Can the same computation secure a blockchain and power AI models? Pearl is a Proof-of-Useful-Work blockchain designed to let miners perform AI inference and compete for blocks using the same computation. The goal is to create two complementary revenue streams: block rewards help subsidize inference, while customer payments help cover the underlying cost of mining. Pearl uses matrix multiplication as its mining primitive, which is also a core operation in AI inference. When a miner processes a compatible inference request, the same calculations can generate mining attempts while producing an output that serves a customer. But miners can also perform arbitrary matrix multiplications solely to compete for block rewards. The protocol verifies that the prescribed computation was performed correctly, not whether the matrices originated from a real inference request. The economic incentive is straightforward. Miners performing real inference can earn customer fees and mining rewards from the same underlying work, potentially improving their economics relative to miners performing synthetic calculations alone. The remaining challenge is converting that incentive into realized utility: how much of the network's total computation is actually serving external demand rather than being performed solely to earn block rewards?