arXiv:2609.09229v1 Announce Type: cross
Abstract: Additional inference compute can increase the number of correctly resolved security-assurance tasks, but repeated success, unique coverage, accepted evidence, and operational protection are different quantities. We develop a resource-constrained framework that separates them. For repeated conditionally independent attempts with latent success probability $\Theta$, coverage is $C_n = 1 – E[(1-\Theta)^n]$, and its limiting value is $1 – P(\Theta = 0)$. Positive pairwise outcome correlation does not by itself imply a ceiling below one: we construct two models with the same mean success and pairwise correlation but different limiting coverage. We distinguish this result from the effective sample size used to estimate a mean, and show why finite-budget observations cannot generally identify an asymptotic support ceiling. We then connect coverage to fallible evidence checking, proper scoring of factual grounding, complete resource accounting, service capacity, and a response model that includes mitigation delay. A conceptual defensive architecture separates evidence analysis, adjudication, and operational authority. An evaluation protocol specifies held-out tasks, paired comparisons, negative cases, and uncertainty reporting. The contribution is a consistent theoretical synthesis and a set of counterexamples to invalid extrapolations, rather than an empirical scaling law. All numerical illustrations are analytic; no model-parity result, hardware benchmark, or general attacker-defender equilibrium is claimed.
Abstract: Additional inference compute can increase the number of correctly resolved security-assurance tasks, but repeated success, unique coverage, accepted evidence, and operational protection are different quantities. We develop a resource-constrained framework that separates them. For repeated conditionally independent attempts with latent success probability $\Theta$, coverage is $C_n = 1 – E[(1-\Theta)^n]$, and its limiting value is $1 – P(\Theta = 0)$. Positive pairwise outcome correlation does not by itself imply a ceiling below one: we construct two models with the same mean success and pairwise correlation but different limiting coverage. We distinguish this result from the effective sample size used to estimate a mean, and show why finite-budget observations cannot generally identify an asymptotic support ceiling. We then connect coverage to fallible evidence checking, proper scoring of factual grounding, complete resource accounting, service capacity, and a response model that includes mitigation delay. A conceptual defensive architecture separates evidence analysis, adjudication, and operational authority. An evaluation protocol specifies held-out tasks, paired comparisons, negative cases, and uncertainty reporting. The contribution is a consistent theoretical synthesis and a set of counterexamples to invalid extrapolations, rather than an empirical scaling law. All numerical illustrations are analytic; no model-parity result, hardware benchmark, or general attacker-defender equilibrium is claimed.
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