WASHINGTON (AP) — Eager for a historic trade agreement, President Donald Trump is claiming done deals with China that aren't measuring up to the hype.

He describes last week's meeting with Chinese President Xi Jinping in Buenos Aires, Argentina, as "extraordinary" and a "big leap forward." China, however, has provided few details and little confirmation about what it actually agreed to do in regard to buying more American products and addressing the Trump administration's assertions that Beijing steals American technology.

Trump claimed that China had agreed to reduce or eliminate its 40 percent tariffs on cars imported from the U.S. His top economic adviser, Larry Kudlow, acknowledged no deal had been "signed and sealed and delivered yet."

The statements marked a week when Trump also claimed without evidence for a second time that Paris protesters were chanting support for him, grossly overstated the costs of illegal immigration and derided U.S. weapons spending as crazy, despite earlier boasts about increasing the military budget.

Meanwhile, Democratic Rep.-elect Alexandria Ocasio-Cortez ignored reality when she suggested the Pentagon has a hidden pot of $21 trillion that could help pay for "Medicare for All." The total defense budget during the period in question only totaled $9 trillion.

A look at the claims and the facts:

PARIS

TRUMP: "The Paris Agreement isn't working out so well for Paris. Protests and riots all over France. People do not want to pay large sums of money, much to third world countries (that are questionably run), in order to maybe protect the environment. Chanting "We Want Trump!" Love France." — tweet Saturday.

THE FACTS: Neither Associated Press journalists covering protests in the city nor any French television networks have shown evidence that supporters were chanting any slogans in support of Trump. The protests that began as a revolt against a gas tax increase have turned increasingly violent and France imposed exceptional security measures Saturday to prevent a repeat of rioting a week ago.

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JERUSALEM

TRUMP: "We quickly moved the American embassy to Jerusalem and we got it built."— remarks Thursday at Hanukkah event.

THE FACTS: Nothing's been built yet. The Trump administration designated an existing U.S. consular facility in Jerusalem for the U.S. Embassy, retrofitting some offices and holding a big dedication ceremony in May. The U.S. has yet to identify a permanent site for the new embassy, a process that is expected to take years. The State Department has estimated that constructing a new embassy would cost more than $500 million.

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TARIFFS

TRUMP: "China has agreed to reduce and remove tariffs on cars coming into China from the U.S. Currently the tariff is 40%." — tweet Sunday.

THE FACTS: Nearly a week later, it's still not clear if this will happen. When asked about the matter, Kudlow would only say that he hoped China would remove its tariffs on U.S. autos. "We don't yet have a specific agreement on that, but I will just tell you, as an involved participant, we expect those tariffs to go to zero," he told reporters on Monday. Pressed again Tuesday, Kudlow told "Fox and Friends" that he expected China to move quickly on removing the tariffs "if they're serious about this."

"I think it's coming, OK?" he said. "It hasn't been signed and sealed and delivered yet."

The White House's confusing and conflicting words have left Wall Street skeptical.

"It doesn't seem like anything was actually agreed to at the dinner and White House officials are contorting themselves into pretzels to reconcile Trump's tweets (which seem if not completely fabricated then grossly exaggerated) with reality," JPMorgan told investors in a trading note.

On Thursday, a Chinese official said that China will "immediately implement the consensus reached by the two sides on farm products, cars and energy," but did not address the auto tariffs specifically or provide any additional details.

Trump has cast doubt on whether a firm agreement had been reached, tweeting Tuesday that his administration will determine "whether or not a REAL deal with China is actually possible."

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TRUMP: "I am a Tariff Man. When people or countries come in to raid the great wealth of our Nation, I want them to pay for the privilege of doing so. It will always be the best way to max out our economic power. We are right now taking in $billions in Tariffs. MAKE AMERICA RICH AGAIN." — tweet Tuesday.

THE FACTS: Trump seems to be claiming that tariffs are some kind of a membership fee for foreign companies to trade in the U.S. economy.

They're not. Tariffs are a tax, per Article I, Section 8 of the Constitution.

The costs of this tax are borne by U.S. consumers and businesses, often in the form of higher prices. Foreign companies may end up selling fewer goods and services if the United States imposes high tariffs. So they pay a price, too.

In some cases, the tariffs exist to protect industries that are vital for national security. Or, the tariffs exist to retaliate against the trade practices of other countries. Or, they might protect politically connected companies.

In the past, White House aides have insisted that Trump's tariffs are a negotiating ploy. Yet the president offered no such qualifications on Tuesday.

Tariffs are not seen as some easy way of generating massive wealth for an economically developed nation. After Trump announced steel and aluminum tariffs earlier this year, the University of Chicago asked leading academic economists in March whether Americans would be better off because of import taxes. Not a single economist surveyed said the country would be wealthier.

Nor do the budget numbers suggest they can come anywhere close to covering the costs of the federal government.

Trump is correct that tariffs did generate $41.3 billion in tax revenues last budget year, according to the Treasury Department. But to put that in perspective, the federal budget exceeds $4.1 trillion.

The taxes collected on imports were equal to about 1 percent of all federal spending.

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MEDICARE

OCASIO-CORTEZ: "$21 TRILLION of Pentagon financial transactions 'could not be traced, documented, or explained.' $21T in Pentagon accounting errors. Medicare for All costs (tilde)$32T. That means 66% of Medicare for All could have been funded already by the Pentagon. And that's before our premiums." — tweet Sunday.

THE FACTS: Ocasio-Cortez is generally correct to suggest that one way of paying for the huge cost of "Medicare for All" would be to cut spending elsewhere. But she is wrong to suggest that there's pot of misspent defense dollars that could cover the new health care expenses. The New York Democrat also misrepresents the findings of an academic study that found the $21 trillion in Pentagon errors to be accounting "adjustments," not a tally of actual money wasted.

The study by Mark Skidmore, an economist at Michigan State University and Catherine Austin Fitts, a former assistant secretary of the Department of Housing and Urban Development, did find $21 trillion in Pentagon transactions from 1998 to 2015 that could not be verified. Their study is a cited in a Nation article retweeted in part by Ocasio-Cortez, even though that article makes clear that not "all of this $21 trillion was secret or misused funding ... the plugs are found on both the positive and the negative sides of the ledger, thus potentially netting each other out."

Total defense spending from 1998 to 2015 was $9 trillion. That means defunding the military entirely would only cover a small portion of the estimated $32 trillion cost over 10 years for the "Medicare for All" legislation by Sen. Bernie Sanders, I-Vt. Ocasio-Cortez wrongly suggests that fixing Pentagon accounting errors would net 66 percent of costs.

"What she was referencing was the total number of transactions that happened with DoD — there's a lot of double and triple counting as money gets moved around in the department," said Todd Harrison, director of defense budget analysis at the Center for Strategic and International Studies. "All of that basically means is that those transactions don't have a full trail," akin to an employee who submits an expense report without providing all the receipts.

"Just because you don't have the proper audit trail for transactions doesn't mean that those transactions are fraudulent," Harrison said.

David Norquist, the Pentagon's comptroller, has attributed the accounting errors to the department's older bookkeeping "systems that do not automatically pass data from one to the other." He said in testimony to the House Armed Services Committee in January that the errors do not amount to a pot of lost money. "I wouldn't want the taxpayer to confuse that with the loss of something like a trillion dollars, it's not. That wouldn't be accurate," Norquist said.

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MILITARY SPENDING

TRUMP: "I am certain that, at some time in the future, President Xi and I, together with President Putin of Russia, will start talking about a meaningful halt to what has become a major and uncontrollable Arms Race. The U.S. spent 716 Billion Dollars this year. Crazy!" — tweet Monday.

THE FACTS: His criticism of U.S. weapons spending as "crazy" vastly overstates the amount spent on the arms race. It also is a sudden change of tone from his previous boasts about increased military spending.

Trump's statement appeared to confuse the total Defense Department budget with America's investment in the missile defense systems and strategic nuclear weapons usually associated with the arms race. The Pentagon's budget for 2019 totals about $716 billion, but that includes everything from health care and pay for service members to the costs of the wars in Afghanistan, Iraq and Syria. The arms race is just a fraction of that amount, totaling about $10 billion this year for a wide range of missile defense and nuclear weapons programs.

Until recently, Trump has bragged about his increase in military spending, railing about what he claims is previous administrations' neglect of America's armed forces. He said his administration is "rebuilding our military." He has occasionally complained about specific programs such as Air Force One and the F-35 Joint Strike Fighter, but his criticism was leveled at the defense contractors and focused on demanding savings.

He has been far more supportive of the broader defense increases, and specifically has endorsed hikes for missile defense in line with a U.S. defense strategy that targets China and Russia as key adversaries.

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IMMIGRATION

TRUMP: "Could somebody please explain to the Democrats (we need their votes) that our Country losses (sic) 250 Billion Dollars a year on illegal immigration, not including the terrible drug flow. Top Border Security, including a Wall, is $25 Billion. Pays for itself in two months. Get it done!" — tweet Tuesday.

THE FACTS: He's inflating the cost of illegal immigration. Trump's numbers left even those sympathetic to the president's position scratching their heads.

"I'm not sure where the president got his numbers," said Dave Ray, a spokesman for the nonprofit group FAIR, the Federation for American Immigration Reform, which advocates for lower immigration numbers.

Neither the White House nor the Department of Homeland Security responded to questions about where the $250 billion estimate had come from.

The Heritage Foundation, for instance, estimated in 2013 that households headed by immigrants living in the U.S. illegally impose a net fiscal burden of around $54.5 billion per year.

Even Trump himself has contradicted the figure. During his 2016 campaign, Trump claimed that illegal immigration cost the country more than $113 billion a year — less than half the number he tweeted Tuesday.

That estimate appeared based on a paper by FAIR, which released an updated report in 2017 that claimed taxpayers "shell out approximately $134.9 billion to cover the costs incurred by the presence of more than 12.5 million illegal aliens, and about 4.2 million citizen children of illegal aliens" at the federal, state and local levels, with "a tax burden of approximately $8,075 per illegal alien family member and a total of $115,894,597,664."

The $116 million figure included services such as health care and education, as well as spending on agencies including U.S. Immigration and Customs Enforcement, minus the $19 billon the group concluded those who are living in the country illegally pay in taxes. But it also included costs associated with the children of those immigrants in its tally, even when they are U.S. citizens. The estimate was criticized for making broad generalizations and other major methodological flaws.

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FENTANYL

TRUMP, about his meeting with Xi at the gathering of leading rich and developing nations: "What he will be doing to fentanyl could be a game changer for the United States — and what fentanyl is doing to our country in terms of killing people. Because he's agreed to put it at the highest level of crime in his country." — aboard Air Force One on Dec. 1.

TRUMP: "One of the very exciting things to come out of my meeting with President Xi of China is his promise to me to criminalize the sale of deadly Fentanyl coming into the United States. It will now be considered a 'controlled substance.'" — tweet Wednesday.

THE FACTS: That's a misreading of what China agreed to do, at least as far as Chinese authorities are concerned.

Fentanyl has been a controlled substance in China for years, according to Chinese regulators. All told, China has already put 25 variants of fentanyl, plus two precursors — chemicals used to make the drug — on its list of controlled substances, Chinese foreign ministry spokesman Geng Shuang said last week.

Now, "China has decided to list all the fentanyl-like substances as controlled substances and start working to adjust related regulations," says China's foreign ministry.

Doing so could help block China's opioid merchants from skirting the law by inventing new chemical variants of fentanyl faster than regulators can declare them illegal.

The standard approach of regulating drugs one by one has failed to control the proliferation of new and deadly synthetic opioids in the United States.

In February, the U.S. said that for at least the next two years, all new chemical versions of fentanyl that weren't already regulated would be classified as illegal controlled substances. U.S. officials had been urging China to do something similar.

But China hasn't always followed through on its promises. "Similar suggestions have failed to gain approval from Chinese regulators in the past," the U.S.-China Economic and Security Review Commission said in a report last week that criticized China for "slow and ineffective" regulation of fentanyl.

In 2016, U.S. negotiators thought they had secured an agreement with Beijing that China would target U.S.-bound exports of substances that were illegal in the United States, even if they weren't illegal in China, but Beijing never implemented the policy, according to the commission, a group formed by the U.S. Congress to monitor economic relations with China.

China's new approach could indeed be game changing, as Trump said. But so far there's no timeline for implementation of the policy.

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Associated Press writers Lori Hinnant in Paris, Josh Boak, Ricardo Alonso-Zaldivar, Jill Colvin and Lolita Baldor in Washington and Erika Kinetz in Shanghai contributed to this report.

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EDITOR'S NOTE _ A look at the veracity of claims by political figures