



This paper proposes a novel localization framework underpinned by a pinching-antenna (PA) system, in which the target location is estimated using received signal strength (RSS) measurements obtained from downlink signals transmitted by the PAs. To develop a comprehensive analytical framework, we employ stochastic geometry to model the spatial distribution of the PAs, enabling tractable and insightful network-level performance analysis. Closed-form expressions for target localizability and the Cramer-Rao lower bound (CRLB) distribution are analytically derived, enabling the evaluation of the fundamental limits of PA-assisted localization systems without extensive simulations. Furthermore, the proposed framework provides practical guidance for selecting the optimal waveguide number to maximize localization performance. Numerical results also highlight the superiority of the PA-assisted approach over conventional fixed-antenna systems in terms of the CRLB.