Yet despite the exhaustive interviews, and a trove of online videos and entries to message boards on gaming Web sites that Loughner made over the years, investigators have been unable to understand what cause him to allegedly erupt into the shocking outburst of violence. Investigators also have yet to nail down why Loughner allegedly targeted Giffords and have not learned of any interaction between the two beyond an event in 2007 at which Loughner asked Giffords a question.

“I haven’t seen anything that says somebody knows, somebody heard him say something, that gave an indication of a path to violence,” the senior federal official said.

An Arizona state legislator who was briefed on the investigation said officials have a good timeline of Loughner’s movements on the day of the killing and before it.

“But I don’t think they have anything with regard to his state of mind because he isn’t talking and the family is very stand-offish,” added the legislator, who spoke on the condition of anonymity because the briefing was private. “They’re not a very tight-knit family, and they’re not able to get into his state of mind without him talking. There’s hope that after a while he might be open to discussion.”