A Unified Generative–Relational Formalism for Market Analysis: From Ontology to Praxis, With a Market Foam Model of Spacetime and Case Studies on Inflation and Justice

A market analysis commits to an ontology, a dynamics, an epistemology, a phenomenology, and a theory of praxis, and established theories fix a subset of these commitments while the remainder stays implicit. This paper designs one formal object in which all five are explicit, typed, and connected by stated maps. A reflexive generative–relational market system consists of a schema of kinds and relations presented as a category, market states as functors, a grammar of guarded rewriting events, accounting invariants given by a kernel condition, a rate law, a family of observers, belief-update rules, admissible actions, and external evaluation frames. Prices arise as potentials of an exchange-ratio cochain and exist exactly on ratio systems with zero holonomy. Market time, distance, and causal order are derived from the process law and are joined in a market foam, a labelled two-complex in which persistent facts are faces, subjects, venues, and ledgers are edges, and events are vertices. The conserved sector of the foam is a spin foam for a torus supplied by the accounting invariants, its non-negative weights come from the rate law, and its sum over histories is the Markov transition kernel. An accounting identity splits the discrepancy between two candidate mechanisms into a part visible under a declared protocol and a part hidden by the protocol, and the system is closed under extension by its participants' models. The design is verified on eleven classical cases and on two extended cases through 95 synthetic numerical checks. Currency inflation separates into a gauge part and a curvature part. Justice separates into reciprocity as cycle holonomy with geometric and dynamical components, distribution as a boundary property read against an external frame, and procedure as a property of non-commuting step operators and of the path measure. The contribution is a single typed language in which market mechanism, observation, learning, action, and evaluation-relevant observables are stated with proportionate claim labels. The implication for empirical work is that event-complete records and designed interventions are the conditions under which mechanism and procedure become identifiable.