This is not a green shoot:
Housing construction hit to a record low in April as a steep drop in apartment building offset a rebound in single-family construction. […] In a disappointing sign for the future, applications for new building permits dropped 3.3 percent to a new record low annual rate of 494,000.
That said, I don’t really see this as “disappointing” or much of a “sign for the future.” The supply of new housing ought to be fairly fundamentals-driven. There are so many people in the country, the population is growing at such-and-such a rate, and demographics are shifting like so. Back during the housing boom, too many houses were built. Consequently, new housing starts need to stay depressed for as long as it takes for people to fill the houses. The “Hangover Theory” of recessions isn’t true as a general matter, but as applied to the specific case of the housing sector it seems like a pretty close approximation.