  We demonstrate that the feedback effect from bosonic excitations on fermions,
which in the past allowed one to verify the phononic mechanism of a
conventional, $s-$wave superconductivity, may also allow one to experimentally
detect the ``fingerprints'' of the pairing mechanism in cuprates. We argue that
for spin-mediated $d-$wave superconductivity, the fermionic spectral function,
the density of states, the tunneling conductance through an insulating
junction, and the optical conductivity are affected by the interaction with
collective spin excitations, which below $T_c$ are propagating, magnon-like
quasiparticles with gap $\Delta_s$.
  We show that the interaction with a propagating spin excitation gives rise to
singularities at frequencies $\Delta + \Delta_s$ for the spectral function and
the density of states, and at
  $2\Delta + \Delta_s$ for tunneling and optical conductivities, where $\Delta$
is the maximum value of the $d-$wave gap. We further argue that recent optical
measurements also allow one to detect subleading singularities at $4\Delta$ and
$2\Delta + 2\Delta_s$. We consider the experimental detection of these
singularities as a strong evidence in favor of the magnetic scenario for
superconductivity in cuprates.
