As Philadelphia transforms, there is a distinct possibility for social gaps to widen, and for the growth to exclude the city’s poor. For the first time in decades, more people are moving to the city than leaving it, and many of the newcomers are better educated or wealthier than the average Philadelphian. But alongside the rehabbed brownstones and loft-style condos, hundreds of thousands of families continue to live in poverty, giving Philly the dubious distinction of having the largest population living in poverty of any major city — 25.6 percent. In the region, that compares to 18.2 percent in Washington, D.C., 19.4 percent in New York, 21.4 percent in Boston and 22.4 percent in Baltimore. And while the numbers vary, the same challenge crops up in all of these fast-gentrifying cities: How to ensure that growth happens without leaving the most vulnerable populations behind?