{
  "checks_passed": 75,
  "parameters": {
    "b1": 1,
    "b0": 4,
    "mu": 1,
    "c": 1,
    "gamma2": 1,
    "gamma3": 1,
    "N": 1
  },
  "rows": [
    {
      "R": 0.1,
      "phase": 0,
      "broad_fraction": 0,
      "current": 0.0,
      "shape2": 3.181949859554436,
      "shape3": 0.0011679079693571134,
      "force_R": -117.96209882077919
    },
    {
      "R": 0.5,
      "phase": 0,
      "broad_fraction": 0,
      "current": 0.0,
      "shape2": 68.88134996766712,
      "shape3": 73.7498955623181,
      "force_R": -2284.9652324199833
    },
    {
      "R": 1,
      "phase": 0,
      "broad_fraction": 0,
      "current": 0.0,
      "shape2": 6524.8026918614405,
      "shape3": 307.68986831205814,
      "force_R": -1525.1524688175728
    },
    {
      "R": 2,
      "phase": 0,
      "broad_fraction": 0,
      "current": 0.0,
      "shape2": 7.97107254862814,
      "shape3": 0.07981175418055565,
      "force_R": 99.64557113363395
    },
    {
      "R": 4,
      "phase": 0,
      "broad_fraction": 0,
      "current": 0.0,
      "shape2": 1.6060888813315152e-18,
      "shape3": 3.9336987248629844e-21,
      "force_R": 4.8679253406431325e-17
    },
    {
      "R": 0.1,
      "phase": 1.0471975511965976,
      "broad_fraction": 0,
      "current": 0.024992384045589,
      "shape2": 5.26658097102841,
      "shape3": 0.007161611806328188,
      "force_R": -188.90334908557418
    },
    {
      "R": 0.5,
      "phase": 1.0471975511965976,
      "broad_fraction": 0,
      "current": 0.1807232249639688,
      "shape2": 335.20831208728083,
      "shape3": 176.95433783770423,
      "force_R": -8631.948487100974
    },
    {
      "R": 1,
      "phase": 1.0471975511965976,
      "broad_fraction": 0,
      "current": 0.0223695816783678,
      "shape2": 12484.414675388121,
      "shape3": 477.91883758103904,
      "force_R": 2425.6544921203704
    },
    {
      "R": 2,
      "phase": 1.0471975511965976,
      "broad_fraction": 0,
      "current": 2.2704351020509958e-07,
      "shape2": 13.346485069485771,
      "shape3": 0.10760343625025212,
      "force_R": 167.01267659452887
    },
    {
      "R": 4,
      "phase": 1.0471975511965976,
      "broad_fraction": 0,
      "current": 4.495604672126863e-28,
      "shape2": 2.612399571246688e-18,
      "shape3": 5.090191847377364e-21,
      "force_R": 7.915160208529223e-17
    },
    {
      "R": 0.1,
      "phase": 2.0943951023931953,
      "broad_fraction": 0,
      "current": 0.18876532579159905,
      "shape2": 28.014310162571142,
      "shape3": 0.8389188656495188,
      "force_R": -782.3504524843406
    },
    {
      "R": 0.5,
      "phase": 2.0943951023931953,
      "broad_fraction": 0,
      "current": 0.40433004479768414,
      "shape2": 24195.819168339527,
      "shape3": 2422.5455985255467,
      "force_R": -287667.9120467901
    },
    {
      "R": 1,
      "phase": 2.0943951023931953,
      "broad_fraction": 0,
      "current": 0.028852379096123846,
      "shape2": 187187.83939961385,
      "shape3": 3440.746540537866,
      "force_R": 166607.3809870523
    },
    {
      "R": 2,
      "phase": 2.0943951023931953,
      "broad_fraction": 0,
      "current": 2.567582589372954e-07,
      "shape2": 159.31189159131793,
      "shape3": 0.6860636469122624,
      "force_R": 1996.0541000954686
    },
    {
      "R": 4,
      "phase": 2.0943951023931953,
      "broad_fraction": 0,
      "current": 4.7883163675138085e-28,
      "shape2": 2.96954668155073e-17,
      "shape3": 3.148427729618749e-20,
      "force_R": 8.991495253128817e-16
    },
    {
      "R": 0.1,
      "phase": 0,
      "broad_fraction": 0.5,
      "current": 0.0,
      "shape2": 0.8531478555065394,
      "shape3": 0.00011416339228594803,
      "force_R": -32.75348232898986
    },
    {
      "R": 0.5,
      "phase": 0,
      "broad_fraction": 0.5,
      "current": 0.0,
      "shape2": 73.23260478982023,
      "shape3": 12.686783247036814,
      "force_R": -177.10312671254206
    },
    {
      "R": 1,
      "phase": 0,
      "broad_fraction": 0.5,
      "current": 0.0,
      "shape2": 1921.3448347002827,
      "shape3": 208.06654127949943,
      "force_R": -8585.560122518707
    },
    {
      "R": 2,
      "phase": 0,
      "broad_fraction": 0.5,
      "current": 0.0,
      "shape2": 297.1296162157094,
      "shape3": 5.7629034772051035,
      "force_R": 1907.7099033219922
    },
    {
      "R": 4,
      "phase": 0,
      "broad_fraction": 0.5,
      "current": 0.0,
      "shape2": 4.19360398326246e-09,
      "shape3": 1.9458960276162303e-11,
      "force_R": 7.678446483849238e-08
    },
    {
      "R": 0.1,
      "phase": 1.0471975511965976,
      "broad_fraction": 0.5,
      "current": 0.013614728087228417,
      "shape2": 1.4545347257010215,
      "shape3": 0.0007362397271386648,
      "force_R": -54.97486907113041
    },
    {
      "R": 0.5,
      "phase": 1.0471975511965976,
      "broad_fraction": 0.5,
      "current": 0.15359326662515724,
      "shape2": 73.98518879628567,
      "shape3": 36.599796487927186,
      "force_R": -604.6321507410574
    },
    {
      "R": 1,
      "phase": 1.0471975511965976,
      "broad_fraction": 0.5,
      "current": 0.06809585927587064,
      "shape2": 4195.226868107775,
      "shape3": 360.9389708260711,
      "force_R": -15320.098320484245
    },
    {
      "R": 2,
      "phase": 1.0471975511965976,
      "broad_fraction": 0.5,
      "current": 7.023672179123135e-05,
      "shape2": 509.8648665753835,
      "shape3": 8.010273551509336,
      "force_R": 3292.83324750443
    },
    {
      "R": 4,
      "phase": 1.0471975511965976,
      "broad_fraction": 0.5,
      "current": 9.637061138613947e-18,
      "shape2": 6.8665520375190215e-09,
      "shape3": 2.5370231522412866e-11,
      "force_R": 1.2565342891460258e-07
    },
    {
      "R": 0.1,
      "phase": 2.0943951023931953,
      "broad_fraction": 0.5,
      "current": 0.10986233006531537,
      "shape2": 9.615603526574844,
      "shape3": 0.10423364293684935,
      "force_R": -316.4719380971986
    },
    {
      "R": 0.5,
      "phase": 2.0943951023931953,
      "broad_fraction": 0.5,
      "current": 0.4577540614578044,
      "shape2": 2780.078668378399,
      "shape3": 703.2590380588558,
      "force_R": -45017.10911886908
    },
    {
      "R": 1,
      "phase": 2.0943951023931953,
      "broad_fraction": 0.5,
      "current": 0.10093424066701961,
      "shape2": 80735.53100627173,
      "shape3": 2970.7650554306865,
      "force_R": -176376.67593232833
    },
    {
      "R": 2,
      "phase": 2.0943951023931953,
      "broad_fraction": 0.5,
      "current": 8.285550192928574e-05,
      "shape2": 6353.647997065417,
      "shape3": 52.23536130783873,
      "force_R": 41385.689953657995
    },
    {
      "R": 4,
      "phase": 2.0943951023931953,
      "broad_fraction": 0.5,
      "current": 1.0500204545528424e-17,
      "shape2": 7.887959727533972e-08,
      "shape3": 1.5799129708477017e-10,
      "force_R": 1.4420469891017545e-06
    },
    {
      "R": 0.1,
      "phase": 0,
      "broad_fraction": 1,
      "current": 0.0,
      "shape2": 0.014351805054544486,
      "shape3": 7.765966574790868e-08,
      "force_R": -0.5731106697608783
    },
    {
      "R": 0.5,
      "phase": 0,
      "broad_fraction": 1,
      "current": 0.0,
      "shape2": 8.201950329788508,
      "shape3": 0.016789042442991498,
      "force_R": -62.537216076668095
    },
    {
      "R": 1,
      "phase": 0,
      "broad_fraction": 1,
      "current": 0.0,
      "shape2": 91.24915020738206,
      "shape3": 1.1523421181612203,
      "force_R": -268.3613199501887
    },
    {
      "R": 2,
      "phase": 0,
      "broad_fraction": 1,
      "current": 0.0,
      "shape2": 159.34362313183456,
      "shape3": 4.807654192375908,
      "force_R": 218.14330807437295
    },
    {
      "R": 4,
      "phase": 0,
      "broad_fraction": 1,
      "current": 0.0,
      "shape2": 0.0536289784574218,
      "shape3": 0.001247058659071182,
      "force_R": 0.3535116519633101
    },
    {
      "R": 0.1,
      "phase": 1.0471975511965976,
      "broad_fraction": 1,
      "current": 0.001643348033570163,
      "shape2": 0.025321003046653936,
      "shape3": 5.298018298132431e-07,
      "force_R": -1.039813673401724
    },
    {
      "R": 0.5,
      "phase": 1.0471975511965976,
      "broad_fraction": 1,
      "current": 0.030133803872421958,
      "shape2": 12.811094284660333,
      "shape3": 0.06765345096813738,
      "force_R": -93.65365850381372
    },
    {
      "R": 1,
      "phase": 1.0471975511965976,
      "broad_fraction": 1,
      "current": 0.05068197777711243,
      "shape2": 122.66024364202272,
      "shape3": 2.7649115287141286,
      "force_R": -337.1930579348176
    },
    {
      "R": 2,
      "phase": 1.0471975511965976,
      "broad_fraction": 1,
      "current": 0.006970412372678566,
      "shape2": 203.63687843012767,
      "shape3": 7.467481837203735,
      "force_R": 266.7588709146869
    },
    {
      "R": 4,
      "phase": 1.0471975511965976,
      "broad_fraction": 1,
      "current": 7.884871410514711e-08,
      "shape2": 0.0784629197560792,
      "shape3": 0.0016813036914101894,
      "force_R": 0.5131736540984104
    },
    {
      "R": 0.1,
      "phase": 2.0943951023931953,
      "broad_fraction": 1,
      "current": 0.014322367921119558,
      "shape2": 0.21527057357369353,
      "shape3": 9.588373404228747e-05,
      "force_R": -8.619897355576358
    },
    {
      "R": 0.5,
      "phase": 2.0943951023931953,
      "broad_fraction": 1,
      "current": 0.1607131212072736,
      "shape2": 67.80872209983008,
      "shape3": 2.5753397110652827,
      "force_R": -462.8134626202864
    },
    {
      "R": 1,
      "phase": 2.0943951023931953,
      "broad_fraction": 1,
      "current": 0.13724785754980134,
      "shape2": 556.0974294425466,
      "shape3": 37.85227497696167,
      "force_R": -1596.3864933017912
    },
    {
      "R": 2,
      "phase": 2.0943951023931953,
      "broad_fraction": 1,
      "current": 0.010538609057368364,
      "shape2": 1225.1738090455785,
      "shape3": 53.76166469590416,
      "force_R": 1184.2577357406174
    },
    {
      "R": 4,
      "phase": 2.0943951023931953,
      "broad_fraction": 1,
      "current": 9.874792474183032e-08,
      "shape2": 0.7127722391583846,
      "shape3": 0.0107197444830041,
      "force_R": 4.564368440406984
    }
  ],
  "small": [
    {
      "h": 0,
      "phase": 0,
      "leading_coefficients": [
        0.0,
        36864.0,
        131072.0
      ],
      "scaled": [
        0.0,
        36863.45933185021,
        131070.42715207812
      ]
    },
    {
      "h": 0,
      "phase": 1.0471975511965976,
      "leading_coefficients": [
        2.6666666666666665,
        65536.0,
        932067.5555555555
      ],
      "scaled": [
        2.6666488890026647,
        65534.543663836324,
        932040.2156473688
      ]
    },
    {
      "h": 0,
      "phase": 2.0943951023931953,
      "leading_coefficients": [
        23.999999999999986,
        589823.9999999995,
        209715199.99999964
      ],
      "scaled": [
        23.999328023038874,
        589775.2441832488,
        209688024.11032727
      ]
    },
    {
      "h": 0.5,
      "phase": 0,
      "leading_coefficients": [
        0.0,
        9252.0,
        12282.5
      ],
      "scaled": [
        0.0,
        9251.924850321957,
        12282.407881838546
      ]
    },
    {
      "h": 0.5,
      "phase": 1.0471975511965976,
      "leading_coefficients": [
        1.4166666666666665,
        16448.0,
        87342.22222222222
      ],
      "scaled": [
        1.4166609409941058,
        16447.79445500181,
        87340.62097523996
      ]
    },
    {
      "h": 0.5,
      "phase": 2.0943951023931953,
      "leading_coefficients": [
        12.749999999999993,
        148031.99999999985,
        19651999.999999966
      ],
      "scaled": [
        12.749791222846207,
        148024.9701827923,
        19650408.30514955
      ]
    },
    {
      "h": 1,
      "phase": 0,
      "leading_coefficients": [
        0.0,
        144.0,
        8.0
      ],
      "scaled": [
        0.0,
        143.99995199997994,
        7.999976000061342
      ]
    },
    {
      "h": 1,
      "phase": 1.0471975511965976,
      "leading_coefficients": [
        0.16666666666666666,
        256.0,
        56.888888888888886
      ],
      "scaled": [
        0.16666643055585414,
        255.99971555611793,
        56.88847170652711
      ]
    },
    {
      "h": 1,
      "phase": 2.0943951023931953,
      "leading_coefficients": [
        1.4999999999999991,
        2303.999999999998,
        12799.999999999978
      ],
      "scaled": [
        1.4999928750376859,
        2303.983104202234,
        12799.585292209103
      ]
    }
  ],
  "large": [
    {
      "R": 3,
      "phase": 0,
      "shape2_ratio": 1.976016575949064
    },
    {
      "R": 4,
      "phase": 0,
      "shape2_ratio": 1.5103845344914384
    },
    {
      "R": 5,
      "phase": 0,
      "shape2_ratio": 1.3145899592512809
    },
    {
      "R": 3,
      "phase": 1.0471975511965976,
      "shape2_ratio": 1.6996697950465602
    },
    {
      "R": 4,
      "phase": 1.0471975511965976,
      "shape2_ratio": 1.370560642597708
    },
    {
      "R": 5,
      "phase": 1.0471975511965976,
      "shape2_ratio": 1.2301528137108055
    },
    {
      "R": 3,
      "phase": 2.0943951023931953,
      "shape2_ratio": 1.2054096552870286
    },
    {
      "R": 4,
      "phase": 2.0943951023931953,
      "shape2_ratio": 1.1129369834338994
    },
    {
      "R": 5,
      "phase": 2.0943951023931953,
      "shape2_ratio": 1.0715127066159422
    }
  ],
  "responses": [
    {
      "R": 0.2,
      "E": 16.509400626996076,
      "phase_response": -13.705324493251679,
      "angle_response": -53.059196542371005
    },
    {
      "R": 1,
      "E": 4556.233934793121,
      "phase_response": -7054.281878163237,
      "angle_response": -19014.116022162852
    },
    {
      "R": 2,
      "E": 517.8752103636151,
      "phase_response": -606.1618996966445,
      "angle_response": 2783.574336359606
    }
  ],
  "sources": {
    "local-pattern-pair-checks.py": "80652db1a2824a31e9f72a0d117b5b4f2d5393bf399e17ecd216013eb73e54d3"
  },
  "historical_sources": {},
  "original_script_sha256": "606fe258bba82143fae6861572edefb403b8b489c4e6fcf4943e6e5fb97ae616",
  "timestamp_utc": "2026-10-13T23:52:00.788678+00:00",
  "exact_identity_checks": 21,
  "numerical_comparison_checks": 54,
  "numerical_scope": "Non-rigorous SciPy quadrature and finite differences with bounded tails; no interval certification.",
  "grounding": {
    "path": "content/notes/topics/contact-operators/flat-space-count-action.md",
    "snapshot": 1096,
    "sha256": "8050a51e5b95601798189747d25c426143ad1273b7ccf482842c987b9da1b832"
  },
  "publication": {
    "originalReportSHA256": "e34be94ba501d47e5a10cc2725e282b4f525f4fc45b439e1815e2f33e7266b9e",
    "omittedPrivateSourceLocations": 4,
    "archivedSourceSHA256": [
      "606fe258bba82143fae6861572edefb403b8b489c4e6fcf4943e6e5fb97ae616",
      "b782a8d89367eefc9958c831500931de8e006bfeb6ba64b3516824c9b8f4fef4",
      "c476d877f6cf437501b7b0e649efd07d7919a430f249f0dd92a6e40f3213668b",
      "f3a38384153e357d72392882a8878ad195b187a00cea84c15ad795c041eb3101"
    ]
  }
}