Nearly a month later, no one has been arrested for the July 30 shooting outside a Chicago liquor store that severely injured Norwood, 30, and killed his brother Omar, 35.

“That’s the norm in this city. We live amongst a lot of killers,” Norwood said, adding that the detectives have stopped calling. “Ain’t nobody been locked up. And they ain’t trying to solve nothing.”

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The Norwood brothers have joined the grim ledger of Chicago violence, part of a wave of summer shootings that has propelled the city, again, to the forefront of the national debate over guns and violence. As of Tuesday, 365 people had been killed in Chicago this year, more than in any other U.S. city.

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Yet the growing death toll obscures a far larger group of victims — more than 1,600 people who, like Deangelo Norwood, have been shot this year and survived. While homicides routinely go unsolved here, the perpetrators of nonfatal shootings are even less likely to be brought to justice.

Since 2010, Chicago police have made arrests in only about 27 percent of homicides, according to a Washington Post analysis of homicide data in more than 50 major U.S. cities — the lowest rate of any city The Post examined.

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For nonfatal shootings, the arrest rate plummets into the single digits, according to data maintained by the University of Chicago Crime Lab. The latest report shows Chicago police made an arrest in 10 percent of nonfatal shootings in 2014, 7 percent in 2015 and just 5 percent — 1 in 20 — in 2016.

While the numbers in Chicago are particularly abysmal, the pattern appears to hold in other cities. Because no comprehensive national data is available on arrest rates for nonfatal shootings, The Post requested the information from 50 major U.S. cities. Only six provided it and only for select years.

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In those places, The Post found that nonfatal shootings were less than half as likely as homicides to result in arrests. In Charlotte, for example, police have made arrests in 71 percent of homicides but in just 30 percent of nonfatal shootings since 2013. In Miami, police made arrests in 1 in 3 homicides but in just 1 in 5 nonfatal shootings between 2014 and 2016. And in Omaha, police made arrests in 67 percent of homicides but in just 18 percent of nonfatal shootings in 2016 and 2017.

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Chicago police officials say they have significantly improved their ability to solve homicides as well as nonfatal shootings by strengthening their relationships with the community. Homicides and nonfatal shootings are both down compared with this time last year. And, police noted, the department had made arrests in 44 percent of homicides committed through mid-August, up from 33 percent during the same period last year.

“We have been making considerable investments,” said police spokesman Anthony Guglielmi, noting that the department plans to hire 300 additional homicide detectives by the end of this year, bringing the total to more than 1,200.

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But in Chicago and throughout the nation, police say the same factors that make it difficult to solve homicides make it difficult to solve nonfatal shootings. Minority communities, which tend to produce the most victims, also tend to distrust police. Witnesses are likely to fear retaliation for “snitching.” And victims may be unwilling to cooperate, because telling the truth about the shooting could implicate them in a crime.

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“The other night, we had three people shot. They all take themselves to the hospital. They don’t wait for the cops or the ambulance. Then . . . they tell us to go ‘F’ ourselves,” said William Evans, the former police commissioner in Boston, where Boston Magazine last year found that police made arrests in just 4 percent of nonfatal shootings between January 2014 and September 2016.

While police say they cannot solve crimes without the cooperation of the public, leaders in the black community say the failure to solve crimes is fueling the distrust — along with a deadly cycle of impunity and retaliation that begets more violence.

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“These communities have degenerated into a lawless vigilante justice, where people have to get justice on their own terms because the police won’t get it for them,” said the Rev. Marshall Hatch Sr., pastor of New Mount Pilgrim Missionary Baptist Church on Chicago’s troubled West Side.

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“People feel like they’ve got to take the law into their own hands,” he said.

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Cook County State’s Attorney Kim Foxx (D) agrees with that assessment. Foxx is the first African American woman elected to head the prosecutor’s office that handles Chicago crime, one of the biggest and busiest in the nation.

The lack of arrests, she said, leaves thousands of families waiting for a justice that never comes.

“It’s heartbreaking,” she said. “Each day that passes, the likelihood of us being able to put together a winning case diminishes.”

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While witnesses might feel an obligation to cooperate with police after someone has been killed, Foxx said, nonfatal shootings can leave people feeling that it is “more pragmatic to deal with this in the street justice system.”

That was how Deshon Hannah saw things four years ago when he was hit with 30 buckshot pellets from a shotgun blast fired by a rival gang member in Chicago’s Back of the Yards neighborhood.

“I didn’t want him to go to jail, to be honest,” Hannah, 20, said of his shooter. “I wanted my retaliation. I wanted to shoot the person who shot me.”

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Hannah, who has since become an anti-violence activist, said he had no interest in cooperating with Chicago police, who he said routinely harassed and mistreated his family, friends and neighbors. The police eventually arrested someone without his help.

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Scores settled in the street often produce “collateral damage,” further raising the victim count as innocent people are caught in the crossfire, said Eric Russell, a Chicago police-accountability activist.

“They’re shooting into crowds. Some of them are high off of drugs and narcotics. They’re reckless,” Russell said this month after 72 people were shot — 12 fatally — in a single Chicago weekend.

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“If there is a silver lining, thank God these shooters can’t aim,” he said. “These kids are just terrible shots.”

Whether a shooting is fatal or nonfatal often comes down to luck: Where the bullet strikes. How quickly someone dials 911. When the ambulance arrives. The distance to the nearest trauma center.

Still, policing experts acknowledge that the public — and in some cases the police — tends to focus almost exclusively on fatal shootings. Many cities do not even track how many nonfatal shootings their police handle, much less how many result in arrests.

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“The homicides get all of the attention and all of the resources,” said Natalie Kroovand Hipple, an Indiana University criminal-justice professor who studies gun violence.

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Tio Hardiman, a longtime community activist in Chicago, tries to stop violence “on the front end,” before it happens. But in a city with thousands of shootings and hundreds of homicides each year, Hardiman spends most of his time with people who are already victims.

“If I’m being straight up, there is a lot of hopelessness,” he said, “and no faith in the police department.”

As Hardiman spoke, he stood sweating in a baggy gray suit in a field on the Far South Side where the bodies of two boys had been discovered four days earlier: Darnelle Flowers, 17, and Raysuan Turner, 16.

Through a steady stream of anonymous tips, Turner’s family had pieced together their best guess at what happened: They believe that the boys were lured to the neighborhood by two girls, one of whom was angry over a schoolyard dispute, and that after meeting the girls and two unidentified males in a park, the boys were led to the overgrown field, shot and left for dead.

But making the leap to an arrest has proved frustrating. The tipsters don’t want to be identified. Two witnesses tracked down by a local activist disappeared when it came time to speak with prosecutors. Two people who had been held as persons of interest have been released.

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“I just hope that somebody has the balls to come forward,” said Turner’s mother, Rayniecia Morris, sliding on sunglasses to hide the tears pooling at the corners of her eyes. “There are people out there who know what happened to my son, and they need to come forward.”

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On the day they were shot, the Norwood brothers had stopped to buy water and a pack of gum from Ziad Certified Liquor, a market in the Bronzeville area where a hand-painted mural of a black trumpeter gazes down at customers from above the Budweiser cooler.

Born to a drug-addicted mother and raised — along with six siblings — by a devoted, diligent grandmother on Chicago’s rough South Side, both were dream chasers who longed to get out. Instead, they got caught up in the chaos. Both went to prison: Deangelo for a stickup and Omar for the unlawful use of a weapon.

But things had been going well since they got out. Deangelo had finished his GED and found a job with Divvy, the city’s bike-share program. Omar worked in food service and began taking classes to become an electrician. The brothers talked about pooling their money and opening a juice bar in Chicago’s booming downtown.

Then Omar started dating a woman with an ex-boyfriend who also had just gotten out of prison. As the woman waffled between them, Omar and the other man began taunting each other on social media, Deangelo said.

He said the shooting occurred when three of the man’s friends spotted the Norwood brothers in the candy aisle of the liquor store. A heated argument led to a fistfight on the sidewalk outside. The Norwoods were winning, Deangelo said — until one of the men pulled out a gun.

Omar died instantly, shot in the back of the head. Deangelo crumpled to the ground next to his brother, bleeding from a hole in his chest.

During 17 hours of surgery, doctors removed his spleen and part of his liver, leaving his abdomen a patchwork of staples, stitches and scars. He spent weeks in the hospital, then decamped to a small apartment in Indiana to heal. These days, just pulling on socks is a painful, complicated task.

Aside from the physical pain, the emotional trauma has left him by turns hopeful and despondent. One minute, he’s making plans to go back to work, save $15,000 and open that juice bar. The next, he’s saying he feels lost without his big brother.

“It’s like I’m half dead and half alive,” he said softly. “I’ll never be the same again.”

Meanwhile, the shooting plays on a loop in his head. He sees the gun, the muzzle flash, the blood. His brother’s pained expression as he falls.