  We present new x-ray and neutron scattering measurements of stripe order in
La(1.875)Ba(0.125)CuO(4), along with low-field susceptibility, thermal
conductivity, and specific heat data. We compare these with previously reported
results for resistivity and thermopower. Temperature-dependent features
indicating transitions (or crossovers) are correlated among the various
experimental quantities. Taking into account recent spectroscopic studies, we
argue that the most likely interpretation of the complete collection of results
is that an unusual form of two-dimensional superconducting correlations appears
together with the onset of spin-stripe order. Recent theoretical proposals for
a sinusoidally-modulated superconducting state compatible with stripe order
provide an intriguing explanation of our results and motivate further
experimental tests. We also discuss evidence for one-dimensional pairing
correlations that appear together with the charge order. With regard to the
overall phenomenology, we consider the degree to which similar behavior may
have been observed in other cuprates, and describe possible connections to
various puzzling phenomena in cuprate superconductors.
