The trace site (T, J) is a small category T equipped with a Grothendieck topology J that indexes traces and their refinements in the GFRTU. Objects of T are traces; morphisms are refinement maps (a morphism t → t’ means t’ refines or extends t). The topology J specifies which families of refinements count as covers.
The trace site is one of the three primitive inputs to the GFRTU construction (alongside the recognition fibers and their dynamics). The choice of trace site determines the granularity and structure of the universe: different trace sites produce different GFRTUs, just as different topological spaces produce different sheaf topoi.
The category of sheaves on the trace site, Sh(T, J), is the sheaf universe — a Grothendieck topos where recognitions assemble as sheaves. The three closure principles of the GFRTU (sheaf completion, fiber stabilization, generative closure) all operate relative to the trace site.