  The Friedmann-Lemaitre-Robertson-Walker (FLRW) metric assumes comoving
spatial rigidity of metrical properties. The curvature term in comoving
coordinates is environment-independent and cannot evolve. In the standard
model, structure formation is interpreted accordingly: structures average out
on the chosen metrical background, which remains rigid in comoving coordinates
despite nonlinear structure growth. The latter claim needs to be tested, since
it is a hypothesis that is not derived using general relativity. We introduce a
test of the comoving rigidity assumption by measuring the two-point
auto-correlation function on comoving scales---assuming FLRW comoving spatial
rigidity---in order to detect shifts in the baryon acoustic oscillation (BAO)
peak location for Large Red Galaxy (LRG) pairs of the Sloan Digital Sky Survey
Data Release 7. In tangential directions, subsets of pairs overlapping with
superclusters or voids show the BAO peak. The tangential BAO peak location for
overlap with Nadathur & Hotchkiss superclusters is $4.3\pm1.6$ Mpc/h less than
that for LRG pairs unselected for supercluster overlap, and $6.6\pm2.8$ Mpc/h
less than that of the complementary pairs. Liivamagi et al. superclusters give
corresponding differences of $3.7\pm2.9$ Mpc/h and $6.3\pm2.6$ Mpc/h,
respectively. We have found moderately significant evidence
(Kolmogorov--Smirnov tests suggest very significant evidence) that the BAO peak
location for supercluster-overlapping pairs is compressed by about 6% compared
to that of the complementary sample, providing a potential challenge to FLRW
models and a benchmark for predictions from models based on an averaging
approach that leaves the spatial metric a priori unspecified.
