WASHINGTON — The Transportation Security Administration unveiled a sweeping overhaul of the nation’s airport checkpoints Tuesday, introducing a continuous Möbius-strip queue that returns every traveler to the front of the line after roughly 45 minutes of steady, orderly progress.

Officials at 40 major airports confirmed the new design is already operational and, by every metric the agency currently tracks, flawless.

“Throughput is up, incident reports are down, and not one passenger has ever once complained from the other side,” said Dale Whitcombe-Ferris, the TSA’s Deputy Assistant Administrator for Perpetual Flow Optimization. “We have received zero complaints from the far side of the checkpoint. Zero. You can draw your own conclusions.”

Whitcombe-Ferris declined to say what conclusions those might be, or whether the “far side” had been visited by anyone at the agency.

The new checkpoint requires travelers to remove their shoes, belts, and laptops, proceed through a full-body scanner, and then rejoin the queue at the point where they first removed their shoes. Agency sources described the process as “deeply thorough.”

Early adopters reported mixed reactions. Marcy Delacroix-Tuttle, a traveler from Dayton, said she had been through the line “either four or eleven times” and had begun to recognize the people ahead of her. “There’s a man named Gary,” she said. “We’re close now. I think I’m in his wedding.”

The TSA has defended the redesign as a logical extension of its long-standing commitment to making sure every passenger feels fully screened. Dr. Ingrid Palomäki-Voss, a senior fellow at the Institute for Topological Approaches to Queueing at the Greater Midwest Center for Applied Lines, said the Möbius configuration solves the single greatest flaw in conventional security: the end.

“A line with an exit is a line with a vulnerability. We have removed the vulnerability, and, as a side effect, the exit.”

Palomäki-Voss added that the design has an elegant single-sided quality. “There is no inside and no outside. There is only the line. Frankly, we’ve been trying to tell people that for years.”

Airlines have responded cautiously. Several carriers noted that flights continue to depart on schedule, though no one has been able to confirm that any passengers were on them. A spokesperson for one major airline said gate agents had begun announcing final boarding calls “out of habit and, increasingly, hope.”

Asked how a traveler might actually reach a gate, Whitcombe-Ferris said the agency was “exploring a pilot program” in which a passenger who has shown sufficient patience would be quietly waved through by an agent. Criteria for sufficient patience have not been established. The agency said it would know it when it saw it, and that it has not yet seen it.

The rollout includes a revised PreCheck program, which now loops back to the beginning faster.

At press time, the TSA had announced plans to expand the Möbius design to baggage claim, where officials said the carousel would finally be “honest about what it is.”