Composable Future: Toward an Algebraic Theory of Paradigmatic Transitions

We introduce Composable Future, a formal structure in which paradigmatic futures are treated as algebraic objects admitting composition. A future F is defined as a 4-tuple (S0, τ, S1, Φ) where S0 and S1 are paradigmatic states, τ : S0 → S1 is atrajectory morphism, and Φ: S1 → P(F) is a typed affordance set. We define four primitive operators—sequential bind (≫=), parallel tensor (⊗), fork (|), and merge (⊕)—and investigate the algebraic laws they satisfy. Identity and closure hold ingeneral; associativity of ≫= holds when τ is stateless and reduces to a fibered structure when τ is path-dependent. Under probabilistic extension the structure forms a Kleisli category over the probability monad. We identify five open problems and position the framework relative to applied category theory, process algebra, branching-time temporal logic, and affordance theory.