A Generative Relational Theory of Temporal Emergence in Large-Scale Heterogeneous Systems

Abstract

This paper develops a generative relational theory of temporal emergence for large-scale heterogeneous systems. Its object is the constitution of temporal organization from change: the minimal relational conditions under which difference, comparability, recurrence, and ordering give rise to temporal structure in systems whose components possess distinct dynamics and share no universally accessed clock. The central hypothesis holds that temporal emergence occurs through relational invariance across generative difference. The paper formalizes repetition as invariance of relational form under an equivalence structure, derives multi-scale temporality from the plurality of such structures, defines distributed temporal emergence through an irreducibility criterion, and sets out categorical and sheaf-theoretic formulations together with a perturbative program that attributes temporal organization among drivers, components, and relations. The brain, ecological systems, and distributed computation serve as three instances of a single problem class. The theory concerns temporal organization within relational systems and advances no claim about the nature of fundamental physical time.