.3167983829649513e-11,
            0.040656259422496566,
            -8.704418728366595e-10
          ],
          [
            4.79798914847143e-12,
            0.020044646128845312,
            -4.43550118189552e-10
          ],
          [
            -3.6208134625692604e-12,
            -0.0005925655756974686,
            -1.7052626730806173e-11
          ]
        ],
        "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": [
          [
            6.250988615619235e-11,
            0.16373039751287433,
            -3.4401299586761525e-09
          ],
          [
            5.439837469367603e-11,
            0.14329437380940258,
            -3.0108105453230394e-09
          ],
          [
            4.624389760010672e-11,
            0.12282629636512066,
            -2.5819203997023976e-09
          ],
          [
            3.8039349448126814e-11,
            0.10232735695897932,
            -2.153434486285022e-09
          ],
          [
            2.9792834865816076e-11,
            0.08179865629189753,
            -1.7253651285464855e-09
          ],
          [
            2.1502466474032644e-11,
            0.061241272392196455,
            -1.2977020569238107e-09
          ],
          [
            1.3168022228171594e-11,
            0.04065625942249662,
            -8.704418852367724e-10
          ],
          [
            4.7979398232200765e-12,
            0.020044646128845267,
            -4.4355014106045587e-10
          ],
          [
            -3.6208258613612543e-12,
            -0.000592565575697479,
            -1.7052637080183786e-11
          ]
        ]
      },
      "reflected": {
        "reached": true,
        "construction": "reflect_displacements_about_reconstructed_parent",
        "energies_eV": [
          -77.65435373501347,
          -77.64989540937623,
          -77.64467164759762,
          -77.63866911960059,
          -77.63187483502935,
          -77.62427625435788,
          -77.61586145802353,
          -77.60661926144296,
          -77.59653931595858
        ],
        "cartesian_polarizations_e_A2": [
          [
            7.67426577042665e-14,
            -7.284212871042842e-06,
            -2.3058961857237196e-13
          ],
          [
            -3.385064578337651e-12,
            -0.0002551836646157924,
            5.5182466750608114e-12
          ],
          [
            -6.84786103056548e-12,
            -0.0005035749659619433,
            1.1266902694198694e-11
          ],
          [
            -1.0311824222466648e-11,
            -0.0007524434271641926,
            1.701529278202877e-11
          ],
          [
            -1.377746356866142e-11,
            -0.0010017748672413128,
            2.276430696869036e-11
          ],
          [
            -1.724529205066046e-11,
            -0.0012515556678968274,
            2.8514038006167745e-11
          ],
          [
            -2.0715411402214105e-11,
            -0.0015017729185967839,
            3.4264566910821024e-11
          ],
          [
            -2.4188244655011453e-11,
            -0.001752414484257818,
            4.001598968918493e-11
          ],
          [
            -2.7663997507458266e-11,
            -0.0020034690479886737,
            4.576859951795957e-11
          ]
        ],
        "raw_reduced_polarization": [
          [
            -3.6153300530412957e-12,
            -0.0005925655756988973,
            -1.704458955162935e-11
          ],
          [
            -1.3011375684294402e-11,
            -0.02075911626769935,
            4.068656101663915e-10
          ],
          [
            -2.2394129434966607e-11,
            -0.04096588350593789,
            8.306580050800768e-10
          ],
          [
            -3.177782450257933e-11,
            -0.06121167288206224,
            1.2543267770040902e-09
          ],
          [
            -4.1161904459935876e-11,
            -0.08149533135192537,
            1.6779380634478748e-09
          ],
          [
            -5.05754452927068e-11,
            -0.10181575162315457,
            2.101499119049956e-09
          ],
          [
            -6.002167621035363e-11,
            -0.12217188395864519,
            2.5250163091938438e-09
          ],
          [
            -6.952378437543917e-11,
            -0.1425627416845923,
            2.9484970818419237e-09
          ],
          [
            -7.908380775863029e-11,
            -0.1629874046692222,
            3.37196338902008e-09
          ]
        ],
        "unwrapped_reduced_polarization": [
          [
            -3.6153300530412957e-12,
            -0.0005925655756988973,
            -1.704458955162935e-11
          ],
          [
            -1.3011375684294402e-11,
            -0.02075911626769935,
            4.068656101663915e-10
          ],
          [
            -2.2394129434966607e-11,
            -0.04096588350593789,
            8.306580050800768e-10
          ],
          [
            -3.177782450257933e-11,
            -0.06121167288206224,
            1.2543267770040902e-09
          ],
          [
            -4.1161904459935876e-11,
            -0.08149533135192537,
            1.6779380634478748e-09
          ],
          [
            -5.05754452927068e-11,
            -0.10181575162315457,
            2.101499119049956e-09
          ],
          [
            -6.002167621035363e-11,
            -0.12217188395864519,
            2.5250163091938438e-09
          ],
          [
            -6.952378437543917e-11,
            -0.1425627416845923,
            2.9484970818419237e-09
          ],
          [
            -7.908380775863029e-11,
            -0.1629874046692222,
            3.37196338902008e-09
          ]
        ],
        "gauge_integer_shift": [
          0,
          0,
          0
        ],
        "expected_opposite_endpoint_reduced_polarization": [
          -6.971639281067467e-11,
          -0.16491557674197038,
          3.40613694769825e-09
        ],
        "actual_opposite_endpoint_branch_residual": 0.0019281720727481748
      },
      "pnp_branch": {
        "construction": "incoming_path_concatenated_with_parent_reflection",
        "reduced_polarization": [
          [
            6.250988560464515e-11,
            0.16373039751287427,
            -3.4401299804395705e-09
          ],
          [
            5.4398418325006816e-11,
            0.14329437380940255,
            -3.0108105698397194e-09
          ],
          [
            4.624386386420589e-11,
            0.12282629636512062,
            -2.5819204269005784e-09
          ],
          [
            3.8039320325692925e-11,
            0.10232735695897938,
            -2.1534345059041735e-09
          ],
          [
            2.9792811955428364e-11,
            0.0817986562918975,
            -1.7253651335626262e-09
          ],
          [
            2.150252046697232e-11,
            0.06124127239219648,
            -1.2977020315845188e-09
          ],
          [
            1.3167983829649513e-11,
            0.040656259422496566,
            -8.704418728366595e-10
          ],
          [
            4.7979891484714306e-12,
            0.020044646128845312,
            -4.43550118189552e-10
          ],
          [
            -3.6208134625692604e-12,
            -0.0005925655756974701,
            -1.7052626730806193e-11
          ],
          [
            -1.3011375684294402e-11,
            -0.02075911626769935,
            4.068656101663915e-10
          ],
          [
            -2.2394129434966607e-11,
            -0.04096588350593789,
            8.306580050800768e-10
          ],
          [
            -3.177782450257933e-11,
            -0.06121167288206224,
            1.2543267770040902e-09
          ],
          [
            -4.1161904459935876e-11,
            -0.08149533135192537,
            1.6779380634478748e-09
          ],
          [
            -5.05754452927068e-11,
            -0.10181575162315457,
            2.101499119049956e-09
          ],
          [
            -6.002167621035363e-11,
            -0.12217188395864519,
            2.5250163091938438e-09
          ],
          [
            -6.952378437543917e-11,
            -0.1425627416845923,
            2.9484970818419237e-09
          ],
          [
            -7.908380775863029e-11,
            -0.1629874046692222,
            3.37196338902008e-09
          ]
        ],
        "unwrapped_reduced_polarization": [
          [
            6.250988560464515e-11,
            0.16373039751287427,
            -3.4401299804395705e-09
          ],
          [
            5.4398418325006816e-11,
            0.14329437380940255,
            -3.0108105698397194e-09
          ],
          [
            4.624386386420589e-11,
            0.12282629636512062,
            -2.5819204269005784e-09
          ],
          [
            3.8039320325692925e-11,
            0.10232735695897938,
            -2.1534345059041735e-09
          ],
          [
            2.9792811955428364e-11,
            0.0817986562918975,
            -1.7253651335626262e-09
          ],
          [
            2.150252046697232e-11,
            0.06124127239219648,
            -1.2977020315845188e-09
          ],
          [
            1.3167983829649513e-11,
            0.040656259422496566,
            -8.704418728366595e-10
          ],
          [
            4.79798914847143e-12,
            0.020044646128845312,
            -4.43550118189552e-10
          ],
          [
            -3.6208134625692604e-12,
            -0.0005925655756974686,
            -1.7052626730806173e-11
          ],
          [
            -1.3011375684294402e-11,
            -0.02075911626769935,
            4.068656101663915e-10
          ],
          [
            -2.2394129434966607e-11,
            -0.04096588350593789,
            8.306580050800768e-10
          ],
          [
            -3.177782450257933e-11,
            -0.06121167288206224,
            1.2543267770040902e-09
          ],
          [
            -4.1161904459935876e-11,
            -0.08149533135192537,
            1.6779380634478748e-09
          ],
          [
            -5.05754452927068e-11,
            -0.10181575162315457,
            2.101499119049956e-09
          ],
          [
            -6.002167621035363e-11,
            -0.12217188395864519,
            2.5250163091938438e-09
          ],
          [
            -6.952378437543917e-11,
            -0.1425627416845923,
            2.9484970818419237e-09
          ],
          [
            -7.908380775863029e-11,
            -0.1629874046692222,
            3.37196338902008e-09
          ]
        ],
        "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": [
          [
            6.250988615619235e-11,
            0.16373039751287433,
            -3.4401299586761525e-09
          ],
          [
            5.439837469367603e-11,
            0.14329437380940258,
            -3.0108105453230394e-09
          ],
          [
            4.624389760010672e-11,
            0.12282629636512066,
            -2.5819203997023976e-09
          ],
          [
            3.8039349448126814e-11,
            0.10232735695897932,
            -2.153434486285022e-09
          ],
          [
            2.9792834865816076e-11,
            0.08179865629189753,
            -1.7253651285464855e-09
          ],
          [
            2.1502466474032644e-11,
            0.061241272392196455,
            -1.2977020569238107e-09
          ],
          [
            1.3168022228171594e-11,
            0.04065625942249662,
            -8.704418852367724e-10
          ],
          [
            4.7979398232200765e-12,
            0.020044646128845267,
            -4.4355014106045587e-10
          ],
          [
            -3.6208258613612543e-12,
            -0.000592565575697479,
            -1.7052637080183786e-11
          ],
          [
            -1.3011369759396985e-11,
            -0.02075911626769933,
            4.0686565228043037e-10
          ],
          [
            -2.239414209626034e-11,
            -0.04096588350593788,
            8.306579868389008e-10
          ],
          [
            -3.177780261154339e-11,
            -0.06121167288206225,
            1.2543267535747304e-09
          ],
          [
            -4.11619072160363e-11,
            -0.08149533135192538,
            1.6779380107578845e-09
          ],
          [
            -5.057543273068177e-11,
            -0.1018157516231546,
            2.1014990858603255e-09
          ],
          [
            -6.002165431340245e-11,
            -0.1221718839586452,
            2.525016307153294e-09
          ],
          [
            -6.952377562541301e-11,
            -0.14256274168459226,
            2.9484971131310544e-09
          ],
          [
            -7.908379506815777e-11,
            -0.16298740466922224,
            3.3719633751871925e-09
          ]
        ]
      },
      "incoming_structure_ids": [
        "incoming_00_000",
        "incoming_00_001",
        "incoming_00_002",
        "incoming_00_003",
        "incoming_00_004",
        "incoming_00_005",
        "incoming_00_006",
        "incoming_00_007",
        "incoming_00_008"
      ],
      "reflected_structure_ids": [
        "reflected_00_001",
        "reflected_00_002",
        "reflected_00_003",
        "reflected_00_004",
        "reflected_00_005",
        "reflected_00_006",
        "reflected_00_007",
        "reflected_00_008"
      ],
      "positive_extension_structure_ids": [
        "extension_plus_00_000",
        "extension_plus_00_001",
        "extension_plus_00_002",
        "extension_plus_00_003"
      ],
      "negative_extension_structure_ids": [
        "extension_minus_00_000",
        "extension_minus_00_001",
        "extension_minus_00_002",
        "extension_minus_00_003"
      ],
      "extension": {
        "enabled": true,
        "fraction_beyond_polar_endpoint": 0.35,
        "images_per_side": 4,
        "construction": "continue fractional atomic displacements and symmetric log strain beyond +P; reflect these structures about N for the -P side",
        "positive_path_coordinates": [
          1.35,
          1.2625,
          1.175,
          1.0875
        ],
        "negative_path_coordinates": [
          -1.0875,
          -1.175,
          -1.2625,
          -1.35
        ]
      },
      "branch_coordinates": [
        1.35,
        1.2625,
        1.175,
        1.0875,
        1.0,
        0.875,
        0.75,
        0.625,
        0.5,
        0.375,
        0.25,
        0.125,
        0.0,
        -0.125,
        -0.25,
        -0.375,
        -0.5,
        -0.625,
        -0.75,
        -0.875,
        -1.0,
        -1.0875,
        -1.175,
        -1.2625,
        -1.35
      ],
      "parent": {
        "candidate_id": "bec_projection_00",
        "source": "MACEField_BEC_backprojection",
        "spacegroup": "P6_3mc",
        "spacegroup_number": 186,
        "pointgroup": "6mm",
        "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": 0.0005925655756990805,
        "parent_symmetrization_rmsd_A": 0.022764896930609443,
        "parent_cell_rmsd_A": 0.009973682936103553,
        "energy_eV": -77.65435373501347,
        "reduced_polarization": [
          -3.61563857547544e-12,
          -0.0005925655756990803,
          -1.7045796533893763e-11
        ],
        "cartesian_polarization_e_A2": [
          7.674727007206441e-14,
          -7.284212871045093e-06,
          -2.3060596337087917e-13
        ],
        "ranking_score": 0.5264434488160334
      }
    }
  ],
  "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": 40,
      "full_response": 8,
      "energy_polarization": 32
    },
    "model_evaluations_for_recovery_and_path_properties": {
      "total": 65,
      "full_response": 33,
      "energy_polarization": 32
    },
    "elapsed_seconds": 174.22413312696153
  }
}