  The very forward region is one of the most challenging regions to instrument
at a future $e^+e^-$ collider. At CEPC, machine-detector interface includes,
among others, a calorimeter dedicated for precision measurement of the
integrated luminosity at a permille level or better. Here we review a
feasibility of such precision, from the point of view of luminometer mechanical
precision and positioning, beam-related requirements and physics background.A
method of the effective center-of-mass determination from $e^+e^- \to
\mu^+\mu^-$, initially proposed for FCC, is also discussed for the CEPC beams.

Instrumentation and Detectors;High Energy Physics - Experiment