Zeno's dichotomy: one step-sequence, three outcomes

Zeno's dichotomy is not a paradox about motion but a demonstration that a single step-sequence yields different outcomes depending on the intention declared at the outset. One process, halving the remaining distance to a target at each step, produces three true descriptions: arrival, if the intention is to stop after a set number of steps; endless approach, if the intention is to keep halving; and invariant self-similar structure, if the intention is to attend only to the rule. The outcome is not a property of the stepping alone but of the stepping together with the declared intention. There is no infinite task, only an infinite recursion that can be exited by a decision. The recursion remains valid; one simply stops participating in it. This is the same structure as the liar paradox: both are genuine open steps, maintained by decision and closed by decision.