The proliferation of generative AI tools has rendered traditional modular assessments in computing and data-centric education increasingly ineffective, creating a disconnect between academic evaluation and authentic skill measurement. This paper presents a theoretically grounded framework for designing AI-resilient assessments, supported by formal analysis and empirical validation. We make three primary contributions. First, we establish two formal propositions. (1) Assessments composed of interconnected problems, in which outputs serve as inputs to subsequent tasks, are inherently more AI-resilient than modular assessments due to their reliance on multi-step reasoning and sustained context. (2) Semi-structured problems with deterministic success criteria provide more reliable measures of student competency than fully open-ended projects, which allow AI systems to default to familiar solution templates. These results challenge widely cited recommendations in recent institutional and policy guidance that promote open-ended assessments as inherently more robust to AI assistance. Second, we validate these propositions through empirical analysis of three university data science courses (N = 117). We observe a substantial AI inflation effect: students achieve near-perfect scores on AI-assisted modular homework, while performance drops by approximately 30 percentage points on proctored exams (Cohen d = 1.51). In contrast, interconnected projects remain strongly aligned with modular assessments (r = 0.954, p < 0.001) while maintaining AI resistance, whereas proctored exams show weaker alignment (r = 0.726, p < 0.001). Third, we translate these findings into a practical assessment design procedure that enables educators to construct evaluations that promote deeper engagement, reflect industry practice, and resist trivial AI delegation.