Random singlet physics in the exchange-disordered two-dimensional triangular material YbCu <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"> <mml:msub> <mml:mi/> <mml:mn>1.14</mml:mn>

Quantum spin liquid (QSL) phases exist in theory, but real candidate QSL materials are often extraordinarily sensitive to structural defects which disrupt the ground state. Here, we investigate candidate triangular QSL material YbCu$_{1.14}$Se$_2$ and discover the absence of magnetic order, but also no compelling evidence of a QSL ground state due to significant structural disorder. We instead look at the results through a lens of a 2-dimensional (2D) random singlet phase. We are able to match thermodynamic measurements using a phenomenological model of a distribution of singlet formation. YbCu$_{1.14}$Se$_2$ behaves strikingly similar to other disordered triangular lattice materials, suggesting universal behavior of random singlet formation in 2D frustrated systems.