Like most incumbents seeking re-election — perhaps even more than most — Gov. Cuomo has a proclivity for exaggerating his record.

One claim isn’t just hype, though. In pushing through a cap on property-tax levies, Cuomo achieved one of the most significant fiscal reforms in New York history.

Enacted in 2011, the cap limits the annual growth in total property-tax levies to 2 percent or the rate of inflation, whichever is less, in all fiscally independent school districts and all counties and municipalities outside New York City.

The cap can be overridden by 60 percent of the members of local governing bodies or by an equally large supermajority of taxpayers voting directly on school budgets.

As long as Cuomo’s cap stays in place, it will continue bending the property-tax curve lower— especially in school districts, where the law gives a simple majority of voters the power to absolutely freeze tax levies at prior-year levels.

But will the cap last? Considering his efforts to appeal to suburban and upstate taxpayers, it’s odd that Cuomo won’t commit to seeking the law’s permanent enactment.

Keep in mind, the governor was able to goad Assembly Democrats into passing the cap in the first place by linking it to an extension of New York City’s rent regulations.

The final version of the tax-cap law, enacted in tandem with a rent-control extender, said the levy limit “shall remain in full force and effect at a minimum until and including June 15, 2016, and shall remain in effect thereafter only so long as” the rent laws continue beyond their own expiration, next set for June 2015.

Rent control’s continuation may be the safest of Albany bets, but the odd wording of the tax-cap statute creates a worrisome loose end.

After all, while limiting property taxes has earned Cuomo plenty of gratitude from taxpayers, it’s also earned the enmity of public employee unions — which remain determined to gut or repeal the cap, sooner or later.

Rob Astorino, the Republican gubernatorial candidate, made it clear early in the campaign that he favors making the cap permanent.

But Cuomo himself had little to say on the topic until last week, when he issued a booklet listing his second-term policy proposals. “Extend the Property Tax Cap” was among them. Notably missing was the word “permanently.”

Cuomo could keep his latest promise merely by retaining the link to rent control and adding a few years to the sunset date — leaving the cap’s ultimate fate in the hands of his successor. For taxpayers, that’s hardly reassuring.

On the subject of property taxes, Cuomo prefers to talk up his recent “property tax freeze.” In reality, this is a temporary state tax credit for homeowners (and only homeowners) living in jurisdictions that have remained within their tax caps.

On top of the $1.5 billion he’s already committed to those tax credits over the next three years, Cuomo says he’ll set aside another $500 million to give local governments a stronger incentive to consolidate or share services — because, he claims in a new TV ad, New York’s high property taxes result from “the waste and duplication of our over 10,000 local governments.”

In fact, that number is inflated by including 6,900 town-only special districts — essentially lines on a map that lack separate taxing authority. Far from adding to taxes, they make sure costs are distributed fairly to the property owners benefitting from specific services.

The true number, as counted by the US Census Bureau, is 3,453. Relative to population, that’s not especially high, and there’s no correlation between the number of local governments and the burden of property taxes in different states.

In fact, the evidence suggests New York’s high local taxes are driven mainly by high employee wages and benefits — but Cuomo has made it clear he won’t pursue reform of the collective-bargaining laws that make it hard for localities to restructure contracts.

In his recent debate with Astorino, Cuomo said: “Rhetoric is fine. Facts are better.” The fact is that the tax cap is working — but it needs to be permanent to make a permanent difference.