DYNAMIC MULTILAYER MODEL M_OSI(T) WITH CROSS-LAYER CONTRACTS AND COMPOSITIONAL CYBER-RESILIENCE PROPERTIES

The paper proposes a dynamic multilayer model M_OSI(t) for formally describing communication-mission cyber resilience. The model combines OSI layers L1–L7 with control and organizational planes in a temporal multilayer graph and represents cross-layer interactions as assume-guarantee contracts containing assumptions, guarantees, invariants, ownership, and authority boundaries. Contract compatibility and refinement conditions, a threshold-based state set, local controllability, stability and non-interference criteria, and a normalized observation-quality indicator are formulated. For a synthetic parameterization, explicit matrices J, B and the function J(w, δ) are given; the resulting local-stability boundary w*(δ) = (1 – r)/g(δ) equals 0.60 at zero delay and 0.45 at δ = 30 ms, and controllability from control-plane inputs reduces to the activity of the cross-layer link. Five synthetic profiles contain 38 components, 5 agents, and 57 temporal dependencies. For the cascade map, the first period-doubling boundary is μ* = 3e^λ ≈ 3.154 at λ = 0.05; in a separate synthetic parameterization, the joint satisfaction region of three contract constraints is nonempty for μ ≤ 2.1. Three counterexamples of incorrect composition are constructed for five demonstration profiles. All quantitative values are illustrative and are not measurements of operational communication stacks; the system meaning of the model parameters and their calibration procedure are summarized in a separate table. The result is a formal specification for subsequent profile verification and empirical calibration.