TUCSON, Ariz. — Investigators on Tuesday revealed more disturbing details about the events leading up to the assassination attempt against U.S. Rep. Gabrielle Giffords, including a menacing handwritten note in the suspect’s home with the words "Die, bitch."

And on the day of the shooting, a mumbling Jared Loughner ran into the desert near his home after his father asked him why he was removing a black bag from the trunk of a family car, sheriff’s officials said. Loughner resurfaced later Saturday when authorities say he showed up at a grocery store in a taxi and shot 19 people, killing six, including a federal judge and a 9-year-old girl.

Investigators provided the new details to The Associated Press and said they’re still searching for the bag. They suspect it could contain clues into Loughner’s motives.

"The bag is very important to us," said Capt. Chris Nanos, head of the Pima County Sheriff’s Department’s criminal investigations division. "What was in that bag and is there any relevance?"

"What if he wrote a note that says, ‘Hey, I’m going to go do these things and I know it’s wrong but I’m still going to do them,’" Nanos said. "That’d be a pretty good piece of evidence."

Authorities previously said they found handwritten notes in Loughner’s safe reading "I planned ahead," ”My assassination" and the name "Giffords." Pima County Chief Rick Kastigar and Nanos told the AP they also found notes with the words "Die, bitch", which they believe referenced Giffords, and "Die, cops."

All the writings were either in an envelope or on an actual form letter Giffords’ office sent him in 2007 after he attended one of her political events, Nanos said.

For all of it, Loughner’s parents, silent and holed up in their home since the shooting spree, apologized Tuesday.

"There are no words that can possibly express how we feel," Randy and Amy Loughner wrote in a statement handed to reporters waiting outside their house. "We wish that there were, so we could make you feel better. We don’t understand why this happened.

"We care very deeply about the victims and their families. We are so very sorry for their loss."

The apparent target of the attack, Giffords, 40, was able to breathe on her own Tuesday at an intensive care unit here, another hopeful sign of her progress, doctors said.

Meanwhile, several hundred mourners filled a Tuscon church for a public Mass to remember the slain and pray for the injured. As people filed in, nine young girls sang "Amazing Grace." The youngest victim of the attack, 9-year-old Christina Taylor Green, was a member of that choir.

Yvonne Ignacio, 53, went to the Mass after learning about the shooting while she was listening to a conservative talk radio Saturday.

"I am dismayed that it’s become political. That’s disrespectful to the victims and that’s why we’re here," said Ignacio, who is a tea party member.

On Wednesday, President Barack Obama will visit Arizona and give a speech honoring those killed.

In addition the new details about the hours before the shooting, interviews with those who knew Loughner or his family painted a picture of a young loner who did try to fit in.

Before everything fell apart, he went through the motions as many young men do nowadays: Living at home with his parents, working low-wage jobs at big brand stores and volunteering time doing things he liked.

None of it worked. His relationship with his parents was strained. He clashed with co-workers and police. And he couldn’t follow the rules at an animal shelter where he spent some time.

One close high school friend who requested anonymity to avoid the publicity surrounding the case said he would wait outside 10 minutes for Jared to leave the house when they were going out.

When Jared would get into the car, he’d say that it took so long because his parents were hassling him.

The parents of another close friend recalled how Loughner’s parents showed up at their doorstep in 2008 looking for their son, who had left home about a week before and broken off contact.

While the friend, Zach Osler, didn’t want to talk with the AP, his parents Roxanne and George Osler IV did.

With the Loughners at their house, Zach Osler told them the name of the local hotel where their only child was staying, Zach’s father said. Jared moved back in, he said.

After that, Osler’s dad sometimes would see Mrs. Loughner at the local supermarket, though they didn’t chat much. He recalled that every time he saw her she had at least one 30-pack of beer in her cart.

Loughner, now 22, would come over several times a week from 2007 to 2008, the Oslers said.

The boys listened to the heavy metal band Slipknot and progressive rockers The Mars Volta, studied the form of meditative movement called tai chi, and watched and discussed movies.

Loughner’s favorites included little-known conspiracy theory documentaries such as "Zeitgeist" and "Loose Change" as well as bigger studio productions with cult followings and themes of brainwashing, science fiction and altered states of consciousness, including "Donnie Darko" and "A Scanner Darkly."

Even in small talk, he struck the Oslers as unusual.

"He always said, ‘Hi, Mrs. Osler. How are you today?’ When he left he made a point of coming over and saying, ‘Thank you for having me over,’" said Roxanne Osler, noting that was not typical for Zach’s friends. "Jared struck me as a young man who craved attention and acceptance."

Once he shared with the Oslers a short story he had written about a reporter meeting an angel during the apocalypse.

George Osler IV read it, thought it was well written, but couldn’t identify the point.

"He seemed like he was kind of offended that I didn’t get the message," George Osler said.

Meanwhile, the unfailingly polite kid they knew was getting into trouble.

Loughner was arrested in October 2008 on a vandalism charge near Tucson after admitting that he vandalized a road sign with a magic marker, scrawling the letters "C” and "X” in a reference to what he said was Christianity.

The case was ultimately dismissed after he paid a $500 fine and completed a diversion program.

Even when Loughner tried to do good, it didn’t work out.

A year ago, he volunteered walking adoptable dogs at the county animal shelter, said Kim Janes, manager of the Pima Animal Care Center. He liked dogs; neighbors remember him as the kid they would see walking his own.

At the shelter, staff became concerned: He was allowing dogs to play in an area that was being disinfected after one had contracted a potentially deadly disease, the parvovirus.

"He didn’t think the disease was that threatening and when we tried to explain how dangerous some of the diseases are. He didn’t get it," Janes said.

He wouldn’t agree to keep dogs from the restricted area, and was asked to come back when he would. He never returned.

Loughner also jumped from paid job to job because he couldn’t get along with co-workers, according to the close high school friend who requested anonymity. Employers included a Quiznos sandwich shop and Banana Republic, the friend said.

On his application at the animal shelter, he listed customer service work at Eddie Bauer.

Loughner grew up on an unremarkable Tucson block of low-slung homes with palm trees and cactus gardens out front. Fittingly, it’s called Soledad Avenue — Spanish for solitude.

Solitude found Loughner, even when he tried to escape it. He had buddies but always fell out of touch, typically severing the friendship with a text message. Zach Osler was one such friend.

Loughner’s father moved into the house as a bachelor, and eventually got married, longtime next-door neighbor George Gayan said. Property records show Randy Loughner has lived there since 1977.

Gayan said he and Randy Loughner had "differences of opinion but nothing where it was radical or violent." He declined to provide specifics. "As time went on, they indicated they wanted privacy," Gayan said.

Unlike other homes on the block, the Loughners’ is obscured by plants. It was assessed in 2010 at $137,842.

Randy Loughner apparently has not worked for years — at least outside his home. He did fix up cars. Gayan said he had three "show cars" and two of Jared Loughner’s friends said he bought a junker 1969 orange Chevrolet Nova and made it pristine.

Amy Loughner got a job with the county parks and recreation department just before Jared was born, and since at least 2002 has been the supervisor for Roy P. Drachman Agua Caliente Park on the outskirts of the city. She earns $25.70 an hour, according to Gwyn Hatcher, Pima County’s human resources director.

"She’s worked hard, done a good job of keeping it looking good," said Charles Ford, a former Tucson City Council member who is a board member of Friends of Agua Caliente Park.

Linda McKinley, 62, has lived down the street from the Loughner family for decades and said the parents could not be nicer — but that she had misgivings about Jared as he got older.

"As a parent, my heart aches for them," she said.

She added that when she was outside watering her plants she would see Jared riding down the street on his bike, often talking to himself or yelling out randomly to no one.

Once he yelled to some children on the street: "I’m coming to get you!" McKinley said.

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Associated Press writers Alicia Chang and Gillian Flaccus in Tucson, Jacques Billeaud in Phoenix, Christy Lemire in Los Angeles and news researcher Julie Reed in Charlotte, N.C., contributed to this report.