4D Systemic Stability Analysis of Canadian Metropolitan Systems: Algorithmic Assessment of Structural Resilience

This publication presents a full analytical demonstration of the 4D Systemic Stability Algorithm (4D SSA) applied to large-scale territorial and infrastructure systems within Canada. The study focuses on three major metropolitan environments and evaluates their systemic stability through a unified algorithmic framework designed to identify structural vulnerabilities, cascade propagation paths, and long-term resilience limits. The analysis is conducted in laboratory observation mode, meaning that the algorithm performs structural diagnostics without proposing policy recommendations or normative interventions. The objective of the study is to demonstrate the operational capability of the algorithm to process complex socio-technical systems composed of multiple interdependent subsystems, including infrastructure networks, economic activity, institutional governance, transportation systems, and human capital structures. The 4D SSA framework evaluates systems along three fundamental analytical axes: • Structure – topological configuration, connectivity, and capacity of system components• Transition – propagation dynamics, cascade behavior, and regime shifts• Time – historical trajectories, acceleration patterns, and structural wear These dimensions are integrated through algorithmic evaluation of system cohesion, propagation potential, and resonance thresholds. The method uses graph-theoretic representations of infrastructure and institutional interdependencies and applies spectral diagnostics to detect hidden structural fragilities that may remain invisible in traditional economic or policy analysis. The study utilizes an Adaptive Data Minimum (ADM) approach, relying primarily on official public data sources including government budgets, infrastructure reports, national statistical datasets, and institutional disclosures. This approach demonstrates that meaningful systemic diagnostics can be generated even under conditions of incomplete information. The primary objective of the publication is methodological:to demonstrate the ability of the 4D SSA algorithm to perform reproducible systemic diagnostics on large-scale territorial systems. This work therefore functions as a demonstration case of algorithmic systemic analysis, illustrating how complex infrastructure-economic systems can be evaluated through a unified structural stability framework.