Act 0 — The computational arena

A formula becomes an algorithm only after its state, arithmetic, and traffic are declared. This act builds that contract from the machine upward: first the bytes that must move, then the state a stream must retain, then the grid on which arithmetic lands, and finally the mode-by-mode dynamics of a solvable quadratic control. The result can distinguish a bandwidth ceiling from a floating-point failure and a flat direction from a sharp one. It still cannot say what high dimension makes typical. Act I turns from one declared execution to the geometry of many possible directions.