Illustration: Aïda Amer/Axios

The surprise has now worn off on the abrupt end to the U.S.-North Korea summit in Hanoi, with the two sides disputing even the terms of what was being negotiated.

Driving the news: The U.S. side claims North Korea offered to close one nuclear facility in exchange for lifting all economic sanctions.The North Korean side claims it only wanted a partial reprieve from economic sanctions.

Why it matters: "Further progress could be difficult now that Mr. Trump has broadcast that he and Mr. Kim have staked out conflicting bottom lines," the N.Y. Times' Edward Wong reports.

The other side: "Trump could have left Hanoi with a deal of any kind just for the sake of it, but he decided that no deal was better than an insubstantial one that could hamper future negotiations," Stanford professor Gi-Wook Shin writes for Axios Expert Voices.

  • "By doing so, he not only appeared as a tough negotiator to his North Korean counterpart, but also shielded himself from the potential criticism of a bad deal, affording him more domestic political slack than the alternative might have."
  • "His decision also sends a warning signal to North Korea that he will not let the country continue to set the tone and pace for the negotiations."

Between the lines: Trump also faced a furor today over comments where he said he believes Kim Jong-un's denial about the mistreatment of Otto Warmbier, the U.S. student who was in a coma when released by North Korea and died shortly after returning home.

  • "He felt badly about it. He felt very badly," Trump said today. "He tells me that he didn't know about it and I will take him at his word."
  • "I don't think that the top leadership knew about it ... I don't believe that he [Kim] would have allowed that to happen."
  • Flashback to January 2018: "You are powerful witnesses to a menace that threatens our world, and your strength inspires us all," Trump told Warmbier's parents during the State of the Union.
  • Former U.N. ambassador Nikki Haley today: "Americans know the cruelty that was placed on Otto Warmbier by the North Korean regime. Our hearts are with the Warmbier family for their strength and courage. We will never forget Otto."

The bottom line: Diplomacy is happening and the freeze in nuclear tests will continue, North Korea confirmed today. But that's about it.

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Why it matters: He was arrested under the new national security law that gives Beijing more powers over the former British colony. Lai is the most prominent person arrested under the law, which prompted the U.S. to sanction Chinese officials, including Hong Kong leader Carrie Lam, over Beijing's efforts to strip the territory of its autonomy.

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Why it matters: It's the lowest single-day positive rate since the start of the pandemic. It's another sign that the state that was once a global coronavirus epicenter is curbing the spread of the virus. "Our daily numbers remain low and steady, despite increasing infection rates across the country, and even in our region," Cuomo said in a statement. "But we must not become complacent: Everyone should continue to wear their masks and socially distance."

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