## 4 Discussion
These applications span a broad range within what is called the critical infrastructure, including medicine and healthcare, transportation, critical industrial facilities, and energy supply. In this context, it is easy to imagine communication systems that must be designed fail-safe. From Section 3, recall the reasons for considering a communication system's analog part. Point 4 list a possible requirement for such a fail-safe system: provided the noise sequence \(\|\mathbf{w}\|_{\infty}\) does not exceed a \"maximum credible amplitude\" \(e_{w}\), correct message transmission must be possible. Outside of communications engineering, such requirements are standard in control theory and correspond to a distinction of design-basis events from beyond-design-basis events. Traditionally, we find this distinction in engineering for safety-critical facilities, such as nuclear power plants. Based on mathematical modeling, the plant is designed to withstand all accidents whose occurrence is considered realistic. Consequently, a model-to-system relationship guides the design process. The replacement of the design process's model-to-system relationship by a metamodel-to system relationship is a distinguishing feature of digital twinning: any machine-readable language necessarily incorporates a formal model of the physical entity it describes. In our case, this formal model consists of the sampling and interpolation theory, as introduced in Section 2. Once the relevant algorithms are implemented on the employed computing hardware, the model itself becomes part of the physical system and its dynamics. Accordingly, a conclusive generalization of the distinction between design-basis and beyond-design-basis events for such systems considers the resulting interaction between computing hardware, implemented algorithms, and physical agents. The analysis of the structural properties of \(\mathfrak{F}_{\star}\) and \(\mathfrak{F}_{\star}\) in Section 3 follows this approach. In order to ensure that the system as a whole can withstand all design-basis events, such as any possible noise sequence not exceeding \"maximum credible amplitude\" \(e_{w}\), we need to prove that the employed algorithm can capture those characteristics of the physical entity that are relevant for design-basis events correctly. In other words, we require the employed machine-readable language to provide sufficient representatives of the analog world. This facet of trustworthiness is known as integrity [4; 9]. To the best of the authors' knowledge, this work is the first to consider the problem of identifying trustworthy digital representations of analog systems. However, the problem is fundamental to digital twinning, and the authors believe that it will receive increased attention in the anticipated generation of communication technology. Conceptualization, H.B. and F.H.P.F. ; methodology, H.B. and Y.N.B. ; validation, H.B., Y.N.B. and U.J.M. ; formal analysis, H.B. and Y.N.B. ; investigation, H.B. and Y.N.B. ; writing--original draft preparation, H.B., Y.N.B. and U.J.M. ; writing--review and editing, H.B., Y.N.B., U.J.M. and F.H.P.F. ; visualization, Y.N.B. ; supervision, H.B. and F.H.P.F. ; project administration, H.B. and F.H.P.F. ; funding acquisition, H.B. and F.H.P.F. All authors have read and agreed to the published version of the manuscript. The work of [PERSON] was supported in part by the German Federal Ministry of Education and Research (BMBF) within the National Initiative on 6G Communication Systems through the Research Hub 6G-life under Grant 16 KISK002; Excellence Cluster Cyber Security in the Age of Large-Scale Adversaries (CASA), Ruhr University Bochum, 44801 Bochum. The work of [PERSON] was supported in part by the BMBF within the national initiative on Post Shannon Communication (NewCom) under Grant 16 KIS1004 and in part by the BMBF within 6G-life under Grant 16 KISK002. The work of [PERSON]\(\ddot{\text{o}}\)nich was supported by the BMBF within NewCom under Grant 16 KIS1003K.