Signatures of a spin-1/2 cooperative paramagnet in the diluted triangular lattice of Y$_2$CuTiO$_6$

We present a combination of thermodynamic and dynamic experimental signatures of a disorder driven dynamic cooperative paramagnet in a 50% site diluted triangular lattice spin-1/2 system, Y$_2$CuTiO$_6$. Magnetic ordering and spin freezing are absent down to 50 mK, far below the Curie Weiss scale of ~-134 K. We observe scaling collapses of the magnetic field- and temperature-dependent magnetic heat capacity and magnetisation data, respectively, in conformity with expectations from the random singlet physics. Our experiments establish the suppression of any freezing scale, if at all present, by more than three orders of magnitude, opening a plethora of interesting possibilities such as disorder-stabilized long range quantum entangled ground states.