This paper presents PolySwarm, a novel multi-agent large language model (LLM) framework designed for real-time prediction market trading and latency arbitrage on decentralized platforms such as Polymarket. PolySwarm deploys a swarm of 50 diverse LLM personas that concurrently evaluate binary outcome markets, aggregating individual probability estimates through confidence-weighted Bayesian combination of swarm consensus with market-implied probabilities, and applying quarter-Kelly position sizing for risk-controlled execution. The system incorporates an information-theoretic market analysis engine using Kullback-Leibler (KL) divergence and Jensen-Shannon (JS) divergence to detect cross-market inefficiencies and negation pair mispricings. A latency arbitrage module exploits stale Polymarket prices by deriving CEX-implied probabilities from a log-normal pricing model and executing trades within the human reaction-time window. We provide a full architectural description, implementation details, and evaluation methodology using Brier scores, calibration analysis, and log-loss metrics benchmarked against human superforecaster performance. We further discuss open challenges including hallucination in agent pools, computational cost at scale, regulatory exposure, and feedback-loop risk, and outline five priority directions for future research. Experimental results demonstrate that swarm aggregation consistently outperforms single-model baselines in probability calibration on Polymarket prediction tasks.