Beyond Constant Fault Rates: Reliability Bounds for Gated Computation and Semantic Mechanization

Abstract

Constant fault intensity, independent segments, fresh retries, and a fixed fault distribution are different assumptions. Earlier papers on gated computation use different subsets of them. We separate these assumptions and examine which conclusions survive their removal. A conditional survival identity replaces the independent-segment product. Uniform conditional gate accuracy and progress bounds preserve logarithmic verification overhead without a Poisson arrival model. A verification floor yields a finite horizon only when its exposure persists along correct prefixes. Unequal difficulty, latent regimes, persistent retry defects, and changing input distributions give counterexamples to predictions based on one average rate. Two positive results locate the 1/σ ceiling multiplier of the first paper. For the ideal gated survival curve, a latent rate drawn once per run preserves it exactly, and a monotone hazard orders it: at most 1/σ for an increasing failure rate and at least 1/σ for a decreasing one. With finite segments, the upper bounds hold after rounding to whole segments. For semantic mechanization, local escape and fallback probabilities replace one volume-weighted closure fraction. The twin result survives changes in the arrival law and dependent or adaptive sampling, provided twins induce the same observation law. We classify all 25 named results of the four earlier papers as arrival-free, conditionally preserved, or stationary-parameter formulas that need replacement, and we give executable finite-model checks. These are mathematical models, not measurements of deployed agents. The contribution is their application and synthesis; the probability identities and inequalities are classical.