The fixed fiber H_t* at a trace t is the subset of the recognition fiber H_t that is stable under both the stabilizer σ_t and the drift operator Δ_t: H_t* = {a ∈ H_t : σ_t(a) = a and Δ_t(a) = a}. Elements of the fixed fiber are recognitions that neither decay under stabilization nor shift under dynamical evolution — they are the fully coherent semantic values at that trace.
Because σ_t and Δ_t commute and both preserve the Heyting structure, the fixed fiber H_t* is itself a Heyting subalgebra of H_t. The fixed fibers at different traces assemble into a subsheaf H* of the sheaf universe, representing the dynamically coherent portion of all recognition data. This subsheaf H* is to the GFRTU what the stable fragment H^st is to the semiotic universe: the portion of the algebra that has reached equilibrium.
The three closure principles of the GFRTU — sheaf completion, fiber stabilization, and generative closure — interact to determine the fixed fibers. Fiber stabilization produces the fixed fibers locally; sheaf completion ensures they glue globally; generative closure ensures the universe contains exactly what these fixed points force.