{
  "run_time": "2026-10-14T19:18:01.960301+09:00",
  "mpmath_version": "1.4.1",
  "numpy_version": "2.3.5",
  "method": "deterministic; no random draws; sampling SE and seed not applicable",
  "scope": "Only explicitly supplied formulas; numerical evidence, no count or theorem certification.",
  "read_scope": "No root proof, referee report, management file, or actual L zeros read.",
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    "entrywise_LDL_reconstruction_exact": true
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      "Hminus7_over_main": "2.0938779544971883139374790975162681193263711175616471789100277128e-29894"
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  ],
  "finite_scale_diagnostics": [
    {
      "epsilon": "1/1000",
      "log10_H_when_T_over_sqrtM_is_0p1_exact": "64000",
      "log10_H_for_unit_constant_logH_over_H_to_2eps_large_crossing": "1809.9399243361776292072221355591205583012886570437855767053188638",
      "warning": "Only a unit-constant crossover; omitted constants are not controlled."
    },
    {
      "epsilon": "1/100",
      "log10_H_when_T_over_sqrtM_is_0p1_exact": "6400",
      "log10_H_for_unit_constant_logH_over_H_to_2eps_large_crossing": "122.52137808379108969593030195804068355639280416359043545753149811",
      "warning": "Only a unit-constant crossover; omitted constants are not controlled."
    },
    {
      "epsilon": "1/32",
      "log10_H_when_T_over_sqrtM_is_0p1_exact": "2048",
      "log10_H_for_unit_constant_logH_over_H_to_2eps_large_crossing": "29.254544455590266515783232183967479155032575385793270549058766282",
      "warning": "Only a unit-constant crossover; omitted constants are not controlled."
    },
    {
      "epsilon": "1/17",
      "log10_H_when_T_over_sqrtM_is_0p1_exact": "1088",
      "log10_H_for_unit_constant_logH_over_H_to_2eps_large_crossing": "12.361412066527082682381681700429890873876869105382663988897739569",
      "warning": "Only a unit-constant crossover; omitted constants are not controlled."
    }
  ],
  "assumptions": [
    "The eight-point Gaussian or arithmetic approximation must be supplied separately.",
    "The fixed-q near/tail count and Jensen/pole-log moments are inputs only.",
    "Bulk sign error H^-5 and the stated Fourier/GC inequalities are inputs, not inferred from exponents.",
    "Quantile main term is z^-2 log(H)/H with H>=e and baseline<=z<=1."
  ],
  "limitations": [
    "High precision is not interval arithmetic; bridge eigenvalue positivity is numerical evidence.",
    "The first exact rational matrix has positive exact LDL pivots, but this does not certify L-function count statements.",
    "Very small eigenvalues produce large density and inverse-covariance constants.",
    "epsilon is fixed before H tends to infinity; no uniformity as epsilon tends to zero is claimed."
  ]
}