## 1 Introduction  
Cyber-physical systems (CPS) are a category of systems that contain both cyberspace and physical components, closely linked to related concepts such as Industrial Control Systems (ICS), Operational Technology (OT), Industry 4.0, and the internet of things (IoT) [1, 2, 3, 4]. Complex CPS enables active feedback loops between logical processes and physical effects, representing multi-domain effects that are rarely limited to the traditional silos of digital systems and real-world physical systems [5]. As CPS often consists of systems of systems, the securitization of these systems can range from complicated to complex [6; 7]. Understanding the cyber security consequences posed by cyber threats to these systems is imperative, as a weakness in the posture of a CPS would have far-reaching implications for the physical domains it interacts with [7; 8; 9]. This evolution gives rise to what are now termed Complex Cyber-Physical-Social Systems (C-CPSS), wherein the complexity of human behavior, decision making, and social structures interacts with and influences the performance and security posture of traditional CPS environments. Cyber security is an applied field that has rapidly evolved in response to technological advancements, legislative demands, and business changes. Mission assurance is a term originally defined by the United States Air Force, which is the \"process to protect or ensure the continued function and resilience of capabilities and assets... critical to the execution of DoD mission-essential functions\" [10]. In a non-military environment, mission assurance involves guaranteeing organization-essential services. The cyber domain inherently contributes to the delivery of such services and, as a fundamental input to capability, must also be resilient to degradation in the event of an outage to provide mission assurance. Thus, understanding how CPS, and more specifically how C-CPSS, impacts the resilience of systems contributing to mission assurance is a pertinent question for cyber security researchers. The security challenges in C-CPSS go beyond traditional threat modeling. Emergent behaviors--caused by nonlinear interactions among cyber, physical, and social components--can manifest in unpredictable ways, undermining system performance and jeopardizing mission assurance [11; 12]. Mission assurance, as defined in both defence and civilian contexts, involves the sustained delivery of essential services under degraded conditions [13; 14]. In C-CPSS environments, threats are not only technical or malicious but can also stem from unintended interactions, misaligned incentives, or cascading failures across domains [3]. Existing CPS security models often overlook these socio-technical interdependencies, leading to resilience strategies that are insufficient for the demands of complex, real-world scenarios. This paper addresses a key research gap: the lack of integrated frameworks that explicitly account for social complexity and emergent cyber risk in CPS, and by extension, C-CPSS [15; 16]. We argue that advancing cyber resilience in such systems requires a fundamental reconceptualization--one that embraces responsible resilience, grounded in trustworthy and explainable AI models, and incorporates the modeling of emergent risk across cyber, physical, and social dimensions. To address these challenges, this paper introduces the concept of responsible resilience--the capacity of C-CPSS to absorb, recover from, and adapt to disruptions through the integration of transparent and trustworthy AI models. We propose the E3R modeling paradigm (Emergent, Risk-Relevant Resilience), a novel framework that combines causal loop diagrams, agent-based simulations, and ontology-driven modeling to capture the dynamics of socio-technical emergence and guide the design of adaptive, mission-oriented resilience strategies. The key contributions of this paper are as follows:  
* A review of recent CPS and cyber security research, highlighting the absence of social-emergent risk modeling in the literature review.