The Atom Learning Model (ALM) tokenises a school curriculum. 757 pages of GCSE and Further Mathematics material were read by machine into 1,934 atoms, each one thing a learner can do in a single step, ordered by 4,616 machine-written prerequisite links. Both sides of a lesson are then expressed in that one structure: a question is a set of atoms plus everything beneath them, a child's ability is a score between 0 and 1 on every atom of the same graph, and whether a question suits a child is arithmetic over one index, with no difficulty parameter fitted for either side. Nobody wrote an atom, a link or a question. Reading the 757 pages cost £55, building the whole structure cost between £615 and £1,230, and against it the system composed 6,648 questions for 373 children in two English secondary schools over seven weeks, at 26p per composed question. Four measurements went against expectation. The cost is in the links, not the pages. The composer's own difficulty label has a rank correlation of -0.0123 with measured facility, so a language model shown a question cannot say how hard it is. Children stop working when a mark takes seven seconds instead of three. And the deployment never served a question deeper than two prerequisite steps, which is exactly where the central premise becomes testable, leaving it unfalsified rather than confirmed.
API buyers purchase a dated contract, not a model name alone: the contract includes the requested and served model, reasoning-effort term or its omission, output rail, service product, prompt, and price schedule. We study the reasoning-effort term through a registered paired contrast of Sonnet 5 with explicit high effort against the same model with effort omitted, using 30 AIME 2026 items and five calls per item. Every paid attempt was assigned one frozen terminal category, and inference resampled items while retaining their repeated calls. Mean delivered cost was \$0.01031 per call higher under the explicit-high contract than under the omitted contract [+\$0.00204, +\$0.01974]. The corresponding accuracy contrast was +0.0133 [-0.0267, +0.0467]; we did not detect an accuracy difference, and the interval permits a gain of up to 4.67 percentage points that this design cannot rule out. Cost per correct answer was \$0.08665 under the high-effort contract and \$0.07662 under the omitted contract, as registered point estimates. A dated contract census, Models-API metadata, and preregistered raw-response probes further documented model-specific omission semantics, including within a provider; claims remained at documentation grade when raw structure was indeterminate. The request registry, parser, terminal taxonomy, statistical plan, and analysis pipeline were frozen before outcomes were examined; the resulting claims are bounded to the model, task, and collection date studied.