Of course, all the speculation, and all the layers of security in the new system, are for scraps of paper that nobody wants. The hope is that under the system, no summons can vanish — which is exactly what they have long had a habit of doing, as officers would try to do favors for some who had been ticketed.

Mayor Michael R. Bloomberg said he put a great deal of faith in the new system.

“Once it gets into the system, it would be very hard to fix it, get rid of it, because it’s just — it’s too easy to track,” Mr. Bloomberg said on his weekly radio program on WOR-AM on Friday. “So, if that practice that’s alleged to have taken place did take place, then at least we’re convinced it won’t in the future.”

Those were the mayor’s first extensive comments on the investigation, in which a grand jury in the Bronx is reviewing the suspicion that scores of officers fixed tickets. Dozens of officers could face criminal charges, and hundreds more could face administrative charges, according to people with knowledge of the investigation. The grand jury is looking at tickets issued before the new system went into operation.

“There seems to be a lot of evidence that there was a practice that should not have taken place,” Mr. Bloomberg said.

Much of the inquiry focuses on police-union delegates, who are believed to have acted as conduits for favor requests. The union has fought back, saying that ticket-fixing is a longstanding courtesy, not corruption, and suggesting that over the years many requests came from high-ranking police officials and other notables.

Under the old system, it was possible to discern a ticket’s disappearance, but that would have involved a more painstaking reconstruction. Once the old forms were distributed, someone in each station house was responsible for manually tallying which summons numbers went to which officers.