Quoting Under a Misspecified Fill Law: Order-Book Queues, Adverse Selection, and Inventory-Control Certificates

A market maker's fill law depends on price, tagged queue priority, order size, order flow, and price changes accompanying execution. This paper connects uncertainty in these book primitives to the loss of a deployed quoting policy. A marked-wealth identity separates offset capture, carried-inventory drift, and simultaneous fill–price jumps. A finite event model retains inventory reservations, batch consumption, partial fills, and costly replacement. A pending cancellation remains executable until acknowledgement. Its value admits an exact residual identity and a perturbation bound in the delay law. Approximating a deterministic delay by mean-matched Erlang stages has a sharp inverse-stage value-error rate, with an explicit leading term and remainder. A performance-difference identity transfers local decision errors into total policy loss. Smooth quote branches admit quadratic certificates accounting for primitive uncertainty, continuation values, HJB residuals, and optimization error. Discrete messages admit a value-interval certificate that preserves state-dependent action gaps and bounds their discounted occupation. It requires neither action curvature nor the true value function. A 74-state queue-and-inventory example gives a rational loss enclosure for a declared uncertainty box. Two lower bounds identify limits: omitting tagged rank causes positive minimax loss with known primitives, while calibration at a replacement boundary has a sharp inverse-square-root duration rate. A separate two-quote experiment gives a statistical certificate for an exponential fill curve. Hybrid margins, finite-book truncation, shutdown thresholds, and information-value ceilings receive explicit assumptions. The guarantees are conditional on specified models and uncertainty sets. Synthetic examples independently check partial-fill laws, cancellation values, controlled policies, and the resulting bounds.