AMNA NAWAZ: Police today said fingerprints and shell casings collected at the scene of last week's murder of UnitedHealthcare CEO Brian Thompson are directly connected to their prime suspect, Luigi Mangione.

The fingerprints match the 26-year-old and the casings match the gun found on him when he was arrested earlier this week in Pennsylvania.

To break down the latest, I'm joined now by William Brangham in New York.

So, William, we have this new evidence now linking the alleged shooter here to the crime.

Police also say that they're in possession of some notes written by him.

What kind of insight is that giving us?

What have we learned, and especially as it relates to motive in this case?

WILLIAM BRANGHAM: That's right, Amna.

Police have at least two different pieces of writing from this suspect.

One is a notebook that is allegedly full of planning details.

And the other is what people have been calling his manifesto.

It's a 260-word handwritten document where, reportedly, he takes credit and claims responsibility for this killing.

Now, the police have not released that manifesto in its entirety.

One journalist claims to have a copy of it, and he's posted it on his Web site, and it is now floating all over the Internet.

But what we know from police sources, details of that, is that the suspect describes the killing as a - - quote -- "symbolic takedown" and generally expresses his now well-documented fury and anger at the health care industry in general.

And that is what has been -- as we have reported, resonated with so many people who seem willing to look past the grisly murderer and still side with him in their complaints as far as health insurance is run in this country.

The notebook that the police have described some of the planning process, reportedly, that he's going to go after an as-yet unnamed health care CEO at a meeting, that that would be -- quote -- "targeted, precise," and it would -- doesn't risk innocents, which apparently the suspect thought about using a bomb at one point, but decided that might injure too many other people that he didn't want to target.

But for right now, the suspect is still in custody in Pennsylvania.

He's fighting extradition, where he would come to New York City to face that serious murder charge.

AMNA NAWAZ: And, William, given that Brian Thompson, the victim here, the 50-year-old father of two, was a health insurance executive, there have been some making the connection between that, the work that he did, and also the reporting around the suspect in this case, who allegedly had a serious back injury and some back pain he was dealing with.

What do we know about that connection?

WILLIAM BRANGHAM: That's right.

For a long period of time, the suspect wrote on the Web site Reddit about his back problems, how it started in his 20s, how he suffered an injury surfing in Hawaii that made it worse, how he had spinal surgery to try to address it.

All those writings have been taken down, but journalists have read some archived versions of them.

In those writings, there is no indication of violent or ill intent towards health care workers or the industry in general, but, again, sort of documents his frustration with that system more broadly.

AMNA NAWAZ: There's another reported detail in the suspect's case here, William.

That is that he once reportedly expressed admiration for Ted Kaczynski, the man known as the Unabomber.

What should we know about that?

WILLIAM BRANGHAM: That's right.

This suspect apparently posted a lot of book reviews on the Web site called Goodreads.

And among them was him giving four stars to Ted Kaczynski, the Unabomber's manifesto.

For people who are old enough to remember, Ted Kaczynski sent mail bombs all around the country, murdered three people, and hurt dozens of other people, but wanted those attacks to draw attention to his manifesto, which was a critique of industrialization and the technological revolution that we were living through.

And that is why some police officials believe that this suspect might have been inspired by Kaczynski, who, as I'm saying, used violence to draw attention to his political beliefs.

AMNA NAWAZ: All right, that is William Brangham with the latest on the killing of that UnitedHealthcare CEO.

William, thank you.

WILLIAM BRANGHAM: Thanks, Amna.