  Identifying universal scaling relations between two or more variables in a
complex system plays a pivotal role in understanding various phenomena in
different branches of science. Examples include the allometric scaling among
food webs in biology, the scaling relationship between fluid flow and fracture
stiffness in geophysics, and the gap-to-$T_c$ ratio, between energy gap,
$\Delta$, and critical transition temperature, $T_c$, hallmarks of
superconductivity. Kinematics, in turn, is the branch of physics that governs
the motion of bodies by imposing constraints correlating their masses, momenta,
and energy; it is an essential ingredient for the analysis of high-energy
quarkonium production, galaxy formation, as well as the $\rho_\circ+AT^2$
contribution to the normal state resistivity in a Fermi liquid (FL),
$\rho_\circ$ being a measure of disorder and $A$ the hallmark of FL. Here, we
report on the identification of a novel, universal kinematic scaling relation
between $T_c(\rho_\circ)$ and $A(\rho_\circ)$ found in a plethora of
defect-bearing conventional and non-conventional superconductors within their
FL regime. We traced back this relation to the triggering and stabilization of
an electron-electron scattering channel within a very specific, yet common,
type of amorphized regions, ubiquitous in all such superconductors. Our
theoretical treatment consisted of, first, analyzing the construct of a
distorted lattice as a mimic of the kinematic aftermath of the formation of
such amorphized regions. Then we applied standard many body techniques to
derive expressions for $T_c(\rho_\circ)$, $A(\rho_\circ)$, and their
correlations. Our results are in agreement with experiments and provide a solid
theoretical foundation for reconciling superconductivity with FL transport in
these systems.
