An IRT-shaped practice score is not a real IQ test

IntelligenceMax updates a learner's ability estimate after each answer and displays it on the familiar IQ scale, using math that resembles item response theory: a sigmoid-based probability model, a posterior precision updated via Fisher information, and a capped per-answer delta. The arithmetic is internally consistent, but it rests on a weak foundation — the difficulty and discrimination parameters for each item are assigned by the same AI that generates the question, not fitted from an empirical norming sample.

This distinction matters for engineers. Calling the update 'IRT-style' only describes the logistic form of the equation; it does not establish that an item labeled difficulty 115 behaves like a 115 on a validated instrument. A separate confidence-calibration score the product reports — a Brier-style measure of stated confidence versus correctness — also does not validate item difficulty or the ability estimate itself.

Within those limits, the estimate can usefully drive an adaptive practice loop: reacting consistently to surprising answers and selecting questions near the current estimate. But it cannot support claims of a clinical Full Scale IQ, a lasting change in general intelligence, or transfer to school or work performance. The commercial brain-training literature shows gains concentrated in trained tasks and close relatives, with broad transfer claims holding up poorly against active control groups. Genuine empirical calibration would require binning responses by predicted probability, reporting sample counts and Brier score or log loss, and using stable, reusable items for item-level residual analysis — a nontrivial challenge when most items are generated one-off.