Then the mayor will be free to do his business in peace and quiet, his message unfiltered, his administration shown only in its best light, through news releases and photo ops.

That is the absurd logic of Mr. de Blasio’s eruption at a news conference on Thursday. He snapped at reporters’ questions as unfit to be answered. And he refused to respond to Yoav Gonen, City Hall bureau chief of The Post, which he belittled as a “right-wing rag.”

[. . .]

“We as a party have moved to a more progressive place, we’ve certainly moved leftward,” he said. “We need to win the election and be organized to actually then implement those changes, so one of the things I’m focused on is connecting with my fellow progressives and urging them to be ready to hit the ground running after the November election.”

“That could come from a party structure, that could come from external progressive forces, that could come from a rich combination of the two,” he continued. “But what I fear from historical perspective is, if it doesn’t come from somewhere, we’re going to look back and say, ‘how did we blow a golden opportunity.'”

This is decidedly a side track at the convention, with both Cuomo and the Clintons keeping de Blasio away from the main stage. It was unclear late Tuesday whether the mayor would be afforded a time to speak at one of his own delegation’s daily breakfasts, or whether Cuomo and de Blasio would ever occupy the same spotlight at the same time.

The caravan then makes the drive down the East Side of Manhattan, a ride familiar to his predecessors, before embarking on a detour: past City Hall, across the East River to his final destination, a Y.M.C.A. on Ninth Street in Park Slope, Brooklyn.

There, for an hour — and sometimes more — Mr. de Blasio runs the nation’s largest city from a gym mat. Or a stationary bicycle. Or the weight room.

For the entirety of his 30 months as mayor, the Y.M.C.A. gym has served as the center of a kind of Camp David for Mr. de Blasio, an archipelago of neighborhood haunts in a roughly three-block radius that was part of his pre-mayoral life and where he now routinely returns.

There is the Colson Patisserie, the mayor’s favorite morning stop; the S & S Cleaners; the nearby Brooklyn Public Library branch where Mr. de Blasio votes; the Little Purity Diner; and Bar Toto, where he has held meetings and made fund-raising calls.

The uniqueness of the mayor’s routine has been noted since his early days in office, before he and his family moved to Gracie Mansion from their Park Slope home. But close observation by a reporter for The New York Times, who is a fellow member of the Y.M.C.A., reveals it to be more rigid, lengthy and leisurely than previously known.

During a recent week, Mr. de Blasio did not miss a single workout — hitting the gym each and every weekday, usually leaving the mansion around 8 a.m. or a bit later.

[. . .]

No one begrudges the mayor’s right to exercise, even though some may take issue with his choice of venue to do so. But his sojourn in Park Slope is hardly a solitary affair.

There is a security detail, as well as a rotating cast of staff members from his press office who stay either outside or across the street at the patisserie before accompanying him to City Hall or other events. One is assigned per day, said Eric F. Phillips, the mayor’s top spokesman, to help Mr. de Blasio “stay connected and efficient while he’s working out.”

[. . .]

Last Tuesday, for example, Mr. de Blasio traveled from the Upper East Side to Brooklyn, before reversing direction to head 15 miles north — straight past Gracie Mansion — to an event in the Bronx at 10:30 a.m.

The routine has also survived a raft of continuing investigations into the mayor’s fund-raising activities by state and federal prosecutors.

As recent observations showed, it is, in many respects, a routine that most busy people can only dream of.

In one week in late June, the mayor emerged on that Monday into the gym’s stretching area in a T-shirt, running shoes and khaki cargo shorts with pockets.

After 15 minutes of stretching and BlackBerry multitasking, he moved to the weight room. By 9:24 a.m., he was wearing headphones on a stationary bicycle, pedaling at a gentle pace while watching CNN. In the first-floor lobby, a communications adviser, Wiley Norvell, sat waiting for the mayor.

At 10:23 a.m., Mr. de Blasio exited the gym wearing a suit and got into a waiting car. Mr. Norvell got in the back seat next to him. Sixteen minutes later, the mayor’s office sent reporters a statement on the Supreme Court’s ruling on Texas abortion laws.

New Yorkers sometimes hear directly from their mayor while he is at the gym, as in one case when a prerecorded interview earlier that Tuesday aired at 9:30 a.m. on NY1. As his voice sounded on the television, Mr. de Blasio was working out.

The mayor also conducts his weekly radio appearances with Brian Lehrer, the WNYC host, from nearby — occasionally in his gym clothes. That Wednesday, he hustled from the stationary bicycle and out of the gym, still in his workout cargo shorts.

One chain concerned charter schools; another dealt with affordable housing in East New York, Brooklyn. Three discussed “the most effective message to employ in raising funds to advance the mayor’s policy agendas.”

These internal discussions about public matters are now part of a court battle here, as lawyers for a nonprofit aligned with the mayor are fighting to keep those emails confidential, resisting subpoenas for that information by the state’s Joint Commission on Public Ethics.

The legal strategy appeared to clarify what had been one of the more puzzling moments of the de Blasio era: the description in May of five outside consultants as “agents of the city.” The designation of “agents” appeared months earlier, in a December letter from the nonprofit’s lawyers to the state ethics panel, and applied to a dozen advisers with close ties to the city.

The de Blasio administration has argued that the nonprofit, the Campaign for One New York, and a small group of outside consultants are so close to City Hall that they essentially work for the city. For that reason, the argument goes, their emails with the mayor and his staff are immune from public disclosure under the state’s Freedom of Information Law.

[. . .]

“If such documents were made public, elected officials might be reluctant — and might not even choose — to obtain the information derived from public opinion surveys,” Ms. Wolfe said.

Arguing before Justice Denise A. Hartman in a courtroom here on Wednesday, a lawyer for the nonprofit, Lawrence A. Mandelker, said that communications between Mr. de Blasio and the nonprofit did not have to be disclosed to the panel because, among other reasons, of a “deliberative process” privilege that applies to executive branch communications.

Scott Kleinberg, who came to New York from the Chicago Tribune, was announced as City Hall’s new social media director in a May 3 memo that boasted that he and his team would “infuse personality and engagement into the social media channels for the Office of the Mayor and City government as a whole.”

Just eight weeks later, Kleinberg said he was out.

“Well, that was fast,” he wrote on Facebook Tuesday night. “I moved to NYC for a dream job and that’s not what I got.

“I tried to stick it out, but it was impossible,” he continued. “I don’t even know the word quit, but for the sake of my health and my sanity, I decided I needed to do just that. Now, for the first time in my life, I’m unemployed… I’ve learned a lot in the past several weeks, including something I’ve ignored in many a fortune cookie: If something seems too good to be true, it probably is.”

[. . .]

“I’m sure it’s impossible for someone of your caliber, with your work ethic and honesty, to survive in a sea of cut-throat political hacks,” one friend commented.

Kleinberg responded with thanks, adding, “I ended up with political hacks plus a boss who just couldn’t get it. It was a bad combination for sure.”

Another wrote that he was impressed Kleinberg had stayed with the job as long as he did, adding, “It clearly was not as advertised.”

A third commented, “Well, you are not the only one to be disappointed with our mayor’s office.”

[. . .]