Heterogeneous Value Circulation in Relational Spacetime: A Topological Formalism

This discussion paper develops a preliminary topological language for heterogeneous value circulation within a Generative Relational (GR) account of relational spacetime. The underlying structure is an oriented two-dimensional cell complex whose vertices are events, edges are couplings, and faces are primitive two-dimensional structures with semantics to be specified by the model. Entities and values are considered potentially emergent, historically constituted structures supported by subcomplexes; the representation does not require each event to be an exchange or each value to occupy a single face. Different value modalities may exhibit distinct topological, geometric, temporal, dynamical, and multiscale properties, while sharing portions of their relational support. Circulation is approached through causally admissible histories and transformations of value-supporting configurations, including transmission, conversion, reproduction, and changes in subsequent generative capacity. Cellular boundaries, homology, quotient constructions, discrete Morse theory, and persistent topology supply candidate analytical tools, with their interpretive conditions explicitly distinguished. The longer-term normative problem concerns how the ordering of feasible histories affects deprivation, obligations, value formation, and future possibilities. The paper treats mathematical structure as a proposed representation rather than evidence of an ultimate ontology or a validated social mechanism. This working release contains Sections 1–11 and Appendices A–E (notation, exact cellular calculations, historical subcomplex constructions, simulation reproducibility, and open mathematical extensions), including reproducible synthetic computational experiments, a preliminary justice-comparison interface, an assessment of mathematical and interpretive scope, and a conclusion; the broader ethical theory remains open.