(Hyperloop One/YouTube)

Transportation pioneer Elon Musk has been known to talk big and sometimes overpromise.

But the Tesla chief and rocket builder took it up a notch Thursday, offering a tantalizing but so-far-undocumented announcement that his tunnel-boring company had received a verbal government green light to build a super-high-speed pod-and-tube transportation system, which he calls Hyperloop, for travel between Washington and New York.

“Just received verbal govt approval for The Boring Company to build an underground NY-Phil-Balt-DC Hyperloop. NY-DC in 29 mins,” he wrote on Twitter.

Questioners on Twitter asked one of the obvious ones: Who gave the permission? Musk did not offer details.

But the Trump administration did not knock the notion down.

Asked if it had given Musk verbal approval, a White House spokesman said, “We have had promising conversations to date, are committed to transformative infrastructure projects, and believe our greatest solutions have often come from the ingenuity and drive of the private sector.”

The system would run from “City center to city center in each case, with up to a dozen or more entry/exit elevators in each city,” Musk said in a later tweet.

His firm intends to build the system underground using an excavation machine. The futuristic concept envisions transporting sealed passenger capsules in a low-pressure tube at hundreds of miles an hour.

Musk appeared to do a little moderating as the day wore on.

“Still a lot of work needed to receive formal approval, but am optimistic that will occur rapidly,” he wrote in a later tweet.

Hours later, he followed with another tweet: “If you want this to happen fast, please let your local & federal elected representatives know. Makes a big difference if they hear from you.”

Even if official federal permission is forthcoming, the need for local ones is a potential major complication.

Leif Dormsjo, director of the District’s Department of Transportation, said, “I’m completely unaware of any request to the District government to permit or review anything related to an Elon Musk project.”

“This is news to City Hall,” said a spokesman for New York Mayor Bill de Blasio (D).

Musk has had “no contact” with city officials, a spokesman for Philadelphia Mayor Jim Kenney said.

“We do not know what he means when he says he has received government approval,” the spokesman said. “There are numerous hurdles for this Hyper­loop technology before it can become a reality.”

A Boring Co. spokesperson said: “We look forward to future conversations with the cities and states along this route and we expect to secure the formal approvals necessary to break ground later this year.”

The electric and autonomous car evangelist first teased the Boring Co. in December, and in April he hinted that his network of Hyperloops could be a nationwide phenomenon.

Musk’s plans appear to draw significant inspiration from Los Angeles’ crushing road traffic, which he has bemoaned on multiple occasions.

In April, he proposed underground tunnels for the city that could ferry cars from one place to another at high speeds. Musk’s tweets on Thursday seemed to refer to these plans, as well as an eventual Hyperloop corridor connecting Los Angeles with San Francisco.

Building a Hyperloop above ground comes with enormous physical and regulatory challenges, which may be one reason Musk is considering an underground approach.

Because Hyperloop technology involves traveling at extremely high speeds, any major turns could subject passengers to undue gravity forces. That suggests that the safest, most efficient way to build the Hyperloop would be in straight lines.

There’s just one problem: Above ground, you need to worry about permits and land rights. Musk’s original vision for the Hyperloop budgeted $1 billion for that alone.

Subterranean land rights may be no less complicated. But go deep enough, and at least you won’t have to worry about plowing through buildings.

Musk isn’t the only one working on Hyperloop technology. Although he has done much to popularize the concept in recent years, by opensourcing the idea, Musk has allowed other companies such as Hyperloop One to compete against each other in an effort to build the first working example.