First results from the CUORE \boldmath$0\nu\beta\beta$ decay experiment

CUORE---the Cryogenic Underground Observatory for Rare Events---is an experiment searching for the $0\nu\beta\beta$ decay of $^{130}$Te, located at the Laboratori Nazionali del Gran Sasso in Italy. The detector comprises 988 $5 \times 5 \times 5$ cm$^3$ TeO$_2$ crystals operated as bolometers at $\sim$10 mK in the world's largest and most powerful dilution refrigerator. CUORE began physics data collection in spring 2017, and has recently published a lower limit of $T_{1/2}^{0\nu} (^{130}Te) > 1.3 \times 10^{25}$ y (90\% C.L.) on the decay half-life---the most sensitive to date for this isotope. We present the analysis leading to this result, including a discussion of spectral line shape modeling and fitting.