The "Ultraviolet" Structure of Recursive Value and Power: Physical Strategies and Formal Architectures for Generative Relational Being

Value and power, when examined at their foundations, exhibit a recursion without evident terminus. Every valuation appears to invoke a higher valuation that would ground it, every exercise of power a legitimation that would authorize it, and every legitimation a further legitimation in its turn, so that the attempt to fix a foundation descends through an unbounded series and the analysis grows less stable the finer its resolution becomes. This paper takes that recursion as its object. It argues that the recursion of value and power shares its formal structure with a problem long familiar in theoretical physics, the problem of ultraviolet behaviour, in which the number of relevant degrees of freedom fails to diminish as one descends toward short distances and the quantities one wishes to compute cease to converge. The paper does not claim that the two are mathematically identical. It claims that they are the same kind of formal problem, and that the discipline which has confronted such problems most directly has accumulated a repertoire of strategies worth examining. The account is built in two movements. The first is diagnostic. It reconstructs the recursion of value and power, identifies the condition under which it fails to terminate, and characterizes that condition in the borrowed and deliberately marked vocabulary of "ultraviolet" structure. The second is comparative and constructive. It sets out the four principal responses that theoretical physics has made to the ultraviolet problem, absorption in renormalization, discretization in dynamical triangulation, extension in string theory, and pre-geometric emergence in group field theory, and it examines what each would mean if carried onto the terrain of a relational and generative account of value and power. It finds that a generative relational account is most consistent with the emergence strategy, on which the recursion terminates at the level where the description in terms of contestable claims ceases to apply. On this basis the paper proposes a layered formal architecture of five offices, ontology, representation, dynamics, criteria, and observation, in which the several formal instruments each occupy a distinct office of a single relational order rather than competing for one, so that representation, generative dynamics, cyclic criteria, and multiscale observation are placed in a definite dependence. It closes, in the manner it requires of itself, on the questions that any formalization of generative value would have to confront. The paper continues a programme that has replaced the individual with generative relational being and carries that programme onto the question of formal foundations.