Spectral Stability, Dissipativity, and Contraction: Necessary and Sufficient Robustness Characterizations for Linear and Nonlinear Systems This deposit is a compact technical note that separates asymptotic spectral stability from uniform transient robustness, and then provides a unified robustness bridge from linear systems to nonlinear systems via contraction theory. For LTI systems , the note proves a necessary-and-sufficient characterization of 2-norm transient robustness: exponential contractivity of the semigroup is equivalent to negative definiteness of the symmetric part . As a corollary, Euclidean dissipativity is equivalent to the absence of transient amplification, clarifying why eigenvalue stability alone is insufficient for robust transient behavior in non-normal dynamics. The note further derives an explicit transient envelope bound using Lyapunov solutions , showing how transient growth limits can be expressed in terms of the conditioning of and associated decay rates. For nonlinear systems , the note extends the robustness framing using uniform contraction in a state-dependent metric , requiring over a forward-invariant set. Under this condition it defines a finite-horizon fragility functional aggregating spectral margin proxies, energy decay, drift accumulation, and basin-thickness terms, and proves an explicit upper bound on fragility in terms of the contraction rate , a drift Lipschitz constant, time horizon , and basin-radius proxy parameters. Together, the results provide a unified backbone: complete (necessary-and-sufficient) robustness classification in the linear 2-norm case, and a sufficient bounded-fragility guarantee for nonlinear systems under contraction, with explicit bounds suitable for audit-style robustness arguments. License: Copeland Resonant Harmonic Formalism (CRHC v1.0) This work is licensed under the Copeland Resonant Harmonic Copyright (CRHC v1.0). Attribution is required for all uses. Collaboration, academic discussion, and non-commercial use are permitted. Commercial use, resale, or incorporation into proprietary systems is not permitted without explicit written permission from the author. Derivative works must preserve attribution and must not remove or alter the stated license terms.