Abstract
<p>Arguments that students should build foundational knowledge before delegating cognitive work to AI tools are typically made from pedagogical theory. This paper argues the same conclusion from a different warrant: the ordering of cognitive layers is a structural constraint on learning systems rather than a preference about instruction, and the clearest evidence comes from how machine learning systems are built. Large models are trained in a fixed sequence, representation before alignment before reasoning before tool use, and no laboratory deviates from it despite training runs costing hundreds of millions of dollars. The same organizations producing those systems market them to students as a substitute for the lower layers.The paper develops the formal basis for that constraint using the statistical mechanics from which neural networks were originally constructed. Learning is treated as descent on an energy landscape at a temperature set externally, a description that is literal for machines and structural for people. Three results follow. The Fundamental Theorem of Calculus gives a precise statement of why a delivered answer and an accumulated answer are different states rather than the same state reached faster. The safe learning rate depends on local curvature, which constrains what standardized pacing can achieve. And the framework yields a test for which tools cause harm: locate the cognitive layer a tool automates. Calculators automate execution above a built concept, and meta-analyses across 133 studies find no harm except at the grade where the underlying operation is still forming. Search relocates storage while leaving reasoning intact. Systems producing finished reasoning automate encoding, conceptual structuring, and self-checking, and two independent randomized trials find measurable harm from unrestricted access, with no harm when the same model is constrained to withhold answers.The test is predictive rather than retrospective and applies to tools that do not yet exist.</p>