FlowLOB: A Continuous-Time Computational Simulator for Event-Level Limit Order Book Counterfactuals

Financial limit order books are irregular, event-driven systems in which a complete counterfactual path is unobserved. FlowLOB is an experimental continuous-time autoregressive simulator for market-by-order event streams coupled to a lightweight book engine. It generates inter-arrival times, message types, sides, relative prices, and sizes, and supports paired rollouts under injected child-order schedules. This preliminary report records the current positive and negative evidence rather than claiming a validated execution model. On a one-use locked AAPL episode test covering four adjacent dates, the 500 ms Pearson correlation is 0.087 with a date-cluster 95% interval of [-0.009, 0.293]. Adding the simulator prediction to an observed-feature baseline lowers Pearson correlation by 0.0568 under the reported frozen-fit procedure. Re-designed paired-schedule experiments show wide, protocol-sensitive exponent intervals rather than confirming a universal square-root impact law. The deposit is a transparent research report and diagnostic baseline, not evidence of robust market-impact prediction or deployable execution performance.