{
  "scope": "Independent direct proof audit plus numerical adversarial probes; no formal proof assistant or hardware certification.",
  "theorem_review": "No blocking derivation error remaining after stated corrections; weighted geometry, graph realizability, covariance martingale, channel bounds, OU identities, radial envelopes and finite-cutoff diagnostics reviewed.",
  "resolved_findings": [
    {
      "id": "R1",
      "severity": "blocking",
      "original_issue": "Arbitrary H(x)>700 infinity shortcut created zero positive-time risk upper bound below positive endpoint lower bound.",
      "resolution": "Reject unsupported beta>650; keep finite supported positive Poisson evaluation."
    },
    {
      "id": "R2",
      "severity": "substantive numerical",
      "original_issue": "FV beta50 produced negative decay eigenvalue, clipped zero exits and mean exit error of five orders.",
      "resolution": "Restrict FV to beta<=15 and cells<=2000; reject nonpositive decay; mark under-resolved exit values NaN."
    },
    {
      "id": "R3",
      "severity": "blocking input validation",
      "original_issue": "NaN restoring rate or horizon erased drift tube allowance and returned a positive robust margin.",
      "resolution": "Finite-value validation added to calibration API."
    },
    {
      "id": "R4",
      "severity": "mathematical hypothesis",
      "original_issue": "Girsanov marginal-path KL equality unjustified for hidden exogenous adapted disturbance.",
      "resolution": "Use energy inequality and explain augmented-space/data-processing distinction."
    },
    {
      "id": "R5",
      "severity": "mathematical hypothesis",
      "original_issue": "Centered OU tracking comparison omitted zero initial condition.",
      "resolution": "Explicitly require Z0=0; general initial error remains covered separately."
    },
    {
      "id": "R6",
      "severity": "numerical bound",
      "original_issue": "Positive Laplace upper bound could underflow to false zero.",
      "resolution": "Positive smallest-float upward underflow rounding plus log_upper and underflow flag."
    }
  ],
  "numerical_probes": [
    {
      "function": "mean_exit_upper",
      "status": "rejected",
      "details": "dimensionless beta exceeds supported range (beta<=650)"
    },
    {
      "function": "mean_exit_upper",
      "status": "rejected",
      "details": "dimensionless beta exceeds supported range (beta<=650)"
    },
    {
      "function": "survival_fv",
      "status": "rejected",
      "details": "validated FV support: 0<beta<=15, 8<=cells<=2000, kappa>0"
    },
    {
      "function": "drift_tube",
      "status": "rejected",
      "details": "all scalar parameters must be finite"
    },
    {
      "function": "drift_tube",
      "status": "rejected",
      "details": "all scalar parameters must be finite"
    },
    {
      "function": "robust_margin",
      "status": "rejected",
      "details": "all scalar parameters must be finite"
    },
    {
      "function": "laplace_chernoff_upper",
      "status": "positive underflow rounding verified",
      "result": {
        "upper": 5e-324,
        "log_upper": -3122.8359746001997,
        "s": 3124499.9929559845,
        "underflow_rounded_up": true
      }
    },
    {
      "function": "FV range edge",
      "beta": 12.5,
      "status": "convergence checked",
      "values": [
        {
          "cells": 200,
          "principal_eigenvalue": 8.490443374381333e-05,
          "mean_relative_error": -0.0001364085863825304
        },
        {
          "cells": 400,
          "principal_eigenvalue": 8.489574726730994e-05,
          "mean_relative_error": -3.410503409517762e-05
        },
        {
          "cells": 800,
          "principal_eigenvalue": 8.489357628752046e-05,
          "mean_relative_error": -8.525187564112358e-06
        },
        {
          "cells": 1600,
          "principal_eigenvalue": 8.489302728264858e-05,
          "mean_relative_error": -2.1302833549396993e-06
        },
        {
          "cells": 2000,
          "principal_eigenvalue": 8.489296355165827e-05,
          "mean_relative_error": -1.3661838982326202e-06
        }
      ]
    },
    {
      "function": "FV range edge",
      "beta": 15,
      "status": "convergence checked",
      "values": [
        {
          "cells": 200,
          "principal_eigenvalue": 8.51419700912485e-06,
          "mean_relative_error": -0.0002028768802967429
        },
        {
          "cells": 400,
          "principal_eigenvalue": 8.512902544710432e-06,
          "mean_relative_error": -5.072161935526509e-05
        },
        {
          "cells": 800,
          "principal_eigenvalue": 8.512576721020274e-06,
          "mean_relative_error": -1.267598048282359e-05
        },
        {
          "cells": 1600,
          "principal_eigenvalue": 8.512492562596715e-06,
          "mean_relative_error": -3.1518842026345695e-06
        },
        {
          "cells": 2000,
          "principal_eigenvalue": 8.512488279738732e-06,
          "mean_relative_error": -2.0560617690623673e-06
        }
      ]
    }
  ],
  "checks_run": {
    "risk_unit_checks": 16,
    "calibration_checks": 5,
    "quantum_algebra_checks": "all passed independently"
  },
  "limits": [
    "Double precision analytic results are not outward-rounded interval certificates.",
    "FV is a spatially approximate solver with an explicit finite support range.",
    "No experiments, quantum advantage or AI capability gain certified."
  ]
}