  Latent order book models have allowed for significant progress in our
understanding of price formation in financial markets. In particular they are
able to reproduce a number of stylized facts, such as the square-root impact
law. An important question that is raised -- if one is to bring such models
closer to real market data -- is that of the connection between the latent
(unobservable) order book and the real (observable) order book. Here we suggest
a simple, consistent mechanism for the revelation of latent liquidity that
allows for quantitative estimation of the latent order book from real market
data. We successfully confront our results to real order book data for over a
hundred assets and discuss market stability. One of our key theoretical results
is the existence of a market instability threshold, where the conversion of
latent order becomes too slow, inducing liquidity crises. Finally we compute
the price impact of a metaorder in different parameter regimes.
