Large language models accelerate literature synthesis but can hallucinate and mis-cite, limiting their usefulness in expert workflows. We present RA-FSM (Research Assistant - Finite State Machine), a modular GPT-based research assistant that wraps generation in a finite-state control loop: Relevance -> Confidence -> Knowledge. The system is grounded in vector retrieval and a deterministic citation pipeline. The controller filters out-of-scope queries, scores answerability, decomposes questions, and triggers retrieval only when needed, and emits answers with confidence labels and in-corpus, de-duplicated references. A ranked-tier ingestion workflow constructs a domain knowledge base from journals, conferences, indices, preprints, and patents, writing both to a dense vector index and to a relational store of normalized metrics. We implement the system for photonics and evaluate it on six task categories: analytical reasoning, numerical analysis, methodological critique, comparative synthesis, factual extraction, and application design. In blinded A/B reviews, domain experts prefer RA-FSM to both a strong Notebook LM (NLM) and a vanilla Default GPT API call single-pass baseline, citing stronger boundary-condition handling and more defensible evidence use. Coverage and novelty analyses indicate that RA-FSM explores beyond the NLM while incurring tunable latency and cost overheads. The design emphasizes transparent, well-cited answers for high-stakes technical work and is generalizable to other scientific domains.