Three former high-ranking administrators have sued Schools Chancellor Richard Carranza, claiming they were demoted because they’re white. It’s an explosive charge, and one that must be proved — but the allegations reflect, at minimum, the intensifying racial tensions since Carranza took charge of the nation’s largest school system 13 months ago.

The chancellor threw down the race gauntlet from Day One. He picked fights with white parents, promised to achieve racial balance in the city’s selective high schools and commissioned a $23 million “implicit-bias” social-conditioning regimen that lies at the heart of the former administrators’ $80 million lawsuit.

The program, first reported by The Post, assumes that students in majority-minority schools struggle because the system’s white-majority teachers and staff, consciously or otherwise, bring racist attitudes to work with them — and that this, rather than bad teaching, administrative inertia and non-classroom-related social issues, is the primary cause of classroom underperformance.

Carranza’s reeducation program is the purported remedy, complete with racialist rhetoric, threats and, if the suit is to be believed, race-based transfers and demotions. Eventually, all of the DOE’s 130,000-plus teachers and administrators will be subjected to such social conditioning.

Yet the DOE, despite repeated requests, can produce no empirical evidence that implicit bias exists in our schools. (This is likely because implicit bias itself is a dubious concept.)

Rather than supplying evidence, the DOE points to a study prepared by an advocacy group, the Perception Institute, which itself makes no explicit case for racial bias in New York schools — or anywhere else. The institute asserts that inequality of outcomes across ethnic groups is all the evidence needed for racial bias.

Its report, “The Impact of Implicit Bias, Racial Anxiety and Stereotype Threat on Student Outcomes,” is an ambitious exercise in rhetorical gymnastics but makes no credible case for Carranza’s race-driven policies.

“Racism­ [is] any act that even unwittingly tolerates, accepts or reinforces racially unequal opportunities or outcomes for children,” writes Glenn Singleton, another DOE consultant, paid $750,000 for his insights.

This is nonsense. Unequal outcomes have many causes, ranging from social dislocation and inequitable resource distribution to uneven student ability and effort — and to differences in teaching competence. Without proper context, disparate outcomes generally tell us little.

But one outcome dramatically undercuts Carranza’s sophistry: The stunning success of most of the city’s charter schools.

Teacher ethnicity is essentially identical in charter and district schools — 42% minority in charters versus 38% in traditional public schools. It’s all but certain that, at some point, a black or Hispanic charter school child will have a white teacher, since charter kids are virtually all black or Hispanic. So whatever harm is done by implicit prejudices should be magnified in charter schools — yet charters for the most part prosper, while most district schools don’t.

The chancellor appears oblivious to this. His reckless race rhetoric, amplified by the increasingly bitter DOE hyperbole on implicit bias, should disturb anyone with memories of the last race-driven crisis in city schools — the near-catastrophe at Ocean Hill-Brownsville, in 1968.

Ocean Hill-Brownsville had more to do with the unionization of the city’s teachers and community empowerment than with education policy, but it proceeded along racial lines that generated decades of bitterness.

Carranza and his associates may not even be aware of the potential explosiveness of the fight they’re picking; or maybe they do know, and assume that the prospect of racial conflict will preempt opposition to their scheme.

It’s a risky bet. Carranza says that he’s combating a “white-supremacy culture,” characterized by such concepts as “individualism,” “objectivity” and “worship of the written word.” It’s hard to imagine any educator disparaging the written word, but Carranza has crossed that Rubicon. As chancellor, he’s never outlined a coherent academic agenda for the city’s 1.1 million pupils. ­Instead, it’s all about race.

Asked for a specific goal, a DOE spokesman answered: “an 84 percent high-school graduation rate by 2026.” That’s likely to be a moving target, given the Empire State’s ever-diminishing graduation standards. Carranza has perpetrated on city schools an empirically baseless, socially destructive program with no substantive objectives. The lawsuit’s plaintiff pool looks certain to grow. If Carranza truly wants to serve New York’s students, he should change course — or resign.

Bob McManus is a contributing editor of City Journal, from which this column was adapted.