The most important thing about the city’s charter schools is that they offer students a chance to excel in neighborhoods where the regular public schools have been failing to offer that opportunity for decades.

Last week’s release of state English and math scores provided fresh evidence of that basic fact.

As Success Academy CEO Eva Moskowitz noted in The Wall Street Journal last week, the number of Central Harlem kids meeting the state math-proficiency standard has more than doubled since 2013 — and children attending the area’s charters account for 96 percent of that growth.

If you include charter scores in the results for Harlem’s District 5, it jumps 12 spots in the rankings of all 56 city districts. Yet if you don’t include them, the district’s ranking has still improved slightly since 2006, when charters started opening there.

All this knocks the heart out of one regular charge against charters: the claim that their performance is so much better merely because they “cherry pick” the best students.

No: What they’re doing is offering opportunity to do well — giving families the chance to “cherry pick” a good school that helps children soar.

Charters enroll mainly minority, lower-income kids, yet in math proficiency, 15 of the top 25 city public schools are charters. (Most of the other 10 are in wealthy ’hoods or have selective admission — whereas charter admission is by lottery.)

In both math and English this year, black New York City children at charters outperformed the city- and statewide averages for white kids. Black and Hispanic charter children massively outdid their peers in regular public schools.

The students deserve cheers for putting in the hard work to excel. But the charters deserve their own cheers for providing the opportunity.

Think about all the potential that’s wasted because the regular public schools don’t offer the same opportunity.

Another related lie is that charters somehow hurt the regular schools in their area, especially if they’re “co-located” in the same building. In fact, a new study by Sarah Cordes of Temple University, using data from 1996 to 2010, shows the reverse.

Co-location or close proximity is actually a slight boost for the non-charter school, she found, bringing small increases in math and reading scores, increased student engagement and school safety, and fewer kids forced to repeat grades.

The greatest boost came when the regular school shared a building with a charter, especially a high-quality one.

There can be no doubt that proximity to high-performing charter schools stokes competition and forces district school “administrators to get their act together,” Cordes told Chalkbeat in an interview.

The city does have many excellent regular public schools: Families with the money spend big-time to live in those zones. But a bad ZIP code shouldn’t mean no hope for the less well-off.

New York’s charters offer that hope — and the special interests seeking to crush them are working to deny it.