Recorded data and provenance for the associated calculation.

Download recorded JSON

timestamp2026-09-12T14:25:17.320342+00:00
execution_modenormal
checks289
maximum_scaled_error1.5183842738686337e-8
scopeIndependent spectral, reciprocal and complete-response checks of Dirac reduction.
View complete data
{
  "timestamp": "2026-09-12T14:25:17.320342+00:00",
  "execution_mode": "normal",
  "checks": 289,
  "maximum_scaled_error": 1.5183842738686337e-08,
  "scope": "Independent spectral, reciprocal and complete-response checks of Dirac reduction.",
  "results": {
    "spectral": [
      {
        "size": 1,
        "epsilon": 0.3,
        "coupling": 0.8,
        "occupation": 0.7,
        "energy": 0.11450973972391323,
        "trace_berry_error": 1.9083068458769503e-11,
        "nonabelian_connection_norm": 1.9083068458769503e-11
      },
      {
        "size": 1,
        "epsilon": 1.2,
        "coupling": -0.6,
        "occupation": 1.3,
        "energy": 0.055299299132866395,
        "trace_berry_error": 6.174116773394189e-12,
        "nonabelian_connection_norm": 6.174116773394189e-12
      },
      {
        "size": 2,
        "epsilon": 0.3,
        "coupling": 0.8,
        "occupation": 0.7,
        "energy": 0.958510057508325,
        "trace_berry_error": 8.892226630935004e-11,
        "nonabelian_connection_norm": 0.23936600305614042
      },
      {
        "size": 2,
        "epsilon": 1.2,
        "coupling": -0.6,
        "occupation": 1.3,
        "energy": 1.2206369048251333,
        "trace_berry_error": 3.6985735382915804e-12,
        "nonabelian_connection_norm": 0.15524504570032197
      },
      {
        "size": 3,
        "epsilon": 0.3,
        "coupling": 0.8,
        "occupation": 0.7,
        "energy": 2.159011224522253,
        "trace_berry_error": 8.955801949531014e-11,
        "nonabelian_connection_norm": 0.4863260691455319
      },
      {
        "size": 3,
        "epsilon": 1.2,
        "coupling": -0.6,
        "occupation": 1.3,
        "energy": 1.8516644496163888,
        "trace_berry_error": 3.706257817968852e-10,
        "nonabelian_connection_norm": 0.2022409464157095
      },
      {
        "size": 4,
        "epsilon": 0.3,
        "coupling": 0.8,
        "occupation": 0.7,
        "energy": 2.910855821532443,
        "trace_berry_error": 4.825993138551917e-10,
        "nonabelian_connection_norm": 0.6020921670935444
      },
      {
        "size": 4,
        "epsilon": 1.2,
        "coupling": -0.6,
        "occupation": 1.3,
        "energy": 3.159136509509886,
        "trace_berry_error": 3.3614933672937685e-10,
        "nonabelian_connection_norm": 0.2171445025752048
      }
    ],
    "reciprocal_action": [
      {
        "size": 1,
        "slow_norm": 1.0,
        "fast_norm": 1.0
      },
      {
        "size": 2,
        "slow_norm": 1.0000000000000002,
        "fast_norm": 1.0000000000000002
      },
      {
        "size": 3,
        "slow_norm": 1.0000000000000002,
        "fast_norm": 0.9999999999999996
      }
    ],
    "projected_master": [
      {
        "depth": 1,
        "retained_degree": 2,
        "fast_degree": 3,
        "trace": 4.0,
        "fast_rank": 4
      },
      {
        "depth": 2,
        "retained_degree": 2,
        "fast_degree": 3,
        "trace": 10.0,
        "fast_rank": 10
      },
      {
        "depth": 3,
        "retained_degree": 2,
        "fast_degree": 2,
        "trace": 10.000000000000002,
        "fast_rank": 10
      },
      {
        "depth": 6,
        "retained_degree": 1,
        "fast_degree": 2,
        "trace": 28.0,
        "fast_rank": 28
      }
    ],
    "assigned_band_controls": [
      {
        "depth": 5,
        "retained_degree": 9,
        "fast_degree": 9,
        "width": 1e-06,
        "fast_rank": 2002,
        "excess_energy": 2001.9979981574936,
        "source_coefficient": 2001.9999998425062,
        "smallest_fast_insertion": 0.0024498586620002693
      },
      {
        "depth": 5,
        "retained_degree": 9,
        "fast_degree": 9,
        "width": 0.001,
        "fast_rank": 2002,
        "excess_energy": 2000.1498700790398,
        "source_coefficient": 2001.85854355615,
        "smallest_fast_insertion": 0.0024498586620002693
      },
      {
        "depth": 5,
        "retained_degree": 9,
        "fast_degree": 9,
        "width": 0.1,
        "fast_rank": 2002,
        "excess_energy": 1923.6943361660224,
        "source_coefficient": 1979.9441823423856,
        "smallest_fast_insertion": 0.0024498586620002693
      },
      {
        "depth": 5,
        "retained_degree": 9,
        "fast_degree": 9,
        "width": 1.0,
        "fast_rank": 2002,
        "excess_energy": 1652.4009939171872,
        "source_coefficient": 1852.7214277619978,
        "smallest_fast_insertion": 0.0024498586620002693
      },
      {
        "depth": 5,
        "retained_degree": 14,
        "fast_degree": 14,
        "width": 1e-06,
        "fast_rank": 11628,
        "excess_energy": 11627.988485810149,
        "source_coefficient": 11627.999886455707,
        "smallest_fast_insertion": 1.4201110588400814e-05
      },
      {
        "depth": 5,
        "retained_degree": 14,
        "fast_degree": 14,
        "width": 0.001,
        "fast_rank": 11628,
        "excess_energy": 11621.894584653373,
        "source_coefficient": 11627.044889368875,
        "smallest_fast_insertion": 1.4201110588400814e-05
      },
      {
        "depth": 5,
        "retained_degree": 14,
        "fast_degree": 14,
        "width": 0.1,
        "fast_rank": 11628,
        "excess_energy": 11402.894227330105,
        "source_coefficient": 11563.564025961228,
        "smallest_fast_insertion": 1.4201110588400814e-05
      },
      {
        "depth": 5,
        "retained_degree": 14,
        "fast_degree": 14,
        "width": 1.0,
        "fast_rank": 11628,
        "excess_energy": 10587.85753730172,
        "source_coefficient": 11221.66038150836,
        "smallest_fast_insertion": 1.4201110588400814e-05
      },
      {
        "depth": 5,
        "retained_degree": 21,
        "fast_degree": 21,
        "width": 1e-06,
        "fast_rank": 65780,
        "excess_energy": 65779.95963781193,
        "source_coefficient": 65779.99608586662,
        "smallest_fast_insertion": 5.240699484550159e-09
      },
      {
        "depth": 5,
        "retained_degree": 21,
        "fast_degree": 21,
        "width": 0.001,
        "fast_rank": 65780,
        "excess_energy": 65764.086691018,
        "source_coefficient": 65777.1440105355,
        "smallest_fast_insertion": 5.240699484550159e-09
      },
      {
        "depth": 5,
        "retained_degree": 21,
        "fast_degree": 21,
        "width": 0.1,
        "fast_rank": 65780,
        "excess_energy": 65216.19913412091,
        "source_coefficient": 65622.00881846614,
        "smallest_fast_insertion": 5.240699484550159e-09
      },
      {
        "depth": 5,
        "retained_degree": 21,
        "fast_degree": 21,
        "width": 1.0,
        "fast_rank": 65780,
        "excess_energy": 63065.04176911321,
        "source_coefficient": 64804.96728269211,
        "smallest_fast_insertion": 5.240699484550159e-09
      },
      {
        "depth": 6,
        "retained_degree": 12,
        "fast_degree": 12,
        "width": 1e-06,
        "fast_rank": 18564,
        "excess_energy": 18563.98145128735,
        "source_coefficient": 18563.99998471281,
        "smallest_fast_insertion": 0.00021462952734159236
      },
      {
        "depth": 6,
        "retained_degree": 12,
        "fast_degree": 12,
        "width": 0.001,
        "fast_rank": 18564,
        "excess_energy": 18551.284993426507,
        "source_coefficient": 18562.14699256638,
        "smallest_fast_insertion": 0.00021462952734159236
      },
      {
        "depth": 6,
        "retained_degree": 12,
        "fast_degree": 12,
        "width": 0.1,
        "fast_rank": 18564,
        "excess_energy": 18101.411298390743,
        "source_coefficient": 18425.10673440405,
        "smallest_fast_insertion": 0.00021462952734159236
      },
      {
        "depth": 6,
        "retained_degree": 12,
        "fast_degree": 12,
        "width": 1.0,
        "fast_rank": 18564,
        "excess_energy": 16518.81197273733,
        "source_coefficient": 17715.319845219638,
        "smallest_fast_insertion": 0.00021462952734159236
      },
      {
        "depth": 6,
        "retained_degree": 34,
        "fast_degree": 34,
        "width": 1e-06,
        "fast_rank": 3838380,
        "excess_energy": 3838379.2534778574,
        "source_coefficient": 3838379.90101164,
        "smallest_fast_insertion": 2.7951632596598144e-15
      },
      {
        "depth": 6,
        "retained_degree": 34,
        "fast_degree": 34,
        "width": 0.001,
        "fast_rank": 3838380,
        "excess_energy": 3838140.612842479,
        "source_coefficient": 3838331.546067902,
        "smallest_fast_insertion": 2.7951632596598144e-15
      },
      {
        "depth": 6,
        "retained_degree": 34,
        "fast_degree": 34,
        "width": 0.1,
        "fast_rank": 3838380,
        "excess_energy": 3830381.033458169,
        "source_coefficient": 3836144.618034565,
        "smallest_fast_insertion": 2.7951632596598144e-15
      },
      {
        "depth": 6,
        "retained_degree": 34,
        "fast_degree": 34,
        "width": 1.0,
        "fast_rank": 3838380,
        "excess_energy": 3798841.3039176995,
        "source_coefficient": 3825132.65383776,
        "smallest_fast_insertion": 2.7951632596598144e-15
      },
      {
        "depth": 10,
        "retained_degree": 22,
        "fast_degree": 22,
        "width": 1e-06,
        "fast_rank": 64512240,
        "excess_energy": 64512197.823477715,
        "source_coefficient": 64512235.10422947,
        "smallest_fast_insertion": 8.265372666000754e-08
      },
      {
        "depth": 10,
        "retained_degree": 22,
        "fast_degree": 22,
        "width": 0.001,
        "fast_rank": 64512240,
        "excess_energy": 64499603.46606164,
        "source_coefficient": 64509361.47589961,
        "smallest_fast_insertion": 8.265372666000754e-08
      },
      {
        "depth": 10,
        "retained_degree": 22,
        "fast_degree": 22,
        "width": 0.1,
        "fast_rank": 64512240,
        "excess_energy": 64158876.91823747,
        "source_coefficient": 64395412.68015899,
        "smallest_fast_insertion": 8.265372666000754e-08
      },
      {
        "depth": 10,
        "retained_degree": 22,
        "fast_degree": 22,
        "width": 1.0,
        "fast_rank": 64512240,
        "excess_energy": 62986481.51663236,
        "source_coefficient": 63900763.459715515,
        "smallest_fast_insertion": 8.265372666000754e-08
      }
    ],
    "distinct_spectral_root": [
      {
        "overlap": 0.0,
        "width": 0.001,
        "spectral_cross": -1.1102230246251565e-16,
        "hs_root_cross": -0.2776251583843316
      },
      {
        "overlap": 0.0,
        "width": 0.1,
        "spectral_cross": -2.220446049250313e-16,
        "hs_root_cross": -0.2776251583843316
      },
      {
        "overlap": 0.2,
        "width": 0.001,
        "spectral_cross": 4.791613030796782e-07,
        "hs_root_cross": -0.21913479533151892
      },
      {
        "overlap": 0.2,
        "width": 0.1,
        "spectral_cross": 0.004314482113929874,
        "hs_root_cross": -0.21913479533151892
      },
      {
        "overlap": 0.7,
        "width": 0.001,
        "spectral_cross": 4.47199272446408e-06,
        "hs_root_cross": -0.07963966888254803
      },
      {
        "overlap": 0.7,
        "width": 0.1,
        "spectral_cross": 0.031170384990417854,
        "hs_root_cross": -0.07963966888254803
      },
      {
        "overlap": 1.0,
        "width": 0.001,
        "spectral_cross": 0.0009983007292725388,
        "hs_root_cross": -1.6653345369377348e-16
      },
      {
        "overlap": 1.0,
        "width": 0.1,
        "spectral_cross": 0.0834466811773511,
        "hs_root_cross": -1.6653345369377348e-16
      }
    ],
    "complete_scalar_square": [
      {
        "depth": 1,
        "slow_degree": 2,
        "fast_degree": 3,
        "slow_current": 0.8,
        "occupation_per_fast_mode": 0.4,
        "coupling": 0.7,
        "complete_slow_frequency": 2.1279999999999997,
        "total_energy": 2.1952000000000003,
        "total_canonical_norm": 2.4000000000000004
      },
      {
        "depth": 2,
        "slow_degree": 2,
        "fast_degree": 2,
        "slow_current": 0.8,
        "occupation_per_fast_mode": 0.4,
        "coupling": 0.7,
        "complete_slow_frequency": 3.024,
        "total_energy": 3.8976000000000006,
        "total_canonical_norm": 3.2
      },
      {
        "depth": 3,
        "slow_degree": 1,
        "fast_degree": 2,
        "slow_current": 0.8,
        "occupation_per_fast_mode": 0.4,
        "coupling": 0.7,
        "complete_slow_frequency": 3.6959999999999997,
        "total_energy": 8.1984,
        "total_canonical_norm": 4.8
      },
      {
        "depth": 6,
        "slow_degree": 1,
        "fast_degree": 1,
        "slow_current": 0.8,
        "occupation_per_fast_mode": 0.4,
        "coupling": 0.7,
        "complete_slow_frequency": 2.94,
        "total_energy": 4.704,
        "total_canonical_norm": 3.6000000000000005
      },
      {
        "depth": 5,
        "slow_degree": 9,
        "fast_degree": 9,
        "per_mode_occupation_one_frequency": 2121.112128146453,
        "fixed_total_fast_norm_one_frequency": 120.11212814645309,
        "cross_only_per_mode_occupation_one_frequency": 2002,
        "slow_self_multiplier": 119.11212814645309
      },
      {
        "depth": 5,
        "slow_degree": 14,
        "fast_degree": 14,
        "per_mode_occupation_one_frequency": 12197.70027303064,
        "fixed_total_fast_norm_one_frequency": 570.7002730306401,
        "cross_only_per_mode_occupation_one_frequency": 11628,
        "slow_self_multiplier": 569.7002730306401
      },
      {
        "depth": 5,
        "slow_degree": 21,
        "fast_degree": 21,
        "per_mode_occupation_one_frequency": 68600.84776513277,
        "fixed_total_fast_norm_one_frequency": 2821.8477651327726,
        "cross_only_per_mode_occupation_one_frequency": 65780,
        "slow_self_multiplier": 2820.8477651327726
      },
      {
        "depth": 6,
        "slow_degree": 12,
        "fast_degree": 12,
        "per_mode_occupation_one_frequency": 19144.39172413793,
        "fixed_total_fast_norm_one_frequency": 581.3917241379311,
        "cross_only_per_mode_occupation_one_frequency": 18564,
        "slow_self_multiplier": 580.3917241379311
      },
      {
        "depth": 6,
        "slow_degree": 34,
        "fast_degree": 34,
        "per_mode_occupation_one_frequency": 3917910.8961571692,
        "fixed_total_fast_norm_one_frequency": 79531.89615716934,
        "cross_only_per_mode_occupation_one_frequency": 3838380,
        "slow_self_multiplier": 79530.89615716934
      },
      {
        "depth": 10,
        "slow_degree": 22,
        "fast_degree": 22,
        "per_mode_occupation_one_frequency": 64686151.62061292,
        "fixed_total_fast_norm_one_frequency": 173912.620612918,
        "cross_only_per_mode_occupation_one_frequency": 64512240,
        "slow_self_multiplier": 173911.620612918
      }
    ]
  },
  "source_sha256": {
    "experiments/dirac_current_reduction_checks.py": "b26dd1108f49c5b7254d56966739b9f67bf04d521def9d289d8b183636b36c7a",
    "experiments/dirac_current_reduction.py": "e9a907c42f83662ade7a9ce8baba55a3c0e880c99ac5480b578beb6e381738e9",
    "experiments/graded_current_tower.py": "cf0f72cb6d078df086ec594550155d6518b00255ed46a16d669790edb093a602",
    "experiments/coherent_mode_algebra.py": "4fbcbb6a1fbaa5a1a7de387746eda4d00f69fe22bbdb1e906c8795f8bb786dff",
    "experiments/spatial_dirac_mode_checks.py": "116a9f6d0f3cbcf9ee2fbe7a762e09c113194a07591191dd6663f5bcb8364552"
  }
}