JDK-6320749 discusses a problem with the assertion originally added to ObjectSynchronizer::FastHashcode,

assert(!SafepointSynchronize::is_at_safepoint(), "invariant");

the reasoning for which was stated as:

"hashCode() can be a heap mutator. Given that, it seems unwise to call hashCode while at a safepoint. Can parallelscavange tolerate the markwords changing at this point? (Are the markwords known intact in this situation?)"

but a "verify_in_progress" relaxation check was added to address the problem in 6320749, and we have since further added a relaxation for DumpSharedSpaces:

 assert(Universe::verify_in_progress() || DumpSharedSpaces ||
 !SafepointSynchronize::is_at_safepoint(), "invariant");

The same initial !is-at-safepoint assertion was also added to ObjectSynchronizer::inflate - with the same basic mutation-of-markword rationale. But monitor deflation, which also mutates the markword, has until recently always been performed at a safepoint and ergo markWord mutation at a safepoint must be safe, and thus both assertions can be removed.

These assertions can be tripped if inflation happens to occur when querying the identity_hash of an object, during a CDS dump safepoint.