This document presents a structured treatment of Adaptive Market Solvers (AMSs), a framework that reconceptualizes markets as computational processes grounded in finite-state machines (FSMs) and updated through metaheuristic optimizers. It integrates formalism with illustrative examples, such as modeling a shortbread production chain as an FSM, to demonstrate the discovery-based nature of market representation. The paper advances a thermodynamic analogy to interpret equilibria and dynamic steady states, while also situating AMSs within blockchain and machine learning infrastructures to ensure trustless execution and adaptive optimization. Through this process, the document positions AMSs as both Turing-complete systems and evolving market mechanisms, capable of self-organization, competition, and Pareto-improving coordination in decentralized economic ecosystems.