{
  "created": "2026-09-12T03:57:25.691689+00:00",
  "status": "conditional_inverse_construction",
  "checks": 219,
  "scope": "Specified independent canonical mode-bundle actions; positive-current coherent branches and smooth physical CP3 controls. No master-action or observed-particle identification.",
  "execution_mode": "optimized",
  "peak_variations": [
    {
      "N": 2,
      "d": 2,
      "energy": 5.14001615701859,
      "expected": 5.140016157018584,
      "first_variation_error": 1.6538859171078002e-10,
      "hessian_errors": [
        1.0593700267271346e-07,
        4.237990925408144e-09,
        1.694576484587523e-10
      ]
    },
    {
      "N": 3,
      "d": 2,
      "energy": 7.619934803287942,
      "expected": 7.619934803287935,
      "first_variation_error": 8.383449490168005e-11,
      "hessian_errors": [
        9.866932568110585e-08,
        3.9464316995130525e-09,
        1.6198384691658594e-10
      ]
    },
    {
      "N": 2,
      "d": 6,
      "energy": 23.76220227539413,
      "expected": 23.762202275394177,
      "first_variation_error": 2.8633273529976577e-10,
      "hessian_errors": [
        9.220533875625502e-08,
        3.6884466591631083e-09,
        1.47394515437571e-10
      ]
    }
  ],
  "smooth_response": [
    {
      "N": 2,
      "full_response_error": 4.8875796561963366e-11
    },
    {
      "N": 3,
      "full_response_error": 7.030158730127034e-11
    }
  ],
  "spatial_response": [
    {
      "mass": 2.0,
      "feedback": 0.0,
      "ell": 1,
      "growth": 2.220446049250313e-16
    },
    {
      "mass": 2.0,
      "feedback": 0.0,
      "ell": 3,
      "growth": 0.0
    },
    {
      "mass": 2.0,
      "feedback": 0.0,
      "ell": 30,
      "growth": 0.0
    },
    {
      "mass": 2.0,
      "feedback": 0.0,
      "ell": 300,
      "growth": 0.0
    },
    {
      "mass": 2.0,
      "feedback": 0.2,
      "ell": 1,
      "growth": -1.1355715307340597e-16
    },
    {
      "mass": 2.0,
      "feedback": 0.2,
      "ell": 3,
      "growth": 4.86959716818167e-16
    },
    {
      "mass": 2.0,
      "feedback": 0.2,
      "ell": 30,
      "growth": -1.0465687112648282e-15
    },
    {
      "mass": 2.0,
      "feedback": 0.2,
      "ell": 300,
      "growth": 5.417888360170764e-14
    },
    {
      "mass": 2.0,
      "feedback": 2.0,
      "ell": 1,
      "growth": 0.0
    },
    {
      "mass": 2.0,
      "feedback": 2.0,
      "ell": 3,
      "growth": 0.0
    },
    {
      "mass": 2.0,
      "feedback": 2.0,
      "ell": 30,
      "growth": 0.0
    },
    {
      "mass": 2.0,
      "feedback": 2.0,
      "ell": 300,
      "growth": 0.0
    },
    {
      "mass": 2.0,
      "feedback": 3.0,
      "ell": 1,
      "growth": 0.8056740287942241
    },
    {
      "mass": 2.0,
      "feedback": 3.0,
      "ell": 3,
      "growth": 1.2526848692520631
    },
    {
      "mass": 2.0,
      "feedback": 3.0,
      "ell": 30,
      "growth": 1.4110055050246526
    },
    {
      "mass": 2.0,
      "feedback": 3.0,
      "ell": 300,
      "growth": 1.414178557808654
    }
  ],
  "large_bands": [
    {
      "N": 12,
      "d": 6,
      "a": 0.0,
      "mean": 5.3867700926509845e-05,
      "logZ": 0.0,
      "susceptibility_ratio": 0.0
    },
    {
      "N": 12,
      "d": 6,
      "a": 1.0,
      "mean": 5.5651055196049e-05,
      "logZ": 5.4741754662024356e-05,
      "susceptibility_ratio": 0.034014422583648854
    },
    {
      "N": 12,
      "d": 6,
      "a": 10.0,
      "mean": 0.00010031978013135772,
      "logZ": 0.0006923143050716618,
      "susceptibility_ratio": 1.327802856355968
    },
    {
      "N": 12,
      "d": 6,
      "a": 30.0,
      "mean": 0.6785436579015974,
      "logZ": 2.1707255104427325,
      "susceptibility_ratio": 3.011659130202846
    },
    {
      "N": 12,
      "d": 6,
      "a": 100.0,
      "mean": 0.937870154455668,
      "logZ": 64.24106933538127,
      "susceptibility_ratio": 0.06876721690745878
    },
    {
      "N": 12,
      "d": 6,
      "a": 200.0,
      "mean": 0.9694948785925447,
      "logZ": 159.97849305743475,
      "susceptibility_ratio": 0.03201224753545165
    },
    {
      "N": 12,
      "d": 6,
      "a": 201.0,
      "mean": 0.9696492713076846,
      "logZ": 160.9480652630255,
      "susceptibility_ratio": 0.031842217762423616
    },
    {
      "N": 12,
      "d": 6,
      "a": 1000.0,
      "mean": 0.9939805686388508,
      "logZ": 950.2426199457461,
      "susceptibility_ratio": 0.006075618111261766
    },
    {
      "N": 12,
      "d": 6,
      "a": 10000.0,
      "mean": 0.999399807320648,
      "logZ": 9936.409694977818,
      "susceptibility_ratio": 0.0006007461016887117
    },
    {
      "N": 12,
      "d": 6,
      "a": 1000000.0,
      "mean": 0.9999939999807498,
      "logZ": 999908.7767672157,
      "susceptibility_ratio": 6.000074501099915e-06
    },
    {
      "N": 12,
      "spatial_normalization": 1694.7631206749377,
      "cubature": [
        0.9999999999999977,
        1.5096357534110287,
        2.662060405881802,
        0.2499999999999994,
        0.24999999999999944,
        0.2499999999999994,
        0.24999999999999947,
        34.77866777016289,
        0.10000000000000035,
        0.028571428571428765,
        0.002380952380952399
      ]
    },
    {
      "N": 34,
      "d": 6,
      "a": 0.0,
      "mean": 2.605265763159794e-07,
      "logZ": 0.0,
      "susceptibility_ratio": 0.0
    },
    {
      "N": 34,
      "d": 6,
      "a": 1.0,
      "mean": 2.662033589633673e-07,
      "logZ": 2.6331698943504733e-07,
      "susceptibility_ratio": 0.022442554734028116
    },
    {
      "N": 34,
      "d": 6,
      "a": 10.0,
      "mean": 3.8841994164264663e-07,
      "logZ": 3.0534754245081785e-06,
      "susceptibility_ratio": 0.856366339309428
    },
    {
      "N": 34,
      "d": 6,
      "a": 30.0,
      "mean": 0.011882526297312054,
      "logZ": 0.015696416622308362,
      "susceptibility_ratio": 22.94408569445451
    },
    {
      "N": 34,
      "d": 6,
      "a": 100.0,
      "mean": 0.9377386329524607,
      "logZ": 58.00452912395123,
      "susceptibility_ratio": 0.06908075838208573
    },
    {
      "N": 34,
      "d": 6,
      "a": 200.0,
      "mean": 0.9694644890638204,
      "logZ": 153.7356337723062,
      "susceptibility_ratio": 0.03207828120712691
    },
    {
      "N": 34,
      "d": 6,
      "a": 201.0,
      "mean": 0.9696191945639804,
      "logZ": 154.70517574516768,
      "susceptibility_ratio": 0.03190754337860918
    },
    {
      "N": 34,
      "d": 6,
      "a": 1000.0,
      "mean": 0.9939794207364446,
      "logZ": 943.9950367824553,
      "susceptibility_ratio": 0.006077950737751542
    },
    {
      "N": 34,
      "d": 6,
      "a": 10000.0,
      "mean": 0.9993997959817943,
      "logZ": 9930.161085040723,
      "susceptibility_ratio": 0.0006007688151895466
    },
    {
      "N": 34,
      "d": 6,
      "a": 1000000.0,
      "mean": 0.9999939999796175,
      "logZ": 999902.528045099,
      "susceptibility_ratio": 6.000076765872079e-06
    },
    {
      "N": 34,
      "spatial_normalization": 3391520233.235542,
      "cubature": [
        0.999999999999997,
        2.835194788111109,
        10.030202895734062,
        0.2499999999999993,
        0.2499999999999993,
        0.2499999999999993,
        0.2499999999999994,
        422.4500106032427,
        0.10000000000000035,
        0.028571428571428765,
        0.002380952380952399
      ]
    },
    {
      "N": 22,
      "d": 10,
      "a": 0.0,
      "mean": 1.5500934396321892e-08,
      "logZ": 2.2204460492503128e-16,
      "susceptibility_ratio": 0.0
    },
    {
      "N": 22,
      "d": 10,
      "a": 1.0,
      "mean": 1.5543257551450578e-08,
      "logZ": 1.5522005680779216e-08,
      "susceptibility_ratio": 0.002758231560754769
    },
    {
      "N": 22,
      "d": 10,
      "a": 10.0,
      "mean": 1.5988713093604628e-08,
      "logZ": 1.573133605603516e-07,
      "susceptibility_ratio": 0.036536144922005236
    },
    {
      "N": 22,
      "d": 10,
      "a": 30.0,
      "mean": 3.638700225029398e-08,
      "logZ": 5.282902471037687e-07,
      "susceptibility_ratio": 8.716270866837627
    },
    {
      "N": 22,
      "d": 10,
      "a": 100.0,
      "mean": 0.8937896241038586,
      "logZ": 38.71172636141961,
      "susceptibility_ratio": 0.12713011184556217
    },
    {
      "N": 22,
      "d": 10,
      "a": 200.0,
      "mean": 0.9485808222509644,
      "logZ": 131.4836172782764,
      "susceptibility_ratio": 0.055827257026138916
    },
    {
      "N": 22,
      "d": 10,
      "a": 201.0,
      "mean": 0.9488442469570453,
      "logZ": 132.43233003873394,
      "susceptibility_ratio": 0.05551668445512908
    },
    {
      "N": 22,
      "d": 10,
      "a": 1000.0,
      "mean": 0.9899467141806649,
      "logZ": 915.1693256274681,
      "susceptibility_ratio": 0.010210017039383575
    },
    {
      "N": 22,
      "d": 10,
      "a": 10000.0,
      "mean": 0.9989994742277319,
      "logZ": 9892.095838178613,
      "susceptibility_ratio": 0.0010020549000328287
    },
    {
      "N": 22,
      "d": 10,
      "a": 1000000.0,
      "mean": 0.9999899999474993,
      "logZ": 999846.0389349603,
      "susceptibility_ratio": 1.0000205004887497e-05
    }
  ],
  "mass_limits": [
    {
      "eta": 1.0,
      "frequency_ratio": 206.83124337625816,
      "energy_ratio": 207.5113445193284,
      "states": [
        {
          "N": 12,
          "frequency": 18557.99896252662,
          "energy": 18496.69697152437,
          "susceptibility_ratio": 0.00032342255645976446
        },
        {
          "N": 34,
          "frequency": 3838373.99999469,
          "energy": 3838274.457727611,
          "susceptibility_ratio": 1.5631646682520125e-06
        }
      ]
    },
    {
      "eta": 0.1,
      "frequency_ratio": 206.77135665579453,
      "energy_ratio": 206.85445252259913,
      "states": [
        {
          "N": 12,
          "frequency": 18563.39998962995,
          "energy": 18555.888052745107,
          "susceptibility_ratio": 3.232278251611021e-05
        },
        {
          "N": 34,
          "frequency": 3838379.399999947,
          "energy": 3838368.0642212275,
          "susceptibility_ratio": 1.5631599789300153e-07
        }
      ]
    },
    {
      "eta": 0.01,
      "frequency_ratio": 206.7653709299556,
      "energy_ratio": 206.7752084932797,
      "states": [
        {
          "N": 12,
          "frequency": 18563.939999896305,
          "energy": 18563.05064923565,
          "susceptibility_ratio": 3.2320836736459557e-06
        },
        {
          "N": 34,
          "frequency": 3838379.9399999995,
          "energy": 3838378.668267013,
          "susceptibility_ratio": 1.563159509999653e-08
        }
      ]
    },
    {
      "eta": 0.0001,
      "frequency_ratio": 206.76471253279627,
      "energy_ratio": 206.76484152961402,
      "states": [
        {
          "N": 12,
          "frequency": 18563.99939999999,
          "energy": 18563.987743389218,
          "susceptibility_ratio": 3.232062271770311e-08
        },
        {
          "N": 34,
          "frequency": 3838379.9994,
          "energy": 3838379.983919569,
          "susceptibility_ratio": 1.5631594584173334e-10
        }
      ]
    }
  ],
  "cusp": {
    "N": 3,
    "d": 2,
    "right_derivative": 4.999999999988347,
    "left_derivative": -4.999999999988347
  },
  "sources": {
    "experiments/coherent_peak_action_checks.py": "66485a4d5b0f604172685439fffb1073469d57c72293ba92ed15ffe30874aff1",
    "experiments/coherent_mode_algebra.py": "4fbcbb6a1fbaa5a1a7de387746eda4d00f69fe22bbdb1e906c8795f8bb786dff",
    "experiments/coherent_spatial_bundle_checks.py": "2fe91619467ae08a40bb053b88fad079deaf0a1b23836f713db8cd83107c207a"
  }
}