This paper presents a comprehensive mathematical framework for enhancing machine learning robustness against adversarial attacks through novel theoretical constructs. We introduce Archive Function Robustness theory, which provides formal bounds on the impact of data corruption in learning systems, and develop an extended Dataset Core methodology for efficient processing of large-scale datasets while preserving information integrity. Our theoretical contributions include: (1) a rigorous characterization of archive function stability under adversarial perturbations with provable Lipschitz-based bounds, (2) stratified and adaptive Dataset Core algorithms that maintain \(\varepsilon \) -approximation guarantees for big data scenarios, and (3) consistency-based verification techniques for poison detection in streaming environments. The framework demonstrates that well-behaved archive functions exhibit bounded degradation under data corruption, with explicit relationships between poisoning rates, data distortion, and system performance. Our approach enables scalable robust learning with theoretical guarantees, providing a foundation for trustworthy AI deployment in adversarial settings.