| { |
| "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." |
| ] |
| } |
|
|
