But, with cameras of the world's press trained on them, they displayed an initial atmosphere of bonhomie as they met on the verandah of the Capella, a refurbished 19th century British regimental officers' mess. After a handshake, they were soon smiling ...
Q: What are North Korea's nuclear capabilities?
North Korea first tested a nuclear weapon in 2006, but no one is sure how many they have produced and stockpiled since then.
"The high U.S. estimate is 60 warheads total, adding 12 each year," Lewis told NBC News. "The low estimate is around 30 warheads."
Nuclear weapons have a wide range of explosive yields, and it's unclear how powerful each warhead is in North Korea's arsenal. But based on expert analyses of their subsequent nuclear tests (they've carried out six so far), the warheads have become larger and more sophisticated over time.
Their most recent test, conducted in September 2017, was especially concerning. North Korea claimed the explosion was from a hydrogen bomb, a more complicated design that requires a nuclear bomb to trigger a secondary explosion that's vastly more destructive. Experts believe the latest explosion was significantly more powerful than previous tests, but getting a precise read is difficult.
"It's very hard to estimate the actual explosive power based on just seismic signals," Lewis said.
At the same time, North Korea has made advances in its ability to deliver a nuclear warhead.
Based on observations of dozens of missile tests over the last three decades, Lewis says experts believe North Korea likely has "several hundred" short- and medium-range missiles that can potentially be launched from mobile platforms, making them harder to detect. These missiles could potentially target South Korea or Japan.
North Korean leader Kim Jong-Un inspects a Hwasong-12 ballistic rocket in 2017.AFP - Getty Images fileBut newer missiles appear to have a farther range, making their ongoing program an issue of serious concern to America and its allies. In November last year, North Korea launched a Hwasong-15, an intercontinental ballistic missile (ICBM) with a range that could potentially put the continental United States in play based on independent estimates.
"It could hit Mar-a-Lago," Lewis said. "We don't know how many of them exist."
Q: What would a deal to get rid of their nuclear program look like?
Secretary of State Mike Pompeo set the bar high last month at his swearing-in ceremony when he called for the "permanent, verifiable, irreversible dismantling of North Korea's weapons of mass destruction program." He made the same point again Monday in Singapore ahead of the summit.
But the CIA, which Pompeo ran until recently, is doubtful that North Korea will ever agree to a deal to get rid of its nuclear weapons, which its leaders see as an essential bulwark against an invasion.
Even assuming Kim agreed to Pompeo's stated demands this week, the process itself would likely be long, technically complicated and filled with potential snags. Siegfried Hecker, a Stanford professor who ran the Los Alamos weapons program and has toured North Korea's nuclear facilities multiple times, has estimated it would take 15 years.
It's a far cry from Trump's claim that he doesn't need to prepare much for his meeting because he'll know "very quickly" whether a deal is at hand.
Lewis thinks it's possible to progress faster if North Korea is determined to cooperate, but at the very least it would be a "multi-year process" with endless possibilities for scientific hurdles or diplomatic impasses over how to carry out denuclearization.
"The North Koreans would first have to make a declaration of all their holdings," Lewis said. "We would then have to verify that declaration, which means being able to visit all their facilities, all their military units, and inspecting them in order to ensure the declaration was complete and correct."
Negotiations over which inspections are allowed and under what circumstances have been highly contentious in the past. But assuming they move past this point, they'd have to then get to work destroying North Korea's nuclear stockpile.
That's also a difficult task: Depending on the design, nuclear weapons can be dangerous to dismantle and American experts would likely have to work closely with the scientists who engineered them to complete the process safely from within North Korea. While unlikely to trigger a nuclear detonation, an accident could still produce a large conventional explosion that sends nuclear material flying. Once removed, the nuclear material would have to be safely taken away and diluted.
There is some precedent for this process. The United States and Russia worked together to remove nuclear weapons and material from former Soviet-controlled nations at the end of the Cold War.
The next big task is dismantling the facilities used to manufacture nuclear weapons. North Korea has a nuclear reactor at Yongbyon and it's possible they have hidden sites as well. In addition to the technical challenges of shutting down and dismantling the facility and related weapons factories, there would be intense talks about which capabilities North Korea could retain that also have conventional military or civilian use and how to verify they're not being used for a covert nuclear program instead.
Q: What happened to prior negotiations?
Trump may be the first sitting president to meet North Korea's leader, but he won't be the first to try to negotiate over their nuclear program. Previous efforts have all ended in failure, which helps explain why outside experts are so skeptical of progress.
The running thread through the talks, according to Lewis, is that North Korea was "always willing to freeze their program and promise at a later date to give things up," while reaching a deal to permanently roll back their capability proved too much.
North Korea allowed international inspectors in to its Yongbyon facility in 1992, but it evolved into a tense standoff over the extent of their ability to review the site. In 1994, the Clinton administration negotiated a new framework that would freeze North Korea's plutonium program in exchange for fuel shipments and allowing the regime to operate light-water nuclear reactors that are more difficult to use for nuclear weapons production. Starting in 1999, the U.S. also eased sanctions in exchange for a freeze on its long-range missile program while they worked on a broader agreement.
Relations broke down during the Bush administration, however, especially after U.S. officials announced in 2002 that North Korea had admitted to a secret uranium enrichment program that provided an alternate path to a weapon. Tensions had also risen over U.S. fuel shipments to North Korea, which were a contentious issue in Congress and sometimes delayed. North Korea withdrew from the Nuclear Non-Proliferation Treaty in 2003 and tested its first weapon in 2006.
The Bush administration held further talks between North Korea along with China, Russia, South Korea and Japan, but those failed to produce a lasting agreement. Similar to Pompeo, U.S. officials set a goal of "complete, verifiable, irreversible dismantlement" which became its own acronym in arms control circles, "CVID."
The U.S. clashed over how to verify a deal and North Korea eventually withdrew from discussions and restarted missile tests in 2009.
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