arXiv:2510.03992v1 Announce Type: cross Abstract: Large language models (LLMs) are increasingly deployed in agentic systems where they map user intents to relevant external tools to fulfill a task. A critical step in this process is tool selection, where a retriever first surfaces candidate tools from a larger pool, after which the LLM selects the most appropriate one. This pipeline presents an underexplored attack surface where errors in selection can lead to severe outcomes like unauthorized data access or denial of service, all without modifying the agent's model or code. While existing evaluations measure task performance in benign settings, they overlook the specific vulnerabilities of the tool selection mechanism under adversarial conditions. To address this gap, we introduce ToolCert, the first statistical framework that formally certifies tool selection robustness. ToolCert models tool selection as a Bernoulli success process and evaluates it against a strong, adaptive attacker who introduces adversarial tools with misleading metadata, and are iteratively refined based on the agent's previous choices. By sampling these adversarial interactions, ToolCert produces a high-confidence lower bound on accuracy, formally quantifying the agent's worst-case performance. Our evaluation with ToolCert uncovers the severe fragility: under attacks injecting deceptive tools or saturating retrieval, the certified accuracy bound drops near zero, an average performance drop of over 60% compared to non-adversarial settings. For attacks targeting the retrieval and selection stages, the certified accuracy bound plummets to less than 20% after just a single round of adversarial adaptation. ToolCert thus reveals previously unexamined security threats inherent to tool selection and provides a principled method to quantify an agent's robustness to such threats, a necessary step for the safe deployment of agentic systems.