Preliminary Notes on Heterogeneous Value Circulation and a Mathematical Representation

This preliminary discussion paper examines one possible mathematical representation of heterogeneous value circulation. It distinguishes typed transfer records, local interpretations, admissible transformations, changing conditions of circulation, and the independent choice of evaluative criteria. Two motivating cases are a bilateral exchange of money and labour service and a three-node route in which delayed receipt can affect a stipulated task threshold. A finite directed graph with locally heterogeneous state spaces supplies a deliberately limited starting representation. Additive inventory laws are separated from service events, replicable artifacts, interpretive assessments, and non-conservative transformation. Typed event accounts, in-transit stocks, local update maps, and set-valued uncertainties are specified explicitly. Equality within a unit, conversion by convention, contextual equivalence, similarity, and incomparability are considered separately. Reproducible synthetic Python studies illustrate receipt delay, threshold-dependent responses, path-composed internal transformations, conflicting sufficiency requirements, selective two-resource diffusion, and conductance feedback with parameter and time-step sensitivity checks. These calculations make formal assumptions inspectable; they are not calibrated economic or biological models and do not establish an ethically privileged objective. The paper compares established mathematical possibilities and identifies conditions for more responsible modeling of circulation and recognition.