Neighborhood revival usually starts with density. The more people who live in an area, the more likely the neighborhood will be able to attract basic retail amenities like grocery stores and coffee shops. If enough of those small shops cluster together, they soon start to form the nucleus of a local business district.

With the completion of its $45 million headquarters on Ridge Avenue in Sharswood, the Philadelphia Housing Authority is trying to flip that script, bringing buildings and retail first, and population density later.

The five-story headquarters, which opened in January, currently stands in virtual isolation, surrounded by parking lots, empty tracts and a scattering of tumbledown retail buildings. In the half century since the Columbia Avenue riots devastated this part of North Philadelphia, the area has lost 65 percent of its population.

That hardly sounds like fertile ground for a retail comeback. But the Housing Authority argues that the situation in Sharswood is so dire that only a big government player can create the conditions for revival on Ridge Avenue, once a bustling commercial center for North Philadelphia’s African American community. Consider the PHA’s investments a test of the “if you build it, they will come” strategy.

The PHA’s strength has always been building houses. Now it has to prove it can do retail, too.

Ironically, its Sharswood master plan started out with housing. Because private housing development has been moving at warp speed along Ridge below Girard Avenue, it was hoped that the PHA could act as a bulwark against gentrification. To realize that goal, the PHA took control of 1,300 parcels between 19th and 27th Streets, from Girard to Cecil B. Moore Avenue, so that it could build hundreds of subsidized homes for Philadelphia’s poorest residents.

So far, the effort to repopulate the neighborhood has been moving slowly. Since the construction began in 2016, the PHA has completed just 57 subsidized homes. Another 83 are in the works. The PHA also will gain 94 apartments for senior citizens when it completes the renovation of a former public housing tower in the neighborhood.

Now, reviving Ridge Avenue has become the PHA’s focus.

Speaking at last month’s ribbon-cutting, the authority’s president, Kelvin Jeremiah, told the crowd that the new headquarters would provide the anchor that Ridge Avenue has long lacked. He noted that the project brings 400 employees to Sharswood every day, as well as a regular stream of PHA tenants and contractors.

Unfortunately, nothing about the new headquarters makes you want to take a stroll up Ridge Avenue. While the building (designed by BLT Architects) succeeds in projecting the gravitas we expect from government offices, its ground floor is less than welcoming. Neither of its two public rooms can be entered directly from Ridge Avenue. (The door to the PHA’s customer service center is on Jefferson.) While the PHA’s plans call for a cafe and bank at the eastern end of the site, the authority has yet to secure tenants.

Given that dull streetscape, what happens next could determine the fate of Ridge Avenue. The PHA owns the large vacant parcel bounded by Jefferson, Redner and 21st Streets, and has long hoped to build supermarket there.

Its initial proposal was predictably suburban: a Save-A-Lot store in an asphalt lot. If Ridge Avenue is going to become a walkable urban corridor again, a big parking lot is the last thing it needs. But thanks to a nudge from the city’s Civic Design Review board, the PHA went back to the drawing board.

The new design is still a shopping center, but now the layout shows buildings lining two sides of the block, along Ridge Avenue and 21st Street. One is a 24-unit apartment house with retail space on the ground floor. If the PHA can pull off this arrangement, the two buildings will form a much-needed street edge, giving the project an urban feel. Among the tenants that have signed up are an urgent care clinic, a Pagano’s restaurant, and a hardware store.

Because retail is not the authority’s strong point, it has hired two private developers to manage Ridge Avenue’s evolution: Mosaic Development Partners and Shift Capital. Both are struggling to ensure that the project sets the tone for the rest of the development, but it has not been easy.

Why? Save-A-Lot, the main tenant, is insisting on having a stand-alone store and a design that breaks up the continuity of Ridge Avenue’s streetscape, explained Brian Murray, who runs Shift Capital.

Rather than occupy one of the Ridge Avenue buildings, the supermarket will sit at the rear of the site, inside a 200-car garage intended mainly for PHA employees. Although the developers and the PHA say they hope to camouflage the parking structure on 20th Street, where it faces the neighborhood, the development still has too much parking and not enough density.

Worst of all, Save-A-Lot has demanded that the developer leave a large gap between the two buildings on Ridge Avenue. The supermarket wants to be sure that passersby are guaranteed a view of its parking lot.

The developers have tried to explain that the demand defeats their effort to create a true street edge along Ridge Avenue. It also interferes with the retail continuity, something that is crucial to the street’s future. But according to Murray, the supermarket has refused to to sign a lease unless it can have its suburban design. And without Save-A-Lot, the whole project falls apart.

“It’s not like there was a rush of tenants saying, ‘This is where we want to be,’ ” he explained.

The real problem? Not enough population density in Sharswood. “Given what’s there, this is the best we can do,” Murray argued.

He may be right, but it’s disappointing that Save-A-Lot is forcing this suburban model on a struggling neighborhood like Sharswood at a time when other supermarkets are figuring out how to operate in an urban setting. Giant Heirloom Market just opened a store in the ground floor of a four-story building at 23rd and Bainbridge and plans three more. None have parking lots.

It’s worth noting that all four Giant stores will be in affluent neighborhoods. The sharp differences in approach between a store like Giant and Save-A-Lot suggests we are heading to a new form of inequality. In the future, urban-scaled buildings and density could be a luxury for the city’s upscale neighborhoods, while Philadelphia’s poorer areas will be forced to make do with surface lots and sprawl.