The Henry Rutgers Houses, a public-housing development built and maintained by the New York City Housing Authority, are located in the Lower East Side of Manhattan. (Drew Angerer/Getty Images)

Emily A. Benfer is the director of the Health Justice Advocacy Clinic and a professor at Columbia Law School.

The New York City Housing Authority, responsible for 176,000 apartments in 2,418 buildings, is by far the biggest public-housing system in the country. Beset by lead-paint hazards, mold, heating failures and chronic mismanagement, NYCHA buildings are also a danger to the authority’s 400,000 residents — the population of a mid-size American city.

On Jan. 31, New York narrowly avoided a complete federal takeover of NYCHA by agreeing to spend $2.2 billion on a decade-long effort to repair NYCHA’s decrepit buildings and by ceding much management responsibility to a powerful federal monitor. Housing and Urban Development Secretary Ben Carson and Mayor Bill de Blasio (D) announced the agreement at HUD’s Lower Manhattan offices on the deadline date set by a federal judge who last fall had rejected an earlier agreement as inadequate.

The new agreement is also inadequate. That was made clear Monday with news that interim NYCHA chairman Stanley Brezenoff refused to sign the agreement. The deal unfairly places “all of the financial burden” on the city and not on the federal government, where it belongs, he told the New York Times. The city had announced last week that he was being replaced.

Last summer, NYCHA estimated that $32 billion would be needed over five years to fix its buildings, which are on average more than 60 years old, according to the New York Times. The city could never afford to spend that much on these essential repairs. Federal funding will be required if the public-health crisis is going to be effectively addressed and HUD is going to fulfill its duty to provide safe and decent housing. HUD provides $2 billion of NYCHA’s $3.2 billion annual operating budget.

The conditions of public housing in New York City are deplorable. More than 59 percent of NYCHA residents surveyed reported mold in their units, and 52 percent reported leaking roofs, windows or plumbing. More than 800 children under age 6 and living in NYCHA housing tested positive for high levels of lead between 2012 and 2016. The housing authority had ignored lead-paint safety regulations for years.

The alarming deterioration of New York’s public housing occurred in tandem with steady federal funding cuts to public housing nationwide, reductions that picked up speed under the Trump administration. According to the Wall Street Journal, the administration made an initial cut of at least $35 million for 2017 as part of an expected $150 million total.

When billions are needed but millions are being cut, the authorization of a federal monitor is the equivalent of nailing a 2-by-4 to a collapsing building.

NYCHA’s neglect has had staggering consequences for children’s health. Lead poisoning can result in reduced IQ, developmental delays, academic failure, juvenile delinquency, behavioral problems, biological and neurological damage and premature death. The Centers for Disease Control and Prevention makes it clear: “There is no known safe level of lead.” A New York state report last year found that 80 percent of NYCHA buildings, where mold is rife, had conditions that could contribute to asthma in children. As the CDC notes, asthma is a leading cause of school absences and reduced daily activities; in 2008 alone, asthma caused 14.2 million missed days of work and 10.5 million missed days of school nationwide, affecting children from low-income families at the highest rates.

Yet NYCHA does not have the funds necessary to address the more than 245,000 open work orders for repairs, let alone employ enough lead-hazard risk investigators or mold remediation specialists to address these problems.

Shockingly, the new NYCHA agreement with HUD provides no supplemental federal funding for mold and lead-hazard inspection and remediation. Instead, the agreement mandates the use of “visual assessments” for lead hazards. As The Post reported in a tragic 2017 story about lead hazards in D.C. public housing, one of the “key weaknesses of federal guidelines” mandated by HUD and followed by the District is that inspectors rely on visual inspections for peeling paint and deteriorating conditions “instead of specifically testing for lead or asthma-inducing mold.” In effect, children in federally assisted housing must develop lead poisoning before meaningful inspections occur.

HUD’s lack of oversight, compliance review and long-term planning is a problem that reaches far beyond NYCHA. June 2018 reports from HUD’s Inspector General and the Government Accountability Office on the conditions of federally assisted housing found wide margins for fraudulent reporting. For example, the East Chicago Housing Authority in Indiana was allowed to falsely self-certify compliance as generations of families were exposed to lead and arsenic while residing in public housing on a Superfund site.

HUD’s perfunctory approach to its responsibilities, combined with inadequate federal funding, has resulted in squalid environments that threaten the health and livelihoods of public-housing residents. By disinvesting in housing for low-income families, Congress and HUD are thwarting progress, perpetuating racial segregation and increasing the cycle of poverty for future generations. The federal government has an obligation to protect those who qualify for federal assistance. If generations of children are going to thrive, they first must live in homes and communities that government neglect and indifference haven’t made dangerous to their health.