Complete passes need eight states: Three binary distinctions, coverage, and closure

Three independent binary distinctions have eight joint states. A complete inspection therefore needs at least eight entries, and a closed route changing one bit per tick attains the bound. Every shortest route flips the coordinates four, two and two times. For a deterministic law depending only on the current three-bit state, complete coverage together with return forces an eight-cycle directly. Reversible one-bit laws without coverage can instead have orders two, four or six; an explicit six-cycle uses all three coordinates while missing two states. The distinction is between the available state set and the states reached by an orbit. Fixed-interval readouts of an eight-cycle see exactly eight divided by the greatest common divisor of eight and the interval. Applying these results to recognition uses the stated spatial and binary-state identifications; a physical duration also needs the duration of a tick.