Constraints on Lepton Number Violation with the 2 tonne$\cdot$yr CUORE Dataset

Matter-antimatter asymmetry underlines the incompleteness of the current understanding of particle physics. Neutrinoless double-beta decay ($0\nu \beta \beta$) may help explain this asymmetry, while unveiling the Majorana nature of the neutrino. The CUORE experiment searches for $0\nu \beta \beta$ of ${}^{130}$Te using a tonne-scale cryogenic calorimeter operated at milli-kelvin temperatures. We report no evidence of $0\nu \beta \beta$ and place a lower limit on the half-life of $T_{1\mathrm{/}2}>3.5\times$ 10${}^{25}$~years (90% C.I.) with over 2~tonne$\cdot$year TeO${}_2$ exposure. The tools and techniques developed for this result and the 5 year stable operation of nearly 1000 detectors demonstrate crucial infrastructure for a future-generation experiment capable of searching for $0\nu \beta \beta$ across multiple isotopes.