For generations, the label has been at once exclusive and widely misapplied, available to millions in earnest, but vulnerable to line-blurring by suburban peers who claimed New York City residency without an address to match.

Could a New Yorker be identified by a harried gait? A brash retort? The knowledge that L trains are to be avoided on weekends?

Perhaps. But beginning this week, the evidence will, for the first time, be wallet-size.

On Monday, New York is expected to introduce the country’s largest municipal-identification program, issuing cards intended as a boon for undocumented immigrants, the homeless and others who strain to navigate the bureaucracy of city services and institutions without government-issued ID. The card will confer discounts for prescription drugs, access to city buildings and free memberships to zoos and museums. It will be accepted as a library card across the city’s three public library systems and recognized as identification to open an account at several banks and credit unions.

“For New Yorkers who couldn’t have an official ID, this card is the key to a fuller life,” Mayor Bill de Blasio said in a statement, adding that it was “fraud-proof, secure and appealing to anyone.”