{
  "schema": "ferrofinder.endpoint_parent_recovery.v4_variable_cell",
  "status": "complete",
  "input_atom_count": 76,
  "input_formula": "As4K4Nb16O52",
  "input_spacegroup": "Cmc2_1",
  "input_pointgroup": "mm2",
  "input_is_polar_point_group": true,
  "input_energy_eV": -596.7873981187169,
  "input_cartesian_polarization_e_A2": [
    -1.4684765218203657e-17,
    -9.830566954797057e-18,
    0.00074813410115824
  ],
  "input_reduced_polarization": [
    -1.5753315783831432e-15,
    -1.0720791865332606e-15,
    0.08402752923463679
  ],
  "input_formal_targets": [
    {
      "orbit_id": 0,
      "representative_formal_class": [
        0.0,
        0.0,
        0.0
      ],
      "target_reduced_polarization": [
        0.0,
        0.0,
        0.0
      ]
    },
    {
      "orbit_id": 1,
      "representative_formal_class": [
        0.0,
        0.0,
        0.5
      ],
      "target_reduced_polarization": [
        0.0,
        0.0,
        0.5
      ]
    },
    {
      "orbit_id": 2,
      "representative_formal_class": [
        0.5,
        0.0,
        0.0
      ],
      "target_reduced_polarization": [
        -0.5,
        0.0,
        0.0
      ]
    },
    {
      "orbit_id": 3,
      "representative_formal_class": [
        0.0,
        0.5,
        0.0
      ],
      "target_reduced_polarization": [
        0.0,
        -0.5,
        0.0
      ]
    },
    {
      "orbit_id": 4,
      "representative_formal_class": [
        0.5,
        0.0,
        0.5
      ],
      "target_reduced_polarization": [
        -0.5,
        0.0,
        0.5
      ]
    },
    {
      "orbit_id": 5,
      "representative_formal_class": [
        0.0,
        0.5,
        0.5
      ],
      "target_reduced_polarization": [
        0.0,
        -0.5,
        0.5
      ]
    },
    {
      "orbit_id": 6,
      "representative_formal_class": [
        0.5,
        0.5,
        0.0
      ],
      "target_reduced_polarization": [
        -0.5,
        -0.5,
        0.0
      ]
    },
    {
      "orbit_id": 7,
      "representative_formal_class": [
        0.5,
        0.5,
        0.5
      ],
      "target_reduced_polarization": [
        -0.5,
        -0.5,
        0.5
      ]
    }
  ],
  "parent_candidates": [
    {
      "candidate_id": "inversion_parent_endpoint_00",
      "source": "same_species_inversion_center_projection_from_endpoint",
      "spacegroup": "Cmcm",
      "spacegroup_number": 63,
      "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": 6.1690334214841615e-15,
      "parent_symmetrization_rmsd_A": 0.6142406847342545,
      "parent_cell_rmsd_A": 0.0,
      "energy_eV": -596.4695882423773,
      "reduced_polarization": [
        -1.3270259317241988e-15,
        -6.019222920449673e-15,
        2.54815552612887e-16
      ],
      "cartesian_polarization_e_A2": [
        -1.2370134969197122e-17,
        -5.519403293955638e-17,
        2.268735093743548e-18
      ],
      "ranking_score": 0.6142406847342669
    },
    {
      "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": 2.059778323365479e-05,
      "parent_symmetrization_rmsd_A": 0.0022388543353353695,
      "parent_cell_rmsd_A": 0.0008686126947571338,
      "energy_eV": -596.7823848069144,
      "reduced_polarization": [
        1.7219066122687932e-15,
        2.865390589428593e-15,
        -2.059778323365479e-05
      ],
      "cartesian_polarization_e_A2": [
        1.605373010328448e-17,
        2.6275219831822e-17,
        -1.834116448921208e-07
      ],
      "ranking_score": 0.502497203075492
    },
    {
      "candidate_id": "inversion_parent_bec_00_00",
      "source": "same_species_inversion_center_projection_after_BEC",
      "spacegroup": "Cmcm",
      "spacegroup_number": 63,
      "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": 8.214625577925185e-15,
      "parent_symmetrization_rmsd_A": 0.6142406868274175,
      "parent_cell_rmsd_A": 0.0008686126947571338,
      "energy_eV": -596.470863472569,
      "reduced_polarization": [
        3.733653499483181e-15,
        -5.737360207882922e-15,
        -4.54121159783392e-15
      ],
      "cartesian_polarization_e_A2": [
        3.480936200805164e-17,
        -5.261098164482332e-17,
        -4.0436928552631835e-17
      ],
      "ranking_score": 0.6144578400011232
    },
    {
      "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": 5.772384015228556e-09,
      "parent_symmetrization_rmsd_A": 0.011107132683095102,
      "parent_cell_rmsd_A": 0.0043133580069436165,
      "energy_eV": -596.7315885116026,
      "reduced_polarization": [
        7.331872195858027e-15,
        -2.12476208715531e-15,
        0.500000005772384
      ],
      "cartesian_polarization_e_A2": [
        8.743790837082748e-17,
        -3.221630038989538e-17,
        0.004449250561236908
      ],
      "ranking_score": 0.512185483729599
    },
    {
      "candidate_id": "bec_projection_02",
      "source": "MACEField_BEC_backprojection",
      "spacegroup": "Cc",
      "spacegroup_number": 9,
      "pointgroup": "m",
      "has_inversion": false,
      "is_polar_point_group": true,
      "nonpolar_parent_hypothesis": false,
      "symmetry_tolerance_A": null,
      "target_reduced_polarization": [
        -0.5,
        0.0,
        0.0
      ],
      "formal_class": [
        0.5,
        0.0,
        0.0
      ],
      "target_residual": 1.2828004167760335e-07,
      "parent_symmetrization_rmsd_A": 0.016587682512991187,
      "parent_cell_rmsd_A": 0.004133481742291701,
      "energy_eV": -596.5401707466799,
      "reduced_polarization": [
        -0.5000000144179044,
        -1.0060894134309677e-15,
        -1.2746722372740736e-07
      ],
      "cartesian_polarization_e_A2": [
        -0.004661569054441921,
        -2.264270174721667e-17,
        -1.919338971764541e-06
      ],
      "ranking_score": 0.5176213095086475
    },
    {
      "candidate_id": "bec_projection_03",
      "source": "MACEField_BEC_backprojection",
      "spacegroup": "Cm",
      "spacegroup_number": 8,
      "pointgroup": "m",
      "has_inversion": false,
      "is_polar_point_group": true,
      "nonpolar_parent_hypothesis": false,
      "symmetry_tolerance_A": null,
      "target_reduced_polarization": [
        0.0,
        -0.5,
        0.0
      ],
      "formal_class": [
        0.0,
        0.5,
        0.0
      ],
      "target_residual": 0.0009713037651615946,
      "parent_symmetrization_rmsd_A": 0.014417149414933748,
      "parent_cell_rmsd_A": 0.016056347101978903,
      "energy_eV": -596.6397629244311,
      "reduced_polarization": [
        1.1140264429415984e-14,
        -0.4996778748849914,
        -0.0009163331351085005
      ],
      "cartesian_polarization_e_A2": [
        1.1839142702297337e-16,
        -0.004581985628481622,
        -5.530909737217958e-07
      ],
      "ranking_score": 0.5203738437207517
    },
    {
      "candidate_id": "bec_projection_04",
      "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": 2.6838977661656266e-07,
      "parent_symmetrization_rmsd_A": 0.019854058141768355,
      "parent_cell_rmsd_A": 0.005915953682437425,
      "energy_eV": -596.4895541030778,
      "reduced_polarization": [
        -0.49999976552607994,
        -1.245298547085811e-16,
        0.4999998694050039
      ],
      "cartesian_polarization_e_A2": [
        -0.004655443247799622,
        -4.8850652559443764e-17,
        0.004447329450565159
      ],
      "ranking_score": 0.5213335833419309
    },
    {
      "candidate_id": "bec_projection_05",
      "source": "MACEField_BEC_backprojection",
      "spacegroup": "Cm",
      "spacegroup_number": 8,
      "pointgroup": "m",
      "has_inversion": false,
      "is_polar_point_group": true,
      "nonpolar_parent_hypothesis": false,
      "symmetry_tolerance_A": null,
      "target_reduced_polarization": [
        0.0,
        -0.5,
        0.5
      ],
      "formal_class": [
        0.0,
        0.5,
        0.5
      ],
      "target_residual": 2.181028777086606e-06,
      "parent_symmetrization_rmsd_A": 0.01812008454122517,
      "parent_cell_rmsd_A": 0.016716307361576307,
      "energy_eV": -596.5922487575464,
      "reduced_polarization": [
        3.7413004172301904e-15,
        -0.5000021749939071,
        0.50000016213584
      ],
      "cartesian_polarization_e_A2": [
        7.336421999612603e-17,
        -0.004591604751830586,
        0.00445689379338245
      ],
      "ranking_score": 0.5223035234391734
    },
    {
      "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": 4.536340215483303e-08,
      "parent_symmetrization_rmsd_A": 0.021885522474870005,
      "parent_cell_rmsd_A": 0.01658703664979201,
      "energy_eV": -596.3974491290919,
      "reduced_polarization": [
        -0.49999995915931716,
        -0.49999998101080606,
        5.411782895723075e-09
      ],
      "cartesian_polarization_e_A2": [
        -0.004661559224441962,
        -0.004584949887182439,
        5.706539500108582e-06
      ],
      "ranking_score": 0.5260323723641224
    },
    {
      "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": 2.65206795093112e-06,
      "parent_symmetrization_rmsd_A": 0.02449533736591403,
      "parent_cell_rmsd_A": 0.017220151711580863,
      "energy_eV": -596.3501422433995,
      "reduced_polarization": [
        -0.499999522124692,
        -0.5000026085439353,
        0.5000000244569821
      ],
      "cartesian_polarization_e_A2": [
        -0.004655417368763493,
        -0.004591615831209187,
        0.004454981223409204
      ],
      "ranking_score": 0.5288056794297111
    }
  ],
  "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": [
              -1.5753315783831432e-15,
              -1.0720791865332606e-15,
              0.08402752923463679
            ],
            "branch_aligned_reduced_polarization": [
              -1.5753315783831432e-15,
              -1.0720791865332606e-15,
              0.08402752923463679
            ],
            "target_residual": 0.08402752923463679,
            "energy_eV": -596.7873981187169,
            "max_atomic_step_A": 0.0036820220412151937,
            "max_log_strain_component": 0.00011858495762589319,
            "step_scale": 1.0,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 1.58445574830528,
            "cell_principal_stretches": [
              1.00000676005118,
              0.9999642571025652,
              0.9998814220732921
            ],
            "cell_volume_ratio": 0.9998524424221681,
            "cell_rmsd_from_input_A": 0.0008686126947571338
          },
          {
            "iteration": 1,
            "reduced_polarization": [
              1.7219066122687932e-15,
              2.865390589428593e-15,
              -2.059778323365479e-05
            ],
            "branch_aligned_reduced_polarization": [
              1.7219066122687932e-15,
              2.865390589428593e-15,
              -2.059778323365479e-05
            ],
            "target_residual": 2.059778323365479e-05,
            "energy_eV": -596.7823848069144
          }
        ],
        "iterations": 1
      },
      "parent": {
        "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": 2.059778323365479e-05,
        "parent_symmetrization_rmsd_A": 0.0022388543353353695,
        "parent_cell_rmsd_A": 0.0008686126947571338,
        "energy_eV": -596.7823848069144,
        "reduced_polarization": [
          1.7219066122687932e-15,
          2.865390589428593e-15,
          -2.059778323365479e-05
        ],
        "cartesian_polarization_e_A2": [
          1.605373010328448e-17,
          2.6275219831822e-17,
          -1.834116448921208e-07
        ],
        "ranking_score": 0.502497203075492
      },
      "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": [
          -596.7873981187167,
          -596.7870688262402,
          -596.7866546208252,
          -596.7861554828893,
          -596.7855713883813,
          -596.7849023087738,
          -596.7841482110641,
          -596.7833090577669,
          -596.7823848069144
        ],
        "cartesian_polarizations_e_A2": [
          [
            -1.908174555440694e-18,
            -1.27361532468553e-17,
            0.0007481341011582245
          ],
          [
            -1.0353212067304935e-17,
            -1.611419455200194e-17,
            0.0006546194504100751
          ],
          [
            -2.5487967046557903e-17,
            -6.041421042268074e-17,
            0.0005610969260093033
          ],
          [
            4.5708013401151836e-17,
            3.1043064705825224e-17,
            0.00046756688754237677
          ],
          [
            -1.5666320544898038e-17,
            -5.085151201240057e-19,
            0.00037402969486938095
          ],
          [
            -9.020302671776662e-18,
            1.0909061304269622e-17,
            0.00028048570811414574
          ],
          [
            1.838478275650005e-17,
            3.4265497197462496e-18,
            0.00018693528765495023
          ],
          [
            1.1553236136435398e-17,
            3.775328305774074e-17,
            9.337879411553798e-05
          ],
          [
            -2.6508569256858384e-18,
            7.536265817200928e-17,
            -1.8341164482037857e-07
          ]
        ],
        "raw_reduced_polarization": [
          [
            -2.0470246473716905e-16,
            -1.3889498820603326e-15,
            0.08402752923463505
          ],
          [
            -1.1030096243326679e-15,
            -1.7656553268423612e-15,
            0.07352329755599159
          ],
          [
            -2.721083517538225e-15,
            -6.602723011976615e-15,
            0.06301847520412637
          ],
          [
            4.919456981813185e-15,
            3.3675642252396953e-15,
            0.052513102595633396
          ],
          [
            -1.663071013822155e-15,
            -7.44639687815058e-17,
            0.04200722017557786
          ],
          [
            -9.512369093911331e-16,
            1.171855762638341e-15,
            0.03150086841638491
          ],
          [
            1.985094186250454e-15,
            3.594266785496066e-16,
            0.020994087816794047
          ],
          [
            1.2468386844806773e-15,
            4.1088011527926944e-15,
            0.01048691890084788
          ],
          [
            -2.8434810739395024e-16,
            8.218499515264579e-15,
            -2.0597783225597882e-05
          ]
        ],
        "unwrapped_reduced_polarization": [
          [
            -2.0470246473716905e-16,
            -1.3889498820603326e-15,
            0.08402752923463505
          ],
          [
            -1.1030096243326679e-15,
            -1.7656553268423612e-15,
            0.07352329755599159
          ],
          [
            -2.721083517538225e-15,
            -6.602723011976615e-15,
            0.06301847520412637
          ],
          [
            4.919456981813185e-15,
            3.367564225239696e-15,
            0.052513102595633396
          ],
          [
            -1.6630710138221552e-15,
            -7.446396878150583e-17,
            0.04200722017557786
          ],
          [
            -9.512369093911331e-16,
            1.171855762638341e-15,
            0.03150086841638491
          ],
          [
            1.9850941862504535e-15,
            3.5942667854960666e-16,
            0.020994087816794047
          ],
          [
            1.2468386844806773e-15,
            4.1088011527926944e-15,
            0.01048691890084788
          ],
          [
            -2.843481073939502e-16,
            8.218499515264579e-15,
            -2.0597783225597896e-05
          ]
        ],
        "berry_integer_shifts": [
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ]
        ],
        "folded_reduced_polarization": [
          [
            -2.220446049250313e-16,
            -1.3877787807814457e-15,
            0.08402752923463508
          ],
          [
            -1.1102230246251565e-15,
            -1.7763568394002505e-15,
            0.07352329755599163
          ],
          [
            -2.7200464103316335e-15,
            -6.6058269965196814e-15,
            0.0630184752041264
          ],
          [
            4.884981308350689e-15,
            3.3306690738754696e-15,
            0.052513102595633354
          ],
          [
            -1.6653345369377348e-15,
            -5.551115123125783e-17,
            0.0420072201755779
          ],
          [
            -9.43689570931383e-16,
            1.2212453270876722e-15,
            0.031500868416384886
          ],
          [
            1.9984014443252818e-15,
            3.3306690738754696e-16,
            0.020994087816794016
          ],
          [
            1.2212453270876722e-15,
            4.107825191113079e-15,
            0.010486918900847852
          ],
          [
            -2.7755575615628914e-16,
            8.215650382226158e-15,
            -2.059778322560657e-05
          ]
        ]
      },
      "reflected": {
        "reached": true,
        "construction": "reflect_displacements_about_reconstructed_parent",
        "energies_eV": [
          -596.7823848069145,
          -596.7811764057776,
          -596.7798826891511,
          -596.7785037160663,
          -596.7770395410648,
          -596.7754902142007,
          -596.7738557810396,
          -596.7721362826599,
          -596.7703317556524
        ],
        "cartesian_polarizations_e_A2": [
          [
            6.3187061882596516e-18,
            4.6532566734420255e-17,
            -1.8341164487041196e-07
          ],
          [
            1.424719221982322e-17,
            3.7620093155997584e-17,
            -9.355373591081508e-05
          ],
          [
            -3.300735300130753e-17,
            1.3474937042775976e-16,
            -0.0001869239206022408
          ],
          [
            3.7515686554510895e-17,
            1.1762656001218578e-16,
            -0.0002802936028467615
          ],
          [
            2.7066578878844413e-17,
            7.959472380226699e-17,
            -0.0003736624197828864
          ],
          [
            2.7992104251849343e-17,
            1.0457057326997366e-16,
            -0.0004670300085700629
          ],
          [
            2.0466300052239596e-17,
            1.3759669367810954e-16,
            -0.0005603960063977684
          ],
          [
            -1.0827867268564248e-17,
            5.713214432073416e-17,
            -0.0006537600504961148
          ],
          [
            8.26079059993192e-18,
            7.480674041094953e-17,
            -0.0007471217781447937
          ]
        ],
        "raw_reduced_polarization": [
          [
            6.777275750466366e-16,
            5.074505348413203e-15,
            -2.0597783231216808e-05
          ],
          [
            1.5205553679141956e-15,
            4.11090091610906e-15,
            -0.010506565764322792
          ],
          [
            -3.553571349176445e-15,
            1.470911414445028e-14,
            -0.020992811220460664
          ],
          [
            4.007840952774258e-15,
            1.284541799375918e-14,
            -0.03147929340355929
          ],
          [
            2.8859746319919454e-15,
            8.69912076356578e-15,
            -0.04196597156447823
          ],
          [
            2.986401741274937e-15,
            1.1421692385520745e-14,
            -0.05245280495414996
          ],
          [
            2.1824133074284023e-15,
            1.5019832583595862e-14,
            -0.06293975282460142
          ],
          [
            -1.1691705528969494e-15,
            6.238868699647465e-15,
            -0.0734267744301448
          ],
          [
            8.861894692297493e-16,
            8.15810011525741e-15,
            -0.08391382902838292
          ]
        ],
        "unwrapped_reduced_polarization": [
          [
            6.777275750466366e-16,
            5.074505348413203e-15,
            -2.0597783231216808e-05
          ],
          [
            1.5205553679141956e-15,
            4.11090091610906e-15,
            -0.010506565764322792
          ],
          [
            -3.553571349176445e-15,
            1.470911414445028e-14,
            -0.020992811220460664
          ],
          [
            4.007840952774258e-15,
            1.284541799375918e-14,
            -0.03147929340355929
          ],
          [
            2.8859746319919454e-15,
            8.69912076356578e-15,
            -0.04196597156447823
          ],
          [
            2.986401741274937e-15,
            1.1421692385520745e-14,
            -0.05245280495414996
          ],
          [
            2.1824133074284023e-15,
            1.5019832583595862e-14,
            -0.06293975282460142
          ],
          [
            -1.1691705528969492e-15,
            6.238868699647465e-15,
            -0.0734267744301448
          ],
          [
            8.861894692297491e-16,
            8.15810011525741e-15,
            -0.08391382902838292
          ]
        ],
        "gauge_integer_shift": [
          0,
          0,
          0
        ],
        "expected_opposite_endpoint_reduced_polarization": [
          -3.640473331325163e-16,
          1.7826402094031932e-14,
          -0.08406872940803514
        ],
        "actual_opposite_endpoint_branch_residual": 0.0001549003796522258
      },
      "pnp_branch": {
        "construction": "incoming_path_concatenated_with_parent_reflection",
        "reduced_polarization": [
          [
            -2.0470246473716905e-16,
            -1.3889498820603326e-15,
            0.08402752923463505
          ],
          [
            -1.1030096243326679e-15,
            -1.7656553268423612e-15,
            0.07352329755599159
          ],
          [
            -2.721083517538225e-15,
            -6.602723011976615e-15,
            0.06301847520412637
          ],
          [
            4.919456981813185e-15,
            3.3675642252396953e-15,
            0.052513102595633396
          ],
          [
            -1.663071013822155e-15,
            -7.44639687815058e-17,
            0.04200722017557786
          ],
          [
            -9.512369093911331e-16,
            1.171855762638341e-15,
            0.03150086841638491
          ],
          [
            1.985094186250454e-15,
            3.594266785496066e-16,
            0.020994087816794047
          ],
          [
            1.2468386844806773e-15,
            4.1088011527926944e-15,
            0.01048691890084788
          ],
          [
            -2.8434810739395024e-16,
            8.218499515264579e-15,
            -2.0597783225597882e-05
          ],
          [
            1.5205553679141956e-15,
            4.11090091610906e-15,
            -0.010506565764322792
          ],
          [
            -3.553571349176445e-15,
            1.470911414445028e-14,
            -0.020992811220460664
          ],
          [
            4.007840952774258e-15,
            1.284541799375918e-14,
            -0.03147929340355929
          ],
          [
            2.8859746319919454e-15,
            8.69912076356578e-15,
            -0.04196597156447823
          ],
          [
            2.986401741274937e-15,
            1.1421692385520745e-14,
            -0.05245280495414996
          ],
          [
            2.1824133074284023e-15,
            1.5019832583595862e-14,
            -0.06293975282460142
          ],
          [
            -1.1691705528969494e-15,
            6.238868699647465e-15,
            -0.0734267744301448
          ],
          [
            8.861894692297493e-16,
            8.15810011525741e-15,
            -0.08391382902838292
          ]
        ],
        "unwrapped_reduced_polarization": [
          [
            -2.0470246473716905e-16,
            -1.3889498820603326e-15,
            0.08402752923463505
          ],
          [
            -1.1030096243326679e-15,
            -1.7656553268423612e-15,
            0.07352329755599159
          ],
          [
            -2.721083517538225e-15,
            -6.602723011976615e-15,
            0.06301847520412637
          ],
          [
            4.919456981813185e-15,
            3.367564225239696e-15,
            0.052513102595633396
          ],
          [
            -1.6630710138221552e-15,
            -7.446396878150583e-17,
            0.04200722017557786
          ],
          [
            -9.512369093911331e-16,
            1.171855762638341e-15,
            0.03150086841638491
          ],
          [
            1.9850941862504535e-15,
            3.5942667854960666e-16,
            0.020994087816794047
          ],
          [
            1.2468386844806773e-15,
            4.1088011527926944e-15,
            0.01048691890084788
          ],
          [
            -2.843481073939502e-16,
            8.218499515264579e-15,
            -2.0597783225597896e-05
          ],
          [
            1.5205553679141954e-15,
            4.11090091610906e-15,
            -0.010506565764322792
          ],
          [
            -3.553571349176445e-15,
            1.470911414445028e-14,
            -0.020992811220460664
          ],
          [
            4.007840952774258e-15,
            1.284541799375918e-14,
            -0.03147929340355929
          ],
          [
            2.8859746319919454e-15,
            8.69912076356578e-15,
            -0.04196597156447823
          ],
          [
            2.986401741274937e-15,
            1.1421692385520745e-14,
            -0.05245280495414996
          ],
          [
            2.1824133074284023e-15,
            1.5019832583595862e-14,
            -0.06293975282460142
          ],
          [
            -1.1691705528969492e-15,
            6.238868699647465e-15,
            -0.0734267744301448
          ],
          [
            8.861894692297491e-16,
            8.15810011525741e-15,
            -0.08391382902838292
          ]
        ],
        "berry_integer_shifts": [
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ]
        ],
        "folded_reduced_polarization": [
          [
            -2.220446049250313e-16,
            -1.3877787807814457e-15,
            0.08402752923463508
          ],
          [
            -1.1102230246251565e-15,
            -1.7763568394002505e-15,
            0.07352329755599163
          ],
          [
            -2.7200464103316335e-15,
            -6.6058269965196814e-15,
            0.0630184752041264
          ],
          [
            4.884981308350689e-15,
            3.3306690738754696e-15,
            0.052513102595633354
          ],
          [
            -1.6653345369377348e-15,
            -5.551115123125783e-17,
            0.0420072201755779
          ],
          [
            -9.43689570931383e-16,
            1.2212453270876722e-15,
            0.031500868416384886
          ],
          [
            1.9984014443252818e-15,
            3.3306690738754696e-16,
            0.020994087816794016
          ],
          [
            1.2212453270876722e-15,
            4.107825191113079e-15,
            0.010486918900847852
          ],
          [
            -2.7755575615628914e-16,
            8.215650382226158e-15,
            -2.059778322560657e-05
          ],
          [
            1.5543122344752192e-15,
            4.107825191113079e-15,
            -0.010506565764322795
          ],
          [
            -3.552713678800501e-15,
            1.4654943925052066e-14,
            -0.02099281122046065
          ],
          [
            3.9968028886505635e-15,
            1.2878587085651816e-14,
            -0.03147929340355926
          ],
          [
            2.886579864025407e-15,
            8.659739592076221e-15,
            -0.04196597156447823
          ],
          [
            2.9976021664879227e-15,
            1.1435297153639112e-14,
            -0.052452804954149945
          ],
          [
            2.220446049250313e-15,
            1.4988010832439613e-14,
            -0.0629397528246014
          ],
          [
            -1.1657341758564144e-15,
            6.217248937900877e-15,
            -0.07342677443014478
          ],
          [
            8.881784197001252e-16,
            8.104628079763643e-15,
            -0.0839138290283829
          ]
        ]
      },
      "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": [
              -1.5753315783831432e-15,
              -1.0720791865332606e-15,
              0.08402752923463679
            ],
            "branch_aligned_reduced_polarization": [
              -1.5753315783831432e-15,
              -1.0720791865332606e-15,
              0.0840275292346368
            ],
            "target_residual": 0.4159724707653632,
            "energy_eV": -596.7873981187169,
            "max_atomic_step_A": 0.018227595406499975,
            "max_log_strain_component": 0.0005870466294624224,
            "step_scale": 1.0,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 1.58445574830528,
            "cell_principal_stretches": [
              1.000587218975058,
              1.0001769615593383,
              0.9999665355073297
            ],
            "cell_volume_ratio": 1.000730794380521,
            "cell_rmsd_from_input_A": 0.004302874367975995
          },
          {
            "iteration": 1,
            "reduced_polarization": [
              -4.58904734267262e-16,
              4.888475781612015e-16,
              0.49899734288350983
            ],
            "branch_aligned_reduced_polarization": [
              -4.58904734267262e-16,
              4.888475781612015e-16,
              0.49899734288350983
            ],
            "target_residual": 0.0010026571164901688,
            "energy_eV": -596.7318887236853,
            "max_atomic_step_A": 4.415011687160644e-05,
            "max_log_strain_component": 1.4295014128188503e-06,
            "step_scale": 1.0,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 1.58445574830528,
            "cell_principal_stretches": [
              1.0005886493169238,
              1.0001773925118767,
              0.999966454020213
            ],
            "cell_volume_ratio": 1.0007325745698683,
            "cell_rmsd_from_input_A": 0.0043133580069436165
          },
          {
            "iteration": 2,
            "reduced_polarization": [
              7.331872195858027e-15,
              -2.12476208715531e-15,
              0.500000005772384
            ],
            "branch_aligned_reduced_polarization": [
              7.331872195858027e-15,
              -2.12476208715531e-15,
              0.500000005772384
            ],
            "target_residual": 5.772384015228556e-09,
            "energy_eV": -596.7315885116026
          }
        ],
        "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": 5.772384015228556e-09,
        "parent_symmetrization_rmsd_A": 0.011107132683095102,
        "parent_cell_rmsd_A": 0.0043133580069436165,
        "energy_eV": -596.7315885116026,
        "reduced_polarization": [
          7.331872195858027e-15,
          -2.12476208715531e-15,
          0.500000005772384
        ],
        "cartesian_polarization_e_A2": [
          8.743790837082748e-17,
          -3.221630038989538e-17,
          0.004449250561236908
        ],
        "ranking_score": 0.512185483729599
      },
      "branch_status": "awaiting_branch_sampling"
    },
    {
      "orbit_id": 2,
      "formal_class": [
        0.5,
        0.0,
        0.0
      ],
      "formal_classes_in_orbit": [
        [
          0.5,
          0.0,
          0.0
        ]
      ],
      "target_reduced_polarization": [
        -0.5,
        0.0,
        0.0
      ],
      "bec_backprojection": {
        "converged_to_target": true,
        "history": [
          {
            "iteration": 0,
            "reduced_polarization": [
              -1.5753315783831432e-15,
              -1.0720791865332606e-15,
              0.08402752923463679
            ],
            "branch_aligned_reduced_polarization": [
              -1.5543122344752192e-15,
              -1.0720791865332606e-15,
              0.08402752923463679
            ],
            "target_residual": 0.5070114650274451,
            "energy_eV": -596.7873981187169,
            "max_atomic_step_A": 0.0307201396978466,
            "max_log_strain_component": 0.0004103358884923008,
            "step_scale": 1.0,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 1.58445574830528,
            "cell_principal_stretches": [
              1.0003964726680217,
              0.9998814220732889,
              0.999574712858826
            ],
            "cell_volume_ratio": 0.9998524424221634,
            "cell_rmsd_from_input_A": 0.004122244023565656
          },
          {
            "iteration": 1,
            "reduced_polarization": [
              -0.49859982301561956,
              3.5466401033771285e-15,
              1.8638867099922622e-05
            ],
            "branch_aligned_reduced_polarization": [
              -0.49859982301561956,
              3.5466401033771285e-15,
              1.8638867099922622e-05
            ],
            "target_residual": 0.0014003010372614436,
            "energy_eV": -596.541527855532,
            "max_atomic_step_A": 8.93952749562508e-05,
            "max_log_strain_component": 1.1660549797393098e-06,
            "step_scale": 1.0,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 1.58445574830528,
            "cell_principal_stretches": [
              1.0003976344760925,
              0.9998813941758987,
              0.9995735451901131
            ],
            "cell_volume_ratio": 0.9998524077073413,
            "cell_rmsd_from_input_A": 0.004133481742291701
          },
          {
            "iteration": 2,
            "reduced_polarization": [
              -0.5000000144179044,
              -1.0060894134309677e-15,
              -1.2746722372740736e-07
            ],
            "branch_aligned_reduced_polarization": [
              -0.5000000144179044,
              -1.0060894134309677e-15,
              -1.2746722372740736e-07
            ],
            "target_residual": 1.2828004167760335e-07,
            "energy_eV": -596.5401707466799
          }
        ],
        "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": [
          -0.5,
          0.0,
          0.0
        ],
        "formal_class": [
          0.5,
          0.0,
          0.0
        ],
        "target_residual": 1.2828004167760335e-07,
        "parent_symmetrization_rmsd_A": 0.016587682512991187,
        "parent_cell_rmsd_A": 0.004133481742291701,
        "energy_eV": -596.5401707466799,
        "reduced_polarization": [
          -0.5000000144179044,
          -1.0060894134309677e-15,
          -1.2746722372740736e-07
        ],
        "cartesian_polarization_e_A2": [
          -0.004661569054441921,
          -2.264270174721667e-17,
          -1.919338971764541e-06
        ],
        "ranking_score": 0.5176213095086475
      },
      "branch_status": "awaiting_branch_sampling"
    },
    {
      "orbit_id": 3,
      "formal_class": [
        0.0,
        0.5,
        0.0
      ],
      "formal_classes_in_orbit": [
        [
          0.0,
          0.5,
          0.0
        ]
      ],
      "target_reduced_polarization": [
        0.0,
        -0.5,
        0.0
      ],
      "bec_backprojection": {
        "converged_to_target": true,
        "history": [
          {
            "iteration": 0,
            "reduced_polarization": [
              -1.5753315783831432e-15,
              -1.0720791865332606e-15,
              0.08402752923463679
            ],
            "branch_aligned_reduced_polarization": [
              -1.5753315783831432e-15,
              -1.0547118733938987e-15,
              0.08402752923463679
            ],
            "target_residual": 0.5070114650274455,
            "energy_eV": -596.7873981187169,
            "max_atomic_step_A": 0.024128902554514414,
            "max_log_strain_component": 0.0016599832895304461,
            "step_scale": 1.0,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 1.58445574830528,
            "cell_principal_stretches": [
              1.0015845898749018,
              1.000006760051182,
              0.9982638446334919
            ],
            "cell_volume_ratio": 0.9998524424221729,
            "cell_rmsd_from_input_A": 0.016056347101978903
          },
          {
            "iteration": 1,
            "reduced_polarization": [
              1.1140264429415984e-14,
              -0.4996778748849914,
              -0.0009163331351085005
            ],
            "branch_aligned_reduced_polarization": [
              1.1140264429415984e-14,
              -0.4996778748849914,
              -0.0009163331351085005
            ],
            "target_residual": 0.0009713037651615946,
            "energy_eV": -596.6397629244311
          }
        ],
        "iterations": 1
      },
      "parent": {
        "candidate_id": "bec_projection_03",
        "source": "MACEField_BEC_backprojection",
        "spacegroup": "Cm",
        "spacegroup_number": 8,
        "pointgroup": "m",
        "has_inversion": false,
        "is_polar_point_group": true,
        "nonpolar_parent_hypothesis": false,
        "symmetry_tolerance_A": null,
        "target_reduced_polarization": [
          0.0,
          -0.5,
          0.0
        ],
        "formal_class": [
          0.0,
          0.5,
          0.0
        ],
        "target_residual": 0.0009713037651615946,
        "parent_symmetrization_rmsd_A": 0.014417149414933748,
        "parent_cell_rmsd_A": 0.016056347101978903,
        "energy_eV": -596.6397629244311,
        "reduced_polarization": [
          1.1140264429415984e-14,
          -0.4996778748849914,
          -0.0009163331351085005
        ],
        "cartesian_polarization_e_A2": [
          1.1839142702297337e-16,
          -0.004581985628481622,
          -5.530909737217958e-07
        ],
        "ranking_score": 0.5203738437207517
      },
      "branch_status": "awaiting_branch_sampling"
    },
    {
      "orbit_id": 4,
      "formal_class": [
        0.5,
        0.0,
        0.5
      ],
      "formal_classes_in_orbit": [
        [
          0.5,
          0.0,
          0.5
        ]
      ],
      "target_reduced_polarization": [
        -0.5,
        0.0,
        0.5
      ],
      "bec_backprojection": {
        "converged_to_target": true,
        "history": [
          {
            "iteration": 0,
            "reduced_polarization": [
              -1.5753315783831432e-15,
              -1.0720791865332606e-15,
              0.08402752923463679
            ],
            "branch_aligned_reduced_polarization": [
              -1.5543122344752192e-15,
              -1.0720791865332606e-15,
              0.0840275292346368
            ],
            "target_residual": 0.6504099449075478,
            "energy_eV": -596.7873981187169,
            "max_atomic_step_A": 0.035834088064589056,
            "max_log_strain_component": 0.0005870466294590083,
            "step_scale": 1.0,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 1.58445574830528,
            "cell_principal_stretches": [
              1.0005872189750549,
              1.0004954711264007,
              0.9996481943278902
            ],
            "cell_volume_ratio": 1.000730794380516,
            "cell_rmsd_from_input_A": 0.005895860747141425
          },
          {
            "iteration": 1,
            "reduced_polarization": [
              -0.498566355099212,
              4.204298391144433e-16,
              0.4984270825432099
            ],
            "branch_aligned_reduced_polarization": [
              -0.498566355099212,
              4.204298391144433e-16,
              0.4984270825432099
            ],
            "target_residual": 0.0021282403594121,
            "energy_eV": -596.4914034144973,
            "max_atomic_step_A": 0.00011767984519418436,
            "max_log_strain_component": 2.2523625384070113e-06,
            "step_scale": 1.0,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 1.58445574830528,
            "cell_principal_stretches": [
              1.000589472662761,
              1.00049700639164,
              0.9996472106737285
            ],
            "cell_volume_ratio": 1.0007335992982402,
            "cell_rmsd_from_input_A": 0.005915953682437425
          },
          {
            "iteration": 2,
            "reduced_polarization": [
              -0.49999976552607994,
              -1.245298547085811e-16,
              0.4999998694050039
            ],
            "branch_aligned_reduced_polarization": [
              -0.49999976552607994,
              -1.245298547085811e-16,
              0.4999998694050039
            ],
            "target_residual": 2.6838977661656266e-07,
            "energy_eV": -596.4895541030778
          }
        ],
        "iterations": 2
      },
      "parent": {
        "candidate_id": "bec_projection_04",
        "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": 2.6838977661656266e-07,
        "parent_symmetrization_rmsd_A": 0.019854058141768355,
        "parent_cell_rmsd_A": 0.005915953682437425,
        "energy_eV": -596.4895541030778,
        "reduced_polarization": [
          -0.49999976552607994,
          -1.245298547085811e-16,
          0.4999998694050039
        ],
        "cartesian_polarization_e_A2": [
          -0.004655443247799622,
          -4.8850652559443764e-17,
          0.004447329450565159
        ],
        "ranking_score": 0.5213335833419309
      },
      "branch_status": "awaiting_branch_sampling"
    },
    {
      "orbit_id": 5,
      "formal_class": [
        0.0,
        0.5,
        0.5
      ],
      "formal_classes_in_orbit": [
        [
          0.0,
          0.5,
          0.5
        ]
      ],
      "target_reduced_polarization": [
        0.0,
        -0.5,
        0.5
      ],
      "bec_backprojection": {
        "converged_to_target": true,
        "history": [
          {
            "iteration": 0,
            "reduced_polarization": [
              -1.5753315783831432e-15,
              -1.0720791865332606e-15,
              0.08402752923463679
            ],
            "branch_aligned_reduced_polarization": [
              -1.5753315783831432e-15,
              -1.0547118733938987e-15,
              0.0840275292346368
            ],
            "target_residual": 0.6504099449075482,
            "energy_eV": -596.7873981187169,
            "max_atomic_step_A": 0.03285305292923889,
            "max_log_strain_component": 0.00165998328953388,
            "step_scale": 1.0,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 1.58445574830528,
            "cell_principal_stretches": [
              1.0020567082197938,
              0.9999665355073317,
              0.998710228912588
            ],
            "cell_volume_ratio": 1.0007307943805255,
            "cell_rmsd_from_input_A": 0.016621776913288856
          },
          {
            "iteration": 1,
            "reduced_polarization": [
              7.72073571780477e-15,
              -0.4973182221412812,
              0.49666850086623326
            ],
            "branch_aligned_reduced_polarization": [
              7.72073571780477e-15,
              -0.4973182221412812,
              0.49666850086623326
            ],
            "target_residual": 0.004276776702354587,
            "energy_eV": -596.5947218069349,
            "max_atomic_step_A": 0.00021779825208952314,
            "max_log_strain_component": 9.122110404990292e-06,
            "step_scale": 1.0,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 1.58445574830528,
            "cell_principal_stretches": [
              1.0020691323244049,
              0.9999662605578147,
              0.9987041154872855
            ],
            "cell_volume_ratio": 1.0007368010144888,
            "cell_rmsd_from_input_A": 0.016716307361576307
          },
          {
            "iteration": 2,
            "reduced_polarization": [
              3.7413004172301904e-15,
              -0.5000021749939071,
              0.50000016213584
            ],
            "branch_aligned_reduced_polarization": [
              3.7413004172301904e-15,
              -0.5000021749939071,
              0.50000016213584
            ],
            "target_residual": 2.181028777086606e-06,
            "energy_eV": -596.5922487575464
          }
        ],
        "iterations": 2
      },
      "parent": {
        "candidate_id": "bec_projection_05",
        "source": "MACEField_BEC_backprojection",
        "spacegroup": "Cm",
        "spacegroup_number": 8,
        "pointgroup": "m",
        "has_inversion": false,
        "is_polar_point_group": true,
        "nonpolar_parent_hypothesis": false,
        "symmetry_tolerance_A": null,
        "target_reduced_polarization": [
          0.0,
          -0.5,
          0.5
        ],
        "formal_class": [
          0.0,
          0.5,
          0.5
        ],
        "target_residual": 2.181028777086606e-06,
        "parent_symmetrization_rmsd_A": 0.01812008454122517,
        "parent_cell_rmsd_A": 0.016716307361576307,
        "energy_eV": -596.5922487575464,
        "reduced_polarization": [
          3.7413004172301904e-15,
          -0.5000021749939071,
          0.50000016213584
        ],
        "cartesian_polarization_e_A2": [
          7.336421999612603e-17,
          -0.004591604751830586,
          0.00445689379338245
        ],
        "ranking_score": 0.5223035234391734
      },
      "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": [
              -1.5753315783831432e-15,
              -1.0720791865332606e-15,
              0.08402752923463679
            ],
            "branch_aligned_reduced_polarization": [
              -1.5543122344752192e-15,
              -1.0547118733938987e-15,
              0.08402752923463679
            ],
            "target_residual": 0.7120818953387842,
            "energy_eV": -596.7873981187169,
            "max_atomic_step_A": 0.042842190964009916,
            "max_log_strain_component": 0.001659983289535457,
            "step_scale": 1.0,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 1.58445574830528,
            "cell_principal_stretches": [
              1.0016384055114458,
              0.9999995316682199,
              0.9982174257530858
            ],
            "cell_volume_ratio": 0.9998524424221679,
            "cell_rmsd_from_input_A": 0.016554301425519422
          },
          {
            "iteration": 1,
            "reduced_polarization": [
              -0.4983035660245325,
              -0.4990494448381733,
              -0.0008771648663860171
            ],
            "branch_aligned_reduced_polarization": [
              -0.4983035660245325,
              -0.4990494448381733,
              -0.0008771648663860171
            ],
            "target_residual": 0.0021332748420252266,
            "energy_eV": -596.3995152018693,
            "max_atomic_step_A": 0.00014064897509801638,
            "max_log_strain_component": 3.1849044011243774e-06,
            "step_scale": 1.0,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 1.58445574830528,
            "cell_principal_stretches": [
              1.001642613096086,
              0.9999995163133437,
              0.9982147985409512
            ],
            "cell_volume_ratio": 0.9998539956254717,
            "cell_rmsd_from_input_A": 0.01658703664979201
          },
          {
            "iteration": 2,
            "reduced_polarization": [
              -0.49999995915931716,
              -0.49999998101080606,
              5.411782895723075e-09
            ],
            "branch_aligned_reduced_polarization": [
              -0.49999995915931716,
              -0.49999998101080606,
              5.411782895723075e-09
            ],
            "target_residual": 4.536340215483303e-08,
            "energy_eV": -596.3974491290919
          }
        ],
        "iterations": 2
      },
      "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": 4.536340215483303e-08,
        "parent_symmetrization_rmsd_A": 0.021885522474870005,
        "parent_cell_rmsd_A": 0.01658703664979201,
        "energy_eV": -596.3974491290919,
        "reduced_polarization": [
          -0.49999995915931716,
          -0.49999998101080606,
          5.411782895723075e-09
        ],
        "cartesian_polarization_e_A2": [
          -0.004661559224441962,
          -0.004584949887182439,
          5.706539500108582e-06
        ],
        "ranking_score": 0.5260323723641224
      },
      "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": [
              -1.5753315783831432e-15,
              -1.0720791865332606e-15,
              0.08402752923463679
            ],
            "branch_aligned_reduced_polarization": [
              -1.5543122344752192e-15,
              -1.0547118733938987e-15,
              0.0840275292346368
            ],
            "target_residual": 0.8203859435866989,
            "energy_eV": -596.7873981187169,
            "max_atomic_step_A": 0.04687193071828116,
            "max_log_strain_component": 0.001659983289538891,
            "step_scale": 1.0,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 1.58445574830528,
            "cell_principal_stretches": [
              1.0020920340000705,
              1.0000035482410183,
              0.9986380587863217
            ],
            "cell_volume_ratio": 1.0007307943805206,
            "cell_rmsd_from_input_A": 0.017103511913343385
          },
          {
            "iteration": 1,
            "reduced_polarization": [
              -0.4982571962357841,
              -0.49668508571417375,
              0.4960820739815886
            ],
            "branch_aligned_reduced_polarization": [
              -0.4982571962357841,
              -0.49668508571417375,
              0.4960820739815886
            ],
            "target_residual": 0.0054199784103523135,
            "energy_eV": -596.3547744171296,
            "max_atomic_step_A": 0.00031067562083425337,
            "max_log_strain_component": 1.1296926208746245e-05,
            "step_scale": 1.0,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 1.58445574830528,
            "cell_principal_stretches": [
              1.0021072052479043,
              1.0000033663560202,
              0.998630199119606
            ],
            "cell_volume_ratio": 1.0007378867445749,
            "cell_rmsd_from_input_A": 0.017220151711580863
          },
          {
            "iteration": 2,
            "reduced_polarization": [
              -0.499999522124692,
              -0.5000026085439353,
              0.5000000244569821
            ],
            "branch_aligned_reduced_polarization": [
              -0.499999522124692,
              -0.5000026085439353,
              0.5000000244569821
            ],
            "target_residual": 2.65206795093112e-06,
            "energy_eV": -596.3501422433995
          }
        ],
        "iterations": 2
      },
      "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": 2.65206795093112e-06,
        "parent_symmetrization_rmsd_A": 0.02449533736591403,
        "parent_cell_rmsd_A": 0.017220151711580863,
        "energy_eV": -596.3501422433995,
        "reduced_polarization": [
          -0.499999522124692,
          -0.5000026085439353,
          0.5000000244569821
        ],
        "cartesian_polarization_e_A2": [
          -0.004655417368763493,
          -0.004591615831209187,
          0.004454981223409204
        ],
        "ranking_score": 0.5288056794297111
      },
      "branch_status": "awaiting_branch_sampling"
    }
  ],
  "sampled_polarization_branches": [
    {
      "orbit_id": 0,
      "candidate_id": "bec_projection_00",
      "formal_class": [
        0.0,
        0.0,
        0.0
      ],
      "construction": "MACEField-BEC-parent plus variable-cell P-N-P path and symmetric log-strain continuation beyond both polar endpoints",
      "geometry_diagnostics": {
        "collision_aware": false,
        "permutations_tested": 1,
        "selected_order": [
          0,
          1,
          2,
          3,
          4,
          5,
          6,
          7,
          8,
          9,
          10,
          11,
          12,
          13,
          14,
          15,
          16,
          17,
          18,
          19,
          20,
          21,
          22,
          23,
          24,
          25,
          26,
          27,
          28,
          29,
          30,
          31,
          32,
          33,
          34,
          35,
          36,
          37,
          38,
          39,
          40,
          41,
          42,
          43,
          44,
          45,
          46,
          47,
          48,
          49,
          50,
          51,
          52,
          53,
          54,
          55,
          56,
          57,
          58,
          59,
          60,
          61,
          62,
          63,
          64,
          65,
          66,
          67,
          68,
          69,
          70,
          71,
          72,
          73,
          74,
          75
        ],
        "endpoint_rmsd_A": 0.0022388543353353695,
        "minimum_distance_A_by_image": [
          1.7058777373779983,
          1.7058720168980201,
          1.7058663485841343,
          1.7058607324354662,
          1.7058551684511236,
          1.7058496566302204,
          1.7058441969718572,
          1.7058387894751386,
          1.7058334341391557
        ],
        "minimum_distance_A": 1.7058334341391557,
        "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": [
          1146.2984537678665,
          1146.2773092748996,
          1146.2561651719639,
          1146.23502145905,
          1146.2138781361516,
          1146.1927352032585,
          1146.1715926603665,
          1146.1504505074677,
          1146.1293087445556
        ],
        "cell_deformation_log_strain_norm": 0.0001240390686048468
      },
      "parent_reduced_polarization": [
        -2.8434810739395024e-16,
        8.218499515264579e-15,
        -2.0597783225597882e-05
      ],
      "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": [
          -596.7873981187167,
          -596.7870688262402,
          -596.7866546208252,
          -596.7861554828893,
          -596.7855713883813,
          -596.7849023087738,
          -596.7841482110641,
          -596.7833090577669,
          -596.7823848069144
        ],
        "cartesian_polarizations_e_A2": [
          [
            -1.908174555440694e-18,
            -1.27361532468553e-17,
            0.0007481341011582245
          ],
          [
            -1.0353212067304935e-17,
            -1.611419455200194e-17,
            0.0006546194504100751
          ],
          [
            -2.5487967046557903e-17,
            -6.041421042268074e-17,
            0.0005610969260093033
          ],
          [
            4.5708013401151836e-17,
            3.1043064705825224e-17,
            0.00046756688754237677
          ],
          [
            -1.5666320544898038e-17,
            -5.085151201240057e-19,
            0.00037402969486938095
          ],
          [
            -9.020302671776662e-18,
            1.0909061304269622e-17,
            0.00028048570811414574
          ],
          [
            1.838478275650005e-17,
            3.4265497197462496e-18,
            0.00018693528765495023
          ],
          [
            1.1553236136435398e-17,
            3.775328305774074e-17,
            9.337879411553798e-05
          ],
          [
            -2.6508569256858384e-18,
            7.536265817200928e-17,
            -1.8341164482037857e-07
          ]
        ],
        "raw_reduced_polarization": [
          [
            -2.0470246473716905e-16,
            -1.3889498820603326e-15,
            0.08402752923463505
          ],
          [
            -1.1030096243326679e-15,
            -1.7656553268423612e-15,
            0.07352329755599159
          ],
          [
            -2.721083517538225e-15,
            -6.602723011976615e-15,
            0.06301847520412637
          ],
          [
            4.919456981813185e-15,
            3.3675642252396953e-15,
            0.052513102595633396
          ],
          [
            -1.663071013822155e-15,
            -7.44639687815058e-17,
            0.04200722017557786
          ],
          [
            -9.512369093911331e-16,
            1.171855762638341e-15,
            0.03150086841638491
          ],
          [
            1.985094186250454e-15,
            3.594266785496066e-16,
            0.020994087816794047
          ],
          [
            1.2468386844806773e-15,
            4.1088011527926944e-15,
            0.01048691890084788
          ],
          [
            -2.8434810739395024e-16,
            8.218499515264579e-15,
            -2.0597783225597882e-05
          ]
        ],
        "unwrapped_reduced_polarization": [
          [
            -2.0470246473716905e-16,
            -1.3889498820603326e-15,
            0.08402752923463505
          ],
          [
            -1.1030096243326679e-15,
            -1.7656553268423612e-15,
            0.07352329755599159
          ],
          [
            -2.721083517538225e-15,
            -6.602723011976615e-15,
            0.06301847520412637
          ],
          [
            4.919456981813185e-15,
            3.367564225239696e-15,
            0.052513102595633396
          ],
          [
            -1.6630710138221552e-15,
            -7.446396878150583e-17,
            0.04200722017557786
          ],
          [
            -9.512369093911331e-16,
            1.171855762638341e-15,
            0.03150086841638491
          ],
          [
            1.9850941862504535e-15,
            3.5942667854960666e-16,
            0.020994087816794047
          ],
          [
            1.2468386844806773e-15,
            4.1088011527926944e-15,
            0.01048691890084788
          ],
          [
            -2.843481073939502e-16,
            8.218499515264579e-15,
            -2.0597783225597896e-05
          ]
        ],
        "berry_integer_shifts": [
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ]
        ],
        "folded_reduced_polarization": [
          [
            -2.220446049250313e-16,
            -1.3877787807814457e-15,
            0.08402752923463508
          ],
          [
            -1.1102230246251565e-15,
            -1.7763568394002505e-15,
            0.07352329755599163
          ],
          [
            -2.7200464103316335e-15,
            -6.6058269965196814e-15,
            0.0630184752041264
          ],
          [
            4.884981308350689e-15,
            3.3306690738754696e-15,
            0.052513102595633354
          ],
          [
            -1.6653345369377348e-15,
            -5.551115123125783e-17,
            0.0420072201755779
          ],
          [
            -9.43689570931383e-16,
            1.2212453270876722e-15,
            0.031500868416384886
          ],
          [
            1.9984014443252818e-15,
            3.3306690738754696e-16,
            0.020994087816794016
          ],
          [
            1.2212453270876722e-15,
            4.107825191113079e-15,
            0.010486918900847852
          ],
          [
            -2.7755575615628914e-16,
            8.215650382226158e-15,
            -2.059778322560657e-05
          ]
        ]
      },
      "reflected": {
        "reached": true,
        "construction": "reflect_displacements_about_reconstructed_parent",
        "energies_eV": [
          -596.7823848069145,
          -596.7811764057776,
          -596.7798826891511,
          -596.7785037160663,
          -596.7770395410648,
          -596.7754902142007,
          -596.7738557810396,
          -596.7721362826599,
          -596.7703317556524
        ],
        "cartesian_polarizations_e_A2": [
          [
            6.3187061882596516e-18,
            4.6532566734420255e-17,
            -1.8341164487041196e-07
          ],
          [
            1.424719221982322e-17,
            3.7620093155997584e-17,
            -9.355373591081508e-05
          ],
          [
            -3.300735300130753e-17,
            1.3474937042775976e-16,
            -0.0001869239206022408
          ],
          [
            3.7515686554510895e-17,
            1.1762656001218578e-16,
            -0.0002802936028467615
          ],
          [
            2.7066578878844413e-17,
            7.959472380226699e-17,
            -0.0003736624197828864
          ],
          [
            2.7992104251849343e-17,
            1.0457057326997366e-16,
            -0.0004670300085700629
          ],
          [
            2.0466300052239596e-17,
            1.3759669367810954e-16,
            -0.0005603960063977684
          ],
          [
            -1.0827867268564248e-17,
            5.713214432073416e-17,
            -0.0006537600504961148
          ],
          [
            8.26079059993192e-18,
            7.480674041094953e-17,
            -0.0007471217781447937
          ]
        ],
        "raw_reduced_polarization": [
          [
            6.777275750466366e-16,
            5.074505348413203e-15,
            -2.0597783231216808e-05
          ],
          [
            1.5205553679141956e-15,
            4.11090091610906e-15,
            -0.010506565764322792
          ],
          [
            -3.553571349176445e-15,
            1.470911414445028e-14,
            -0.020992811220460664
          ],
          [
            4.007840952774258e-15,
            1.284541799375918e-14,
            -0.03147929340355929
          ],
          [
            2.8859746319919454e-15,
            8.69912076356578e-15,
            -0.04196597156447823
          ],
          [
            2.986401741274937e-15,
            1.1421692385520745e-14,
            -0.05245280495414996
          ],
          [
            2.1824133074284023e-15,
            1.5019832583595862e-14,
            -0.06293975282460142
          ],
          [
            -1.1691705528969494e-15,
            6.238868699647465e-15,
            -0.0734267744301448
          ],
          [
            8.861894692297493e-16,
            8.15810011525741e-15,
            -0.08391382902838292
          ]
        ],
        "unwrapped_reduced_polarization": [
          [
            6.777275750466366e-16,
            5.074505348413203e-15,
            -2.0597783231216808e-05
          ],
          [
            1.5205553679141956e-15,
            4.11090091610906e-15,
            -0.010506565764322792
          ],
          [
            -3.553571349176445e-15,
            1.470911414445028e-14,
            -0.020992811220460664
          ],
          [
            4.007840952774258e-15,
            1.284541799375918e-14,
            -0.03147929340355929
          ],
          [
            2.8859746319919454e-15,
            8.69912076356578e-15,
            -0.04196597156447823
          ],
          [
            2.986401741274937e-15,
            1.1421692385520745e-14,
            -0.05245280495414996
          ],
          [
            2.1824133074284023e-15,
            1.5019832583595862e-14,
            -0.06293975282460142
          ],
          [
            -1.1691705528969492e-15,
            6.238868699647465e-15,
            -0.0734267744301448
          ],
          [
            8.861894692297491e-16,
            8.15810011525741e-15,
            -0.08391382902838292
          ]
        ],
        "gauge_integer_shift": [
          0,
          0,
          0
        ],
        "expected_opposite_endpoint_reduced_polarization": [
          -3.640473331325163e-16,
          1.7826402094031932e-14,
          -0.08406872940803514
        ],
        "actual_opposite_endpoint_branch_residual": 0.0001549003796522258
      },
      "pnp_branch": {
        "construction": "incoming_path_concatenated_with_parent_reflection",
        "reduced_polarization": [
          [
            -2.0470246473716905e-16,
            -1.3889498820603326e-15,
            0.08402752923463505
          ],
          [
            -1.1030096243326679e-15,
            -1.7656553268423612e-15,
            0.07352329755599159
          ],
          [
            -2.721083517538225e-15,
            -6.602723011976615e-15,
            0.06301847520412637
          ],
          [
            4.919456981813185e-15,
            3.3675642252396953e-15,
            0.052513102595633396
          ],
          [
            -1.663071013822155e-15,
            -7.44639687815058e-17,
            0.04200722017557786
          ],
          [
            -9.512369093911331e-16,
            1.171855762638341e-15,
            0.03150086841638491
          ],
          [
            1.985094186250454e-15,
            3.594266785496066e-16,
            0.020994087816794047
          ],
          [
            1.2468386844806773e-15,
            4.1088011527926944e-15,
            0.01048691890084788
          ],
          [
            -2.8434810739395024e-16,
            8.218499515264579e-15,
            -2.0597783225597882e-05
          ],
          [
            1.5205553679141956e-15,
            4.11090091610906e-15,
            -0.010506565764322792
          ],
          [
            -3.553571349176445e-15,
            1.470911414445028e-14,
            -0.020992811220460664
          ],
          [
            4.007840952774258e-15,
            1.284541799375918e-14,
            -0.03147929340355929
          ],
          [
            2.8859746319919454e-15,
            8.69912076356578e-15,
            -0.04196597156447823
          ],
          [
            2.986401741274937e-15,
            1.1421692385520745e-14,
            -0.05245280495414996
          ],
          [
            2.1824133074284023e-15,
            1.5019832583595862e-14,
            -0.06293975282460142
          ],
          [
            -1.1691705528969494e-15,
            6.238868699647465e-15,
            -0.0734267744301448
          ],
          [
            8.861894692297493e-16,
            8.15810011525741e-15,
            -0.08391382902838292
          ]
        ],
        "unwrapped_reduced_polarization": [
          [
            -2.0470246473716905e-16,
            -1.3889498820603326e-15,
            0.08402752923463505
          ],
          [
            -1.1030096243326679e-15,
            -1.7656553268423612e-15,
            0.07352329755599159
          ],
          [
            -2.721083517538225e-15,
            -6.602723011976615e-15,
            0.06301847520412637
          ],
          [
            4.919456981813185e-15,
            3.367564225239696e-15,
            0.052513102595633396
          ],
          [
            -1.6630710138221552e-15,
            -7.446396878150583e-17,
            0.04200722017557786
          ],
          [
            -9.512369093911331e-16,
            1.171855762638341e-15,
            0.03150086841638491
          ],
          [
            1.9850941862504535e-15,
            3.5942667854960666e-16,
            0.020994087816794047
          ],
          [
            1.2468386844806773e-15,
            4.1088011527926944e-15,
            0.01048691890084788
          ],
          [
            -2.843481073939502e-16,
            8.218499515264579e-15,
            -2.0597783225597896e-05
          ],
          [
            1.5205553679141954e-15,
            4.11090091610906e-15,
            -0.010506565764322792
          ],
          [
            -3.553571349176445e-15,
            1.470911414445028e-14,
            -0.020992811220460664
          ],
          [
            4.007840952774258e-15,
            1.284541799375918e-14,
            -0.03147929340355929
          ],
          [
            2.8859746319919454e-15,
            8.69912076356578e-15,
            -0.04196597156447823
          ],
          [
            2.986401741274937e-15,
            1.1421692385520745e-14,
            -0.05245280495414996
          ],
          [
            2.1824133074284023e-15,
            1.5019832583595862e-14,
            -0.06293975282460142
          ],
          [
            -1.1691705528969492e-15,
            6.238868699647465e-15,
            -0.0734267744301448
          ],
          [
            8.861894692297491e-16,
            8.15810011525741e-15,
            -0.08391382902838292
          ]
        ],
        "berry_integer_shifts": [
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ]
        ],
        "folded_reduced_polarization": [
          [
            -2.220446049250313e-16,
            -1.3877787807814457e-15,
            0.08402752923463508
          ],
          [
            -1.1102230246251565e-15,
            -1.7763568394002505e-15,
            0.07352329755599163
          ],
          [
            -2.7200464103316335e-15,
            -6.6058269965196814e-15,
            0.0630184752041264
          ],
          [
            4.884981308350689e-15,
            3.3306690738754696e-15,
            0.052513102595633354
          ],
          [
            -1.6653345369377348e-15,
            -5.551115123125783e-17,
            0.0420072201755779
          ],
          [
            -9.43689570931383e-16,
            1.2212453270876722e-15,
            0.031500868416384886
          ],
          [
            1.9984014443252818e-15,
            3.3306690738754696e-16,
            0.020994087816794016
          ],
          [
            1.2212453270876722e-15,
            4.107825191113079e-15,
            0.010486918900847852
          ],
          [
            -2.7755575615628914e-16,
            8.215650382226158e-15,
            -2.059778322560657e-05
          ],
          [
            1.5543122344752192e-15,
            4.107825191113079e-15,
            -0.010506565764322795
          ],
          [
            -3.552713678800501e-15,
            1.4654943925052066e-14,
            -0.02099281122046065
          ],
          [
            3.9968028886505635e-15,
            1.2878587085651816e-14,
            -0.03147929340355926
          ],
          [
            2.886579864025407e-15,
            8.659739592076221e-15,
            -0.04196597156447823
          ],
          [
            2.9976021664879227e-15,
            1.1435297153639112e-14,
            -0.052452804954149945
          ],
          [
            2.220446049250313e-15,
            1.4988010832439613e-14,
            -0.0629397528246014
          ],
          [
            -1.1657341758564144e-15,
            6.217248937900877e-15,
            -0.07342677443014478
          ],
          [
            8.881784197001252e-16,
            8.104628079763643e-15,
            -0.0839138290283829
          ]
        ]
      },
      "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": "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": 2.059778323365479e-05,
        "parent_symmetrization_rmsd_A": 0.0022388543353353695,
        "parent_cell_rmsd_A": 0.0008686126947571338,
        "energy_eV": -596.7823848069144,
        "reduced_polarization": [
          1.7219066122687932e-15,
          2.865390589428593e-15,
          -2.059778323365479e-05
        ],
        "cartesian_polarization_e_A2": [
          1.605373010328448e-17,
          2.6275219831822e-17,
          -1.834116448921208e-07
        ],
        "ranking_score": 0.502497203075492
      }
    }
  ],
  "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": 47,
      "full_response": 15,
      "energy_polarization": 32
    },
    "model_evaluations_for_recovery_and_path_properties": {
      "total": 72,
      "full_response": 40,
      "energy_polarization": 32
    },
    "elapsed_seconds": 1304.9490520189865
  }
}
