Concrete example first
Suppose you study three observation contexts:
t0: a rough event log,t1: a cleaned log,t2: a cleaned log plus annotations.
You can move from rough to cleaned, and from cleaned to annotated. Those moves are morphisms between traces. Now pick which families of moves count as enough information to reconstruct a trace. For example, you may say that two complementary cleaned views together cover t2.
That pair — the category of traces and the coverage rule — is the trace site.
Formal definition
A trace site is a pair ((T,J)) where:
- (T) is a small category whose objects are traces and whose morphisms are refinement or transport maps, and
- (J) is a Grothendieck topology on (T), specifying which sieves (or covering families) count as covers.
In GFRTU, the trace site is primitive data. It determines locality, gluing, and the ambient sheaf topos (\mathbf{Sh}(T,J)).
Why it matters in GFRTU
- It tells you what “local” means.
- It determines when local recognition data can glue.
- It anchors every later construction: fibers, sheaf semantics, fixed layer, and generative closure.