The Non-Composability of Resilience Certificates Across Critical Infrastructure Domains

Modern critical infrastructure is governed at once across four resiliencendomains – cybersecurity, operational-technology functional safety, crisis andnemergency management, and AI-governance for cyber-physical systems, eachndefining and certifying resilience differently. Comparing them across definitions,nformal models, and metrics, it is showed they share a common structural skeleton,nwhich this paper formalises as a tuple F = (D, S, R, 𝜙, 𝜌,𝑄) whose final elementn 𝑄 records each domain’s quantification mode – worst-case, expected-value, orndescriptive. These quantification modes do not align across domain boundaries,nyielding a non-composability result for certificates (Proposition 1). Componentlevelncertificates, with the coupling, leave the composed system-level guaranteenunderdetermined unless an explicit bridging assumption is supplied – illustrated on ansmart-water configuration where aworst-case-monitored detector feeds an expectedvalue-ncertified safety function. The paper characterises three structural gaps sharednacross the four domains, and states five requirements a unified framework mustnsatisfy. The result is one of certificate insufficiency, not a failed unification: anunified framework remains achievable, but any cross-domain certification mustnadd an explicit bridge between quantification modes.