Elwood Norris, the California man referred to as Woody who invented it, was a serial creator of futuristic devices, some extra whimsical than others. He developed early hands-free headsets and different refined sound gear but in addition the AirScooter, a private flying machine that by no means gained reputation.

Mr. Cohen, one other founder, was a enterprise capitalist who had invested in oil and gasoline in addition to in fledgling firms whose shares, referred to as penny shares, are traded on flippantly regulated over-the-counter markets. He had beforehand put cash — together with Mr. Kestenbaum and his household — into an organization that made what it mentioned was a wholesome youngsters’s beverage referred to as AquaBall earlier than pivoting to provide vaping liquids for e-cigarettes.

Wrap Applied sciences began buying and selling on an over-the-counter change for $5 a share in Could 2018.

By then, Mr. Carone was serving to Mr. Adams place himself for a mayoral run in 2021 and introducing him to potential donors who may assist gas his marketing campaign.

Among the many donations Mr. Adams acquired in the summertime of 2018 was $1,500 from the Wrap Applied sciences chairman, Mr. Cohen, data present.

Mr. Carone mentioned he didn’t introduce Mr. Cohen to Mr. Adams or ask him for donations.

The mayor’s spokesman, Mr. Younger, mentioned Mr. Adams was not conscious of Mr. Cohen’s donation on the time and didn’t meet him till months later.

Mr. Cohen’s June 2018 contribution got here as Wrap Applied sciences was embarking on its first advertising blitz, staging BolaWrap demonstrations for police and the media in Utah, Missouri and elsewhere.

Native newspapers covered a demonstration for the Yonkers, N.Y., Police Division on Oct. 2, 2018.

A couple of week later, firm representatives held a non-public BolaWrap exhibiting for New York police officers at a division firing vary within the Bronx. The officers rejected the machine, concluding amongst different issues that the loud crack it made when being fired — its flying tether on the time was propelled by a clean 9-millimeter pistol spherical — might be mistaken for gunfire and trigger different officers to begin capturing, folks aware of the assembly mentioned.