CAD.3:4.6 - Separate recognition, mathematical assurance and physical reliance

A shrinking error trace or plausible margin recognizes a promising design. The invariance and continuation arguments establish conditional properties of a mathematical model. Model validation, parameter and disturbance bounds, execution timing and physical tests determine whether those properties support the intended engineering use.

A decrease condition that applies only outside a threshold does not, in discrete time, prevent a jump from inside to outside. Use an actual invariant-set inclusion or a one-step bound valid on the entire proposed set. Likewise, a small average error is not a worst-case constraint bound.