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TMZ has received a 4th email from the man claiming to know who kidnapped Nancy Guthrie and where she is ... and we have a proposition for that person.

The email -- with the same bitcoin account as the other 3 notes -- says in part, "I know what I saw 5 days ago south of the border and I was told to shut up so I know who he is and that was definitely Nancy with them."

This is the second reference he's made to there being more than one person involved in the purported abduction. In the third letter, received by TMZ on Friday, he said, "... be prepared to go International."

10:09 AM PT -- The Pima County Sheriff's Department disputed the report, saying ... "PCSD has never stated that this was a burglary gone wrong. Any reports indicating otherwise are inaccurate. This remains a very active investigation."

There’s a major new development in the Nancy Guthrie case ... authorities now reportedly believe her kidnapping may have stemmed from a burglary gone wrong.

According to AZFamily, citing an inside source, Savannah Guthrie's mother is believed to have been abducted during a botched home invasion -- instead of a carefully planned abduction.

What's more ... the source also tells the outlet there is belief among investigators that Nancy could be alive.

The theory comes on the heels of the FBI's announcement that DNA was recovered from a glove found near the scene ... the glove appears to visually match the gloves worn by the alleged perpetrator. As you know, the masked intruder was caught on a doorbell camera lurking around Nancy's home just before she was abducted on February 1.

Tragedy in Las Vegas ... a mother allegedly shot and killed her 11-year-old cheerleader daughter before turning the gun on herself in a suspected murder-suicide.

Cops say 38-year-old Tawnia McGeehan and her daughter, Addi Smith, were found dead Sunday in a room at the Rio Hotel & Casino, with what appeared to be a suicide note left behind.

The Utah mom and daughter were in town for a cheer competition ... but when they didn’t show, their team, Utah Xtreme Cheer, sounded the alarm on social media, asking for help finding them.

Jaylen Brown says Beverly Hills screwed up -- and he’s not staying quiet about it.

Beverly Hills police shut down his All-Star Weekend panel event on Saturday night, and the Celtics star isn't holding back ... going scorched earth on the city following Sunday's All-Star Game festivities.

“Beverly Hills is so trash," Brown posted to X. "I’m offended had a great panel about the future of culture with great guest people worked hard for this how dare yall.”

He then tagged the city's police department ... saying "300k down the drain."

It wasn't the first time Brown -- who started for runner-up Team USA Stripes in the All-Star Game -- went in on Bev Hills this weekend ... after organizers suggested he applied for a permit, was denied, and moved forward anyway.

He says that version is flat-out wrong.

Pima County Sheriff Chris Nanos isn't taking any crap from people criticizing how he and his investigators are handling the Nancy Guthrie kidnapping.

On Sunday, Nanos was interviewed by a Daily Mail reporter about the case and, at one point, their convo turned to the sheriff's critics, who have slammed him and his detectives for allegedly packing up and leaving the crime scene early.

But Nanos stood his ground, insisting his officers thoroughly investigated Guthrie's property and he feels confident they did their job properly before the FBI swooped in and did another sweep.

The sheriff noted, "My officers were there for almost 20 hours, and they processed their scene, got it done, and brought in all the evidence." Nanos then said the FBI came in and "did their thing."

Authorities are using advanced Bluetooth detection technology as part of the search for Nancy Guthrie, who has been missing for two weeks.

A Pima County Sheriff's Department helicopter has been flying in a low, methodical grid pattern over the Tucson area near Guthrie’s home in an effort to detect a signal from her pacemaker, according to Fox News. Investigators are using specialized equipment capable of identifying nearby Bluetooth-enabled devices.

Guthrie was last seen around 9:30 PM on January 31 and was reported missing February 1. According to reports, her pacemaker disconnected from its companion phone app shortly before 2 AM on February 1. Around the same time, her Nest home security camera also went offline.

The investigation into Nancy Guthrie's case just took a major forensic turn ... TMZ has confirmed.

An FBI spokesperson tells TMZ ... a glove recovered in the case appears to visually match the gloves worn by the unidentified subject captured on the security camera footage released from Nancy's front door camera ... and DNA found inside the glove has been sent for analysis.

According to the feds, investigators collected roughly 16 gloves scattered around areas near the house. But authorities say most of those belonged to volunteer searchers who tossed them aside while combing the neighborhood.

Nancy Guthrie could be found one hour from now ... or it could take weeks ... or even years to locate her.

Pima County Sheriff Chris Nanos made the sobering remarks in a recent interview with the New York Times, underscoring the very real possibility Nancy's kidnapping case could drag on for quite some time.

But Nanos also assured the public that investigators will ultimately "find" the suspect, or suspects, responsible for abducting Nancy from her Tucson, Arizona, home in the wee hours of February 1.

Nancy Guthrie's kidnapper has eluded authorities for 2 weeks, but the ransom note TMZ received is of intense interest to the FBI, and Harvey Levin and Mark Geragos both agree ... it may be the key to cracking the case.

H&M's latest "2 Angry Men" podcast makes it clear ... the FBI is laser focused on that ransom letter, for reasons we cannot publicly discuss. They are also interested in the man who has sent TMZ 3 demand emails asking for bitcoin in return for giving up the kidnapper's name. BTW ... the man says the kidnapper is the "main individual" -- meaning there's more than one person involved.

Law enforcement's dramatic move Friday night apparently did not yield results, but there are a number of clues, including unknown DNA found in Nancy's house. It's currently being analyzed.

The swat operation Friday night -- leading to the detention of a driver in the Tucson area and the search of a home -- appears to be something other than a direct lead from the ransom note TMZ received.

Harvey Levin appeared on CNN Saturday morning, breaking down the limited information we know at this time. A law enforcement source involved in the investigation told him this morning neither the ransom note we received nor the reward demand emails we received were the trigger for last night's action.

We have not confirmed, but it appears ... the main target last night was someone in a vehicle in the Tucson area. Again, it appears but is not confirmed ... the search of the house is connected to the traffic stop. 2 people were taken out of the house, and it was searched for several hours.

Police reportedly detained at least 3 people in connection with the Nancy Guthrie kidnapping ... and now we're seeing the first image of a man in handcuffs.

FOX News Digital obtained the photo showing the man sitting half in and half out of a Pima County Sheriff vehicle surrounded by law enforcement in Tucson, Arizona, on Friday night. The man's hands are cuffed in front of him with a hoodie partially covering his face.

Sources told FOX ... Pima County deputies pulled the man over in a Range Rover during a traffic stop in the parking lot of a Culver's restaurant about 2 miles from Nancy's home.

11 AM PST -- The Prima County Sheriff's Office tells TMZ ... "Last night, a federal court-ordered search warrant was executed at a residence near E. Orange Grove Rd. and N. First Ave. in connection with the Guthrie case. The warrant was based on a lead we received. No arrests were made."

They add ... "A traffic stop was also conducted, and a person was questioned but no arrests resulted from that incident. There are no further details available at this time."

Federal agents in Arizona may have snagged another crucial lead in the search for Nancy Guthrie ... because cops were seen poking around a potential vehicle of interest at a Tucson restaurant near her home Friday night.

Another clue about Nancy Guthrie's potential kidnapper is tucked into an email from a man who claims he knows the individual who abducted Nancy ... and it sounds like the suspect may have crossed the border.

The latest money demand sent to TMZ ends with this ... "for the man hunt of the main individual that can give you all the answers and be prepared to go International."

It sounds to us like the guy demanding the $100,000 FBI reward implies that Nancy's kidnapper is hiding out in Mexico.

Nancy was abducted from her home near Tucson, Arizona ... and Mexico is a short drive south.

It's unlikely the kidnappers would have taken Nancy on a commercial jet ... that would require ID and the jig would be up. Plus, a previous ransom note sent by the alleged kidnapper themselves indicated Nancy was within a 700-mile radius of Tucson, which further supports the theory this kidnapper may be in Mexico.

Our sources tell us the FBI is hyper focused on the ransom note we received ... and they're also very interested in this latest batch of emails demanding bitcoin in return for information on Nancy's kidnapper.

The phrase "the main individual" is also significant ... it clearly suggest there are accomplices.

TMZ just received a third email from the man who claims he knows the identity of Nancy Guthrie's kidnapper ... and he has upped his price.

The email says he's contacting TMZ because he doesn't trust law enforcement. He's essentially using TMZ as an intermediary, telling authorities -- you don't trust me, and I don't trust you.

He suggests the reward being doubled to $100,000 was a move designed "to discredit me."

Nancy Guthrie's family has taken to social media to beg for her return ... but cops say that doesn't mean they've been cleared of wrongdoing yet -- because no one has.

Pima County Sheriff Chris Nanos sat down with Briana Whitney -- a true-crime reporter for Arizona's KTVK-TV -- who asked him if Nancy's fam has officially been cleared in her Tucson-area disappearance.

Sheriff Nanos explains that everyone -- Nancy's family especially -- has been cooperating with the investigation ... including giving statements and submitting to DNA testing.

New video's surfaced in the search for Nancy Guthrie's kidnappers ... a man in Tucson with a goatee, who creepily approached a doorbell camera one week before Nancy was taken, and TMZ has learned cops are giving it a hard look.

The video was originally posted January 23 on Ring's Neighbors app, and it shows the guy intentionally backing up to the front door of a home about 6.5 miles from where Savannah Guthrie's mother lives.

The man clearly didn't want to be seen, but the camera still got a good shot of him as he rang the doorbell around 5 AM. The homeowner who posted the vid says the would-be intruder fled when their dogs started barking.