Abstract
Computing inherited an incomplete formal account of the mutable world around it. Its foundational unit, y=f(x), has no place for time or persistent entities, and breaks precisely where real-world entities enter the relation: a result holds when computed and becomes history once its input changes. Practice compensates by hand, outside the unit, with polling loops, event pipelines, and diffing logic that keep results correct as state moves. We name this recurring work State Engineering and argue that the obligation it discharges, convergence, belongs in the formal unit of computation itself. We propose the Convergent Machine, a computational unit whose semantic contract obliges its output y to remain converged on f(xⓜ,s) as state s moves. We give the contract a trace semantics in which y=f(x) is the static case, and prove that machines compose with nothing to re-establish at the join. The obligation moves from the engineer to the model, and to the substrate beneath it.