  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.
