Standardized examinations are typically treated as uniform syllabus coverage problems. We argue they are better understood as adversarial systems with stable latent cognitive structures diverging systematically from official syllabi. We introduce LearnOpt, which recovers this structure from historical question papers and generates personalized, time-bounded study plans. Applied to nine years of NEET questions (2016-2024, n=1,496), LearnOpt builds an exam knowledge graph from LLM-tagged questions, extracts a five-category latent skill distribution, and formulates study planning as a knapsack-variant optimization over prerequisite-aware subgraphs with Bayesian Knowledge Tracing. Central finding: NEET's latent skill distribution is stable within a syllabus regime (consecutive-year KL divergence 0.004-0.032 for 2016-2021, non-significant under permutation testing) but shifts significantly with NCERT's 2023 syllabus rationalization: pooling 2016-2021 (n=1,072) vs 2023-2024 (n=392) gives KL=0.040 (p=0.0005), with Elimination/Negation questions rising from ~20-29% to ~31-35%. Latent structure, while not permanently stationary, is piecewise stable, with shifts detectable and attributable to curricular events. Within either regime, subject predicts skill profile more strongly than year. An optimization evaluation, using one real and two synthetic mastery profiles, shows the skill-weighted objective produces a modest but real reordering of recommended topics over a mastery-conditioned frequency baseline. Applying the pipeline to JEE Advanced reveals a profile dominated by Multi-concept Integration (80.9% vs. 33.3% for NEET), with a JEE-vs-NEET divergence (KL=0.505) exceeding NEET's largest cross-subject divergence: exam tier shapes latent cognitive structure more than subject, which shapes it more than time within a regime. Code, knowledge graph, and annotated dataset are released publicly.

翻译：标准化考试通常被视为统一的考纲覆盖问题。我们认为，更合理的理解是将其视为具有稳定潜在认知结构且系统性地偏离官方考纲的对抗系统。我们提出LearnOpt，该方法从历史试题中恢复该结构，并生成个性化、时间受限的学习计划。应用于九年NEET试题（2016-2024，n=1,496），LearnOpt构建了基于大语言模型标注试题的考试知识图谱，提取五类潜在技能分布，并将学习计划制定为基于贝叶斯知识追踪的先决条件感知子图上的背包变体优化问题。核心发现：在考纲体制内，NEET的潜在技能分布保持稳定（2016-2021年相邻年份KL散度为0.004-0.032，置换检验下不显著），但在NCERT 2023年考纲标准化后发生显著变化：汇集2016-2021年（n=1,072）与2023-2024年（n=392）数据得出KL=0.040（p=0.0005），其中消除/否定类题型占比从约20-29%升至约31-35%。潜在结构虽非永久平稳，但呈分段稳定状态，其变化可检测且可归因于课程改革事件。在任一体制内，科目对技能特征的预测能力强于年份。基于一个真实与两个合成精通度分布模型的优化评估表明，与精通度条件频率基线相比，技能加权目标函数对推荐主题产生了适度但真实的重新排序。将分析流程应用于JEE Advanced，发现其分布以多概念整合为主（80.9% vs. NEET的33.3%），且JEE与NEET的差异（KL=0.505）超过NEET内部最大跨科目差异：考试层级对潜在认知结构的影响大于科目，而科目在体制内的影响大于时间因素。代码、知识图谱及带标注的数据集均已公开。