Sigh: The infinite-cash-for-the-schools lobby is back at it, claiming the state is failing to fork over anything like the funds it’s supposed to under the 2006 decision in the Campaign for Fiscal Equity suit. Guess it’s time to unpack the deceptions, yet again.

Mayor de Blasio pretty well summed up the claims on Brian Lehrer’s show the other week: The courts, he said, ruled that “school systems around the state and a lot of rural school systems had been underfunded, according to their level of need and the income of parents.”

Not so. Yes, the state’s highest court did uphold a trial judge’s finding that New York City’s schools don’t get enough money to provide “the opportunity for a sound, basic education” — a right that the courts had read into the state constitution some years earlier.

But the ruling didn’t address any school systems outside the city, nor order any specific remedy.

No state court has the power to so do that. Under New York’s constitution, only the Legislature can appropriate money; courts can’t force lawmakers to spend a dime.

Thus, too, the Court of Appeals rejected the specific sum the trial judge had demanded — which turned its order into little more than a shout of Do something.

Soon enough, the state Education Department crunched the numbers and found that the city should get an extra $1.9 billion — which it got, long ago. (Naturally, Albany dealmaking turned this into statewide boosts in school aid.)

It’s true that Gov. Eliot Spitzer, in his year-plus in office, got the Legislature to agree to plan for year after year of huge hikes in state school aid — and he happily cited the CFE decision as justification.

But the Legislature, working with Spitzer’s successors amid the budget pressures of the Great Recession, later decided not to goose spending that much. (Naturally, the spend-more crowd declares these not-as-large increases to be “cuts.”)

Even so, Cuomo has increased state aid by $6 billion in his six years in office, with 40 percent of that going to the city. Indeed, the gov notes that the state has increased its spending on New York City schools at a faster pace than has the city itself — including since de Blasio became mayor.

Bottom line: The cash continues to rain down. Too bad that the real problem isn’t a lack of money — but how it gets spent. Sadly, all those billions in extra state aid have done a lot more to boost teachers’ pay than to actually help the city’s kids learn.

Wouldn’t it be great if the courts dared to recognize those facts?