President Donald Trump made at times outlandish claims about the safety of American voting systems in a White House address on Thursday night, drawing selectively from documents his aides published online to falsely claim elections were “rigged” and “stolen.”

Trump, who has in recent months increasingly pressed his yearslong and unsubstantiated argument that the outcomes of U.S. elections have been tampered with, also laid out a purported effort by the Chinese government to undermine him in 2019. But the documents posted by the White House, although heavily redacted, were far more guarded in their conclusions.

Despite dozens of investigations, audits, recounts and court proceedings at the local, state and federal levels that have failed to produce examples of major voter fraud, Trump has long claimed the 2020 election was rigged against him. Trump’s fixation on the 2020 election — which he lost by some 7 million votes during the coronavirus pandemic — was a recurring theme in the 2024 race. He has called his victory that year over Joe Biden’s vice president, Kamala Harris, “too big to rig.”

There has never been any public evidence to corroborate claims by Trump and his allies of foreign manipulation either in the casting or tabulation of votes in the 2020 contest, or other recent elections, or of significant fraud involving paper ballots. Some of the top officials during Trump’s first term — including his attorney general, William P. Barr — said following his defeat in 2020 that there was no evidence of widespread fraud.

Here’s what else to know:

• Michigan: Trump discussed documents regarding an investigation into a voter registration group in Muskegon, Michigan, that he said were just declassified, although the investigation itself has long been known to the public. In the documents, which had not previously been made public, former employees of the organization said they were encouraged to fill out fake information on voter registration forms in order to achieve quotas and get paid. But in October 2020, the local clerk there said hundreds of “irregular” applications had been caught, and none of them had resulted in any ballots being sent out incorrectly.

• Venezuela: Trump overstated, again, what newly declassified documents said about Venezuela’s ability to rig vote counts. Documents posted by the White House featured an analysis by the CIA that found that officials there had “some capability in manipulating electronic voting systems” to influence the outcomes of races in Venezuela, but determined that the Venezuelan government did not have the ability to rig elections outside its own country.

• Election Security: Repeated investigations and audits have debunked claims by the president and his allies of widespread fraud or manipulation of votes, whether by foreign powers or officials at the state or federal levels, in 2020 or other elections. Federal officials have over the years highlighted some genuine concerns around election vulnerabilities, particularly as they related to foreign influence actors; however, Trump’s false claims have at times either exaggerated or obscured those concerns.

This article originally appeared in The New York Times.