We measured the ratio $P_{x}/P_{z}$ of the transverse to longitudinal components of polarization transferred from electrons to bound protons in $^{12}mathrm{C}$ by the $^{12}mathrm{C}(vec{e},evec{p})$ process at the Mainz Microtron (MAMI). We observed consistent deviations from unity of this ratio normalized to the free-proton ratio, $(P_{x}/P_{z})_{^{12}mathrm{C}}/(P_{x}/P_{z})_{^{1}mathrm{H}}$, for both $s$- and $p$-shell knocked out protons, even though they are embedded in averaged local densities that differ by about a factor of two. The dependence of the double ratio on proton virtuality is similar to the one for knocked out protons from $^{2}mathrm{H}$ and $^{4}mathrm{He}$, suggesting a universal behavior. It further implies no dependence on average local nuclear density.
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