A recognition fiber H_t is the local semantic structure at a trace t in the GFRTU: a finite Heyting algebra equipped with two commuting endomorphisms — a stabilizer σ_t and a drift operator Δ_t. The elements of H_t represent the recognitions (semantic values) available at trace t; the Heyting structure provides the local logic of meet, join, and implication.
The stabilizer σ_t is idempotent and monotone: it projects recognitions onto their stable part. The drift Δ_t is monotone and moves recognitions along a temporal or dynamical axis. Their commutation (σ_t ∘ Δ_t = Δ_t ∘ σ_t) ensures that stabilization and evolution are compatible. The fixed fiber H_t* = {a : σ_t(a) = a = Δ_t(a)} consists of recognitions that are both stable and stationary.
Recognition fibers are the second primitive input to the GFRTU (alongside the trace site). They are fibered over the trace site: restriction maps connect fibers at different traces, and the sheaf condition ensures that compatible recognition data across traces glues into global sections of the sheaf universe.