Meanwhile, police have released a detailed timeline of his movements around the city, and say the suspect the mystery man fled the city by bus very soon after carrying out his premeditated crime on Wednesday morning. 

At 6:44 am, the suspect shot the 50-year-old Thompson -- who was arriving at the New York Hilton Midtown for an investors' meeting -- in the back and leg before leaving first by foot, then using an e-bike he rode through Central Park. Police think he entered the park by riding north up 6th Avenue, and then exited the park at West 77th Street -- minus the backpack he wore before and during the killing and as he rolled into the park.

Concluding the pack was likely somewhere in the park -- and within it, perhaps the murder weapon -- NYPD assigned more than 100 police officers to comb the 840-acre expanse. They hit paydirt, with the New York Post reporting that cops found the apparent backpack in a treed area south of the Carousel near Heckscher Playground near Central Park South.

So far, police haven't leaked anything about the contents of the backpack, which appears to be an Everyday Backpack sold by Peak Designs between 2016 and 2019. Marketed for use by photographers but also used by others, the latest version goes for about $250. Police have yet to find the killer's getaway bike, which he seems to have abandoned somewhere after he exited Central Park and before he made his way to a bus station.

On Friday, police provided their most detailed accounting yet of the suspect's moves around New York City since he arrived on a Greyhound bus 10 days before carrying out the killing -- along with what they've learned from questioning of witnesses, including people who stayed at the same hostel he did: 

Friday, Nov 24: The Killer Arrives

Suspect arrives in New York City at 10:11 pm on a Greyhound bus that originated in Atlanta and made six or seven stops along its journey. Police are unsure where he got on. He immediately takes a cab to the site of the assassination -- the New York Hilton Midtown -- and walks around the area for a half hour before heading to the HI New York City Hostel at Amsterdam Avenue and West 103rd Street, on the Upper West Side near Central Park.

Per earlier reports, the suspect was said to have checked out of the hostel on Friday, Nov. 29, only to return and check back in the very next day. However, police now say the check-out appears to have only happened via an administrative entry in the hostel's systems, and that the suspect actually stayed there for all the 10 days before the attack.