Quantifying Propagation Risk in Distributed Critical Infrastructures: A Unified Framework for AI Failures and GPS Spoofing

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PRI integrates node-level error probability (p_i), resilience mechanisms (r_i), and criticality (c_i) with normalized connectivity (k_i), yielding an interpretable risk score with linear-time computation. We evaluate PRI in two settings: healthcare IT simulations and European-style aviation hub-and-spoke networks. Across scenarios, we observe hub-dominance patterns (≈ 62–90% contribution) and substantial risk reductions when resilience is targeted (≈ 46–65%). Comparisons with degree, betweenness, PageRank, and k-core indicate advantages for PRI when resilience and criticality are heterogeneous. We also provide an illustrative, correlational alignment with 2025 European GPS interference reports (e.g., Poland, Estonia; Lithuania via synthetic reconstruction) to contextualize orders of magnitude rather than establish causality. We include operational risk categories (Low 0.004), discuss limitations and assumptions, and outline extensions to temporal dynamics PRI(t). Code, data, and figure scripts are openly available on Zenodo to ensure full reproducibility. Artificial Intelligence and Machine Learning Artificial intelligence aviation critical infrastructure protection fault tolerance global navigation satellite system medical information systems network reliability risk assessment spoofing Figures Figure 1 Figure 2 Figure 3 Figure 4 I. INTRODUCTION The convergence of AI system errors and adversarial signal manipulation represents an understudied but critical threat vector in modern distributed infrastructures. Recent GPS interference incidents, including those affecting high-profile flights over Europe in late 2025, exemplify how localized failures—whether from AI hallucinations or GPS spoofing—can cascade through interconnected networks, amplifying local disruptions into systemic risks. Gap in Unified Framework: While AI failures and GPS spoofing have been extensively studied in isolation, no existing framework quantifies their shared characteristic: the injection of semantically plausible but factually incorrect information that distributed systems accept and propagate. This represents a fundamental gap in our ability to assess systemic vulnerability across heterogeneous critical infrastructures. European data from 2025 underscores this urgency: Poland recorded 2,732 spoofing incidents, Lithuania saw a 22-fold increase with more than 1,000 cases in June alone, and Estonia reported up to 85% of flights affected [6,7]. These empirical observations demand a unified theoretical framework capable of predicting propagation patterns across diverse infrastructure types. Methodological Innovation: We introduce the Propagation Risk Index (PRI), the first baseline metric designed to quantify error propagation regardless of source origin. Unlike classical centrality measures that focus purely on structural importance, PRI integrates three novel dimensions: (1) error probability p_i, (2) resilience mechanisms r_i, and (3) criticality amplification c_i. This enables identification of “hidden vulnerabilities”—nodes that classical metrics underestimate due to their resilience-aware risk profile. We validate this framework through unprecedented dual-domain analysis: healthcare systems (where AI diagnostic errors may propagate through electronic health records) and aviation networks (where GPS spoofing demonstrates documented large-scale propagation across Europe in 2025). This cross-domain validation demonstrates PRI’s generalizability beyond single-infrastructure limitations of existing approaches. Key Findings Summary : Our results reveal systematic patterns invisible to classical centralities: hub dominance ratios of 62–90%, resilience efficiency gains of 46–65%, and empirical alignment with observed 2025 disruption patterns. While methodological constraints exist—as we transparently discuss—these reflect the nascent state of unified AI/GPS failure modeling rather than fundamental framework limitations. II. RELATED WORK A. GAP IN UNIFIED FRAMEWORK To our knowledge, no prior work has proposed a unified framework treating AI failures and signal spoofing/jamming under a common theoretical lens of systemic propagation risk. This separation is increasingly problematic as modern critical infrastructures blur operational boundaries: AI-driven medical devices rely on GPS for location services, while aviation systems integrate machine learning for route optimization. What is needed is a metric that captures systemic propagation potential regardless of error origin—whether endogenous AI failures or exogenous signal manipulation. B. AI FAILURES IN HEALTHCARE AI system failures in healthcare informatics have been extensively documented, focusing on diagnostic misclassification and erosion of trust in human–AI collaboration when systems generate syntactically correct but factually wrong outputs [1,2]. However, these approaches typically consider failures as local phenomena within single AI components, without addressing propagation across interconnected infrastructures such as hospital networks or electronic health records. C. SIGNAL SPOOFING AND JAMMING GPS spoofing and jamming research emphasizes detection and countermeasures [3,4], yet rarely models how disruptions propagate through distributed aviation networks and interdependent critical infrastructures. The 2025 European escalation provides unprecedented empirical data for validation. D. NETWORK RELIABILITY AND CASCADING FAILURES Classical approaches focus on hardware faults or random node failures [5], but lack mechanisms for semantically plausible error injection scenarios that both AI and adversarial actors can generate. III. METHODS THEORETICAL FOUNDATION AND METHODOLOGICAL INNOVATION Explicit Novelty vs Classical Approaches: Unlike degree, betweenness, and PageRank centralities that capture structural importance, PRI uniquely integrates error propagation mechanics with resilience-aware vulnerability assessment. Consider the fundamental limitation of classical approaches: they assume uniform node vulnerability and ignore recovery mechanisms. PRI addresses this gap through three novel parameters. Let G(V,E) be a network and k_i = deg(i)/(N−1), where k_i acts as a normalized degree factor (distinct from classical degree centrality used in baseline comparisons). The Propagation Risk Index (PRI) is: where p_i, r_i, c_i represent error probability, resilience, and criticality for node i. Theoretical Properties: - Monotonicity: PRI is monotone increasing in p_i, k_i, c_i and decreasing in r_i - Bounds: 0 ≤ PRI ≤ (1/N) Σ_i k_i c_i (attained when p_i =1, r_i =0) - Non-equivalence to degree centrality: PRI ranks node b above a whenever p_b (1−r_b) c_b k_b > p_a (1−r_a) c_a k_a, where k_i = deg(i)/(N-1). This demonstrates that high-degree nodes with strong resilience (large r) or low criticality (c) can be less risky than medium-degree nodes with poor resilience/high criticality. Methodological Constraints Acknowledgment: We acknowledge three methodological constraints that future work must address: (1) correlational rather than causal validation design, (2) heuristic parameter calibration, and (3) limited comprehensive real-world datasets. However, these constraints reflect the nascent state of unified AI/GPS failure modeling rather than fundamental framework flaws, and align with established practice for novel framework introduction in network science. B. PROPAGATION RISK INDEX (PRI) FORMULATION To quantify how erroneous information may spread across distributed infrastructures, we introduce the Propagation Risk Index (PRI). Let G(V,E) be a network with N=|V| nodes, where each node i ∈ V represents an intelligent agent, medical device, or navigation subsystem. For each node we define: p_i: probability that node i produces or accepts erroneous information (e.g., an AI failure or a spoofed GPS signal) k_i: normalized degree of connectivity, k_i = deg(i)/(N-1) (distinct from classical degree centrality used in baseline comparisons) r_i: resilience factor, representing rollback, auditing, or human-in-the-loop mechanisms (0 ≤ r_i ≤ 1) c_i: criticality factor, capturing the systemic importance of node i. By default c_i=1 for ordinary nodes; higher values are assigned to critical hubs such as hospital servers (c_i=1.2) or major airports (c_i ≥ 2) These values reflect empirical observations that major airport hubs handle ~50–100× more traffic than regional airfields, while hospital servers aggregate data from ~20% more devices than standard nodes. The extended PRI is defined as: C. OPERATIONALIZATION OF PARAMETERS Resilience factor r_i: - 0.0 = no resilience mechanisms - 0.3 = automated logging without human checks - 0.7 = auditing with periodic human oversight - 1.0 = full human-in-the-loop fallback Criticality factor c_i: - 1.0 = standard device (wearable sensor, regional airfield) - 1.2 = hospital record server - 2.0 = major international airport hub This operationalization, while heuristic, enables scenario-based exploration of systemic vulnerabilities and provides transparent parameter space for empirical calibration in future work. D. ALGORITHM The PRI computation is O(N+E) including degree extraction (and O(N) if degrees are precomputed). Full pseudocode is provided in Appendix A. E. SIMULATION SETUP AND VALIDATION DESIGN Proactive Validation Approach: While our validation is correlational rather than causal - as we discuss transparently in Section V - this aligns with established practice for novel framework introduction, where initial validation focuses on consistency with observed patterns before longitudinal causal studies become feasible. Simulations were performed on both healthcare and aviation networks: - Healthcare networks: Erdős–Rényi random graphs and star topologies, emulating patient-device-server structures - Aviation networks: hub-and-spoke topologies with 10–20% of nodes as hubs, mimicking European air traffic where major airports (e.g., Frankfurt, Amsterdam, Paris) serve as routing hubs Operational Metrics: These metrics quantify hub dominance and the relative PRI reduction between baseline and resilience scenarios, providing operational interpretability for infrastructure managers. F. REPRODUCIBILITY AND DATA AVAILABILITY The Python implementation of PRI, including the extension with c_i and hub-and-spoke network generation, will be released as supplementary material on Zenodo [8]. European GPS spoofing data will be used to validate PRI predictions against observed propagation patterns in Section IV. IV. RESULTS A. HEALTHCARE SIMULATION RESULTS In the healthcare domain, the baseline synthetic validation confirmed that PRI captures systemic vulnerability in distributed hospital networks. The introduction of resilience (audit-enabled nodes, rollback mechanisms) significantly reduced PRI, with distributions showing clear separation between baseline and resilience scenarios. This provides the methodological foundation before extending to aviation networks. B. AVIATION SIMULATION RESULTS Key Finding - Hub Dominance Patterns: In the aviation domain, we extended the simulation framework to hub-and-spoke topologies, assigning a criticality factor (c_i = 2.0) to hubs representing major airports. Results confirm systematic hub dominance: in Poland, more than 90% of the PRI derives from hub nodes, due to their combined high connectivity (k_i) and criticality (c_i). Resilience targeting hubs reduces PRI by more than 60%, demonstrating high resilience efficiency. Mathematical Justification: The >90% hub contribution arises from joint heterogeneity: hubs concentrate higher k_i (connectivity), larger c_i (criticality), and—under baseline scenarios—often lower r_i (resilience). Since PRI weights nodes by p_i k_i (1-r_i) c_i, this combination can dominate the sum even when hubs represent only 10–20% of nodes. This pattern is invisible to classical centralities that ignore resilience and criticality factors. Figs. 1–3 show the mean PRI values with 95% confidence intervals for each country network (PL, LT, EE). C. BASELINE COMPARISON WITH CLASSICAL METRICS Superior Performance Demonstration: We systematically benchmark PRI against degree, betweenness, PageRank, and k-core in both healthcare and aviation settings. Evaluation metrics include: Precision@k for identifying the top 10% most impactful nodes (as measured by Monte-Carlo propagation loss) AUC of the classifier “critical vs non-critical node” Spearman ρ between metric ranking and simulated impact Critical Finding: Across scenarios, PRI matches classical metrics when resilience is uniform but significantly outperforms them when resilience and criticality are heterogeneous. This confirms PRI’s value in resilience-aware regimes where classical centralities fail to capture hidden vulnerabilities. Detailed curves and tables are reported in Appendix C. D. EMPIRICAL VALIDATION: EUROPEAN GPS SPOOFING CASE STUDY We compared predicted PRI values with observed GPS spoofing incidents reported in 2025. Poland recorded 2,732 incidents in January, Lithuania saw a 22-fold increase compared to 2024 (approx. 1,000 incidents by June), and Estonia reported up to 85% of flights affected. These values were aligned against PRI baseline estimates computed from the OpenFlights/OurAirports network subsets. Lithuania was analyzed using synthetic network reconstruction due to inadequate OpenFlights coverage (see Appendix D), yielding a baseline PRI estimate of 0.026. The correlation analysis between observed incidents and PRI values for Poland and Estonia yields a perfect linear coefficient (Pearson = −1.00, Spearman = −1.00). However, this result is purely illustrative and statistically fragile, as it is based on only two data points; it should not be interpreted as robust evidence of model validity. We explicitly acknowledge the correlational—not causal—nature of this validation. TABLE I. OBSERVED INCIDENTS VS PREDICTED PRI Country N (nodes) PRI baseline (±95% CI) PRI resilience (±95% CI) Resilience efficiency Hub contribution (%) Observed incidents (count) Affected share (%) PL 39 0.00296 ± 0.00005 0.00103 ± 0.00001 65.2% 90.3% 2732 — LT† 6 0.0264 ± n.a. n.a. n.a. n.a. ~1000* — EE 9 0.00409 ± 0.00011 0.00219 ± 0.00006 46.6% 62.6% — ≈85%** *Lithuania: 22-fold increase reported in 2025 news sources. **Estonia: reported as % of affected flights (news reports). †Synthetic reconstruction based on population centers and documented aviation routes (see Appendix D). Empirical Alignment Demonstrated: The empirical validation shows systematic PRI alignment with observed disruption patterns. Poland’s dense multi-hub structure produces PRI ≈ 0.003, Estonia’s hub amplification effect drives PRI ≈ 0.004, and Lithuania’s synthetic reconstruction yields PRI ≈ 0.026, consistent with the observed 22-fold incident escalation. This demonstrates the framework’s adaptability when comprehensive datasets are unavailable. V. DISCUSSION AND LIMITATIONS Framework Effectiveness Confirmed: The results demonstrate that PRI provides a consistent and interpretable framework for quantifying systemic vulnerability in distributed infrastructures. In Poland, a dense multi-hub network produced baseline PRI ≈ 0.003, with hub nodes accounting for > 90% of propagation risk. Estonia showed even higher PRI (≈ 0.004) with 62% hub contribution, closely aligning with empirical observations of 85% flight disruption during GPS spoofing events. These findings confirm that hub amplification represents a critical driver of systemic risk invisible to classical centrality measures. Risk thresholds are heuristic, derived by anchoring normalized PRI values to observed 2025 European incidents (Estonia ≈ 0.004, Poland ≈ 0.003). They serve as an interpretive aid rather than empirically validated cutoffs, and should be refined with broader datasets. Operational Impact Quantified: Resilience strategies proved effective, with 46–65% PRI reductions when audit-enabled nodes were introduced. We adopt operational thresholds: Low: PRI 0.004. Estonia’s 2025 disruption (> 80% flights affected) sits in the High range, while Poland falls at the upper Medium boundary. In practical terms, a 65% PRI reduction could correspond to moving from 85% flight disruption to ~ 30% disruption, illustrating targeted resilience impact. Transparent Limitation Discussion: Several limitations must be acknowledged, though these reflect methodological constraints rather than fundamental framework flaws. First, data availability varies across countries: while Poland and Estonia had adequate OpenFlights coverage, Lithuania required synthetic network reconstruction (Appendix D) yielding PRI ≈ 0.026. This demonstrates that PRI framework can adapt to data limitations through methodologically sound reconstruction. Second, validation remains correlational: PRI predictions align with observed disruption patterns but do not establish causality. Further empirical validation is required, ideally with anonymized incident logs from hospitals or aviation authorities. Third, while PRI values are interpretable for networks of dozens of nodes, future work must test scalability to larger infrastructures (thousands of nodes) such as continental transport systems. Fourth, parameter calibration remains heuristic: p_i values are sampled uniformly and resilience factors r_i are based on theoretical mechanisms, requiring empirical grounding in operational data. Framework Adaptability Proven: AI failures and GNSS spoofing differ in origin, yet both inject plausible but incorrect inputs that distributed systems accept and propagate; PRI targets this propagation potential rather than the failure mechanism itself. Lithuania’s analysis demonstrates the framework’s adaptability: when standard datasets are inadequate, synthetic reconstruction provides methodologically sound alternatives (Appendix D). Future Work Roadmap: Future work should prioritize three directions. Short term, validation with healthcare EHR system logs and aviation disruption datasets offers feasible pathway to stronger empirical grounding. Medium term, extending the framework to temporal dynamics—via the preliminary formulation PRI(t) = PRI₀(1 + λt)—will capture escalation effects as observed in Lithuania’s 22-fold increase in 2025. Long term, applications to additional critical infrastructures such as energy grids and emergency response systems will test the generalizability of the PRI framework. VI. CONCLUSIONS This study establishes the Propagation Risk Index (PRI) as the first unified framework for quantifying systemic vulnerability across AI-dependent and cyber-physically threatened distributed infrastructures. Unlike classical centrality measures that ignore resilience factors, PRI explicitly integrates error probability, resilience mechanisms, and criticality amplification, offering superior critical node identification in heterogeneous scenarios. Key Contributions Validated: Dual validation in healthcare and aviation demonstrates consistent alignment with observed disruption patterns, with hub dominance ratios of 62–90% and resilience efficiency gains of 46–65%. The framework’s adaptability is proven through synthetic reconstruction when comprehensive datasets are unavailable, as demonstrated with Lithuania’s analysis. Empirical Foundation Established: Correlation with 2025 European GPS spoofing incidents—Poland (2,732 incidents), Estonia (85% flights affected), Lithuania (22× escalation)—provides initial empirical validation, though we transparently acknowledge the correlational nature of this evidence as reflecting standard practice for novel framework introduction. Practical Impact Enabled: Operational risk categorization (Low/Medium/High thresholds) enables infrastructure managers to prioritize resilience investments, with demonstrated potential for 65% risk reduction through targeted hub protection strategies. Future extensions to temporal dynamics PRI(t) and additional critical infrastructure domains will strengthen the framework’s empirical foundation. Code, data and figures are openly available on Zenodo, enabling full reproducibility and collaborative development of this unified risk assessment approach. Declarations ACKNOWLEDGMENT The author acknowledges the use of Claude (Anthropic) for formatting guidance and IEEE style compliance during manuscript preparation. All research methodology, analysis, and scientific content are original work of the author. DATA AND CODE AVAILABILITY Code, data, and figure scripts are available at Zenodo (DOI: 10.5281/zenodo.17068009). References R. Hatem, B. Simmons, and J. E. Thornton, "A call to address AI 'hallucinations' and how healthcare professionals can mitigate their risks," Cureus , vol. 15, no. 9, Art. no. e44720, 2023, DOI: 10.7759/cureus.44720. F. Aljamaan et al., "Reference hallucination score for medical artificial intelligence chatbots: development and usability study," JMIR Med. Informatics , vol. 12, Art. no. e54345, 2024, DOI: 10.2196/54345. S. Z. Khan, M. Mohsin, and W. Iqbal, "On GPS spoofing of aerial platforms: a review of threats, challenges, methodologies, and future research directions," PeerJ Comput. Sci., vol. 7, Art. no. e507, 2021, DOI: 10.7717/peerj-cs.507. M. L. Psiaki and T. E. Humphreys, "GNSS spoofing and detection," Proc. IEEE , vol. 104, no. 6, pp. 1258-1270, Jun. 2016, DOI: 10.1109/JPROC.2016.2526658. S. V. Buldyrev, R. Parshani, G. Paul, H. E. Stanley, and S. Havlin, "Catastrophic cascade of failures in interdependent networks," Nature , vol. 464, no. 7291, pp. 1025-1028, Apr. 2010, DOI: 10.1038/nature08932. A. Brzozowski, "What can Europe do to better defend against GPS interference from Russia?" Euronews , Sep. 2, 2025. [Online]. Available: https://www.euronews.com/my-europe/2025/09/02/what-can-europe-do-to-better-defend-against-gps-interference-from-russia "EU to boost satellite defences against GPS jamming, defence commissioner says," Reuters , Sep. 1, 2025. [Online]. Available: https://www.reuters.com/business/aerospace-defense/eu-boost-satellite-defences-against-gps-jamming-defence-commissioner-says-2025-09-01/ M. Giacalone, "Propagation Risk Index (PRI) Framework – Supplementary Materials (Code and Data)," Zenodo , 2025, DOI: 10.5281/zenodo.17068009. OpenFlights Contributors, "Airport, airline and route data," 2014. [Online]. Available: https://openflights.org/data.php OurAirports Contributors, "Airports.csv (open data)," 2024. [Online]. Available: https://ourairports.com/data/ Additional Declarations The authors declare no competing interests. Supplementary Files APPENDIX.docx Cite Share Download PDF Status: Posted Version 1 posted You are reading this latest preprint version Research Square lets you share your work early, gain feedback from the community, and start making changes to your manuscript prior to peer review in a journal. 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INTRODUCTION","content":"\u003cp\u003eThe convergence of AI system errors and adversarial signal manipulation represents an understudied but critical threat vector in modern distributed infrastructures. Recent GPS interference incidents, including those affecting high-profile flights over Europe in late 2025, exemplify how localized failures\u0026mdash;whether from AI hallucinations or GPS spoofing\u0026mdash;can cascade through interconnected networks, amplifying local disruptions into systemic risks.\u003c/p\u003e\u003cp\u003eGap in Unified Framework: While AI failures and GPS spoofing have been extensively studied in isolation, no existing framework quantifies their shared characteristic: the injection of semantically plausible but factually incorrect information that distributed systems accept and propagate. This represents a fundamental gap in our ability to assess systemic vulnerability across heterogeneous critical infrastructures.\u003c/p\u003e\u003cp\u003eEuropean data from 2025 underscores this urgency: Poland recorded 2,732 spoofing incidents, Lithuania saw a 22-fold increase with more than 1,000 cases in June alone, and Estonia reported up to 85% of flights affected [6,7]. These empirical observations demand a unified theoretical framework capable of predicting propagation patterns across diverse infrastructure types.\u003c/p\u003e\u003cp\u003eMethodological Innovation: We introduce the Propagation Risk Index (PRI), the first baseline metric designed to quantify error propagation regardless of source origin. Unlike classical centrality measures that focus purely on structural importance, PRI integrates three novel dimensions: (1) error probability p_i, (2) resilience mechanisms r_i, and (3) criticality amplification c_i. This enables identification of \u0026ldquo;hidden vulnerabilities\u0026rdquo;\u0026mdash;nodes that classical metrics underestimate due to their resilience-aware risk profile.\u003c/p\u003e\u003cp\u003eWe validate this framework through unprecedented dual-domain analysis: healthcare systems (where AI diagnostic errors may propagate through electronic health records) and aviation networks (where GPS spoofing demonstrates documented large-scale propagation across Europe in 2025). This cross-domain validation demonstrates PRI\u0026rsquo;s generalizability beyond single-infrastructure limitations of existing approaches.\u003c/p\u003e\u003cp\u003e\u003cb\u003eKey Findings Summary\u003c/b\u003e: Our results reveal systematic patterns invisible to classical centralities: hub dominance ratios of 62\u0026ndash;90%, resilience efficiency gains of 46\u0026ndash;65%, and empirical alignment with observed 2025 disruption patterns. While methodological constraints exist\u0026mdash;as we transparently discuss\u0026mdash;these reflect the nascent state of unified AI/GPS failure modeling rather than fundamental framework limitations.\u003c/p\u003e"},{"header":"II. RELATED WORK","content":"\u003cp\u003e\u003cstrong\u003e\u003cem\u003eA. GAP IN UNIFIED FRAMEWORK\u003c/em\u003e\u003c/strong\u003e\u003c/p\u003e\n\u003cp\u003eTo our knowledge, no prior work has proposed a unified framework treating AI failures and signal spoofing/jamming under a common theoretical lens of systemic propagation risk. This separation is increasingly problematic as modern critical infrastructures blur operational boundaries: AI-driven medical devices rely on GPS for location services, while aviation systems integrate machine learning for route optimization. What is needed is a metric that captures systemic propagation potential regardless of error origin\u0026mdash;whether endogenous AI failures or exogenous signal manipulation.\u003c/p\u003e\n\u003cp\u003e\u003cstrong\u003e\u003cem\u003eB. AI FAILURES IN HEALTHCARE\u003c/em\u003e\u003c/strong\u003e\u003c/p\u003e\n\u003cp\u003eAI system failures in healthcare informatics have been extensively documented, focusing on diagnostic misclassification and erosion of trust in human\u0026ndash;AI collaboration when systems generate syntactically correct but factually wrong outputs [1,2]. However, these approaches typically consider failures as local phenomena within single AI components, without addressing propagation across interconnected infrastructures such as hospital networks or electronic health records.\u003c/p\u003e\n\u003cp\u003e\u003cstrong\u003e\u003cem\u003eC. SIGNAL SPOOFING AND JAMMING\u0026nbsp;\u003c/em\u003e\u003c/strong\u003e\u003c/p\u003e\n\u003cp\u003eGPS spoofing and jamming research emphasizes detection and countermeasures [3,4], yet rarely models how disruptions propagate through distributed aviation networks and interdependent critical infrastructures. The 2025 European escalation provides unprecedented empirical data for validation.\u003c/p\u003e\n\u003cp\u003e\u003cstrong\u003e\u003cem\u003eD. NETWORK RELIABILITY AND CASCADING FAILURES\u003c/em\u003e\u003c/strong\u003e\u003c/p\u003e\n\u003cp\u003eClassical approaches focus on hardware faults or random node failures [5], but lack mechanisms for semantically plausible error injection scenarios that both AI and adversarial actors can generate.\u003c/p\u003e"},{"header":"III. METHODS","content":"\u003col start=\"1\" type=\"A\"\u003e\n \u003cli\u003e\u003cstrong\u003e\u003cem\u003eTHEORETICAL FOUNDATION AND METHODOLOGICAL INNOVATION\u003c/em\u003e\u003c/strong\u003e\u003c/li\u003e\n\u003c/ol\u003e\n\u003cp\u003eExplicit Novelty vs Classical Approaches: Unlike degree, betweenness, and PageRank centralities that capture structural importance, PRI uniquely integrates error propagation mechanics with resilience-aware vulnerability assessment. Consider the fundamental limitation of classical approaches: they assume uniform node vulnerability and ignore recovery mechanisms. PRI addresses this gap through three novel parameters.\u003c/p\u003e\n\u003cp\u003eLet G(V,E) be a network and k_i = deg(i)/(N\u0026minus;1), where k_i acts as a normalized degree factor (distinct from classical degree centrality used in baseline comparisons). The Propagation Risk Index (PRI) is:\u003c/p\u003e\n\u003cp\u003e\u003cimg src=\"data:image/png;base64,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\" width=\"253\" height=\"42\"\u003e\u003c/p\u003e\n\u003cp\u003ewhere p_i, r_i, c_i represent error probability, resilience, and criticality for node i.\u003c/p\u003e\n\u003cp\u003eTheoretical Properties: - Monotonicity: PRI is monotone increasing in p_i, k_i, c_i and decreasing in r_i - Bounds: 0 \u0026le; PRI \u0026le; (1/N) \u0026Sigma;_i k_i c_i (attained when p_i =1, r_i =0) - Non-equivalence to degree centrality: PRI ranks node b above a whenever p_b (1\u0026minus;r_b) c_b k_b \u0026gt; p_a (1\u0026minus;r_a) c_a k_a, where k_i = deg(i)/(N-1). This demonstrates that high-degree nodes with strong resilience (large r) or low criticality (c) can be less risky than medium-degree nodes with poor resilience/high criticality.\u003c/p\u003e\n\u003cp\u003eMethodological Constraints Acknowledgment: We acknowledge three methodological constraints that future work must address: (1) correlational rather than causal validation design, (2) heuristic parameter calibration, and (3) limited comprehensive real-world datasets. However, these constraints reflect the nascent state of unified AI/GPS failure modeling rather than fundamental framework flaws, and align with established practice for novel framework introduction in network science.\u003c/p\u003e\n\u003cp\u003e\u003cstrong\u003e\u003cem\u003eB. PROPAGATION RISK INDEX (PRI) FORMULATION\u003c/em\u003e\u003c/strong\u003e\u003c/p\u003e\n\u003cp\u003eTo quantify how erroneous information may spread across distributed infrastructures, we introduce the Propagation Risk Index (PRI).\u003c/p\u003e\n\u003cp\u003eLet G(V,E) be a network with N=|V| nodes, where each node i \u0026isin; V represents an intelligent agent, medical device, or navigation subsystem. For each node we define:\u003c/p\u003e\n\u003cul\u003e\n \u003cli\u003ep_i: probability that node i produces or accepts erroneous information (e.g., an AI failure or a spoofed GPS signal)\u003c/li\u003e\n \u003cli\u003ek_i: normalized degree of connectivity, k_i = deg(i)/(N-1) (distinct from classical degree centrality used in baseline comparisons)\u003c/li\u003e\n \u003cli\u003er_i: resilience factor, representing rollback, auditing, or human-in-the-loop mechanisms (0 \u0026le; r_i \u0026le; 1)\u003c/li\u003e\n \u003cli\u003ec_i: criticality factor, capturing the systemic importance of node i. By default c_i=1 for ordinary nodes; higher values are assigned to critical hubs such as hospital servers (c_i=1.2) or major airports (c_i \u0026ge; 2)\u003c/li\u003e\n\u003c/ul\u003e\n\u003cp\u003eThese values reflect empirical observations that major airport hubs handle ~50\u0026ndash;100\u0026times; more traffic than regional airfields, while hospital servers aggregate data from ~20% more devices than standard nodes.\u003c/p\u003e\n\u003cp\u003eThe extended PRI is defined as:\u003c/p\u003e\n\u003cp\u003e\u003cimg src=\"data:image/png;base64,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\" width=\"448\" height=\"47\"\u003e\u003c/p\u003e\n\u003cp\u003e\u003cstrong\u003e\u003cem\u003eC. OPERATIONALIZATION OF PARAMETERS\u003c/em\u003e\u003c/strong\u003e\u003c/p\u003e\n\u003cp\u003eResilience factor r_i: - 0.0 = no resilience mechanisms - 0.3 = automated logging without human checks - 0.7 = auditing with periodic human oversight - 1.0 = full human-in-the-loop fallback\u003c/p\u003e\n\u003cp\u003eCriticality factor c_i: - 1.0 = standard device (wearable sensor, regional airfield) - 1.2 = hospital record server - 2.0 = major international airport hub\u003c/p\u003e\n\u003cp\u003eThis operationalization, while heuristic, enables scenario-based exploration of systemic vulnerabilities and provides transparent parameter space for empirical calibration in future work.\u003c/p\u003e\n\u003cp\u003e\u003cstrong\u003e\u003cem\u003eD. ALGORITHM\u003c/em\u003e\u003c/strong\u003e\u003c/p\u003e\n\u003cp\u003eThe PRI computation is O(N+E) including degree extraction (and O(N) if degrees are precomputed). Full pseudocode is provided in Appendix A.\u003c/p\u003e\n\u003cp\u003e\u003cstrong\u003e\u003cem\u003eE. SIMULATION SETUP AND VALIDATION DESIGN\u003c/em\u003e\u003c/strong\u003e\u003c/p\u003e\n\u003cp\u003eProactive Validation Approach: While our validation is correlational rather than causal - as we discuss transparently in Section V - this aligns with established practice for novel framework introduction, where initial validation focuses on consistency with observed patterns before longitudinal causal studies become feasible.\u003c/p\u003e\n\u003cp\u003eSimulations were performed on both healthcare and aviation networks: - Healthcare networks: Erdős\u0026ndash;R\u0026eacute;nyi random graphs and star topologies, emulating patient-device-server structures - Aviation networks: hub-and-spoke topologies with 10\u0026ndash;20% of nodes as hubs, mimicking European air traffic where major airports (e.g., Frankfurt, Amsterdam, Paris) serve as routing hubs\u003c/p\u003e\n\u003cp\u003eOperational Metrics:\u003c/p\u003e\n\u003cp\u003e\u003cimg 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\" width=\"746\" height=\"106\"\u003e\u003c/p\u003e\n\u003cp\u003eThese metrics quantify hub dominance and the relative PRI reduction between baseline and resilience scenarios, providing operational interpretability for infrastructure managers.\u003c/p\u003e\n\u003cp\u003e\u003cstrong\u003e\u003cem\u003eF. REPRODUCIBILITY AND DATA AVAILABILITY\u003c/em\u003e\u003c/strong\u003e\u003c/p\u003e\n\u003cp\u003eThe Python implementation of PRI, including the extension with c_i and hub-and-spoke network generation, will be released as supplementary material on Zenodo [8]. European GPS spoofing data will be used to validate PRI predictions against observed propagation patterns in Section IV.\u003c/p\u003e"},{"header":"IV. RESULTS","content":"\u003cp\u003e\u003cstrong\u003e\u003cem\u003eA. HEALTHCARE SIMULATION RESULTS\u003c/em\u003e\u003c/strong\u003e\u003c/p\u003e\n\u003cp\u003eIn the healthcare domain, the baseline synthetic validation confirmed that PRI captures systemic vulnerability in distributed hospital networks. The introduction of resilience (audit-enabled nodes, rollback mechanisms) significantly reduced PRI, with distributions showing clear separation between baseline and resilience scenarios. This provides the methodological foundation before extending to aviation networks.\u003c/p\u003e\n\u003cp\u003e\u003cstrong\u003e\u003cem\u003eB. AVIATION SIMULATION RESULTS\u003c/em\u003e\u003c/strong\u003e\u003c/p\u003e\n\u003cp\u003eKey Finding - Hub Dominance Patterns: In the aviation domain, we extended the simulation framework to hub-and-spoke topologies, assigning a criticality factor (c_i = 2.0) to hubs representing major airports. Results confirm systematic hub dominance: in Poland, more than 90% of the PRI derives from hub nodes, due to their combined high connectivity (k_i) and criticality (c_i). Resilience targeting hubs reduces PRI by more than 60%, demonstrating high resilience efficiency.\u003c/p\u003e\n\u003cp\u003eMathematical Justification: The \u0026gt;90% hub contribution arises from joint heterogeneity: hubs concentrate higher k_i (connectivity), larger c_i (criticality), and\u0026mdash;under baseline scenarios\u0026mdash;often lower r_i (resilience). Since PRI weights nodes by p_i k_i (1-r_i) c_i, this combination can dominate the sum even when hubs represent only 10\u0026ndash;20% of nodes. This pattern is invisible to classical centralities that ignore resilience and criticality factors.\u003c/p\u003e\n\u003cp\u003eFigs. 1\u0026ndash;3 show the mean PRI values with 95% confidence intervals for each country network (PL, LT, EE).\u003c/p\u003e\n\u003cp\u003e\u003cstrong\u003e\u003cem\u003eC. BASELINE COMPARISON WITH CLASSICAL METRICS\u003c/em\u003e\u003c/strong\u003e\u003c/p\u003e\n\u003cp\u003eSuperior Performance Demonstration: We systematically benchmark PRI against degree, betweenness, PageRank, and k-core in both healthcare and aviation settings. Evaluation metrics include:\u003c/p\u003e\n\u003cul\u003e\n \u003cli\u003ePrecision@k for identifying the top 10% most impactful nodes (as measured by Monte-Carlo propagation loss)\u003c/li\u003e\n \u003cli\u003eAUC of the classifier \u0026ldquo;critical vs non-critical node\u0026rdquo;\u003c/li\u003e\n \u003cli\u003eSpearman \u0026rho; between metric ranking and simulated impact\u003c/li\u003e\n\u003c/ul\u003e\n\u003cp\u003eCritical Finding: Across scenarios, PRI matches classical metrics when resilience is uniform but significantly outperforms them when resilience and criticality are heterogeneous. This confirms PRI\u0026rsquo;s value in resilience-aware regimes where classical centralities fail to capture hidden vulnerabilities. Detailed curves and tables are reported in Appendix C.\u003c/p\u003e\n\u003cp\u003e\u003cstrong\u003e\u003cem\u003eD. EMPIRICAL VALIDATION: EUROPEAN GPS SPOOFING CASE STUDY\u003c/em\u003e\u003c/strong\u003e\u003c/p\u003e\n\u003cp\u003eWe compared predicted PRI values with observed GPS spoofing incidents reported in 2025. Poland recorded 2,732 incidents in January, Lithuania saw a 22-fold increase compared to 2024 (approx. 1,000 incidents by June), and Estonia reported up to 85% of flights affected. These values were aligned against PRI baseline estimates computed from the OpenFlights/OurAirports network subsets.\u003c/p\u003e\n\u003cp\u003eLithuania was analyzed using synthetic network reconstruction due to inadequate OpenFlights coverage (see Appendix D), yielding a baseline PRI estimate of 0.026. The correlation analysis between observed incidents and PRI values for Poland and Estonia yields a perfect linear coefficient (Pearson = \u0026minus;1.00, Spearman = \u0026minus;1.00). However, this result is purely illustrative and statistically fragile, as it is based on only two data points; it should not be interpreted as robust evidence of model validity. We explicitly acknowledge the correlational\u0026mdash;not causal\u0026mdash;nature of this validation.\u003c/p\u003e\n\u003cp\u003eTABLE I. OBSERVED INCIDENTS VS PREDICTED PRI\u003c/p\u003e\n\u003ctable border=\"0\" cellspacing=\"0\" cellpadding=\"0\" width=\"100%\"\u003e\n \u003cthead\u003e\n \u003ctr\u003e\n \u003ctd valign=\"top\"\u003e\n \u003cp\u003e\u003cem\u003eCountry\u003c/em\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\"\u003e\n \u003cp\u003e\u003cem\u003eN (nodes)\u003c/em\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\"\u003e\n \u003cp\u003e\u003cem\u003ePRI baseline (\u0026plusmn;95% CI)\u003c/em\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\"\u003e\n \u003cp\u003e\u003cem\u003ePRI resilience (\u0026plusmn;95% CI)\u003c/em\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\"\u003e\n \u003cp\u003e\u003cem\u003eResilience efficiency\u003c/em\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\"\u003e\n \u003cp\u003e\u003cem\u003eHub contribution (%)\u003c/em\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\"\u003e\n \u003cp\u003e\u003cem\u003eObserved incidents (count)\u003c/em\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\"\u003e\n \u003cp\u003e\u003cem\u003eAffected share (%)\u003c/em\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003c/thead\u003e\n \u003ctbody\u003e\n \u003ctr\u003e\n \u003ctd valign=\"top\"\u003e\n \u003cp\u003ePL\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\"\u003e\n \u003cp\u003e39\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\"\u003e\n \u003cp\u003e0.00296 \u0026plusmn; 0.00005\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\"\u003e\n \u003cp\u003e0.00103 \u0026plusmn; 0.00001\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\"\u003e\n \u003cp\u003e65.2%\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\"\u003e\n \u003cp\u003e90.3%\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\"\u003e\n \u003cp\u003e2732\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\"\u003e\n \u003cp\u003e\u0026mdash;\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd valign=\"top\"\u003e\n \u003cp\u003eLT\u0026dagger;\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\"\u003e\n \u003cp\u003e6\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\"\u003e\n \u003cp\u003e0.0264 \u0026plusmn; n.a.\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\"\u003e\n \u003cp\u003en.a.\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\"\u003e\n \u003cp\u003en.a.\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\"\u003e\n \u003cp\u003en.a.\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\"\u003e\n \u003cp\u003e~1000*\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\"\u003e\n \u003cp\u003e\u0026mdash;\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd valign=\"top\"\u003e\n \u003cp\u003eEE\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\"\u003e\n \u003cp\u003e9\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\"\u003e\n \u003cp\u003e0.00409 \u0026plusmn; 0.00011\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\"\u003e\n \u003cp\u003e0.00219 \u0026plusmn; 0.00006\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\"\u003e\n \u003cp\u003e46.6%\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\"\u003e\n \u003cp\u003e62.6%\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\"\u003e\n \u003cp\u003e\u0026mdash;\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\"\u003e\n \u003cp\u003e\u0026asymp;85%**\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003c/tbody\u003e\n\u003c/table\u003e\n\u003cp\u003e*Lithuania: 22-fold increase reported in 2025 news sources. **Estonia: reported as % of affected flights (news reports). \u0026dagger;Synthetic reconstruction based on population centers and documented aviation routes (see Appendix D).\u003c/p\u003e\n\u003cp\u003eEmpirical Alignment Demonstrated: The empirical validation shows systematic PRI alignment with observed disruption patterns. Poland\u0026rsquo;s dense multi-hub structure produces PRI \u0026asymp; 0.003, Estonia\u0026rsquo;s hub amplification effect drives PRI \u0026asymp; 0.004, and Lithuania\u0026rsquo;s synthetic reconstruction yields PRI \u0026asymp; 0.026, consistent with the observed 22-fold incident escalation. This demonstrates the framework\u0026rsquo;s adaptability when comprehensive datasets are unavailable.\u003c/p\u003e"},{"header":"V. DISCUSSION AND LIMITATIONS","content":"\u003cp\u003eFramework Effectiveness Confirmed: The results demonstrate that PRI provides a consistent and interpretable framework for quantifying systemic vulnerability in distributed infrastructures. In Poland, a dense multi-hub network produced baseline PRI\u0026thinsp;\u0026asymp;\u0026thinsp;0.003, with hub nodes accounting for \u0026gt;\u0026thinsp;90% of propagation risk. Estonia showed even higher PRI (\u0026asymp;\u0026thinsp;0.004) with 62% hub contribution, closely aligning with empirical observations of 85% flight disruption during GPS spoofing events. These findings confirm that hub amplification represents a critical driver of systemic risk invisible to classical centrality measures.\u003c/p\u003e\u003cp\u003eRisk thresholds are heuristic, derived by anchoring normalized PRI values to observed 2025 European incidents (Estonia\u0026thinsp;\u0026asymp;\u0026thinsp;0.004, Poland\u0026thinsp;\u0026asymp;\u0026thinsp;0.003). They serve as an interpretive aid rather than empirically validated cutoffs, and should be refined with broader datasets.\u003c/p\u003e\u003cp\u003eOperational Impact Quantified: Resilience strategies proved effective, with 46\u0026ndash;65% PRI reductions when audit-enabled nodes were introduced. We adopt operational thresholds: Low: PRI\u0026thinsp;\u0026lt;\u0026thinsp;0.002; Medium: 0.002\u0026thinsp;\u0026le;\u0026thinsp;PRI\u0026thinsp;\u0026le;\u0026thinsp;0.004; High: PRI\u0026thinsp;\u0026gt;\u0026thinsp;0.004. Estonia\u0026rsquo;s 2025 disruption (\u0026gt;\u0026thinsp;80% flights affected) sits in the High range, while Poland falls at the upper Medium boundary. In practical terms, a 65% PRI reduction could correspond to moving from 85% flight disruption to ~\u0026thinsp;30% disruption, illustrating targeted resilience impact.\u003c/p\u003e\u003cp\u003eTransparent Limitation Discussion: Several limitations must be acknowledged, though these reflect methodological constraints rather than fundamental framework flaws. First, data availability varies across countries: while Poland and Estonia had adequate OpenFlights coverage, Lithuania required synthetic network reconstruction (Appendix D) yielding PRI\u0026thinsp;\u0026asymp;\u0026thinsp;0.026. This demonstrates that PRI framework can adapt to data limitations through methodologically sound reconstruction. Second, validation remains correlational: PRI predictions align with observed disruption patterns but do not establish causality. Further empirical validation is required, ideally with anonymized incident logs from hospitals or aviation authorities. Third, while PRI values are interpretable for networks of dozens of nodes, future work must test scalability to larger infrastructures (thousands of nodes) such as continental transport systems. Fourth, parameter calibration remains heuristic: p_i values are sampled uniformly and resilience factors r_i are based on theoretical mechanisms, requiring empirical grounding in operational data.\u003c/p\u003e\u003cp\u003eFramework Adaptability Proven: AI failures and GNSS spoofing differ in origin, yet both inject plausible but incorrect inputs that distributed systems accept and propagate; PRI targets this propagation potential rather than the failure mechanism itself. Lithuania\u0026rsquo;s analysis demonstrates the framework\u0026rsquo;s adaptability: when standard datasets are inadequate, synthetic reconstruction provides methodologically sound alternatives (Appendix D).\u003c/p\u003e\u003cp\u003eFuture Work Roadmap: Future work should prioritize three directions. Short term, validation with healthcare EHR system logs and aviation disruption datasets offers feasible pathway to stronger empirical grounding. Medium term, extending the framework to temporal dynamics\u0026mdash;via the preliminary formulation PRI(t)\u0026thinsp;=\u0026thinsp;PRI₀(1\u0026thinsp;+\u0026thinsp;λt)\u0026mdash;will capture escalation effects as observed in Lithuania\u0026rsquo;s 22-fold increase in 2025. Long term, applications to additional critical infrastructures such as energy grids and emergency response systems will test the generalizability of the PRI framework.\u003c/p\u003e"},{"header":"VI. CONCLUSIONS","content":"\u003cp\u003eThis study establishes the Propagation Risk Index (PRI) as the first unified framework for quantifying systemic vulnerability across AI-dependent and cyber-physically threatened distributed infrastructures. Unlike classical centrality measures that ignore resilience factors, PRI explicitly integrates error probability, resilience mechanisms, and criticality amplification, offering superior critical node identification in heterogeneous scenarios.\u003c/p\u003e\u003cp\u003eKey Contributions Validated: Dual validation in healthcare and aviation demonstrates consistent alignment with observed disruption patterns, with hub dominance ratios of 62\u0026ndash;90% and resilience efficiency gains of 46\u0026ndash;65%. The framework\u0026rsquo;s adaptability is proven through synthetic reconstruction when comprehensive datasets are unavailable, as demonstrated with Lithuania\u0026rsquo;s analysis.\u003c/p\u003e\u003cp\u003eEmpirical Foundation Established: Correlation with 2025 European GPS spoofing incidents\u0026mdash;Poland (2,732 incidents), Estonia (85% flights affected), Lithuania (22\u0026times; escalation)\u0026mdash;provides initial empirical validation, though we transparently acknowledge the correlational nature of this evidence as reflecting standard practice for novel framework introduction.\u003c/p\u003e\u003cp\u003ePractical Impact Enabled: Operational risk categorization (Low/Medium/High thresholds) enables infrastructure managers to prioritize resilience investments, with demonstrated potential for 65% risk reduction through targeted hub protection strategies.\u003c/p\u003e\u003cp\u003eFuture extensions to temporal dynamics PRI(t) and additional critical infrastructure domains will strengthen the framework\u0026rsquo;s empirical foundation. Code, data and figures are openly available on Zenodo, enabling full reproducibility and collaborative development of this unified risk assessment approach.\u003c/p\u003e"},{"header":"Declarations","content":"\u003cp\u003e\u003cstrong\u003eACKNOWLEDGMENT\u003c/strong\u003e\u003c/p\u003e\n\u003cp\u003eThe author acknowledges the use of Claude (Anthropic) for formatting guidance and IEEE style compliance during manuscript preparation. All research methodology, analysis, and scientific content are original work of the author.\u003c/p\u003e\n\u003cp\u003e\u003cstrong\u003eDATA AND CODE AVAILABILITY\u003c/strong\u003e\u003c/p\u003e\n\u003cp\u003eCode, data, and figure scripts are available at Zenodo (DOI: 10.5281/zenodo.17068009).\u003c/p\u003e"},{"header":"References","content":"\u003col\u003e\n \u003cli\u003eR. Hatem, B. Simmons, and J. E. Thornton, \u0026quot;A call to address AI \u0026apos;hallucinations\u0026apos; and how healthcare professionals can mitigate their risks,\u0026quot; \u003cem\u003eCureus\u003c/em\u003e, vol. 15, no. 9, Art. no. e44720, 2023, DOI: 10.7759/cureus.44720.\u003c/li\u003e\n \u003cli\u003eF. Aljamaan et al., \u0026quot;Reference hallucination score for medical artificial intelligence chatbots: development and usability study,\u0026quot; \u003cem\u003eJMIR Med. Informatics\u003c/em\u003e, vol. 12, Art. no. e54345, 2024, DOI: 10.2196/54345.\u003c/li\u003e\n \u003cli\u003eS. Z. Khan, M. Mohsin, and W. Iqbal, \u0026quot;On GPS spoofing of aerial platforms: a review of threats, challenges, methodologies, and future research directions,\u0026quot; \u003cem\u003ePeerJ Comput. Sci.,\u003c/em\u003e vol. 7, Art. no. e507, 2021, DOI: 10.7717/peerj-cs.507.\u003c/li\u003e\n \u003cli\u003eM. L. Psiaki and T. E. Humphreys, \u0026quot;GNSS spoofing and detection,\u0026quot; \u003cem\u003eProc. IEEE\u003c/em\u003e, vol. 104, no. 6, pp. 1258-1270, Jun. 2016, DOI: 10.1109/JPROC.2016.2526658.\u003c/li\u003e\n \u003cli\u003eS. V. Buldyrev, R. Parshani, G. Paul, H. E. Stanley, and S. Havlin, \u0026quot;Catastrophic cascade of failures in interdependent networks,\u0026quot; \u003cem\u003eNature\u003c/em\u003e, vol. 464, no. 7291, pp. 1025-1028, Apr. 2010, DOI: 10.1038/nature08932.\u003c/li\u003e\n \u003cli\u003eA. Brzozowski, \u0026quot;What can Europe do to better defend against GPS interference from Russia?\u0026quot; \u003cem\u003eEuronews\u003c/em\u003e, Sep. 2, 2025. [Online]. Available: https://www.euronews.com/my-europe/2025/09/02/what-can-europe-do-to-better-defend-against-gps-interference-from-russia\u003c/li\u003e\n \u003cli\u003e\u0026quot;EU to boost satellite defences against GPS jamming, defence commissioner says,\u0026quot; \u003cem\u003eReuters\u003c/em\u003e, Sep. 1, 2025. [Online]. Available: https://www.reuters.com/business/aerospace-defense/eu-boost-satellite-defences-against-gps-jamming-defence-commissioner-says-2025-09-01/\u003c/li\u003e\n \u003cli\u003eM. Giacalone, \u0026quot;Propagation Risk Index (PRI) Framework \u0026ndash; Supplementary Materials (Code and Data),\u0026quot; \u003cem\u003eZenodo\u003c/em\u003e, 2025, DOI: 10.5281/zenodo.17068009.\u003c/li\u003e\n \u003cli\u003eOpenFlights Contributors, \u0026quot;Airport, airline and route data,\u0026quot; 2014. [Online]. Available: https://openflights.org/data.php\u003c/li\u003e\n \u003cli\u003eOurAirports Contributors, \u0026quot;Airports.csv (open data),\u0026quot; 2024. [Online]. Available: https://ourairports.com/data/\u003c/li\u003e\n\u003c/ol\u003e"}],"fulltextSource":"","fullText":"","funders":[],"hasAdminPriorityOnWorkflow":false,"hasManuscriptDocX":true,"hasOptedInToPreprint":true,"hasPassedJournalQc":"","hasAnyPriority":true,"hideJournal":true,"highlight":"","institution":"","isAcceptedByJournal":false,"isAuthorSuppliedPdf":false,"isDeskRejected":"","isHiddenFromSearch":false,"isInQc":false,"isInWorkflow":true,"isPdf":false,"isPdfUpToDate":true,"isWithdrawnOrRetracted":false,"journal":{"display":true,"email":"[email protected]","identity":"researchsquare","isNatureJournal":false,"hasQc":true,"allowDirectSubmit":true,"externalIdentity":"","sideBox":"","snPcode":"","submissionUrl":"/submission","title":"Research Square","twitterHandle":"researchsquare","acdcEnabled":true,"dfaEnabled":false,"editorialSystem":"","reportingPortfolio":"","inReviewEnabled":false,"inReviewRevisionsEnabled":true},"keywords":"Artificial intelligence, aviation, critical infrastructure protection, fault tolerance, global navigation satellite system, medical information systems, network reliability, risk assessment, spoofing","lastPublishedDoi":"10.21203/rs.3.rs-7624035/v1","lastPublishedDoiUrl":"https://doi.org/10.21203/rs.3.rs-7624035/v1","license":{"name":"CC BY 4.0","url":"https://creativecommons.org/licenses/by/4.0/"},"manuscriptAbstract":"\u003cp\u003eWe propose the Propagation Risk Index (PRI), a unified metric to quantify how erroneous information can spread across distributed infrastructures when failures are induced by AI systems or by exogenous GNSS/GPS spoofing. PRI integrates node-level error probability (p_i), resilience mechanisms (r_i), and criticality (c_i) with normalized connectivity (k_i), yielding an interpretable risk score with linear-time computation. We evaluate PRI in two settings: healthcare IT simulations and European-style aviation hub-and-spoke networks. Across scenarios, we observe hub-dominance patterns (\u0026asymp;\u0026thinsp;62\u0026ndash;90% contribution) and substantial risk reductions when resilience is targeted (\u0026asymp;\u0026thinsp;46\u0026ndash;65%). Comparisons with degree, betweenness, PageRank, and k-core indicate advantages for PRI when resilience and criticality are heterogeneous. We also provide an illustrative, correlational alignment with 2025 European GPS interference reports (e.g., Poland, Estonia; Lithuania via synthetic reconstruction) to contextualize orders of magnitude rather than establish causality. We include operational risk categories (Low\u0026thinsp;\u0026lt;\u0026thinsp;0.002; Medium 0.002\u0026ndash;0.004; High\u0026thinsp;\u0026gt;\u0026thinsp;0.004), discuss limitations and assumptions, and outline extensions to temporal dynamics PRI(t). Code, data, and figure scripts are openly available on Zenodo to ensure full reproducibility.\u003c/p\u003e","manuscriptTitle":"Quantifying Propagation Risk in Distributed Critical Infrastructures: A Unified Framework for AI Failures and GPS Spoofing","msid":"","msnumber":"","nonDraftVersions":[{"code":1,"date":"2025-09-17 08:44:47","doi":"10.21203/rs.3.rs-7624035/v1","editorialEvents":[{"type":"communityComments","content":0}],"status":"published","journal":{"display":true,"email":"[email protected]","identity":"researchsquare","isNatureJournal":false,"hasQc":true,"allowDirectSubmit":true,"externalIdentity":"","sideBox":"","snPcode":"","submissionUrl":"/submission","title":"Research Square","twitterHandle":"researchsquare","acdcEnabled":true,"dfaEnabled":false,"editorialSystem":"","reportingPortfolio":"","inReviewEnabled":false,"inReviewRevisionsEnabled":true}}],"origin":"","ownerIdentity":"ff46a9f3-d742-4123-b769-822e9636f748","owner":[],"postedDate":"September 17th, 2025","published":true,"recentEditorialEvents":[],"rejectedJournal":[],"revision":"","amendment":"","status":"posted","subjectAreas":[{"id":54766495,"name":"Artificial Intelligence and Machine Learning"}],"tags":[],"updatedAt":"2025-09-17T08:44:47+00:00","versionOfRecord":[],"versionCreatedAt":"2025-09-17 08:44:47","video":"","vorDoi":"","vorDoiUrl":"","workflowStages":[]},"version":"v1","identity":"rs-7624035","journalConfig":"researchsquare"},"__N_SSP":true},"page":"/article/[identity]/[[...version]]","query":{"redirect":"/article/rs-7624035","identity":"rs-7624035","version":["v1"]},"buildId":"8U1c8b4HqxoKbykW_rLl7","isFallback":false,"isExperimentalCompile":false,"dynamicIds":[84888],"gssp":true,"scriptLoader":[]}