We never bought Schools Chancellor Carmen Fariña’s promise of “zero tolerance” on grade-fixing — but it’s now plain she meant zero accountability.

Last week, an arbitrator reinstated ex-Dewey HS principal Kathleen Elvin — after Fariña’s Department of Education, which in theory was trying to fire Elvin, utterly punted on making its case.

Elvin was fired last summer after The Post caught her running a grade-fixing diploma mill: Students in “credit recovery” programs to make up for failed courses barely had to lift a finger to pass.

A Department of Education investigation showed several other administrators and teachers were involved — but only Elvin faced the ax.

Except that she’s now off the hook (with back pay, no less), pulling her $158,000 salary.

Incidentally, the program broke multiple provisions of the United Federation of Teachers contract — by, for example, making teachers responsible for too many classes a day. But when members complained to the union, it did nothing.

In today’s Post, Susan Edelman details how little DOE did to make the Elvin firing stick. But the key fact is that the ruling said her programs must have met DOE approval — because DOE later OK’d all those bogus “recovered credits.”

DOE’s lawyers “explained” that Team Fariña didn’t want to make the 100-plus students retake the classes for real; it might’ve held up their graduations.

So they got worthless diplomas: ones based on “work” for which, to quote the investigators’ report, “students were not required to receive instruction to obtain credit” and where “no instruction was provided.”

Fariña’s crew fired the principal for mass cheating, then declared the cheating kosher so it could still tout Dewey as having a graduation rate above 60% — and not level with the parents about the mass fraud.

All this, mind you, in a high-profile case with mountains of smoking-gun evidence. Sends a pretty clear message to all the other schools looking to boost graduation rates, doesn’t it?

The arbitrator’s ruling reinstates Elvin with all back pay and benefits. But the ruling says nothing about the “graduates” cheated out of a quality education.

Many of Fariña’s graduates move on to CUNY — where they wind up having to take a year or even two of remedial classes to make up for what their high schools failed to teach.

Bronx Borough President Ruben Diaz recently proposed that the DOE repay CUNY for those costs — a provocative idea that highlights only part of the fraud: Doesn’t it owe the students, too?

Zero accountability guarantees more cheating — and more cheated kids.

We look forward to the day when New York City has a schools chancellor who truly believes in making diplomas worth more than the paper they’re printed on.