  Two drastically different theories predict the marginal criticality of
jamming. The full replica symmetry breaking (fullRSB) theory [1-4] predicts the
power-law distributions of weak contact forces and small inter-particle gaps in
infinite-dimensional hard-sphere glass, with two nontrivial exponents
$\theta_f=0.42311...$ and $\gamma=0.41269...$, respectively. While the marginal
mechanical stability (MMS) analysis [5-8] predicts that the isostatic random
packings of hard frictionless spheres under external stress are marginally
stable and provides inequality relationships for the exponents of the
weak-force and inter-particle-gap distributions. Here we measure precisely
contact forces and particle positions in isotropic jammed bidisperse
photoelastic disks and find the clear power-law distributions of weak forces
and small inter-particle gaps, with both exponents $\theta_f=0.44(2)$ and
$\gamma = 0.43(3) $ in an excellent agreement with the fullRSB theory. As the
jammed packing subject to area-conserved cyclic pure shear approaches the
yielding point, the two exponents change substantially from those of the
isotropic case but they still satisfy the scaling relationship provided by the
MMS argument. Our results provide strong experimental evidences for the
robustness of the infinite-dimensional theory and the MMS analysis in
real-world amorphous materials.
