Prerequisite-Aware AI Delegation in Mathematics Education: A Graph-Theoretic Framework for Competency-Sensitive Automation

Generative AI increasingly allows learners to obtain mathematical output without performing all of the cognitive work through which competence is formed. This preprint proposes a theoretical framework for competency-level, process-replacing AI delegation in mathematics education. Mathematical competencies are represented by a prerequisite network. Learner mastery and AI-delegation intensity are modeled separately, while a strictly downstream prerequisite centrality measures how strongly later competencies depend on a given skill. A mastery gate provides local protection against premature delegation independently of graph position. The resulting framework distinguishes three factors: what the learner has already mastered, how much cognitive work is delegated to AI, and how structurally important the competency is for subsequent learning. A continuous optimization model is introduced as an analytical relaxation, together with a discrete classroom interpretation. Monte Carlo stress tests compare graph-aware and simpler delegation policies at equal immediate productivity under several structural data-generating mechanisms. The graph-aware policy is deliberately shown to perform worse when downstream prerequisite structure is irrelevant, and to become advantageous only when downstream propagation is sufficiently important. A 25-competency case study in measure theory, probability, martingales, and mathematical finance illustrates the framework. The paper concludes with a preregistrable empirical hypothesis: the effect of a process-replacing AI-access regime on later autonomous mathematical performance should become less favorable when baseline unmasteredness and downstream prerequisite centrality are jointly high. This is a theoretical and simulation-based preprint. No human-subject experimental results are reported.