San Francisco’s $1.6 billion Central Subway is finally arriving. After decades of planning, the city this week chose a construction company that will begin digging the tunnel from South of Market to Chinatown later this year.

And it is all because former Mayor Willie Brown Jr., following the 1989 Loma Prieta earthquake, promised a subway to Chinatown leaders who feared that their community would suffer when the city tore down the Embarcadero Freeway.

Or, some say, it is all because Brown promised the subway to Rose Pak, the Chinatown power broker, in exchange for her political support in his bid for mayor.

Whatever the truth or motive, Brown’s promise has become lore, used by both supporters and critics of the 1.7-mile subway to argue for and against the project.

Besides engineers, studies, construction crews and concrete, large transportation projects like the Central Subway need one more key ingredient: a creation myth.

“Did it happen? Nobody knows but Rose and Willie. But even if it did, who cares?” said Tom Radulovich, a member of the BART board who has criticized the project. These stories are “really compelling to people who want the project built.”

Radulovich should know. BART has begun work on a new train line that will run from Pittsburg to Hillcrest in Contra Costa County. This $462 million project is the fulfillment of a promise reportedly made more than 50 years ago at a Martinez doughnut shop to an opportunistic county supervisor.

Joe Silva, the story goes, was the swing vote on the Contra Costa County Board of Supervisors on the issue of whether the county should join Alameda and San Francisco Counties to form BART. Politicians who wanted BART arranged the meeting with Silva where, according to some versions, he received a phone call from Gov. Pat Brown and was promised that BART would extend into eastern Contra Costa if he voted yes.

Silva and the others who were at the meeting are dead. Survivors who have heard the tale offer varying accounts. But over the years it has become a rallying cry for residents in places like Brentwood who believe that BART owes them a train.

Joel Keller, the BART director who represents the eastern Contra Costa area and who pushed for the new BART line, said that if he withdrew his support, “you’d be writing about the former BART director who foolishly spoke in the face of rural legend.”

The Central Subway is set to open in 2018. It will extend Third Street light rail service underground to Chinatown, where Pak has long held sway.

In an interview this week, Pak said that Brown did indeed promise the Chinatown community a subway as politicians had done before. She laughed off the story of a back-room deal between her and Brown, saying, “People always like a good conspiracy theory.”

But, she said, “The myth, of course, helps.”