In agentic search, an LLM agent searches the web, reads the pages it finds, and decides what to look for next before returning an answer. But can we trust an answer simply because the agent returns it? Often not, and even a correct answer can be a lucky guess: on questions with several constraints, we find that agents conclude the task is complete while a constraint remains unverified in up to 48% of their correct answers. We call this illusory completion. To see how it arises, we introduce the Epistemic Ledger, which tracks at every turn what the retrieved pages establish about each constraint and what the agent claims. Across 13 agents, from 7B RL-trained models to frontier LLMs, training and scale raise accuracy but change the pattern of verification failures rather than eliminating them: constraints may be left unchecked, assumed without support, or retained despite refuting evidence. To measure what agents lose without tracking their constraints, we show them each constraint's state, approximated by LiveLedger, a lightweight 4B tracker. Agents then answer 4.4-16.1 points more questions correctly, suggesting that on their own, they may not track what they have verified and what remains.

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