A fiber in the GFRTU is the local recognition structure attached to a trace — the semantic data available at a single point of the trace site. Formally, a fiber over trace t is the recognition fiber H_t: a finite Heyting algebra equipped with a stabilizer σ_t and a drift operator Δ_t.
The term “fiber” comes from the language of fibrations: the total structure is a fibered category over the trace site, and the fiber at each trace is the “slice” of the total structure above that point. Restriction maps connect fibers at different traces: if t → t’ is a refinement, there is a restriction map H_t’ → H_t that extracts the coarser data from the finer record.
The fixed fiber H_t* = {a ∈ H_t : σ_t(a) = a = Δ_t(a)} is the subset of a fiber that is stable under both stabilizer and drift — the recognitions that neither decay nor shift. The fixed fibers assemble into a subsheaf H* of the sheaf universe, representing the dynamically coherent portion of the recognition data.