Three race-baiting SUNY-Albany coeds were arraigned on assault and other charges in a capital-city courtroom Monday in a case that offers both Gov. Cuomo and top university officials an unparalleled leadership opportunity.

Want to bet they boot it?

The coeds, who are African-American, brought charges sufficiently serious to attract the attention even of Democratic presidential front-runner Hillary Clinton — advancing a lurid tale of early-morning racist assaults by white students aboard a public bus bound for the SUNY campus on Jan. 30.

“I just got jumped on a bus while people hit us and called us the “ ‘n’ word,” Asha Burwell, one of the three students, tweeted. “NO ONE helped us.”

“A whole bunch of guys started hitting me and my two friends, punching us in the head,” Burwell later charged on social media — adding that the bus driver “let the bus sit . . . while my friend got beat in the head by white guys.”

Not a word of it was true, according to authorities — who arraigned the trio on charges including misdemeanor assault and the filing of false police reports.

Not the crime of the century, to be sure — but definitely a cautionary event that left people in high places looking sadly foolish.

These would include Clinton: “There’s no excuse for racism and violence on a college campus,” declared a campaign tweet, which linked to a national newspaper report on the allegations.

Closer to campus, and much more worrisome, was the reflexive response of UAlbany President Robert J. Jones — an estimable fellow who initially swallowed the tale whole.

“Early this morning, three of our students were harassed and assaulted while riding a bus in Albany,” said his statement. “I am deeply concerned, saddened and angry about this incident. There is no place in the UAlbany community for violence, no place for racial intolerance and no place for gender violence.”

One would hope not.

Then again, nothing actually happened — unless, of course, it matters that one of the trio is now alleged to have assaulted a white coed who was riding the bus. Or unless it matters that the only racial slurs heard on the video came from one of the black students.

All of this seems clear from video footage of the bus ride. (Who knew one bus would carry 12 cameras, covering all the angles? Clearly not the three students.)

To be sure, as soon as Jones actually saw the video, he began to back away from his unconditional acceptance o`f the coeds’ claims.

This seems to have bled energy from what clearly was escalating into another in a national series of ugly, race-driven but factually dubious campus confrontations. (#BlackLivesMatter was on the case, it’s worth noting.)

So, good for Dr. Jones. And good for Albany County District Attorney David Soares — a left-leaning George Soros acolyte who also did his best to tamp down the racial rhetoric. (Though it remains to be seen how the charges will be handled.)

But it would be a mistake to assume the issue has been laid to rest. Hoaxes that enjoy official approbation, even temporarily, generate real, if repressed, bitterness — and this can have consequences.

Certainly the SUNY-Albany incident demonstrates how quickly social media can accelerate seemingly minor incidents into real crises. Actual mobs get tired and run out of steam soon enough, and folks go home. Twitter generates its own critical mass — which rarely dissipates on its own, especially when race is involved.

That’s why it’s so important that leadership gets things right early on; Jones didn’t, even if he did seem to recover quickly.

Now comes the next step.

Now it’s time for the State University’s top leadership — board Chairman H. Carl McCall and Chancellor Nancy Zimpher — to make it clear that there is no place for racial fakery at any of the 64 institutions they oversee.

Not just that would-be hoaxers won’t be tolerated. It should go without saying that those who try it will be directed to go elsewhere for their education — but, sadly, it does need to be said.

More importantly, administrators and staff need to understand that the university’s default when race-based charges surface is this: First, verify; then commiserate.

Cuomo, who’s lately been sticking his oar into the City University’s pond, needs to declare zero tolerance for SUNY campus race-baiting. None of the usual thunder, thank you, just a public acknowledgement that a McCall-Zimpher crackdown will have his full backing.

Dream on? Probably.

But the next hoax — and assuredly there will be one — may not end quite as pacifically as this one.

And then it will be too late.