Advances in cosmic microwave background (CMB) science depend on increasing the number of sensitive detectors observing the sky. New instruments deploy large arrays of superconducting transition-edge sensor (TES) bolometers tiled densely into ever larger focal planes. High multiplexing factors reduce the thermal loading on the cryogenic receivers and simplify their design. We present the design of focal-plane modules with an order of magnitude higher multiplexing factor than has previously been achieved with TES bolometers. We focus on the novel cold readout component, which employs microwave SQUID multiplexing ($mu$mux). Simons Observatory will use 49 modules containing 60,000 bolometers to make exquisitely sensitive measurements of the CMB. We validate the focal-plane module design, presenting measurements of the readout component with and without a prototype detector array of 1728 polarization-sensitive bolometers coupled to feedhorns. The readout component achieves a $95%$ yield and a 910 multiplexing factor. The median white noise of each readout channel is 65 $mathrm{pA/sqrt{Hz}}$. This impacts the projected SO mapping speed by $< 8%$, which is less than is assumed in the sensitivity projections. The results validate the full functionality of the module. We discuss the measured performance in the context of SO science requirements, which are exceeded.
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