Transverse geometry reshapes current and tracer fluctuation amplitudes in quasi-one-dimensional single files.

Single-file transport means no overtaking: particles move in a narrow channel while preserving their longitudinal order. This simple constraint has profound dynamical consequences, most notably tracer subdiffusion, and has made single-file transport a paradigmatic form of confined many-body motion, observed from molecular transport in zeolites to single-file diffusion of colloids in narrow channels. The standard view is that, once overtaking is suppressed, collective transport reduces to that of a strictly one-dimensional file. Here we show that this reduction fails in experimentally relevant finite-width channels: even when exchange is forbidden, the transverse equilibrium structure controls the transport laws and can qualitatively reshape them. Starting from the Brownian dynamics in the full confined geometry, we derive an exact large-scale one-dimensional fluctuating hydrodynamics for the longitudinal density, whose coefficients are fixed by the confined equilibrium equation of state. In the minimal hard-core setting, this yields a collective diffusivity that can become non-monotonic in density. This geometric anomaly propagates to exact large-scale predictions for integrated-current fluctuations, tracer displacement fluctuations and the associated density profiles. The effect is robust to the interaction potential, channel geometry, initial preparation and microscopic dynamics. Quasi one-dimensional single-file transport therefore defines a distinct regime in which forbidding overtaking does not erase geometry from collective transport.