Experts and laypeople alike increasingly encounter the scientific literature by posing questions to large language models (LLMs) rather than through database searches, making a model’s cited sources the reader’s main window into the original literature. Yet LLMs frequently suffer from citation hallucinations. Because source existence is objective and externally checkable, it provides an unusually clean signal for reinforcement learning with verifiable rewards (RLVR). We train LLaMA-3.1-8B-Instruct and LLaMA-3.2-3B-Instruct with GRPO and LoRA against a deterministic verifier that resolves each generated reference against scholarly databases CrossRef and OpenAlex. On 40 common medical questions in the MedAESQA dataset, the hallucination rate decreases from 85.5% for the base 8B model to 76.7% (p < 1e-4) for the best post-trained checkpoint. The post-trained model produces 71% more verified references at unchanged citation density, generates fewer misleading DOIs (down to 14% vs 54% for the base), and favors canonical sources such as the New England Journal of Medicine. A six-part audit finds no evidence of reward hacking. Ultimately, this deterministic verifier supplies a practical, objective signal that reduces hallucinated references, offering a novel method to improve citation accuracy and a stepping stone toward fully verifiable LLM answers for literature-based QA.