
This note presents a formal and self-contained resolution of Zeno’s Achilles paradox within the framework of Return Theory (RT). The paradox is shown to arise purely from a nonlinear projection between shell-time and observer-time, rather than from any physical or logical inconsistency in motion or spacetime. Using the RT time-projection law, the note demonstrates that any Zeno-type infinite subdivision of motion in observer-time corresponds to a Riemann partition of a finite shell-time interval. The resulting infinite series of observer-time increments is proven to converge to a finite value, ensuring that Achilles reaches the target in finite observer-time and finite physical time. No modification of spacetime structure, continuity, or dynamical laws is required. The resolution is purely geometric and relies only on standard assumptions of smoothness and boundedness within the RT framework. This document is intended as a formal reference note within the RT Bookstore collection and complements the main Return Theory framework archived on Zenodo (DOI: 10.5281/zenodo.17857410).
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