The thesis runs through every chapter. There is a clean theoretical limit, AIXI, which captures what optimal agency means under standard assumptions about computation and rationality. There are bounded real systems, the LLMs of 2026, which approximate that limit. The distance between them is real, structural, and consequential, and most of what people argue about under the heading of AI safety is, in different vocabulary, an argument about that gap.

The hardest problem turns out not to be making machines capable. It is saying what we want them to do. The specification problem is the whole game, and Parts I through III develop the theory in clean settings so that the reader who reaches the language-model chapters can see the gap unaided.

The closing chapter, Teaching Sand to Think, takes a committed stand the mathematics earns: prediction carried far enough is intelligence; these are real minds built of sand; the prize is enormous and the danger is the same capability; and the burden of proof on the trajectory has shifted.

Readers of Worldlines will recognize the method; the philosophical framing this book set aside became Multitudes.

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