A Network Model of Information Aging Keywords: Memory, Time, Event Network, Associativity, Archiving, Time Paradox, Information Aging, Time Paradoxes, Burton.Kebler Model

In this paper, we propose a quantitative model of information aging that advances the concept of memory as a dynamic projection of an event network, in which time emerges not as an absolute quantity but as a partial order induced by causal relationships. In contrast to the classical Burton-Kebler model, which describes utility as the exponential decay of the value of individual documents (stable and current), our work formalizes information utility as a function of the integrity of causal paths between historically significant "anchors." The model explicitly distinguishes between the forgetting of events, S(v,.), and the forgetting of their linkcausal R C (e, .) and associative R A (e,.)and corroborates the empirical hypothesis that causal links degrade faster than events themselves (. > .). The model incorporates phase transitions in information aging: when a critical "bridge" between clusters of anchors is lost, utility does not merely decline but drops discontinuously to zero, as network connectivity is severed. This phenomenon is analogous to a percolation transition in complex network theory. Based on this, we derive a generalized utility formula that combines a smooth exponential component (for bulk decay) and a threshold function (for critical points). The model has been validated on a 30-year news archive (>1 billion records) and is accompanied by a Python implementation. Results confirm that the strategic preservation of "bridges" not only mitigates gradual aging but also eliminates the risk of catastrophic collapse of meaning.