Why Formal Monitors Fail: Attack Distribution Entropy as a Coverage Bound for LTL-Based LLM Agent Safety

Several properties safety monitors are asked to certify, among them cross-tenant noninterference, sandbagging and evaluation awareness, are 2-safety hyperproperties, witnessed only by two executions. The standard consequence is a binary impossibility: one trace cannot decide them. We replace the binary with a measurement. A tight bound puts the balanced accuracy of any single-trace monitor at $\tfrac12+\tfrac12\,TV(P_0,P_1)$, turning undecidability into a graded detectability frontier and defining an oversight gap: a monitor's shortfall below it. On a leak family with closed-form $TV$, nine LLM monitors are optimal at $TV=0$ but capture little signal as $TV$ grows; at $TV=1$, where a 20-line membership check scores $100\%$, they average $60.9\%$. That shortfall is mostly not capability: naming what to check closes $61\%$ of it while leaving the $TV=0$ control at chance. The same split runs through a $2{\times}2$ factorial: an imagined second run leaves monitors at chance ($50.4\%$) while the same rule on an executed second run reaches $90.0\%$, and a stored oracle without a comparison procedure yields only $68.2\%$. Information and procedure are each necessary and neither is capability. Under nondeterminism, replay tracks a closed-form $k$-replay curve only under the right projection, and a projection frontier shows the resulting dilemma is forced: narrow misses $98.6\%$ of off-channel leaks, broad flags $75.7\%$ of clean traffic, and attainable accuracy decays like $1/(qm)$ in the benign-variation rate and the channel count. Finally, two frontier LLM judges certified an earlier version of our own benchmark as sound while a sign test found a directional bias ($p=2.7\times10^{-5}$) that invalidated three of our findings. Construction validity for hyperproperty benchmarks should be proved mechanically, not audited by models.

This position paper argues that enforcing LLM agent safety within a single abstraction layer is not merely suboptimal but categorically insufficient for deployed LLM agents -- a structural consequence of how agent execution works, not a contingent limitation of current systems. The three dimensions that jointly constitute safe operation -- semantic intent and policy compliance, environmental validity, and dynamical feasibility -- each depend on a strictly distinct set of information that becomes available at different stages of execution. No single guardrail can certify all three. We argue that the community must respond with a contract-based architecture in which each safety dimension is enforced by an independently certified layer whose probabilistic guarantee satisfies the next layer's assumption. We sketch such an architecture and derive the compositional system-level safety bounds it admits via the chain rule of probability. Three open problems stand between this and a deployable standard: bound estimation from non-i.i.d.\ traces, graceful degradation of contracts under deployment drift, and extension to multi-agent settings -- the most important unfinished business in LLM agent runtime assurance.

Despite alignment training, LLMs remain prone to generating unsafe outputs at deployment time. Monitoring outputs online and raising an alarm when safety can no longer be assumed is therefore critical. We study a simple real-time monitor that turns a verifier signal from an external model into an alarm decision by thresholding, with the threshold calibrated via risk control. In experiments on mathematical reasoning and red teaming datasets, we show that this simple design is competitive with more advanced monitors based on sequential hypothesis testing.