{
  "schema": "ferrofinder.endpoint_parent_recovery.v4_variable_cell",
  "status": "complete",
  "input_atom_count": 80,
  "input_formula": "N44Si24Y12",
  "input_spacegroup": "P4bm",
  "input_pointgroup": "4mm",
  "input_is_polar_point_group": true,
  "input_energy_eV": -662.2728113172923,
  "input_cartesian_polarization_e_A2": [
    3.498818210515769e-08,
    -8.486321376082243e-11,
    -0.005790248794704333
  ],
  "input_reduced_polarization": [
    2.410050180953962e-06,
    -5.845533873863524e-09,
    -1.1497131937567364
  ],
  "input_formal_targets": [
    {
      "orbit_id": 0,
      "representative_formal_class": [
        0.0,
        0.0,
        0.0
      ],
      "target_reduced_polarization": [
        0.0,
        0.0,
        -1.0
      ]
    },
    {
      "orbit_id": 1,
      "representative_formal_class": [
        0.0,
        0.0,
        0.5
      ],
      "target_reduced_polarization": [
        0.0,
        0.0,
        -1.5
      ]
    },
    {
      "orbit_id": 2,
      "representative_formal_class": [
        0.5,
        0.0,
        0.0
      ],
      "target_reduced_polarization": [
        0.5,
        0.0,
        -1.0
      ]
    },
    {
      "orbit_id": 3,
      "representative_formal_class": [
        0.5,
        0.0,
        0.5
      ],
      "target_reduced_polarization": [
        0.5,
        0.0,
        -1.5
      ]
    },
    {
      "orbit_id": 4,
      "representative_formal_class": [
        0.5,
        0.5,
        0.0
      ],
      "target_reduced_polarization": [
        0.5,
        -0.5,
        -1.0
      ]
    },
    {
      "orbit_id": 5,
      "representative_formal_class": [
        0.5,
        0.5,
        0.5
      ],
      "target_reduced_polarization": [
        0.5,
        -0.5,
        -1.5
      ]
    }
  ],
  "parent_candidates": [
    {
      "candidate_id": "inversion_parent_endpoint_00",
      "source": "same_species_inversion_center_projection_from_endpoint",
      "spacegroup": "P4/mbm",
      "spacegroup_number": 127,
      "pointgroup": "4/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": 1.730309240443814e-14,
      "parent_symmetrization_rmsd_A": 0.6921888318754509,
      "parent_cell_rmsd_A": 0.0,
      "energy_eV": -604.8633308788264,
      "reduced_polarization": [
        1.0681781688540798e-14,
        1.3612266693792474e-14,
        -5.236575166450328e-17
      ],
      "cartesian_polarization_e_A2": [
        1.5507400048337148e-16,
        1.9761765531283009e-16,
        -2.637272774685856e-19
      ],
      "ranking_score": 0.6921888318754855
    },
    {
      "candidate_id": "bec_projection_00",
      "source": "MACEField_BEC_backprojection",
      "spacegroup": "P4bm",
      "spacegroup_number": 100,
      "pointgroup": "4mm",
      "has_inversion": false,
      "is_polar_point_group": true,
      "nonpolar_parent_hypothesis": false,
      "symmetry_tolerance_A": null,
      "target_reduced_polarization": [
        0.0,
        0.0,
        -1.0
      ],
      "formal_class": [
        0.0,
        0.0,
        0.0
      ],
      "target_residual": 0.00048256575899662544,
      "parent_symmetrization_rmsd_A": 0.0032047630158849563,
      "parent_cell_rmsd_A": 0.008526957764424038,
      "energy_eV": -662.287422945732,
      "reduced_polarization": [
        -5.573662668765394e-09,
        1.2423588549484047e-11,
        -1.0004825657589644
      ],
      "cartesian_polarization_e_A2": [
        -1.9722982557497968e-10,
        4.4310079666600937e-13,
        -0.005043891527152815
      ],
      "ranking_score": 0.5063016339749842
    },
    {
      "candidate_id": "inversion_parent_bec_00_00",
      "source": "same_species_inversion_center_projection_after_BEC",
      "spacegroup": "P4/mbm",
      "spacegroup_number": 127,
      "pointgroup": "4/mmm",
      "has_inversion": true,
      "is_polar_point_group": false,
      "nonpolar_parent_hypothesis": true,
      "symmetry_tolerance_A": null,
      "target_reduced_polarization": [
        0.0,
        0.0,
        -1.0
      ],
      "formal_class": [
        0.0,
        0.0,
        0.0
      ],
      "target_residual": 1.0260964113495672e-14,
      "parent_symmetrization_rmsd_A": 0.6921888648702684,
      "parent_cell_rmsd_A": 0.008526957764424038,
      "energy_eV": -604.3978230262303,
      "reduced_polarization": [
        3.5867379752521606e-16,
        5.827867615965427e-15,
        8.439138687263443e-15
      ],
      "cartesian_polarization_e_A2": [
        5.200162149881392e-18,
        8.449418685262334e-17,
        4.254556920221529e-17
      ],
      "ranking_score": 0.694320604311395
    },
    {
      "candidate_id": "bec_projection_01",
      "source": "MACEField_BEC_backprojection",
      "spacegroup": "P4bm",
      "spacegroup_number": 100,
      "pointgroup": "4mm",
      "has_inversion": false,
      "is_polar_point_group": true,
      "nonpolar_parent_hypothesis": false,
      "symmetry_tolerance_A": null,
      "target_reduced_polarization": [
        0.0,
        0.0,
        -1.5
      ],
      "formal_class": [
        0.0,
        0.0,
        0.5
      ],
      "target_residual": 1.0863706107373175e-05,
      "parent_symmetrization_rmsd_A": 0.0074875272057225335,
      "parent_cell_rmsd_A": 0.01982188301712359,
      "energy_eV": -662.1237328047603,
      "reduced_polarization": [
        1.1708222188175983e-11,
        5.845367222507864e-16,
        -1.4999891362938926
      ],
      "cartesian_polarization_e_A2": [
        -1.68817500562061e-10,
        4.778946892144918e-13,
        -0.007536233077433417
      ],
      "ranking_score": 0.5124647253722182
    },
    {
      "candidate_id": "bec_projection_02",
      "source": "MACEField_BEC_backprojection",
      "spacegroup": "Cm",
      "spacegroup_number": 8,
      "pointgroup": "m",
      "has_inversion": false,
      "is_polar_point_group": true,
      "nonpolar_parent_hypothesis": false,
      "symmetry_tolerance_A": null,
      "target_reduced_polarization": [
        0.5,
        0.0,
        -1.0
      ],
      "formal_class": [
        0.5,
        0.0,
        0.0
      ],
      "target_residual": 1.6349419971755606e-05,
      "parent_symmetrization_rmsd_A": 0.041502235659489864,
      "parent_cell_rmsd_A": 0.027035900169439117,
      "energy_eV": -661.1793727190218,
      "reduced_polarization": [
        0.49998479396026596,
        -1.6068559367309263e-13,
        -0.999993993346271
      ],
      "cartesian_polarization_e_A2": [
        0.0072738721588669125,
        4.1871329817720627e-13,
        -0.005075289648591712
      ],
      "ranking_score": 0.5482939095417931
    },
    {
      "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": [
        0.5,
        0.0,
        -1.5
      ],
      "formal_class": [
        0.5,
        0.0,
        0.5
      ],
      "target_residual": 4.3427316962470555e-05,
      "parent_symmetrization_rmsd_A": 0.04226705679154945,
      "parent_cell_rmsd_A": 0.033409375486832656,
      "energy_eV": -661.0281598587248,
      "reduced_polarization": [
        0.49998200408510285,
        -2.859576026437647e-13,
        -1.5000395231439232
      ],
      "cartesian_polarization_e_A2": [
        0.007318191695009063,
        6.361087511572749e-13,
        -0.007570352186425305
      ],
      "ranking_score": 0.5507062552971825
    },
    {
      "candidate_id": "bec_projection_04",
      "source": "MACEField_BEC_backprojection",
      "spacegroup": "Pc",
      "spacegroup_number": 7,
      "pointgroup": "m",
      "has_inversion": false,
      "is_polar_point_group": true,
      "nonpolar_parent_hypothesis": false,
      "symmetry_tolerance_A": null,
      "target_reduced_polarization": [
        0.5,
        -0.5,
        -1.0
      ],
      "formal_class": [
        0.5,
        0.5,
        0.0
      ],
      "target_residual": 4.6772750966832216e-05,
      "parent_symmetrization_rmsd_A": 0.058615661070073946,
      "parent_cell_rmsd_A": 0.03730214541333417,
      "energy_eV": -660.0633502037492,
      "reduced_polarization": [
        0.4999685853629595,
        -0.4999685851798867,
        -1.000014626000474
      ],
      "cartesian_polarization_e_A2": [
        0.007274799722212135,
        -0.007274799555522038,
        -0.0051092402790510315
      ],
      "ranking_score": 0.5680347429253412
    },
    {
      "candidate_id": "bec_projection_05",
      "source": "MACEField_BEC_backprojection",
      "spacegroup": "Pc",
      "spacegroup_number": 7,
      "pointgroup": "m",
      "has_inversion": false,
      "is_polar_point_group": true,
      "nonpolar_parent_hypothesis": false,
      "symmetry_tolerance_A": null,
      "target_reduced_polarization": [
        0.5,
        -0.5,
        -1.5
      ],
      "formal_class": [
        0.5,
        0.5,
        0.5
      ],
      "target_residual": 0.0001286911918366049,
      "parent_symmetrization_rmsd_A": 0.0593168067328845,
      "parent_cell_rmsd_A": 0.04293406108298026,
      "energy_eV": -659.924435906486,
      "reduced_polarization": [
        0.4999648402055646,
        -0.4999648401119487,
        -1.5001186970681348
      ],
      "cartesian_polarization_e_A2": [
        0.0073191134451355945,
        -0.007319113329945339,
        -0.007604614175183266
      ],
      "ranking_score": 0.5703077043873028
    }
  ],
  "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,
        -1.0
      ],
      "bec_backprojection": {
        "converged_to_target": true,
        "history": [
          {
            "iteration": 0,
            "reduced_polarization": [
              2.410050180953962e-06,
              -5.845533873863524e-09,
              -1.1497131937567364
            ],
            "branch_aligned_reduced_polarization": [
              2.410050180953962e-06,
              -5.845533873863524e-09,
              -1.1497131937567364
            ],
            "target_residual": 0.14971319377613476,
            "energy_eV": -662.2728113172923,
            "max_atomic_step_A": 0.002670782576652799,
            "max_log_strain_component": 0.0018475752662717314,
            "step_scale": 1.0,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 15.443197682181713,
            "cell_principal_stretches": [
              1.001849283085293,
              0.9994837746218318,
              0.9994837746198466
            ],
            "cell_volume_ratio": 1.0008151900147026,
            "cell_rmsd_from_input_A": 0.008526957764424038
          },
          {
            "iteration": 1,
            "reduced_polarization": [
              -5.573662668765394e-09,
              1.2423588549484047e-11,
              -1.0004825657589644
            ],
            "branch_aligned_reduced_polarization": [
              -5.573662668765394e-09,
              1.2423588549484047e-11,
              -1.0004825657589644
            ],
            "target_residual": 0.00048256575899662544,
            "energy_eV": -662.287422945732
          }
        ],
        "iterations": 1
      },
      "parent": {
        "candidate_id": "bec_projection_00",
        "source": "MACEField_BEC_backprojection",
        "spacegroup": "P4bm",
        "spacegroup_number": 100,
        "pointgroup": "4mm",
        "has_inversion": false,
        "is_polar_point_group": true,
        "nonpolar_parent_hypothesis": false,
        "symmetry_tolerance_A": null,
        "target_reduced_polarization": [
          0.0,
          0.0,
          -1.0
        ],
        "formal_class": [
          0.0,
          0.0,
          0.0
        ],
        "target_residual": 0.00048256575899662544,
        "parent_symmetrization_rmsd_A": 0.0032047630158849563,
        "parent_cell_rmsd_A": 0.008526957764424038,
        "energy_eV": -662.287422945732,
        "reduced_polarization": [
          -5.573662668765394e-09,
          1.2423588549484047e-11,
          -1.0004825657589644
        ],
        "cartesian_polarization_e_A2": [
          -1.9722982557497968e-10,
          4.4310079666600937e-13,
          -0.005043891527152815
        ],
        "ranking_score": 0.5063016339749842
      },
      "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": [
          -662.2728113172923,
          -662.2762295100911,
          -662.2791899006013,
          -662.2816940038263,
          -662.2837433306073,
          -662.2853393876492,
          -662.2864836775376,
          -662.2871776987614,
          -662.2874229457321
        ],
        "cartesian_polarizations_e_A2": [
          [
            3.4988182081044444e-08,
            -8.486321251776312e-11,
            -0.005790248794704315
          ],
          [
            3.058850003982703e-08,
            -7.419518151609253e-11,
            -0.005696892733331807
          ],
          [
            2.6189249392617665e-08,
            -6.352859952541833e-11,
            -0.005603554284228543
          ],
          [
            2.179042962456172e-08,
            -5.28633441546191e-11,
            -0.005510233412818276
          ],
          [
            1.7392040103082924e-08,
            -4.219942902682338e-11,
            -0.005416930084753412
          ],
          [
            1.2994080213546194e-08,
            -3.153688645957543e-11,
            -0.005323644265917566
          ],
          [
            8.596549088304501e-09,
            -2.0875567582037825e-11,
            -0.005230375922428312
          ],
          [
            4.199446093192534e-09,
            -1.0215603058806203e-11,
            -0.005137125020641105
          ],
          [
            -1.972298550687565e-10,
            4.430655472908744e-13,
            -0.005043891527152679
          ]
        ],
        "raw_reduced_polarization": [
          [
            2.4100501792929974e-06,
            -5.845533788239318e-09,
            -1.1497131937567329
          ],
          [
            2.108476193729027e-06,
            -5.114111287388514e-09,
            -1.131030377990576
          ],
          [
            1.806794013083952e-06,
            -4.3824603650136775e-09,
            -1.1123558624671854
          ],
          [
            1.505003599982096e-06,
            -3.650572594252041e-09,
            -1.0936896380409367
          ],
          [
            1.203104908880985e-06,
            -2.918448917714583e-09,
            -1.0750316956156352
          ],
          [
            9.010978954173004e-07,
            -2.186091567353184e-09,
            -1.0563820261449994
          ],
          [
            5.98982497725725e-07,
            -1.4534902834866258e-09,
            -1.0377406206331659
          ],
          [
            2.967586699742879e-07,
            -7.206540768957492e-10,
            -1.0191074701354388
          ],
          [
            -5.573664703057357e-09,
            1.2421157273446756e-11,
            -1.0004825657589371
          ]
        ],
        "unwrapped_reduced_polarization": [
          [
            2.4100501792929974e-06,
            -5.845533788239318e-09,
            -1.1497131937567329
          ],
          [
            2.108476193729027e-06,
            -5.114111287388514e-09,
            -1.131030377990576
          ],
          [
            1.806794013083952e-06,
            -4.3824603650136775e-09,
            -1.1123558624671854
          ],
          [
            1.505003599982096e-06,
            -3.650572594252041e-09,
            -1.0936896380409367
          ],
          [
            1.203104908880985e-06,
            -2.918448917714583e-09,
            -1.0750316956156352
          ],
          [
            9.010978954173004e-07,
            -2.186091567353184e-09,
            -1.0563820261449994
          ],
          [
            5.98982497725725e-07,
            -1.4534902834866258e-09,
            -1.0377406206331659
          ],
          [
            2.967586699742879e-07,
            -7.206540768957492e-10,
            -1.0191074701354388
          ],
          [
            -5.573664703057377e-09,
            1.2421157273446791e-11,
            -1.0004825657589371
          ]
        ],
        "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": [
          [
            2.4100501793133944e-06,
            -5.845533779247347e-09,
            -0.14971319375673287
          ],
          [
            2.1084761937517627e-06,
            -5.114111301107727e-09,
            -0.13103037799057593
          ],
          [
            1.8067940130706006e-06,
            -4.382460339069638e-09,
            -0.11235586246718543
          ],
          [
            1.5050035999664146e-06,
            -3.6505726219715484e-09,
            -0.09368963804093666
          ],
          [
            1.2031049089200607e-06,
            -2.9184489269695746e-09,
            -0.07503169561563516
          ],
          [
            9.010978954115956e-07,
            -2.1860915855320684e-09,
            -0.05638202614499943
          ],
          [
            5.98982497712619e-07,
            -1.4534902725849008e-09,
            -0.037740620633165856
          ],
          [
            2.9675866997092015e-07,
            -7.206540919568738e-10,
            -0.019107470135438787
          ],
          [
            -5.5736646964454906e-09,
            1.2421175199506251e-11,
            -0.0004825657589371257
          ]
        ]
      },
      "reflected": {
        "reached": true,
        "construction": "reflect_displacements_about_reconstructed_parent",
        "energies_eV": [
          -662.2874229457323,
          -662.2807999234542,
          -662.273988994124,
          -662.2669905685633,
          -662.2598050578625,
          -662.2524328732652,
          -662.2448744260513,
          -662.2371301274326,
          -662.2292003884489
        ],
        "cartesian_polarizations_e_A2": [
          [
            -1.9722982732860578e-10,
            4.430680358350793e-13,
            -0.0050438915271528
          ],
          [
            -4.486472484424814e-09,
            1.0837922524262767e-11,
            -0.00498755917065917
          ],
          [
            -8.778350418765585e-09,
            2.1239252604963188e-11,
            -0.004931286463899015
          ],
          [
            -1.3072860801071724e-08,
            3.1647072758082906e-11,
            -0.004875073906843877
          ],
          [
            -1.7370000532633464e-08,
            4.206143003679935e-11,
            -0.004818922002698951
          ],
          [
            -2.1669767323852817e-08,
            5.248224907580676e-11,
            -0.004762831257669809
          ],
          [
            -2.5972158291605068e-08,
            6.290978617449768e-11,
            -0.004706802180728563
          ],
          [
            -3.0277170668664744e-08,
            7.334350073079938e-11,
            -0.004650835283382564
          ],
          [
            -3.4584801783068885e-08,
            8.378389766953321e-11,
            -0.004594931079445719
          ]
        ],
        "raw_reduced_polarization": [
          [
            -5.573662789719311e-09,
            1.2421328917280324e-11,
            -1.000482565758961
          ],
          [
            -3.0244900002202893e-07,
            7.317122233545144e-10,
            -0.9894364626397127
          ],
          [
            -5.99385076477623e-07,
            1.4511602463385608e-09,
            -0.978399325681801
          ],
          [
            -8.963816673735338e-07,
            2.1707662364568965e-09,
            -0.9673712581226243
          ],
          [
            -1.1934385299018237e-06,
            2.890533356306099e-09,
            -0.9563523638936464
          ],
          [
            -1.4905554775773808e-06,
            3.6104563306573418e-09,
            -0.9453427475745226
          ],
          [
            -1.7877322835460266e-06,
            4.33055274197683e-09,
            -0.9343425143470788
          ],
          [
            -2.0849687294959606e-06,
            5.05078526077316e-09,
            -0.9233517699497701
          ],
          [
            -2.3822646042320417e-06,
            5.7711886011282865e-09,
            -0.9123706206326121
          ]
        ],
        "unwrapped_reduced_polarization": [
          [
            -5.573662789719311e-09,
            1.2421328917280324e-11,
            -1.000482565758961
          ],
          [
            -3.0244900002202893e-07,
            7.317122233545144e-10,
            -0.9894364626397127
          ],
          [
            -5.99385076477623e-07,
            1.4511602463385608e-09,
            -0.978399325681801
          ],
          [
            -8.963816673735338e-07,
            2.1707662364568965e-09,
            -0.9673712581226243
          ],
          [
            -1.1934385299018237e-06,
            2.890533356306099e-09,
            -0.9563523638936464
          ],
          [
            -1.4905554775773808e-06,
            3.6104563306573418e-09,
            -0.9453427475745226
          ],
          [
            -1.7877322835460266e-06,
            4.33055274197683e-09,
            -0.9343425143470788
          ],
          [
            -2.0849687294959606e-06,
            5.05078526077316e-09,
            -0.9233517699497701
          ],
          [
            -2.3822646042320417e-06,
            5.7711886011282865e-09,
            -0.9123706206326121
          ]
        ],
        "gauge_integer_shift": [
          0,
          0,
          0
        ],
        "expected_opposite_endpoint_reduced_polarization": [
          -2.4372212878958597e-06,
          5.906572123938698e-09,
          -0.8533194365333321
        ],
        "actual_opposite_endpoint_branch_residual": 0.059051184099305584
      },
      "pnp_branch": {
        "construction": "incoming_path_concatenated_with_parent_reflection",
        "reduced_polarization": [
          [
            2.4100501792929974e-06,
            -5.845533788239318e-09,
            -1.1497131937567329
          ],
          [
            2.108476193729027e-06,
            -5.114111287388514e-09,
            -1.131030377990576
          ],
          [
            1.806794013083952e-06,
            -4.3824603650136775e-09,
            -1.1123558624671854
          ],
          [
            1.505003599982096e-06,
            -3.650572594252041e-09,
            -1.0936896380409367
          ],
          [
            1.203104908880985e-06,
            -2.918448917714583e-09,
            -1.0750316956156352
          ],
          [
            9.010978954173004e-07,
            -2.186091567353184e-09,
            -1.0563820261449994
          ],
          [
            5.98982497725725e-07,
            -1.4534902834866258e-09,
            -1.0377406206331659
          ],
          [
            2.967586699742879e-07,
            -7.206540768957492e-10,
            -1.0191074701354388
          ],
          [
            -5.573664703057357e-09,
            1.2421157273446756e-11,
            -1.0004825657589371
          ],
          [
            -3.0244900002202893e-07,
            7.317122233545144e-10,
            -0.9894364626397127
          ],
          [
            -5.99385076477623e-07,
            1.4511602463385608e-09,
            -0.978399325681801
          ],
          [
            -8.963816673735338e-07,
            2.1707662364568965e-09,
            -0.9673712581226243
          ],
          [
            -1.1934385299018237e-06,
            2.890533356306099e-09,
            -0.9563523638936464
          ],
          [
            -1.4905554775773808e-06,
            3.6104563306573418e-09,
            -0.9453427475745226
          ],
          [
            -1.7877322835460266e-06,
            4.33055274197683e-09,
            -0.9343425143470788
          ],
          [
            -2.0849687294959606e-06,
            5.05078526077316e-09,
            -0.9233517699497701
          ],
          [
            -2.3822646042320417e-06,
            5.7711886011282865e-09,
            -0.9123706206326121
          ]
        ],
        "unwrapped_reduced_polarization": [
          [
            2.4100501792929974e-06,
            -5.845533788239318e-09,
            -1.1497131937567329
          ],
          [
            2.108476193729027e-06,
            -5.114111287388514e-09,
            -1.131030377990576
          ],
          [
            1.806794013083952e-06,
            -4.3824603650136775e-09,
            -1.1123558624671854
          ],
          [
            1.505003599982096e-06,
            -3.650572594252041e-09,
            -1.0936896380409367
          ],
          [
            1.203104908880985e-06,
            -2.918448917714583e-09,
            -1.0750316956156352
          ],
          [
            9.010978954173004e-07,
            -2.186091567353184e-09,
            -1.0563820261449994
          ],
          [
            5.98982497725725e-07,
            -1.4534902834866258e-09,
            -1.0377406206331659
          ],
          [
            2.967586699742879e-07,
            -7.206540768957492e-10,
            -1.0191074701354388
          ],
          [
            -5.573664703057377e-09,
            1.2421157273446791e-11,
            -1.0004825657589371
          ],
          [
            -3.0244900002202893e-07,
            7.317122233545144e-10,
            -0.9894364626397127
          ],
          [
            -5.99385076477623e-07,
            1.4511602463385608e-09,
            -0.978399325681801
          ],
          [
            -8.963816673735338e-07,
            2.1707662364568965e-09,
            -0.9673712581226243
          ],
          [
            -1.1934385299018237e-06,
            2.890533356306099e-09,
            -0.9563523638936464
          ],
          [
            -1.4905554775773808e-06,
            3.6104563306573418e-09,
            -0.9453427475745226
          ],
          [
            -1.7877322835460266e-06,
            4.33055274197683e-09,
            -0.9343425143470788
          ],
          [
            -2.0849687294959606e-06,
            5.05078526077316e-09,
            -0.9233517699497701
          ],
          [
            -2.3822646042320417e-06,
            5.7711886011282865e-09,
            -0.9123706206326121
          ]
        ],
        "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": [
          [
            2.4100501793133944e-06,
            -5.845533779247347e-09,
            -0.14971319375673287
          ],
          [
            2.1084761937517627e-06,
            -5.114111301107727e-09,
            -0.13103037799057593
          ],
          [
            1.8067940130706006e-06,
            -4.382460339069638e-09,
            -0.11235586246718543
          ],
          [
            1.5050035999664146e-06,
            -3.6505726219715484e-09,
            -0.09368963804093666
          ],
          [
            1.2031049089200607e-06,
            -2.9184489269695746e-09,
            -0.07503169561563516
          ],
          [
            9.010978954115956e-07,
            -2.1860915855320684e-09,
            -0.05638202614499943
          ],
          [
            5.98982497712619e-07,
            -1.4534902725849008e-09,
            -0.037740620633165856
          ],
          [
            2.9675866997092015e-07,
            -7.206540919568738e-10,
            -0.019107470135438787
          ],
          [
            -5.5736646964454906e-09,
            1.2421175199506251e-11,
            -0.0004825657589371257
          ],
          [
            -3.024490000114177e-07,
            7.317122463490477e-10,
            0.010563537360287256
          ],
          [
            -5.993850764607345e-07,
            1.4511601920119688e-09,
            0.02160067431819901
          ],
          [
            -8.963816673923652e-07,
            2.1707662334335964e-09,
            0.032628741877375744
          ],
          [
            -1.1934385298895123e-06,
            2.890533368216097e-09,
            0.04364763610635358
          ],
          [
            -1.4905554776012409e-06,
            3.6104563783112553e-09,
            0.054657252425477365
          ],
          [
            -1.7877322835424536e-06,
            4.3305526942205574e-09,
            0.06565748565292118
          ],
          [
            -2.084968729498815e-06,
            5.050785234494981e-09,
            0.07664823005022992
          ],
          [
            -2.3822646042503948e-06,
            5.7711886380928945e-09,
            0.0876293793673879
          ]
        ]
      },
      "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,
        -1.5
      ],
      "bec_backprojection": {
        "converged_to_target": true,
        "history": [
          {
            "iteration": 0,
            "reduced_polarization": [
              2.410050180953962e-06,
              -5.845533873863524e-09,
              -1.1497131937567364
            ],
            "branch_aligned_reduced_polarization": [
              2.410050180953962e-06,
              -5.845533873863524e-09,
              -1.1497131937567364
            ],
            "target_residual": 0.35028680625155445,
            "energy_eV": -662.2728113172923,
            "max_atomic_step_A": 0.006248880768317031,
            "max_log_strain_component": 0.004322806982086468,
            "step_scale": 1.0,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 15.443197682181713,
            "cell_principal_stretches": [
              1.0012088642870514,
              1.0012088642834684,
              0.9956865228993259
            ],
            "cell_volume_ratio": 0.9980952777023695,
            "cell_rmsd_from_input_A": 0.019971784163873078
          },
          {
            "iteration": 1,
            "reduced_polarization": [
              1.0453633726912293e-08,
              -3.1557966777674455e-11,
              -1.5026677095833727
            ],
            "branch_aligned_reduced_polarization": [
              1.0453633726912293e-08,
              -3.1557966777674455e-11,
              -1.5026677095833727
            ],
            "target_residual": 0.0026677095833931835,
            "energy_eV": -662.1219661829269,
            "max_atomic_step_A": 4.689077058887815e-05,
            "max_log_strain_component": 3.242150180206278e-05,
            "step_scale": 1.0,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 15.443197682181713,
            "cell_principal_stretches": [
              1.0011997922423754,
              1.0011997922388194,
              0.9957188050750361
            ],
            "cell_volume_ratio": 0.9981095498059629,
            "cell_rmsd_from_input_A": 0.01982188301712359
          },
          {
            "iteration": 2,
            "reduced_polarization": [
              1.1708222188175983e-11,
              5.845367222507864e-16,
              -1.4999891362938926
            ],
            "branch_aligned_reduced_polarization": [
              1.1708222188175983e-11,
              5.845367222507864e-16,
              -1.4999891362938926
            ],
            "target_residual": 1.0863706107373175e-05,
            "energy_eV": -662.1237328047603
          }
        ],
        "iterations": 2
      },
      "parent": {
        "candidate_id": "bec_projection_01",
        "source": "MACEField_BEC_backprojection",
        "spacegroup": "P4bm",
        "spacegroup_number": 100,
        "pointgroup": "4mm",
        "has_inversion": false,
        "is_polar_point_group": true,
        "nonpolar_parent_hypothesis": false,
        "symmetry_tolerance_A": null,
        "target_reduced_polarization": [
          0.0,
          0.0,
          -1.5
        ],
        "formal_class": [
          0.0,
          0.0,
          0.5
        ],
        "target_residual": 1.0863706107373175e-05,
        "parent_symmetrization_rmsd_A": 0.0074875272057225335,
        "parent_cell_rmsd_A": 0.01982188301712359,
        "energy_eV": -662.1237328047603,
        "reduced_polarization": [
          1.1708222188175983e-11,
          5.845367222507864e-16,
          -1.4999891362938926
        ],
        "cartesian_polarization_e_A2": [
          -1.68817500562061e-10,
          4.778946892144918e-13,
          -0.007536233077433417
        ],
        "ranking_score": 0.5124647253722182
      },
      "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
        ],
        [
          0.0,
          0.5,
          0.0
        ]
      ],
      "target_reduced_polarization": [
        0.5,
        0.0,
        -1.0
      ],
      "bec_backprojection": {
        "converged_to_target": true,
        "history": [
          {
            "iteration": 0,
            "reduced_polarization": [
              2.410050180953962e-06,
              -5.845533873863524e-09,
              -1.1497131937567364
            ],
            "branch_aligned_reduced_polarization": [
              2.410050180978729e-06,
              -5.845533873863524e-09,
              -1.1497131937567364
            ],
            "target_residual": 0.521930675799449,
            "energy_eV": -662.2728113172923,
            "max_atomic_step_A": 0.042485534350388425,
            "max_log_strain_component": 0.004741479960458302,
            "step_scale": 1.0,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 15.443197682181713,
            "cell_principal_stretches": [
              1.0055676285071167,
              0.9994837504785178,
              0.9957879265010067
            ],
            "cell_volume_ratio": 1.0008151665282317,
            "cell_rmsd_from_input_A": 0.02734001496419284
          },
          {
            "iteration": 1,
            "reduced_polarization": [
              0.5009182769586643,
              -2.5185881934113984e-12,
              -0.9842384504382897
            ],
            "branch_aligned_reduced_polarization": [
              0.5009182769586643,
              -2.5185881934113984e-12,
              -0.9842384504382897
            ],
            "target_residual": 0.015788276573428246,
            "energy_eV": -661.1746183368987,
            "max_atomic_step_A": 0.0002885109625979271,
            "max_log_strain_component": 0.0001949226091512461,
            "step_scale": 1.0,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 15.443197682181713,
            "cell_principal_stretches": [
              1.0054609362426385,
              0.9995382006768897,
              0.9957537330537015
            ],
            "cell_volume_ratio": 1.0007291311551847,
            "cell_rmsd_from_input_A": 0.027035900169439117
          },
          {
            "iteration": 2,
            "reduced_polarization": [
              0.49998479396026596,
              -1.6068559367309263e-13,
              -0.999993993346271
            ],
            "branch_aligned_reduced_polarization": [
              0.49998479396026596,
              -1.6068559367309263e-13,
              -0.999993993346271
            ],
            "target_residual": 1.6349419971755606e-05,
            "energy_eV": -661.1793727190218
          }
        ],
        "iterations": 2
      },
      "parent": {
        "candidate_id": "bec_projection_02",
        "source": "MACEField_BEC_backprojection",
        "spacegroup": "Cm",
        "spacegroup_number": 8,
        "pointgroup": "m",
        "has_inversion": false,
        "is_polar_point_group": true,
        "nonpolar_parent_hypothesis": false,
        "symmetry_tolerance_A": null,
        "target_reduced_polarization": [
          0.5,
          0.0,
          -1.0
        ],
        "formal_class": [
          0.5,
          0.0,
          0.0
        ],
        "target_residual": 1.6349419971755606e-05,
        "parent_symmetrization_rmsd_A": 0.041502235659489864,
        "parent_cell_rmsd_A": 0.027035900169439117,
        "energy_eV": -661.1793727190218,
        "reduced_polarization": [
          0.49998479396026596,
          -1.6068559367309263e-13,
          -0.999993993346271
        ],
        "cartesian_polarization_e_A2": [
          0.0072738721588669125,
          4.1871329817720627e-13,
          -0.005075289648591712
        ],
        "ranking_score": 0.5482939095417931
      },
      "branch_status": "awaiting_branch_sampling"
    },
    {
      "orbit_id": 3,
      "formal_class": [
        0.5,
        0.0,
        0.5
      ],
      "formal_classes_in_orbit": [
        [
          0.5,
          0.0,
          0.5
        ],
        [
          0.0,
          0.5,
          0.5
        ]
      ],
      "target_reduced_polarization": [
        0.5,
        0.0,
        -1.5
      ],
      "bec_backprojection": {
        "converged_to_target": true,
        "history": [
          {
            "iteration": 0,
            "reduced_polarization": [
              2.410050180953962e-06,
              -5.845533873863524e-09,
              -1.1497131937567364
            ],
            "branch_aligned_reduced_polarization": [
              2.410050180978729e-06,
              -5.845533873863524e-09,
              -1.1497131937567364
            ],
            "target_residual": 0.6104903247257347,
            "energy_eV": -662.2728113172923,
            "max_atomic_step_A": 0.04253326021254547,
            "max_log_strain_component": 0.0047414808100497054,
            "step_scale": 1.0,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 15.443197682181713,
            "cell_principal_stretches": [
              1.003939442172874,
              1.0012088400984835,
              0.992978392508061
            ],
            "cell_volume_ratio": 0.9980952542797278,
            "cell_rmsd_from_input_A": 0.032815037459719844
          },
          {
            "iteration": 1,
            "reduced_polarization": [
              0.4972852015454238,
              -4.7130027104899335e-11,
              -1.4864901162486435
            ],
            "branch_aligned_reduced_polarization": [
              0.4972852015454238,
              -4.7130027104899335e-11,
              -1.4864901162486435
            ],
            "target_residual": 0.01377995245362394,
            "energy_eV": -661.0484811020694,
            "max_atomic_step_A": 0.00030588491986839904,
            "max_log_strain_component": 0.00016743885216228245,
            "step_scale": 1.0,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 15.443197682181713,
            "cell_principal_stretches": [
              1.003957052268543,
              1.0012556932620662,
              0.992841188291138
            ],
            "cell_volume_ratio": 0.9980215500308607,
            "cell_rmsd_from_input_A": 0.033409375486832656
          },
          {
            "iteration": 2,
            "reduced_polarization": [
              0.49998200408510285,
              -2.859576026437647e-13,
              -1.5000395231439232
            ],
            "branch_aligned_reduced_polarization": [
              0.49998200408510285,
              -2.859576026437647e-13,
              -1.5000395231439232
            ],
            "target_residual": 4.3427316962470555e-05,
            "energy_eV": -661.0281598587248
          }
        ],
        "iterations": 2
      },
      "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": [
          0.5,
          0.0,
          -1.5
        ],
        "formal_class": [
          0.5,
          0.0,
          0.5
        ],
        "target_residual": 4.3427316962470555e-05,
        "parent_symmetrization_rmsd_A": 0.04226705679154945,
        "parent_cell_rmsd_A": 0.033409375486832656,
        "energy_eV": -661.0281598587248,
        "reduced_polarization": [
          0.49998200408510285,
          -2.859576026437647e-13,
          -1.5000395231439232
        ],
        "cartesian_polarization_e_A2": [
          0.007318191695009063,
          6.361087511572749e-13,
          -0.007570352186425305
        ],
        "ranking_score": 0.5507062552971825
      },
      "branch_status": "awaiting_branch_sampling"
    },
    {
      "orbit_id": 4,
      "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,
        -1.0
      ],
      "bec_backprojection": {
        "converged_to_target": true,
        "history": [
          {
            "iteration": 0,
            "reduced_polarization": [
              2.410050180953962e-06,
              -5.845533873863524e-09,
              -1.1497131937567364
            ],
            "branch_aligned_reduced_polarization": [
              2.410050180978729e-06,
              -5.84553389026965e-09,
              -1.1497131937567364
            ],
            "target_residual": 0.7227804815398211,
            "energy_eV": -662.2728113172923,
            "max_atomic_step_A": 0.04903143565615776,
            "max_log_strain_component": 0.00474150299883238,
            "step_scale": 1.0,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 15.443197682181713,
            "cell_principal_stretches": [
              1.0075024343259469,
              0.999483827143842,
              0.9938755409149407
            ],
            "cell_volume_ratio": 1.0008151664765383,
            "cell_rmsd_from_input_A": 0.03771494394956941
          },
          {
            "iteration": 1,
            "reduced_polarization": [
              0.5008998478716346,
              -0.5008997887683109,
              -0.9677289038492618
            ],
            "branch_aligned_reduced_polarization": [
              0.5008998478716346,
              -0.5008997887683109,
              -0.9677289038492618
            ],
            "target_residual": 0.0322961761326299,
            "energy_eV": -660.0525066173421,
            "max_atomic_step_A": 0.0005823300514432441,
            "max_log_strain_component": 0.0003996692566495417,
            "step_scale": 1.0,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 15.443197682181713,
            "cell_principal_stretches": [
              1.0073091424975178,
              0.9995954748667144,
              0.9937800349608308
            ],
            "cell_volume_ratio": 1.0006387675053745,
            "cell_rmsd_from_input_A": 0.03730214541333417
          },
          {
            "iteration": 2,
            "reduced_polarization": [
              0.4999685853629595,
              -0.4999685851798867,
              -1.000014626000474
            ],
            "branch_aligned_reduced_polarization": [
              0.4999685853629595,
              -0.4999685851798867,
              -1.000014626000474
            ],
            "target_residual": 4.6772750966832216e-05,
            "energy_eV": -660.0633502037492
          }
        ],
        "iterations": 2
      },
      "parent": {
        "candidate_id": "bec_projection_04",
        "source": "MACEField_BEC_backprojection",
        "spacegroup": "Pc",
        "spacegroup_number": 7,
        "pointgroup": "m",
        "has_inversion": false,
        "is_polar_point_group": true,
        "nonpolar_parent_hypothesis": false,
        "symmetry_tolerance_A": null,
        "target_reduced_polarization": [
          0.5,
          -0.5,
          -1.0
        ],
        "formal_class": [
          0.5,
          0.5,
          0.0
        ],
        "target_residual": 4.6772750966832216e-05,
        "parent_symmetrization_rmsd_A": 0.058615661070073946,
        "parent_cell_rmsd_A": 0.03730214541333417,
        "energy_eV": -660.0633502037492,
        "reduced_polarization": [
          0.4999685853629595,
          -0.4999685851798867,
          -1.000014626000474
        ],
        "cartesian_polarization_e_A2": [
          0.007274799722212135,
          -0.007274799555522038,
          -0.0051092402790510315
        ],
        "ranking_score": 0.5680347429253412
      },
      "branch_status": "awaiting_branch_sampling"
    },
    {
      "orbit_id": 5,
      "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,
        -1.5
      ],
      "bec_backprojection": {
        "converged_to_target": true,
        "history": [
          {
            "iteration": 0,
            "reduced_polarization": [
              2.410050180953962e-06,
              -5.845533873863524e-09,
              -1.1497131937567364
            ],
            "branch_aligned_reduced_polarization": [
              2.410050180978729e-06,
              -5.84553389026965e-09,
              -1.1497131937567364
            ],
            "target_residual": 0.7891124322542379,
            "energy_eV": -662.2728113172923,
            "max_atomic_step_A": 0.04935584028689878,
            "max_log_strain_component": 0.004741502988034072,
            "step_scale": 1.0,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 15.443197682181713,
            "cell_principal_stretches": [
              1.005712235460557,
              1.001208916898692,
              0.9912279693876092
            ],
            "cell_volume_ratio": 0.9980952542281749,
            "cell_rmsd_from_input_A": 0.04189220819477805
          },
          {
            "iteration": 1,
            "reduced_polarization": [
              0.49725124738041393,
              -0.4972511768438796,
              -1.470038485572887
            ],
            "branch_aligned_reduced_polarization": [
              0.49725124738041393,
              -0.4972511768438796,
              -1.470038485572887
            ],
            "target_residual": 0.030212646631392746,
            "energy_eV": -659.9661840366127,
            "max_atomic_step_A": 0.0005976123015217615,
            "max_log_strain_component": 0.000371238484692445,
            "step_scale": 1.0,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 15.443197682181713,
            "cell_principal_stretches": [
              1.0057093713545096,
              1.0013128014083335,
              0.9909656878598616
            ],
            "cell_volume_ratio": 0.9979318476782025,
            "cell_rmsd_from_input_A": 0.04293406108298026
          },
          {
            "iteration": 2,
            "reduced_polarization": [
              0.4999648402055646,
              -0.4999648401119487,
              -1.5001186970681348
            ],
            "branch_aligned_reduced_polarization": [
              0.4999648402055646,
              -0.4999648401119487,
              -1.5001186970681348
            ],
            "target_residual": 0.0001286911918366049,
            "energy_eV": -659.924435906486
          }
        ],
        "iterations": 2
      },
      "parent": {
        "candidate_id": "bec_projection_05",
        "source": "MACEField_BEC_backprojection",
        "spacegroup": "Pc",
        "spacegroup_number": 7,
        "pointgroup": "m",
        "has_inversion": false,
        "is_polar_point_group": true,
        "nonpolar_parent_hypothesis": false,
        "symmetry_tolerance_A": null,
        "target_reduced_polarization": [
          0.5,
          -0.5,
          -1.5
        ],
        "formal_class": [
          0.5,
          0.5,
          0.5
        ],
        "target_residual": 0.0001286911918366049,
        "parent_symmetrization_rmsd_A": 0.0593168067328845,
        "parent_cell_rmsd_A": 0.04293406108298026,
        "energy_eV": -659.924435906486,
        "reduced_polarization": [
          0.4999648402055646,
          -0.4999648401119487,
          -1.5001186970681348
        ],
        "cartesian_polarization_e_A2": [
          0.0073191134451355945,
          -0.007319113329945339,
          -0.007604614175183266
        ],
        "ranking_score": 0.5703077043873028
      },
      "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,
          76,
          77,
          78,
          79
        ],
        "endpoint_rmsd_A": 0.0032047630158849563,
        "minimum_distance_A_by_image": [
          1.6852475600664438,
          1.685126666551771,
          1.685005838994871,
          1.6848850775189232,
          1.6847643822472356,
          1.6846437533032603,
          1.6845231908105807,
          1.6844026948929127,
          1.684282265674115
        ],
        "minimum_distance_A": 1.684282265674115,
        "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": [
          970.6236125616406,
          970.7224826400699,
          970.8213627896473,
          970.9202530113969,
          971.0191533063428,
          971.1180636755139,
          971.2169841199362,
          971.3159146406344,
          971.4148552386349
        ],
        "cell_deformation_log_strain_norm": 0.0019866521880321196
      },
      "parent_reduced_polarization": [
        -5.573664703057357e-09,
        1.2421157273446756e-11,
        -1.0004825657589371
      ],
      "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": [
          -662.2728113172923,
          -662.2762295100911,
          -662.2791899006013,
          -662.2816940038263,
          -662.2837433306073,
          -662.2853393876492,
          -662.2864836775376,
          -662.2871776987614,
          -662.2874229457321
        ],
        "cartesian_polarizations_e_A2": [
          [
            3.4988182081044444e-08,
            -8.486321251776312e-11,
            -0.005790248794704315
          ],
          [
            3.058850003982703e-08,
            -7.419518151609253e-11,
            -0.005696892733331807
          ],
          [
            2.6189249392617665e-08,
            -6.352859952541833e-11,
            -0.005603554284228543
          ],
          [
            2.179042962456172e-08,
            -5.28633441546191e-11,
            -0.005510233412818276
          ],
          [
            1.7392040103082924e-08,
            -4.219942902682338e-11,
            -0.005416930084753412
          ],
          [
            1.2994080213546194e-08,
            -3.153688645957543e-11,
            -0.005323644265917566
          ],
          [
            8.596549088304501e-09,
            -2.0875567582037825e-11,
            -0.005230375922428312
          ],
          [
            4.199446093192534e-09,
            -1.0215603058806203e-11,
            -0.005137125020641105
          ],
          [
            -1.972298550687565e-10,
            4.430655472908744e-13,
            -0.005043891527152679
          ]
        ],
        "raw_reduced_polarization": [
          [
            2.4100501792929974e-06,
            -5.845533788239318e-09,
            -1.1497131937567329
          ],
          [
            2.108476193729027e-06,
            -5.114111287388514e-09,
            -1.131030377990576
          ],
          [
            1.806794013083952e-06,
            -4.3824603650136775e-09,
            -1.1123558624671854
          ],
          [
            1.505003599982096e-06,
            -3.650572594252041e-09,
            -1.0936896380409367
          ],
          [
            1.203104908880985e-06,
            -2.918448917714583e-09,
            -1.0750316956156352
          ],
          [
            9.010978954173004e-07,
            -2.186091567353184e-09,
            -1.0563820261449994
          ],
          [
            5.98982497725725e-07,
            -1.4534902834866258e-09,
            -1.0377406206331659
          ],
          [
            2.967586699742879e-07,
            -7.206540768957492e-10,
            -1.0191074701354388
          ],
          [
            -5.573664703057357e-09,
            1.2421157273446756e-11,
            -1.0004825657589371
          ]
        ],
        "unwrapped_reduced_polarization": [
          [
            2.4100501792929974e-06,
            -5.845533788239318e-09,
            -1.1497131937567329
          ],
          [
            2.108476193729027e-06,
            -5.114111287388514e-09,
            -1.131030377990576
          ],
          [
            1.806794013083952e-06,
            -4.3824603650136775e-09,
            -1.1123558624671854
          ],
          [
            1.505003599982096e-06,
            -3.650572594252041e-09,
            -1.0936896380409367
          ],
          [
            1.203104908880985e-06,
            -2.918448917714583e-09,
            -1.0750316956156352
          ],
          [
            9.010978954173004e-07,
            -2.186091567353184e-09,
            -1.0563820261449994
          ],
          [
            5.98982497725725e-07,
            -1.4534902834866258e-09,
            -1.0377406206331659
          ],
          [
            2.967586699742879e-07,
            -7.206540768957492e-10,
            -1.0191074701354388
          ],
          [
            -5.573664703057377e-09,
            1.2421157273446791e-11,
            -1.0004825657589371
          ]
        ],
        "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": [
          [
            2.4100501793133944e-06,
            -5.845533779247347e-09,
            -0.14971319375673287
          ],
          [
            2.1084761937517627e-06,
            -5.114111301107727e-09,
            -0.13103037799057593
          ],
          [
            1.8067940130706006e-06,
            -4.382460339069638e-09,
            -0.11235586246718543
          ],
          [
            1.5050035999664146e-06,
            -3.6505726219715484e-09,
            -0.09368963804093666
          ],
          [
            1.2031049089200607e-06,
            -2.9184489269695746e-09,
            -0.07503169561563516
          ],
          [
            9.010978954115956e-07,
            -2.1860915855320684e-09,
            -0.05638202614499943
          ],
          [
            5.98982497712619e-07,
            -1.4534902725849008e-09,
            -0.037740620633165856
          ],
          [
            2.9675866997092015e-07,
            -7.206540919568738e-10,
            -0.019107470135438787
          ],
          [
            -5.5736646964454906e-09,
            1.2421175199506251e-11,
            -0.0004825657589371257
          ]
        ]
      },
      "reflected": {
        "reached": true,
        "construction": "reflect_displacements_about_reconstructed_parent",
        "energies_eV": [
          -662.2874229457323,
          -662.2807999234542,
          -662.273988994124,
          -662.2669905685633,
          -662.2598050578625,
          -662.2524328732652,
          -662.2448744260513,
          -662.2371301274326,
          -662.2292003884489
        ],
        "cartesian_polarizations_e_A2": [
          [
            -1.9722982732860578e-10,
            4.430680358350793e-13,
            -0.0050438915271528
          ],
          [
            -4.486472484424814e-09,
            1.0837922524262767e-11,
            -0.00498755917065917
          ],
          [
            -8.778350418765585e-09,
            2.1239252604963188e-11,
            -0.004931286463899015
          ],
          [
            -1.3072860801071724e-08,
            3.1647072758082906e-11,
            -0.004875073906843877
          ],
          [
            -1.7370000532633464e-08,
            4.206143003679935e-11,
            -0.004818922002698951
          ],
          [
            -2.1669767323852817e-08,
            5.248224907580676e-11,
            -0.004762831257669809
          ],
          [
            -2.5972158291605068e-08,
            6.290978617449768e-11,
            -0.004706802180728563
          ],
          [
            -3.0277170668664744e-08,
            7.334350073079938e-11,
            -0.004650835283382564
          ],
          [
            -3.4584801783068885e-08,
            8.378389766953321e-11,
            -0.004594931079445719
          ]
        ],
        "raw_reduced_polarization": [
          [
            -5.573662789719311e-09,
            1.2421328917280324e-11,
            -1.000482565758961
          ],
          [
            -3.0244900002202893e-07,
            7.317122233545144e-10,
            -0.9894364626397127
          ],
          [
            -5.99385076477623e-07,
            1.4511602463385608e-09,
            -0.978399325681801
          ],
          [
            -8.963816673735338e-07,
            2.1707662364568965e-09,
            -0.9673712581226243
          ],
          [
            -1.1934385299018237e-06,
            2.890533356306099e-09,
            -0.9563523638936464
          ],
          [
            -1.4905554775773808e-06,
            3.6104563306573418e-09,
            -0.9453427475745226
          ],
          [
            -1.7877322835460266e-06,
            4.33055274197683e-09,
            -0.9343425143470788
          ],
          [
            -2.0849687294959606e-06,
            5.05078526077316e-09,
            -0.9233517699497701
          ],
          [
            -2.3822646042320417e-06,
            5.7711886011282865e-09,
            -0.9123706206326121
          ]
        ],
        "unwrapped_reduced_polarization": [
          [
            -5.573662789719311e-09,
            1.2421328917280324e-11,
            -1.000482565758961
          ],
          [
            -3.0244900002202893e-07,
            7.317122233545144e-10,
            -0.9894364626397127
          ],
          [
            -5.99385076477623e-07,
            1.4511602463385608e-09,
            -0.978399325681801
          ],
          [
            -8.963816673735338e-07,
            2.1707662364568965e-09,
            -0.9673712581226243
          ],
          [
            -1.1934385299018237e-06,
            2.890533356306099e-09,
            -0.9563523638936464
          ],
          [
            -1.4905554775773808e-06,
            3.6104563306573418e-09,
            -0.9453427475745226
          ],
          [
            -1.7877322835460266e-06,
            4.33055274197683e-09,
            -0.9343425143470788
          ],
          [
            -2.0849687294959606e-06,
            5.05078526077316e-09,
            -0.9233517699497701
          ],
          [
            -2.3822646042320417e-06,
            5.7711886011282865e-09,
            -0.9123706206326121
          ]
        ],
        "gauge_integer_shift": [
          0,
          0,
          0
        ],
        "expected_opposite_endpoint_reduced_polarization": [
          -2.4372212878958597e-06,
          5.906572123938698e-09,
          -0.8533194365333321
        ],
        "actual_opposite_endpoint_branch_residual": 0.059051184099305584
      },
      "pnp_branch": {
        "construction": "incoming_path_concatenated_with_parent_reflection",
        "reduced_polarization": [
          [
            2.4100501792929974e-06,
            -5.845533788239318e-09,
            -1.1497131937567329
          ],
          [
            2.108476193729027e-06,
            -5.114111287388514e-09,
            -1.131030377990576
          ],
          [
            1.806794013083952e-06,
            -4.3824603650136775e-09,
            -1.1123558624671854
          ],
          [
            1.505003599982096e-06,
            -3.650572594252041e-09,
            -1.0936896380409367
          ],
          [
            1.203104908880985e-06,
            -2.918448917714583e-09,
            -1.0750316956156352
          ],
          [
            9.010978954173004e-07,
            -2.186091567353184e-09,
            -1.0563820261449994
          ],
          [
            5.98982497725725e-07,
            -1.4534902834866258e-09,
            -1.0377406206331659
          ],
          [
            2.967586699742879e-07,
            -7.206540768957492e-10,
            -1.0191074701354388
          ],
          [
            -5.573664703057357e-09,
            1.2421157273446756e-11,
            -1.0004825657589371
          ],
          [
            -3.0244900002202893e-07,
            7.317122233545144e-10,
            -0.9894364626397127
          ],
          [
            -5.99385076477623e-07,
            1.4511602463385608e-09,
            -0.978399325681801
          ],
          [
            -8.963816673735338e-07,
            2.1707662364568965e-09,
            -0.9673712581226243
          ],
          [
            -1.1934385299018237e-06,
            2.890533356306099e-09,
            -0.9563523638936464
          ],
          [
            -1.4905554775773808e-06,
            3.6104563306573418e-09,
            -0.9453427475745226
          ],
          [
            -1.7877322835460266e-06,
            4.33055274197683e-09,
            -0.9343425143470788
          ],
          [
            -2.0849687294959606e-06,
            5.05078526077316e-09,
            -0.9233517699497701
          ],
          [
            -2.3822646042320417e-06,
            5.7711886011282865e-09,
            -0.9123706206326121
          ]
        ],
        "unwrapped_reduced_polarization": [
          [
            2.4100501792929974e-06,
            -5.845533788239318e-09,
            -1.1497131937567329
          ],
          [
            2.108476193729027e-06,
            -5.114111287388514e-09,
            -1.131030377990576
          ],
          [
            1.806794013083952e-06,
            -4.3824603650136775e-09,
            -1.1123558624671854
          ],
          [
            1.505003599982096e-06,
            -3.650572594252041e-09,
            -1.0936896380409367
          ],
          [
            1.203104908880985e-06,
            -2.918448917714583e-09,
            -1.0750316956156352
          ],
          [
            9.010978954173004e-07,
            -2.186091567353184e-09,
            -1.0563820261449994
          ],
          [
            5.98982497725725e-07,
            -1.4534902834866258e-09,
            -1.0377406206331659
          ],
          [
            2.967586699742879e-07,
            -7.206540768957492e-10,
            -1.0191074701354388
          ],
          [
            -5.573664703057377e-09,
            1.2421157273446791e-11,
            -1.0004825657589371
          ],
          [
            -3.0244900002202893e-07,
            7.317122233545144e-10,
            -0.9894364626397127
          ],
          [
            -5.99385076477623e-07,
            1.4511602463385608e-09,
            -0.978399325681801
          ],
          [
            -8.963816673735338e-07,
            2.1707662364568965e-09,
            -0.9673712581226243
          ],
          [
            -1.1934385299018237e-06,
            2.890533356306099e-09,
            -0.9563523638936464
          ],
          [
            -1.4905554775773808e-06,
            3.6104563306573418e-09,
            -0.9453427475745226
          ],
          [
            -1.7877322835460266e-06,
            4.33055274197683e-09,
            -0.9343425143470788
          ],
          [
            -2.0849687294959606e-06,
            5.05078526077316e-09,
            -0.9233517699497701
          ],
          [
            -2.3822646042320417e-06,
            5.7711886011282865e-09,
            -0.9123706206326121
          ]
        ],
        "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": [
          [
            2.4100501793133944e-06,
            -5.845533779247347e-09,
            -0.14971319375673287
          ],
          [
            2.1084761937517627e-06,
            -5.114111301107727e-09,
            -0.13103037799057593
          ],
          [
            1.8067940130706006e-06,
            -4.382460339069638e-09,
            -0.11235586246718543
          ],
          [
            1.5050035999664146e-06,
            -3.6505726219715484e-09,
            -0.09368963804093666
          ],
          [
            1.2031049089200607e-06,
            -2.9184489269695746e-09,
            -0.07503169561563516
          ],
          [
            9.010978954115956e-07,
            -2.1860915855320684e-09,
            -0.05638202614499943
          ],
          [
            5.98982497712619e-07,
            -1.4534902725849008e-09,
            -0.037740620633165856
          ],
          [
            2.9675866997092015e-07,
            -7.206540919568738e-10,
            -0.019107470135438787
          ],
          [
            -5.5736646964454906e-09,
            1.2421175199506251e-11,
            -0.0004825657589371257
          ],
          [
            -3.024490000114177e-07,
            7.317122463490477e-10,
            0.010563537360287256
          ],
          [
            -5.993850764607345e-07,
            1.4511601920119688e-09,
            0.02160067431819901
          ],
          [
            -8.963816673923652e-07,
            2.1707662334335964e-09,
            0.032628741877375744
          ],
          [
            -1.1934385298895123e-06,
            2.890533368216097e-09,
            0.04364763610635358
          ],
          [
            -1.4905554776012409e-06,
            3.6104563783112553e-09,
            0.054657252425477365
          ],
          [
            -1.7877322835424536e-06,
            4.3305526942205574e-09,
            0.06565748565292118
          ],
          [
            -2.084968729498815e-06,
            5.050785234494981e-09,
            0.07664823005022992
          ],
          [
            -2.3822646042503948e-06,
            5.7711886380928945e-09,
            0.0876293793673879
          ]
        ]
      },
      "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": "P4bm",
        "spacegroup_number": 100,
        "pointgroup": "4mm",
        "has_inversion": false,
        "is_polar_point_group": true,
        "nonpolar_parent_hypothesis": false,
        "symmetry_tolerance_A": null,
        "target_reduced_polarization": [
          0.0,
          0.0,
          -1.0
        ],
        "formal_class": [
          0.0,
          0.0,
          0.0
        ],
        "target_residual": 0.00048256575899662544,
        "parent_symmetrization_rmsd_A": 0.0032047630158849563,
        "parent_cell_rmsd_A": 0.008526957764424038,
        "energy_eV": -662.287422945732,
        "reduced_polarization": [
          -5.573662668765394e-09,
          1.2423588549484047e-11,
          -1.0004825657589644
        ],
        "cartesian_polarization_e_A2": [
          -1.9722982557497968e-10,
          4.4310079666600937e-13,
          -0.005043891527152815
        ],
        "ranking_score": 0.5063016339749842
      }
    }
  ],
  "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": 44,
      "full_response": 12,
      "energy_polarization": 32
    },
    "model_evaluations_for_recovery_and_path_properties": {
      "total": 69,
      "full_response": 37,
      "energy_polarization": 32
    },
    "elapsed_seconds": 1931.0627999670105
  }
}
