Coupling Capacity as Structural Reserve: K as Lyapunov Stability Radius in La Profilée

K — Coupling capacity in La Profilée — is the Lyapunov stability radius of the Frame attractor under Module perturbation: the maximal perturbation magnitude the system can absorb while remaining within the basin of attraction of its identity-bearing Frame. This paper proves it structurally. A preliminary theorem (K0) establishes the multiplicative necessity of F·M·K from LP’s axioms M1–M3. Eight further theorems derive K’s structural consequences. K1–K6 form the theoretical core: K1 grounds the IR equation in basin dynamics; K2–K3 formalize depletion and development; K4 derives T_visible geometrically from basin erosion; K5 establishes K_min as the structural collapse boundary; K6 unifies all K-functions as aspects of the same basin geometry. K7 derives Q4 (Structural Self-Priority) as K-differentiation. K8 extends the architecture to phenomenal valence under Q3 and Σ-completeness. The paper connects LP's K-concept to Lyapunov stability theory, structural stability, and basin-of-attraction analysis. No new mathematical objects are required: K was always already a stability radius. This paper makes that precise.