{
  "schema": "ferrofinder.endpoint_parent_recovery.v4_variable_cell",
  "status": "complete",
  "input_atom_count": 36,
  "input_formula": "Mo6O24Rb4Se2",
  "input_spacegroup": "P6_3",
  "input_pointgroup": "6",
  "input_is_polar_point_group": true,
  "input_energy_eV": -225.99380790510943,
  "input_cartesian_polarization_e_A2": [
    -1.9168087742868236e-10,
    0.023233080188845255,
    -1.7515691505797616e-10
  ],
  "input_reduced_polarization": [
    -2.2951251298684598e-08,
    1.0885348570258597,
    -1.5853327107734258e-08
  ],
  "input_formal_targets": [
    {
      "orbit_id": 0,
      "representative_formal_class": [
        0.0,
        0.0,
        0.0
      ],
      "target_reduced_polarization": [
        0.0,
        1.0,
        0.0
      ]
    },
    {
      "orbit_id": 1,
      "representative_formal_class": [
        0.0,
        0.5,
        0.0
      ],
      "target_reduced_polarization": [
        0.0,
        1.5,
        0.0
      ]
    },
    {
      "orbit_id": 2,
      "representative_formal_class": [
        0.5,
        0.0,
        0.0
      ],
      "target_reduced_polarization": [
        -0.5,
        1.0,
        0.0
      ]
    },
    {
      "orbit_id": 3,
      "representative_formal_class": [
        0.5,
        0.5,
        0.0
      ],
      "target_reduced_polarization": [
        -0.5,
        1.5,
        0.0
      ]
    }
  ],
  "parent_candidates": [
    {
      "candidate_id": "inversion_parent_endpoint_00",
      "source": "same_species_inversion_center_projection_from_endpoint",
      "spacegroup": "P6_3/m",
      "spacegroup_number": 176,
      "pointgroup": "6/m",
      "has_inversion": true,
      "is_polar_point_group": false,
      "nonpolar_parent_hypothesis": true,
      "symmetry_tolerance_A": null,
      "target_reduced_polarization": [
        0.0,
        0.0,
        0.0
      ],
      "formal_class": [
        0.0,
        0.0,
        0.0
      ],
      "target_residual": 1.0582478647377274e-14,
      "parent_symmetrization_rmsd_A": 0.5597314937314476,
      "parent_cell_rmsd_A": 0.0,
      "energy_eV": -214.3177352005554,
      "reduced_polarization": [
        -6.658356314361669e-15,
        -1.1852513488195793e-15,
        -8.13943024746311e-15
      ],
      "cartesian_polarization_e_A2": [
        -3.302540228361075e-17,
        -2.5297342986608742e-17,
        -8.992922954196047e-17
      ],
      "ranking_score": 0.5597314937314688
    },
    {
      "candidate_id": "bec_projection_00",
      "source": "MACEField_BEC_backprojection",
      "spacegroup": "P6_3",
      "spacegroup_number": 173,
      "pointgroup": "6",
      "has_inversion": false,
      "is_polar_point_group": true,
      "nonpolar_parent_hypothesis": false,
      "symmetry_tolerance_A": null,
      "target_reduced_polarization": [
        0.0,
        1.0,
        0.0
      ],
      "formal_class": [
        0.0,
        0.0,
        0.0
      ],
      "target_residual": 2.5712726285932298e-06,
      "parent_symmetrization_rmsd_A": 0.013628568307740676,
      "parent_cell_rmsd_A": 0.02142600415316681,
      "energy_eV": -225.90928874263554,
      "reduced_polarization": [
        -6.169436358147267e-13,
        1.0000025712726286,
        -3.24600214377954e-13
      ],
      "cartesian_polarization_e_A2": [
        -1.2037080531627463e-12,
        0.02135152055411792,
        -9.494325691040515e-13
      ],
      "ranking_score": 0.5189902118912896
    },
    {
      "candidate_id": "inversion_parent_bec_00_00",
      "source": "same_species_inversion_center_projection_after_BEC",
      "spacegroup": "P6_3/m",
      "spacegroup_number": 176,
      "pointgroup": "6/m",
      "has_inversion": true,
      "is_polar_point_group": false,
      "nonpolar_parent_hypothesis": true,
      "symmetry_tolerance_A": null,
      "target_reduced_polarization": [
        0.0,
        1.0,
        0.0
      ],
      "formal_class": [
        0.0,
        0.0,
        0.0
      ],
      "target_residual": 3.753046095307979e-15,
      "parent_symmetrization_rmsd_A": 0.5597345184178834,
      "parent_cell_rmsd_A": 0.02142600415316681,
      "energy_eV": -214.27345197967213,
      "reduced_polarization": [
        -1.983830564022683e-15,
        -3.0892442636369467e-15,
        6.97298499782208e-16
      ],
      "cartesian_polarization_e_A2": [
        -2.970442294460365e-17,
        -6.595989278953952e-17,
        7.690465487276026e-18
      ],
      "ranking_score": 0.5650910194561826
    },
    {
      "candidate_id": "bec_projection_01",
      "source": "MACEField_BEC_backprojection",
      "spacegroup": "P6_3",
      "spacegroup_number": 173,
      "pointgroup": "6",
      "has_inversion": false,
      "is_polar_point_group": true,
      "nonpolar_parent_hypothesis": false,
      "symmetry_tolerance_A": null,
      "target_reduced_polarization": [
        0.0,
        1.5,
        0.0
      ],
      "formal_class": [
        0.0,
        0.5,
        0.0
      ],
      "target_residual": 0.00011814154149014658,
      "parent_symmetrization_rmsd_A": 0.0971007435023417,
      "parent_cell_rmsd_A": 0.17366560921879137,
      "energy_eV": -219.6023476010312,
      "reduced_polarization": [
        -1.6650768410894093e-12,
        1.4998818584585099,
        -2.0644711564464393e-12
      ],
      "cartesian_polarization_e_A2": [
        -7.620893855714344e-14,
        0.031913482349419244,
        -2.7692878598432903e-12
      ],
      "ranking_score": 0.6407534288900198
    },
    {
      "candidate_id": "bec_projection_02",
      "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,
        1.0,
        0.0
      ],
      "formal_class": [
        0.5,
        0.0,
        0.0
      ],
      "target_residual": 3.230114557012047e-06,
      "parent_symmetrization_rmsd_A": 0.026280411248895102,
      "parent_cell_rmsd_A": 0.027935369172329312,
      "energy_eV": -225.74852417529013,
      "reduced_polarization": [
        -0.49999681747054403,
        1.0000004631385129,
        -3.010797754754382e-07
      ],
      "cartesian_polarization_e_A2": [
        -0.006330821287029521,
        0.021340725157742095,
        8.546714866649843e-07
      ],
      "ranking_score": 0.5332707137710915
    },
    {
      "candidate_id": "bec_projection_03",
      "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,
        1.5,
        0.0
      ],
      "formal_class": [
        0.5,
        0.5,
        0.0
      ],
      "target_residual": 0.00012451579421493512,
      "parent_symmetrization_rmsd_A": 0.09983797495395418,
      "parent_cell_rmsd_A": 0.17410912148350904,
      "energy_eV": -219.49310474566602,
      "reduced_polarization": [
        -0.49997149765753907,
        1.499879106549141,
        -8.75060127219821e-06
      ],
      "cartesian_polarization_e_A2": [
        -0.00641214795184368,
        0.03190182226261337,
        9.490896314389495e-07
      ],
      "ranking_score": 0.6436142869132613
    }
  ],
  "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,
        1.0,
        0.0
      ],
      "bec_backprojection": {
        "converged_to_target": true,
        "history": [
          {
            "iteration": 0,
            "reduced_polarization": [
              -2.2951251298684598e-08,
              1.0885348570258597,
              -1.5853327107734258e-08
            ],
            "branch_aligned_reduced_polarization": [
              -2.2951251298684598e-08,
              1.0885348570258597,
              -1.5853327107734258e-08
            ],
            "target_residual": 0.08853485702586412,
            "energy_eV": -225.99380790510943,
            "max_atomic_step_A": 0.021952982773950358,
            "max_log_strain_component": 0.002004380443147584,
            "step_scale": 1.0,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 2.30358951047877,
            "cell_principal_stretches": [
              1.0020063905564145,
              0.9998085885140492,
              0.9998085803546517
            ],
            "cell_volume_ratio": 1.0016228280297812,
            "cell_rmsd_from_input_A": 0.021825289345833866
          },
          {
            "iteration": 1,
            "reduced_polarization": [
              1.284786220346184e-10,
              0.9982556068394245,
              9.285329932891532e-11
            ],
            "branch_aligned_reduced_polarization": [
              1.284786220346184e-10,
              0.9982556068394245,
              9.285329932891532e-11
            ],
            "target_residual": 0.0017443931605755152,
            "energy_eV": -225.9052821004856,
            "max_atomic_step_A": 0.0004173892591513172,
            "max_log_strain_component": 3.659752758819162e-05,
            "step_scale": 1.0,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 2.30358951047877,
            "cell_principal_stretches": [
              1.001969720270917,
              0.9998120831245277,
              0.9998120751140828
            ],
            "cell_volume_ratio": 1.0015931735902084,
            "cell_rmsd_from_input_A": 0.02142600415316681
          },
          {
            "iteration": 2,
            "reduced_polarization": [
              -6.169436358147267e-13,
              1.0000025712726286,
              -3.24600214377954e-13
            ],
            "branch_aligned_reduced_polarization": [
              -6.169436358147267e-13,
              1.0000025712726286,
              -3.24600214377954e-13
            ],
            "target_residual": 2.5712726285932298e-06,
            "energy_eV": -225.90928874263554
          }
        ],
        "iterations": 2
      },
      "parent": {
        "candidate_id": "bec_projection_00",
        "source": "MACEField_BEC_backprojection",
        "spacegroup": "P6_3",
        "spacegroup_number": 173,
        "pointgroup": "6",
        "has_inversion": false,
        "is_polar_point_group": true,
        "nonpolar_parent_hypothesis": false,
        "symmetry_tolerance_A": null,
        "target_reduced_polarization": [
          0.0,
          1.0,
          0.0
        ],
        "formal_class": [
          0.0,
          0.0,
          0.0
        ],
        "target_residual": 2.5712726285932298e-06,
        "parent_symmetrization_rmsd_A": 0.013628568307740676,
        "parent_cell_rmsd_A": 0.02142600415316681,
        "energy_eV": -225.90928874263554,
        "reduced_polarization": [
          -6.169436358147267e-13,
          1.0000025712726286,
          -3.24600214377954e-13
        ],
        "cartesian_polarization_e_A2": [
          -1.2037080531627463e-12,
          0.02135152055411792,
          -9.494325691040515e-13
        ],
        "ranking_score": 0.5189902118912896
      },
      "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": [
          -225.99380790510943,
          -225.99677607912184,
          -225.9957345292761,
          -225.99075838037467,
          -225.98191979781433,
          -225.96928812475923,
          -225.95293002667984,
          -225.93290964264395,
          -225.90928874263562
        ],
        "cartesian_polarizations_e_A2": [
          [
            -1.9168087068880436e-10,
            0.023233080188845227,
            -1.751569217015702e-10
          ],
          [
            -1.6797070095776064e-10,
            0.02300222138445392,
            -1.534756126491181e-10
          ],
          [
            -1.44231466107018e-10,
            0.02277006172496052,
            -1.3176749594576074e-10
          ],
          [
            -1.2046379324885238e-10,
            0.022536641101770845,
            -1.1003254734593739e-10
          ],
          [
            -9.66680449148722e-11,
            0.022301992222149035,
            -8.827081988494811e-11
          ],
          [
            -7.284420682686241e-11,
            0.02206614065506799,
            -6.64817078659935e-11
          ],
          [
            -4.899234276660069e-11,
            0.0218291049179258,
            -4.4665450926780683e-11
          ],
          [
            -2.511218648589789e-11,
            0.02159089660448798,
            -2.2821600087847952e-11
          ],
          [
            -1.2036474426816247e-12,
            0.021351520554118084,
            -9.493092332637994e-13
          ]
        ],
        "raw_reduced_polarization": [
          [
            -2.295125107104387e-08,
            1.0885348570258584,
            -1.5853327709041203e-08
          ],
          [
            -2.0097633964443547e-08,
            1.0776678406401012,
            -1.3882517291900748e-08
          ],
          [
            -1.723962990430195e-08,
            1.066740900016309,
            -1.1908637739625817e-08
          ],
          [
            -1.4377287356091393e-08,
            1.0557559124333178,
            -9.931686903890027e-09
          ],
          [
            -1.151063746641653e-08,
            1.0447144182840578,
            -7.951669569492334e-09
          ],
          [
            -8.639651920639025e-09,
            1.0336176233023704,
            -5.9685307898785615e-09
          ],
          [
            -5.764346763709747e-09,
            1.022466402703352,
            -3.98229215220819e-09
          ],
          [
            -2.884680913178302e-09,
            1.0112613072534562,
            -1.992912826541035e-09
          ],
          [
            -6.06592858203984e-13,
            1.0000025712726364,
            -3.1341728949245786e-13
          ]
        ],
        "unwrapped_reduced_polarization": [
          [
            -2.295125107104387e-08,
            1.0885348570258584,
            -1.5853327709041203e-08
          ],
          [
            -2.0097633964443547e-08,
            1.0776678406401012,
            -1.3882517291900748e-08
          ],
          [
            -1.723962990430195e-08,
            1.066740900016309,
            -1.1908637739625817e-08
          ],
          [
            -1.4377287356091393e-08,
            1.0557559124333178,
            -9.931686903890027e-09
          ],
          [
            -1.151063746641653e-08,
            1.0447144182840578,
            -7.951669569492334e-09
          ],
          [
            -8.639651920639025e-09,
            1.0336176233023704,
            -5.9685307898785615e-09
          ],
          [
            -5.764346763709747e-09,
            1.022466402703352,
            -3.98229215220819e-09
          ],
          [
            -2.884680913178302e-09,
            1.0112613072534562,
            -1.992912826541035e-09
          ],
          [
            -6.065928582038749e-13,
            1.0000025712726364,
            -3.13417289492404e-13
          ]
        ],
        "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": [
          [
            -2.295125106632767e-08,
            0.0885348570258584,
            -1.585332770615011e-08
          ],
          [
            -2.009763394594799e-08,
            0.07766784064010124,
            -1.3882517302388209e-08
          ],
          [
            -1.7239629890308805e-08,
            0.06674090001630906,
            -1.1908637742585881e-08
          ],
          [
            -1.4377287360645141e-08,
            0.05575591243331779,
            -9.931686917319382e-09
          ],
          [
            -1.1510637443201688e-08,
            0.044714418284057755,
            -7.951669545036566e-09
          ],
          [
            -8.63965193831362e-09,
            0.03361762330237039,
            -5.968530780720016e-09
          ],
          [
            -5.7643467776813395e-09,
            0.022466402703352095,
            -3.98229216269641e-09
          ],
          [
            -2.884680938564088e-09,
            0.011261307253456199,
            -1.9929128347584424e-09
          ],
          [
            -6.065703495039543e-13,
            2.5712726363646965e-06,
            -3.134159598516817e-13
          ]
        ]
      },
      "reflected": {
        "reached": true,
        "construction": "reflect_displacements_about_reconstructed_parent",
        "energies_eV": [
          -225.90928874263557,
          -225.88634815359137,
          -225.86074439621223,
          -225.8325008611405,
          -225.8016398014839,
          -225.76818248456073,
          -225.7321492978345,
          -225.693559836098,
          -225.65243299972965
        ],
        "cartesian_polarizations_e_A2": [
          [
            -1.2037143977967734e-12,
            0.021351520554117986,
            -9.49415553949161e-13
          ],
          [
            2.2705907565087658e-11,
            0.021119604566635104,
            2.099690576969608e-11
          ],
          [
            4.663013203538309e-11,
            0.020886712269776533,
            4.296680427865015e-11
          ],
          [
            7.056963993930964e-11,
            0.02065284189548882,
            6.49604893007274e-11
          ],
          [
            9.452449942046076e-11,
            0.02041798843958611,
            8.697748369350169e-11
          ],
          [
            1.1849502886272467e-10,
            0.020182142939942103,
            1.09017989481385e-10
          ],
          [
            1.4248156412851335e-10,
            0.01994529250426403,
            1.3108246697562323e-10
          ],
          [
            1.6648472431504884e-10,
            0.019707420606451358,
            1.5317055137821013e-10
          ],
          [
            1.9050483852058426e-10,
            0.01946850738156175,
            1.7528223297988644e-10
          ]
        ],
        "raw_reduced_polarization": [
          [
            -6.166704489585298e-13,
            1.0000025712726317,
            -3.2305744142529747e-13
          ],
          [
            2.852739692906842e-09,
            0.9891872169075194,
            1.977593923596701e-09
          ],
          [
            5.7074056829439946e-09,
            0.9783251140655391,
            3.956997018815074e-09
          ],
          [
            8.563442951692618e-09,
            0.9674161734100938,
            5.937902944884551e-09
          ],
          [
            1.1420836377604604e-08,
            0.9564601539950387,
            7.920268735967463e-09
          ],
          [
            1.4279621243629998e-08,
            0.9454566294151066,
            9.90411298077933e-09
          ],
          [
            1.7139845889051274e-08,
            0.934404989063509,
            1.1889477653603343e-08
          ],
          [
            2.0001543506834852e-08,
            0.9233044519732531,
            1.3876330019064897e-08
          ],
          [
            2.286474065248992e-08,
            0.9121540805971161,
            1.5864669543217592e-08
          ]
        ],
        "unwrapped_reduced_polarization": [
          [
            -6.166704489585298e-13,
            1.0000025712726317,
            -3.2305744142529747e-13
          ],
          [
            2.852739692906842e-09,
            0.9891872169075194,
            1.977593923596701e-09
          ],
          [
            5.7074056829439946e-09,
            0.9783251140655391,
            3.956997018815074e-09
          ],
          [
            8.563442951692618e-09,
            0.9674161734100938,
            5.937902944884551e-09
          ],
          [
            1.1420836377604604e-08,
            0.9564601539950387,
            7.920268735967463e-09
          ],
          [
            1.4279621243629998e-08,
            0.9454566294151066,
            9.90411298077933e-09
          ],
          [
            1.7139845889051274e-08,
            0.934404989063509,
            1.1889477653603343e-08
          ],
          [
            2.0001543506834852e-08,
            0.9233044519732531,
            1.3876330019064897e-08
          ],
          [
            2.286474065248992e-08,
            0.9121540805971161,
            1.5864669543217592e-08
          ]
        ],
        "gauge_integer_shift": [
          0,
          0,
          0
        ],
        "expected_opposite_endpoint_reduced_polarization": [
          2.2676637952281455e-08,
          0.9122221829141665,
          1.5681485109548716e-08
        ],
        "actual_opposite_endpoint_branch_residual": 6.81023170508509e-05
      },
      "pnp_branch": {
        "construction": "incoming_path_concatenated_with_parent_reflection",
        "reduced_polarization": [
          [
            -2.295125107104387e-08,
            1.0885348570258584,
            -1.5853327709041203e-08
          ],
          [
            -2.0097633964443547e-08,
            1.0776678406401012,
            -1.3882517291900748e-08
          ],
          [
            -1.723962990430195e-08,
            1.066740900016309,
            -1.1908637739625817e-08
          ],
          [
            -1.4377287356091393e-08,
            1.0557559124333178,
            -9.931686903890027e-09
          ],
          [
            -1.151063746641653e-08,
            1.0447144182840578,
            -7.951669569492334e-09
          ],
          [
            -8.639651920639025e-09,
            1.0336176233023704,
            -5.9685307898785615e-09
          ],
          [
            -5.764346763709747e-09,
            1.022466402703352,
            -3.98229215220819e-09
          ],
          [
            -2.884680913178302e-09,
            1.0112613072534562,
            -1.992912826541035e-09
          ],
          [
            -6.06592858203984e-13,
            1.0000025712726364,
            -3.1341728949245786e-13
          ],
          [
            2.852739692906842e-09,
            0.9891872169075194,
            1.977593923596701e-09
          ],
          [
            5.7074056829439946e-09,
            0.9783251140655391,
            3.956997018815074e-09
          ],
          [
            8.563442951692618e-09,
            0.9674161734100938,
            5.937902944884551e-09
          ],
          [
            1.1420836377604604e-08,
            0.9564601539950387,
            7.920268735967463e-09
          ],
          [
            1.4279621243629998e-08,
            0.9454566294151066,
            9.90411298077933e-09
          ],
          [
            1.7139845889051274e-08,
            0.934404989063509,
            1.1889477653603343e-08
          ],
          [
            2.0001543506834852e-08,
            0.9233044519732531,
            1.3876330019064897e-08
          ],
          [
            2.286474065248992e-08,
            0.9121540805971161,
            1.5864669543217592e-08
          ]
        ],
        "unwrapped_reduced_polarization": [
          [
            -2.295125107104387e-08,
            1.0885348570258584,
            -1.5853327709041203e-08
          ],
          [
            -2.0097633964443547e-08,
            1.0776678406401012,
            -1.3882517291900748e-08
          ],
          [
            -1.723962990430195e-08,
            1.066740900016309,
            -1.1908637739625817e-08
          ],
          [
            -1.4377287356091393e-08,
            1.0557559124333178,
            -9.931686903890027e-09
          ],
          [
            -1.151063746641653e-08,
            1.0447144182840578,
            -7.951669569492334e-09
          ],
          [
            -8.639651920639025e-09,
            1.0336176233023704,
            -5.9685307898785615e-09
          ],
          [
            -5.764346763709747e-09,
            1.022466402703352,
            -3.98229215220819e-09
          ],
          [
            -2.884680913178302e-09,
            1.0112613072534562,
            -1.992912826541035e-09
          ],
          [
            -6.065928582038749e-13,
            1.0000025712726364,
            -3.13417289492404e-13
          ],
          [
            2.852739692906842e-09,
            0.9891872169075194,
            1.977593923596701e-09
          ],
          [
            5.7074056829439946e-09,
            0.9783251140655391,
            3.956997018815074e-09
          ],
          [
            8.563442951692618e-09,
            0.9674161734100938,
            5.937902944884551e-09
          ],
          [
            1.1420836377604604e-08,
            0.9564601539950387,
            7.920268735967463e-09
          ],
          [
            1.4279621243629998e-08,
            0.9454566294151066,
            9.90411298077933e-09
          ],
          [
            1.7139845889051274e-08,
            0.934404989063509,
            1.1889477653603343e-08
          ],
          [
            2.0001543506834852e-08,
            0.9233044519732531,
            1.3876330019064897e-08
          ],
          [
            2.286474065248992e-08,
            0.9121540805971161,
            1.5864669543217592e-08
          ]
        ],
        "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": [
          [
            -2.295125106632767e-08,
            0.0885348570258584,
            -1.585332770615011e-08
          ],
          [
            -2.009763394594799e-08,
            0.07766784064010124,
            -1.3882517302388209e-08
          ],
          [
            -1.7239629890308805e-08,
            0.06674090001630906,
            -1.1908637742585881e-08
          ],
          [
            -1.4377287360645141e-08,
            0.05575591243331779,
            -9.931686917319382e-09
          ],
          [
            -1.1510637443201688e-08,
            0.044714418284057755,
            -7.951669545036566e-09
          ],
          [
            -8.63965193831362e-09,
            0.03361762330237039,
            -5.968530780720016e-09
          ],
          [
            -5.7643467776813395e-09,
            0.022466402703352095,
            -3.98229216269641e-09
          ],
          [
            -2.884680938564088e-09,
            0.011261307253456199,
            -1.9929128347584424e-09
          ],
          [
            -6.065703495039543e-13,
            2.5712726363646965e-06,
            -3.134159598516817e-13
          ],
          [
            2.85273971112332e-09,
            -0.010812783092480682,
            1.9775939774646645e-09
          ],
          [
            5.7074056591943645e-09,
            -0.021674885934460875,
            3.956997063347956e-09
          ],
          [
            8.563442954745426e-09,
            -0.032583826589906106,
            5.9379029471173794e-09
          ],
          [
            1.1420836387721067e-08,
            -0.04353984600496119,
            7.920268774164185e-09
          ],
          [
            1.4279621263213471e-08,
            -0.05454337058489345,
            9.904112974190582e-09
          ],
          [
            1.713984587592421e-08,
            -0.0655950109364909,
            1.1889477624649203e-08
          ],
          [
            2.000154353254402e-08,
            -0.07669554802674705,
            1.3876329973960821e-08
          ],
          [
            2.286474065638089e-08,
            -0.08784591940288378,
            1.5864669578036228e-08
          ]
        ]
      },
      "incoming_structure_ids": [
        "incoming_00_000",
        "incoming_00_001",
        "incoming_00_002",
        "incoming_00_003",
        "incoming_00_004",
        "incoming_00_005",
        "incoming_00_006",
        "incoming_00_007",
        "incoming_00_008"
      ],
      "reflected_structure_ids": [
        "reflected_00_001",
        "reflected_00_002",
        "reflected_00_003",
        "reflected_00_004",
        "reflected_00_005",
        "reflected_00_006",
        "reflected_00_007",
        "reflected_00_008"
      ]
    },
    {
      "orbit_id": 1,
      "formal_class": [
        0.0,
        0.5,
        0.0
      ],
      "formal_classes_in_orbit": [
        [
          0.0,
          0.5,
          0.0
        ]
      ],
      "target_reduced_polarization": [
        0.0,
        1.5,
        0.0
      ],
      "bec_backprojection": {
        "converged_to_target": true,
        "history": [
          {
            "iteration": 0,
            "reduced_polarization": [
              -2.2951251298684598e-08,
              1.0885348570258597,
              -1.5853327107734258e-08
            ],
            "branch_aligned_reduced_polarization": [
              -2.2951251298684598e-08,
              1.0885348570258597,
              -1.5853327107734258e-08
            ],
            "target_residual": 0.4114651429741412,
            "energy_eV": -225.99380790510943,
            "max_atomic_step_A": 0.10202633679961465,
            "max_log_strain_component": 0.009315344411449145,
            "step_scale": 1.0,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 2.30358951047877,
            "cell_principal_stretches": [
              1.0008901025563295,
              1.0008900645945662,
              0.9907279089983051
            ],
            "cell_volume_ratio": 0.9924923551803477,
            "cell_rmsd_from_input_A": 0.10029618327105216
          },
          {
            "iteration": 1,
            "reduced_polarization": [
              -1.1817778013755072e-09,
              1.4136172718187991,
              -4.235019865694773e-10
            ],
            "branch_aligned_reduced_polarization": [
              -1.1817778013755072e-09,
              1.4136172718187991,
              -4.235019865694773e-10
            ],
            "target_residual": 0.08638272818120087,
            "energy_eV": -221.71795857637883,
            "max_atomic_step_A": 0.028895282602538153,
            "max_log_strain_component": 0.005770770071517954,
            "step_scale": 1.0,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 2.30358951047877,
            "cell_principal_stretches": [
              1.0014419102801113,
              1.001441848767492,
              0.9850271108502634
            ],
            "cell_volume_ratio": 0.9878697395809889,
            "cell_rmsd_from_input_A": 0.1615009279350453
          },
          {
            "iteration": 2,
            "reduced_polarization": [
              -1.4856188445601154e-10,
              1.487344049592743,
              -1.2549910003213297e-10
            ],
            "branch_aligned_reduced_polarization": [
              -1.4856188445601154e-10,
              1.487344049592743,
              -1.2549910003213297e-10
            ],
            "target_residual": 0.012655950407256979,
            "energy_eV": -219.73746403846704,
            "max_atomic_step_A": 0.0049487098220317455,
            "max_log_strain_component": 0.00105070358604013,
            "step_scale": 1.0,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 2.30358951047877,
            "cell_principal_stretches": [
              1.0015424125079184,
              1.0015423467045221,
              0.983992682866308
            ],
            "cell_volume_ratio": 0.9870304042142377,
            "cell_rmsd_from_input_A": 0.17256911802740182
          },
          {
            "iteration": 3,
            "reduced_polarization": [
              -1.7738470284646378e-11,
              1.4987614639001157,
              -2.0222279302956527e-11
            ],
            "branch_aligned_reduced_polarization": [
              -1.7738470284646378e-11,
              1.4987614639001157,
              -2.0222279302956527e-11
            ],
            "target_residual": 0.0012385360998843355,
            "energy_eV": -219.61368951090589,
            "max_atomic_step_A": 0.0004906024644576348,
            "max_log_strain_component": 0.00010420983525188913,
            "step_scale": 1.0,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 2.30358951047877,
            "cell_principal_stretches": [
              1.001552380969419,
              1.0015523147404126,
              0.9838901464936797
            ],
            "cell_volume_ratio": 0.9869471969730408,
            "cell_rmsd_from_input_A": 0.17366560921879137
          },
          {
            "iteration": 4,
            "reduced_polarization": [
              -1.6650768410894093e-12,
              1.4998818584585099,
              -2.0644711564464393e-12
            ],
            "branch_aligned_reduced_polarization": [
              -1.6650768410894093e-12,
              1.4998818584585099,
              -2.0644711564464393e-12
            ],
            "target_residual": 0.00011814154149014658,
            "energy_eV": -219.6023476010312
          }
        ],
        "iterations": 4
      },
      "parent": {
        "candidate_id": "bec_projection_01",
        "source": "MACEField_BEC_backprojection",
        "spacegroup": "P6_3",
        "spacegroup_number": 173,
        "pointgroup": "6",
        "has_inversion": false,
        "is_polar_point_group": true,
        "nonpolar_parent_hypothesis": false,
        "symmetry_tolerance_A": null,
        "target_reduced_polarization": [
          0.0,
          1.5,
          0.0
        ],
        "formal_class": [
          0.0,
          0.5,
          0.0
        ],
        "target_residual": 0.00011814154149014658,
        "parent_symmetrization_rmsd_A": 0.0971007435023417,
        "parent_cell_rmsd_A": 0.17366560921879137,
        "energy_eV": -219.6023476010312,
        "reduced_polarization": [
          -1.6650768410894093e-12,
          1.4998818584585099,
          -2.0644711564464393e-12
        ],
        "cartesian_polarization_e_A2": [
          -7.620893855714344e-14,
          0.031913482349419244,
          -2.7692878598432903e-12
        ],
        "ranking_score": 0.6407534288900198
      },
      "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,
          0.0,
          0.5
        ],
        [
          0.5,
          0.0,
          0.5
        ]
      ],
      "target_reduced_polarization": [
        -0.5,
        1.0,
        0.0
      ],
      "bec_backprojection": {
        "converged_to_target": true,
        "history": [
          {
            "iteration": 0,
            "reduced_polarization": [
              -2.2951251298684598e-08,
              1.0885348570258597,
              -1.5853327107734258e-08
            ],
            "branch_aligned_reduced_polarization": [
              -2.2951251288372276e-08,
              1.0885348570258597,
              -1.5853327107734258e-08
            ],
            "target_residual": 0.5077779021947872,
            "energy_eV": -225.99380790510943,
            "max_atomic_step_A": 0.051980486275664615,
            "max_log_strain_component": 0.0020043804569507546,
            "step_scale": 1.0,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 2.30358951047877,
            "cell_principal_stretches": [
              1.0029504389388344,
              0.9998085837447793,
              0.998867494102587
            ],
            "cell_volume_ratio": 1.0016228280543633,
            "cell_rmsd_from_input_A": 0.0280080645949759
          },
          {
            "iteration": 1,
            "reduced_polarization": [
              -0.5018082713667349,
              0.9998152112795075,
              -4.374023307794121e-05
            ],
            "branch_aligned_reduced_polarization": [
              -0.5018082713667349,
              0.9998152112795075,
              -4.374023307794121e-05
            ],
            "target_residual": 0.0018182148979051572,
            "energy_eV": -225.74702346713258,
            "max_atomic_step_A": 0.0001782582054275807,
            "max_log_strain_component": 6.128297604655432e-06,
            "step_scale": 1.0,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 2.30358951047877,
            "cell_principal_stretches": [
              1.0029422896963538,
              0.9998089617228849,
              0.9988720340035213
            ],
            "cell_volume_ratio": 1.0016196206487755,
            "cell_rmsd_from_input_A": 0.027935369172329312
          },
          {
            "iteration": 2,
            "reduced_polarization": [
              -0.49999681747054403,
              1.0000004631385129,
              -3.010797754754382e-07
            ],
            "branch_aligned_reduced_polarization": [
              -0.49999681747054403,
              1.0000004631385129,
              -3.010797754754382e-07
            ],
            "target_residual": 3.230114557012047e-06,
            "energy_eV": -225.74852417529013
          }
        ],
        "iterations": 2
      },
      "parent": {
        "candidate_id": "bec_projection_02",
        "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,
          1.0,
          0.0
        ],
        "formal_class": [
          0.5,
          0.0,
          0.0
        ],
        "target_residual": 3.230114557012047e-06,
        "parent_symmetrization_rmsd_A": 0.026280411248895102,
        "parent_cell_rmsd_A": 0.027935369172329312,
        "energy_eV": -225.74852417529013,
        "reduced_polarization": [
          -0.49999681747054403,
          1.0000004631385129,
          -3.010797754754382e-07
        ],
        "cartesian_polarization_e_A2": [
          -0.006330821287029521,
          0.021340725157742095,
          8.546714866649843e-07
        ],
        "ranking_score": 0.5332707137710915
      },
      "branch_status": "awaiting_branch_sampling"
    },
    {
      "orbit_id": 3,
      "formal_class": [
        0.5,
        0.5,
        0.0
      ],
      "formal_classes_in_orbit": [
        [
          0.5,
          0.5,
          0.0
        ],
        [
          0.0,
          0.5,
          0.5
        ],
        [
          0.5,
          0.5,
          0.5
        ]
      ],
      "target_reduced_polarization": [
        -0.5,
        1.5,
        0.0
      ],
      "bec_backprojection": {
        "converged_to_target": true,
        "history": [
          {
            "iteration": 0,
            "reduced_polarization": [
              -2.2951251298684598e-08,
              1.0885348570258597,
              -1.5853327107734258e-08
            ],
            "branch_aligned_reduced_polarization": [
              -2.2951251288372276e-08,
              1.0885348570258597,
              -1.5853327107734258e-08
            ],
            "target_residual": 0.6475365170640797,
            "energy_eV": -225.99380790510943,
            "max_atomic_step_A": 0.11523759324811488,
            "max_log_strain_component": 0.009315344397645975,
            "step_scale": 1.0,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 2.30358951047877,
            "cell_principal_stretches": [
              1.0011721213618696,
              1.0008900868540784,
              0.9904488102056676
            ],
            "cell_volume_ratio": 0.9924923552047057,
            "cell_rmsd_from_input_A": 0.10175284564171957
          },
          {
            "iteration": 1,
            "reduced_polarization": [
              -0.47675551061520743,
              1.4140655634880426,
              -0.00572017689441308
            ],
            "branch_aligned_reduced_polarization": [
              -0.47675551061520743,
              1.4140655634880426,
              -0.00572017689441308
            ],
            "target_residual": 0.08920624467541918,
            "energy_eV": -221.55493321435617,
            "max_atomic_step_A": 0.03567787227027678,
            "max_log_strain_component": 0.005681717540732786,
            "step_scale": 1.0,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 2.30358951047877,
            "cell_principal_stretches": [
              1.0016396193111463,
              1.0014333677917215,
              0.9849119738840851
            ],
            "cell_volume_ratio": 0.9879409103952626,
            "cell_rmsd_from_input_A": 0.16160237673549604
          },
          {
            "iteration": 2,
            "reduced_polarization": [
              -0.49579693949988474,
              1.4871178171993984,
              0.0006824447063801325
            ],
            "branch_aligned_reduced_polarization": [
              -0.49579693949988474,
              1.4871178171993984,
              0.0006824447063801325
            ],
            "target_residual": 0.013567685213514176,
            "energy_eV": -219.64048839070924,
            "max_atomic_step_A": 0.005099946918882032,
            "max_log_strain_component": 0.001084503730591086,
            "step_scale": 1.0,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 2.30358951047877,
            "cell_principal_stretches": [
              1.0017336835814277,
              1.0015371004976485,
              0.9838539282454529
            ],
            "cell_volume_ratio": 0.987074523829197,
            "cell_rmsd_from_input_A": 0.1729743481809448
          },
          {
            "iteration": 3,
            "reduced_polarization": [
              -0.49966846597175224,
              1.498733808112896,
              -7.259816482148903e-05
            ],
            "branch_aligned_reduced_polarization": [
              -0.49966846597175224,
              1.498733808112896,
              -7.259816482148903e-05
            ],
            "target_residual": 0.0013108879434908065,
            "energy_eV": -219.50546826646226,
            "max_atomic_step_A": 0.0005089965997746718,
            "max_log_strain_component": 0.00010829421043162452,
            "step_scale": 1.0,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 2.30358951047877,
            "cell_principal_stretches": [
              1.001743144057257,
              1.0015474594383031,
              0.9837482725502268
            ],
            "cell_volume_ratio": 0.9869880516612191,
            "cell_rmsd_from_input_A": 0.17410912148350904
          },
          {
            "iteration": 4,
            "reduced_polarization": [
              -0.49997149765753907,
              1.499879106549141,
              -8.75060127219821e-06
            ],
            "branch_aligned_reduced_polarization": [
              -0.49997149765753907,
              1.499879106549141,
              -8.75060127219821e-06
            ],
            "target_residual": 0.00012451579421493512,
            "energy_eV": -219.49310474566602
          }
        ],
        "iterations": 4
      },
      "parent": {
        "candidate_id": "bec_projection_03",
        "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,
          1.5,
          0.0
        ],
        "formal_class": [
          0.5,
          0.5,
          0.0
        ],
        "target_residual": 0.00012451579421493512,
        "parent_symmetrization_rmsd_A": 0.09983797495395418,
        "parent_cell_rmsd_A": 0.17410912148350904,
        "energy_eV": -219.49310474566602,
        "reduced_polarization": [
          -0.49997149765753907,
          1.499879106549141,
          -8.75060127219821e-06
        ],
        "cartesian_polarization_e_A2": [
          -0.00641214795184368,
          0.03190182226261337,
          9.490896314389495e-07
        ],
        "ranking_score": 0.6436142869132613
      },
      "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
        ],
        "endpoint_rmsd_A": 0.013628568307740676,
        "minimum_distance_A_by_image": [
          1.710630618451604,
          1.7148631379826125,
          1.719098265882908,
          1.7233359990831423,
          1.7275763345472075,
          1.7318192692719006,
          1.7360648002865697,
          1.7403129246527989,
          1.7445636394640351
        ],
        "minimum_distance_A": 1.710630618451604,
        "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": [
          576.5357438740546,
          576.6504791160374,
          576.7652371912548,
          576.8800181042503,
          576.9948218595692,
          577.1096484617572,
          577.2244979153609,
          577.339370224928,
          577.4542653950065
        ],
        "cell_deformation_log_strain_norm": 0.001985651377372829
      },
      "parent_reduced_polarization": [
        -6.06592858203984e-13,
        1.0000025712726364,
        -3.1341728949245786e-13
      ],
      "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": [
          -225.99380790510943,
          -225.99677607912184,
          -225.9957345292761,
          -225.99075838037467,
          -225.98191979781433,
          -225.96928812475923,
          -225.95293002667984,
          -225.93290964264395,
          -225.90928874263562
        ],
        "cartesian_polarizations_e_A2": [
          [
            -1.9168087068880436e-10,
            0.023233080188845227,
            -1.751569217015702e-10
          ],
          [
            -1.6797070095776064e-10,
            0.02300222138445392,
            -1.534756126491181e-10
          ],
          [
            -1.44231466107018e-10,
            0.02277006172496052,
            -1.3176749594576074e-10
          ],
          [
            -1.2046379324885238e-10,
            0.022536641101770845,
            -1.1003254734593739e-10
          ],
          [
            -9.66680449148722e-11,
            0.022301992222149035,
            -8.827081988494811e-11
          ],
          [
            -7.284420682686241e-11,
            0.02206614065506799,
            -6.64817078659935e-11
          ],
          [
            -4.899234276660069e-11,
            0.0218291049179258,
            -4.4665450926780683e-11
          ],
          [
            -2.511218648589789e-11,
            0.02159089660448798,
            -2.2821600087847952e-11
          ],
          [
            -1.2036474426816247e-12,
            0.021351520554118084,
            -9.493092332637994e-13
          ]
        ],
        "raw_reduced_polarization": [
          [
            -2.295125107104387e-08,
            1.0885348570258584,
            -1.5853327709041203e-08
          ],
          [
            -2.0097633964443547e-08,
            1.0776678406401012,
            -1.3882517291900748e-08
          ],
          [
            -1.723962990430195e-08,
            1.066740900016309,
            -1.1908637739625817e-08
          ],
          [
            -1.4377287356091393e-08,
            1.0557559124333178,
            -9.931686903890027e-09
          ],
          [
            -1.151063746641653e-08,
            1.0447144182840578,
            -7.951669569492334e-09
          ],
          [
            -8.639651920639025e-09,
            1.0336176233023704,
            -5.9685307898785615e-09
          ],
          [
            -5.764346763709747e-09,
            1.022466402703352,
            -3.98229215220819e-09
          ],
          [
            -2.884680913178302e-09,
            1.0112613072534562,
            -1.992912826541035e-09
          ],
          [
            -6.06592858203984e-13,
            1.0000025712726364,
            -3.1341728949245786e-13
          ]
        ],
        "unwrapped_reduced_polarization": [
          [
            -2.295125107104387e-08,
            1.0885348570258584,
            -1.5853327709041203e-08
          ],
          [
            -2.0097633964443547e-08,
            1.0776678406401012,
            -1.3882517291900748e-08
          ],
          [
            -1.723962990430195e-08,
            1.066740900016309,
            -1.1908637739625817e-08
          ],
          [
            -1.4377287356091393e-08,
            1.0557559124333178,
            -9.931686903890027e-09
          ],
          [
            -1.151063746641653e-08,
            1.0447144182840578,
            -7.951669569492334e-09
          ],
          [
            -8.639651920639025e-09,
            1.0336176233023704,
            -5.9685307898785615e-09
          ],
          [
            -5.764346763709747e-09,
            1.022466402703352,
            -3.98229215220819e-09
          ],
          [
            -2.884680913178302e-09,
            1.0112613072534562,
            -1.992912826541035e-09
          ],
          [
            -6.065928582038749e-13,
            1.0000025712726364,
            -3.13417289492404e-13
          ]
        ],
        "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": [
          [
            -2.295125106632767e-08,
            0.0885348570258584,
            -1.585332770615011e-08
          ],
          [
            -2.009763394594799e-08,
            0.07766784064010124,
            -1.3882517302388209e-08
          ],
          [
            -1.7239629890308805e-08,
            0.06674090001630906,
            -1.1908637742585881e-08
          ],
          [
            -1.4377287360645141e-08,
            0.05575591243331779,
            -9.931686917319382e-09
          ],
          [
            -1.1510637443201688e-08,
            0.044714418284057755,
            -7.951669545036566e-09
          ],
          [
            -8.63965193831362e-09,
            0.03361762330237039,
            -5.968530780720016e-09
          ],
          [
            -5.7643467776813395e-09,
            0.022466402703352095,
            -3.98229216269641e-09
          ],
          [
            -2.884680938564088e-09,
            0.011261307253456199,
            -1.9929128347584424e-09
          ],
          [
            -6.065703495039543e-13,
            2.5712726363646965e-06,
            -3.134159598516817e-13
          ]
        ]
      },
      "reflected": {
        "reached": true,
        "construction": "reflect_displacements_about_reconstructed_parent",
        "energies_eV": [
          -225.90928874263557,
          -225.88634815359137,
          -225.86074439621223,
          -225.8325008611405,
          -225.8016398014839,
          -225.76818248456073,
          -225.7321492978345,
          -225.693559836098,
          -225.65243299972965
        ],
        "cartesian_polarizations_e_A2": [
          [
            -1.2037143977967734e-12,
            0.021351520554117986,
            -9.49415553949161e-13
          ],
          [
            2.2705907565087658e-11,
            0.021119604566635104,
            2.099690576969608e-11
          ],
          [
            4.663013203538309e-11,
            0.020886712269776533,
            4.296680427865015e-11
          ],
          [
            7.056963993930964e-11,
            0.02065284189548882,
            6.49604893007274e-11
          ],
          [
            9.452449942046076e-11,
            0.02041798843958611,
            8.697748369350169e-11
          ],
          [
            1.1849502886272467e-10,
            0.020182142939942103,
            1.09017989481385e-10
          ],
          [
            1.4248156412851335e-10,
            0.01994529250426403,
            1.3108246697562323e-10
          ],
          [
            1.6648472431504884e-10,
            0.019707420606451358,
            1.5317055137821013e-10
          ],
          [
            1.9050483852058426e-10,
            0.01946850738156175,
            1.7528223297988644e-10
          ]
        ],
        "raw_reduced_polarization": [
          [
            -6.166704489585298e-13,
            1.0000025712726317,
            -3.2305744142529747e-13
          ],
          [
            2.852739692906842e-09,
            0.9891872169075194,
            1.977593923596701e-09
          ],
          [
            5.7074056829439946e-09,
            0.9783251140655391,
            3.956997018815074e-09
          ],
          [
            8.563442951692618e-09,
            0.9674161734100938,
            5.937902944884551e-09
          ],
          [
            1.1420836377604604e-08,
            0.9564601539950387,
            7.920268735967463e-09
          ],
          [
            1.4279621243629998e-08,
            0.9454566294151066,
            9.90411298077933e-09
          ],
          [
            1.7139845889051274e-08,
            0.934404989063509,
            1.1889477653603343e-08
          ],
          [
            2.0001543506834852e-08,
            0.9233044519732531,
            1.3876330019064897e-08
          ],
          [
            2.286474065248992e-08,
            0.9121540805971161,
            1.5864669543217592e-08
          ]
        ],
        "unwrapped_reduced_polarization": [
          [
            -6.166704489585298e-13,
            1.0000025712726317,
            -3.2305744142529747e-13
          ],
          [
            2.852739692906842e-09,
            0.9891872169075194,
            1.977593923596701e-09
          ],
          [
            5.7074056829439946e-09,
            0.9783251140655391,
            3.956997018815074e-09
          ],
          [
            8.563442951692618e-09,
            0.9674161734100938,
            5.937902944884551e-09
          ],
          [
            1.1420836377604604e-08,
            0.9564601539950387,
            7.920268735967463e-09
          ],
          [
            1.4279621243629998e-08,
            0.9454566294151066,
            9.90411298077933e-09
          ],
          [
            1.7139845889051274e-08,
            0.934404989063509,
            1.1889477653603343e-08
          ],
          [
            2.0001543506834852e-08,
            0.9233044519732531,
            1.3876330019064897e-08
          ],
          [
            2.286474065248992e-08,
            0.9121540805971161,
            1.5864669543217592e-08
          ]
        ],
        "gauge_integer_shift": [
          0,
          0,
          0
        ],
        "expected_opposite_endpoint_reduced_polarization": [
          2.2676637952281455e-08,
          0.9122221829141665,
          1.5681485109548716e-08
        ],
        "actual_opposite_endpoint_branch_residual": 6.81023170508509e-05
      },
      "pnp_branch": {
        "construction": "incoming_path_concatenated_with_parent_reflection",
        "reduced_polarization": [
          [
            -2.295125107104387e-08,
            1.0885348570258584,
            -1.5853327709041203e-08
          ],
          [
            -2.0097633964443547e-08,
            1.0776678406401012,
            -1.3882517291900748e-08
          ],
          [
            -1.723962990430195e-08,
            1.066740900016309,
            -1.1908637739625817e-08
          ],
          [
            -1.4377287356091393e-08,
            1.0557559124333178,
            -9.931686903890027e-09
          ],
          [
            -1.151063746641653e-08,
            1.0447144182840578,
            -7.951669569492334e-09
          ],
          [
            -8.639651920639025e-09,
            1.0336176233023704,
            -5.9685307898785615e-09
          ],
          [
            -5.764346763709747e-09,
            1.022466402703352,
            -3.98229215220819e-09
          ],
          [
            -2.884680913178302e-09,
            1.0112613072534562,
            -1.992912826541035e-09
          ],
          [
            -6.06592858203984e-13,
            1.0000025712726364,
            -3.1341728949245786e-13
          ],
          [
            2.852739692906842e-09,
            0.9891872169075194,
            1.977593923596701e-09
          ],
          [
            5.7074056829439946e-09,
            0.9783251140655391,
            3.956997018815074e-09
          ],
          [
            8.563442951692618e-09,
            0.9674161734100938,
            5.937902944884551e-09
          ],
          [
            1.1420836377604604e-08,
            0.9564601539950387,
            7.920268735967463e-09
          ],
          [
            1.4279621243629998e-08,
            0.9454566294151066,
            9.90411298077933e-09
          ],
          [
            1.7139845889051274e-08,
            0.934404989063509,
            1.1889477653603343e-08
          ],
          [
            2.0001543506834852e-08,
            0.9233044519732531,
            1.3876330019064897e-08
          ],
          [
            2.286474065248992e-08,
            0.9121540805971161,
            1.5864669543217592e-08
          ]
        ],
        "unwrapped_reduced_polarization": [
          [
            -2.295125107104387e-08,
            1.0885348570258584,
            -1.5853327709041203e-08
          ],
          [
            -2.0097633964443547e-08,
            1.0776678406401012,
            -1.3882517291900748e-08
          ],
          [
            -1.723962990430195e-08,
            1.066740900016309,
            -1.1908637739625817e-08
          ],
          [
            -1.4377287356091393e-08,
            1.0557559124333178,
            -9.931686903890027e-09
          ],
          [
            -1.151063746641653e-08,
            1.0447144182840578,
            -7.951669569492334e-09
          ],
          [
            -8.639651920639025e-09,
            1.0336176233023704,
            -5.9685307898785615e-09
          ],
          [
            -5.764346763709747e-09,
            1.022466402703352,
            -3.98229215220819e-09
          ],
          [
            -2.884680913178302e-09,
            1.0112613072534562,
            -1.992912826541035e-09
          ],
          [
            -6.065928582038749e-13,
            1.0000025712726364,
            -3.13417289492404e-13
          ],
          [
            2.852739692906842e-09,
            0.9891872169075194,
            1.977593923596701e-09
          ],
          [
            5.7074056829439946e-09,
            0.9783251140655391,
            3.956997018815074e-09
          ],
          [
            8.563442951692618e-09,
            0.9674161734100938,
            5.937902944884551e-09
          ],
          [
            1.1420836377604604e-08,
            0.9564601539950387,
            7.920268735967463e-09
          ],
          [
            1.4279621243629998e-08,
            0.9454566294151066,
            9.90411298077933e-09
          ],
          [
            1.7139845889051274e-08,
            0.934404989063509,
            1.1889477653603343e-08
          ],
          [
            2.0001543506834852e-08,
            0.9233044519732531,
            1.3876330019064897e-08
          ],
          [
            2.286474065248992e-08,
            0.9121540805971161,
            1.5864669543217592e-08
          ]
        ],
        "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": [
          [
            -2.295125106632767e-08,
            0.0885348570258584,
            -1.585332770615011e-08
          ],
          [
            -2.009763394594799e-08,
            0.07766784064010124,
            -1.3882517302388209e-08
          ],
          [
            -1.7239629890308805e-08,
            0.06674090001630906,
            -1.1908637742585881e-08
          ],
          [
            -1.4377287360645141e-08,
            0.05575591243331779,
            -9.931686917319382e-09
          ],
          [
            -1.1510637443201688e-08,
            0.044714418284057755,
            -7.951669545036566e-09
          ],
          [
            -8.63965193831362e-09,
            0.03361762330237039,
            -5.968530780720016e-09
          ],
          [
            -5.7643467776813395e-09,
            0.022466402703352095,
            -3.98229216269641e-09
          ],
          [
            -2.884680938564088e-09,
            0.011261307253456199,
            -1.9929128347584424e-09
          ],
          [
            -6.065703495039543e-13,
            2.5712726363646965e-06,
            -3.134159598516817e-13
          ],
          [
            2.85273971112332e-09,
            -0.010812783092480682,
            1.9775939774646645e-09
          ],
          [
            5.7074056591943645e-09,
            -0.021674885934460875,
            3.956997063347956e-09
          ],
          [
            8.563442954745426e-09,
            -0.032583826589906106,
            5.9379029471173794e-09
          ],
          [
            1.1420836387721067e-08,
            -0.04353984600496119,
            7.920268774164185e-09
          ],
          [
            1.4279621263213471e-08,
            -0.05454337058489345,
            9.904112974190582e-09
          ],
          [
            1.713984587592421e-08,
            -0.0655950109364909,
            1.1889477624649203e-08
          ],
          [
            2.000154353254402e-08,
            -0.07669554802674705,
            1.3876329973960821e-08
          ],
          [
            2.286474065638089e-08,
            -0.08784591940288378,
            1.5864669578036228e-08
          ]
        ]
      },
      "incoming_structure_ids": [
        "incoming_00_000",
        "incoming_00_001",
        "incoming_00_002",
        "incoming_00_003",
        "incoming_00_004",
        "incoming_00_005",
        "incoming_00_006",
        "incoming_00_007",
        "incoming_00_008"
      ],
      "reflected_structure_ids": [
        "reflected_00_001",
        "reflected_00_002",
        "reflected_00_003",
        "reflected_00_004",
        "reflected_00_005",
        "reflected_00_006",
        "reflected_00_007",
        "reflected_00_008"
      ],
      "positive_extension_structure_ids": [
        "extension_plus_00_000",
        "extension_plus_00_001",
        "extension_plus_00_002",
        "extension_plus_00_003"
      ],
      "negative_extension_structure_ids": [
        "extension_minus_00_000",
        "extension_minus_00_001",
        "extension_minus_00_002",
        "extension_minus_00_003"
      ],
      "extension": {
        "enabled": true,
        "fraction_beyond_polar_endpoint": 0.35,
        "images_per_side": 4,
        "construction": "continue fractional atomic displacements and symmetric log strain beyond +P; reflect these structures about N for the -P side",
        "positive_path_coordinates": [
          1.35,
          1.2625,
          1.175,
          1.0875
        ],
        "negative_path_coordinates": [
          -1.0875,
          -1.175,
          -1.2625,
          -1.35
        ]
      },
      "branch_coordinates": [
        1.35,
        1.2625,
        1.175,
        1.0875,
        1.0,
        0.875,
        0.75,
        0.625,
        0.5,
        0.375,
        0.25,
        0.125,
        0.0,
        -0.125,
        -0.25,
        -0.375,
        -0.5,
        -0.625,
        -0.75,
        -0.875,
        -1.0,
        -1.0875,
        -1.175,
        -1.2625,
        -1.35
      ],
      "parent": {
        "candidate_id": "bec_projection_00",
        "source": "MACEField_BEC_backprojection",
        "spacegroup": "P6_3",
        "spacegroup_number": 173,
        "pointgroup": "6",
        "has_inversion": false,
        "is_polar_point_group": true,
        "nonpolar_parent_hypothesis": false,
        "symmetry_tolerance_A": null,
        "target_reduced_polarization": [
          0.0,
          1.0,
          0.0
        ],
        "formal_class": [
          0.0,
          0.0,
          0.0
        ],
        "target_residual": 2.5712726285932298e-06,
        "parent_symmetrization_rmsd_A": 0.013628568307740676,
        "parent_cell_rmsd_A": 0.02142600415316681,
        "energy_eV": -225.90928874263554,
        "reduced_polarization": [
          -6.169436358147267e-13,
          1.0000025712726286,
          -3.24600214377954e-13
        ],
        "cartesian_polarization_e_A2": [
          -1.2037080531627463e-12,
          0.02135152055411792,
          -9.494325691040515e-13
        ],
        "ranking_score": 0.5189902118912896
      }
    }
  ],
  "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": 45,
      "full_response": 13,
      "energy_polarization": 32
    },
    "model_evaluations_for_recovery_and_path_properties": {
      "total": 70,
      "full_response": 38,
      "energy_polarization": 32
    },
    "elapsed_seconds": 630.0727170489845
  }
}
