  The in-plane and out-of-plane superconducting stiffness of LSCO rings appear
to vanish at different transition temperatures, which contradicts
thermodynamical expectation. In addition, we observe a surprisingly strong
dependence of the out-of-plane stiffness transition on sample width. With
evidence from Monte Carlo simulations, this effect is explained by very small
ratio $\alpha$ of interplane over intraplane superconducting stiffnesses. For
three dimensional rings of millimeter dimensions, a crossover from layered
three dimensional to quasi one dimensional behavior occurs at temperatures near
the thermodynamic transition temperature $T_{\rm c}$, and the out of-plane
stiffness appears to vanish below $T_{\rm c}$ by a temperature shift of order
$\alpha L_a/\xi^\parallel$, where $L_a/\xi^\parallel$ is the sample's width
over coherence length. Including the effects of layer-correlated disorder, the
measured temperature shifts can be fit by $\alpha=4.1\times 10^{-5}$ near
$T_{\rm c}$, which is significantly lower than its previously measured value
near zero temperature.
