(NEW YORK) — Data scientists and independent election observers have claimed statistical analysis suggests there was massive falsification of votes in a referendum this week that overwhelming approved constitutional changes to grant Russian President Vladimir Putin the right to extend his rule until 2036.

The week-long referendum on a package of constitutional amendments that “reset” Putin’s term limits concluded in Russia on Wednesday with a result hailed by the Kremlin as a “triumph.” The official tally showed 77.92% of voters backing the amendments and 21.27% against, with a turnout of 65%.

Those numbers are significantly above what most independent political observers and pollsters said would be realistic to expect. The Kremlin’s spokesman, Dmitry Peskov, a day later declared it a “triumphant referendum on confidence” in Putin.

But independent election observers and opposition figures have said the size of the result actually was the product of unprecedented fraud made possible because the vote was deliberately held without the legal safeguards typically applied to voting in Russia.

Roman Udot, who’s monitored Russian elections for two decades and runs Golos, a nongovernmental organization that collects reports of possible ballot fraud, told ABC News a day after voting ended: “The falsification that was found yesterday, it was the national record since the fall of the Soviet Union.”

A prominent Russian physicist, Sergey Shpilkin, on Thursday published what he said was statistical evidence showing results of the referendum far more dubious than in previous contests under Putin.

Shpilkin previously suggested there’s a clear indicator of fraud: If polling stations with abnormally high turnouts also return unusually high results that favor of one outcome, that correlation indicates either ballot stuffing or that voters were pressured into voting a certain way.

The indicator is clearly visible in graphs tracking voting results. In manipulated votes, according to the theory, there will be a spike in the number of ballots for the desired result around turnouts that exceed the average. In fair votes, results are expected to grow proportionally and remain relatively flat across polling sites.

In graphs posted by Shpilkin, using data from the constitutional referendum that compares results with turnout, there’s a huge spike in votes in favor of the amendments among turnouts 70% or greater.

Shpilkin’s analysis of 88 million votes shows many polling stations with above average turnouts returned results favoring the amendments of nearly 100%. The correlation is particularly strong in Russia’s most authoritarian regions, such as Chechnya, which reported a turnout of 95%, with over 97% of votes in favor.

His evidence suggests that as many as 22 million votes — roughly 1 in 4 — may have been cast fraudulently, he told Forbes Russia on Thursday.

Shpilkin said he estimated the real turnout was likely 44%, not 65%. He calculated the real percentage of votes in favor of the amendments to be around 65%, compared with 35% against.

When compared to the actual, lower turnout, that meant only around 29% of Russia’s eligible voters — about 31 million people — supported the amendments, he wrote. Many opponents also boycotted the vote in protest, suggesting the real number of those against the changes likely was higher still.

Shpilkin has conducted similar analysis for other votes in Russia, including Putin’s 2018 presidential election and the 2011 parliamentary elections during which ballot stuffing was so egregious it prompted mass street demonstrations.

In an article for Proekt, he wrote that the falsification seen in the referendum “exceeded anything seen before” in recent Russian elections, calling it an “unprecedented situation.”

Russia’s elections commission and Interior ministry have said the vote took place without any serious violations. The head of the elections commission, Ella Pamfilova, praised the voting process, saying it took place “with maximum openness.”

“The vote happened fairly, the results are reliable and the legitimacy of the results of the vote are indisputable,” she said at a briefing on Saturday.

Before the vote, the Kremlin had portrayed the referendum as largely unrelated to Putin’s future, saying the constitution needed to be updated to reflect modern Russian society. Russians were asked to vote a single “yes” or “no” on an entire package containing more than 200 amendments, including social welfare guarantees as well as insertions meant to attract conservative voters, such as a ban on same-sex marriage.

The key amendment, however, reset the count on Putin’s presidential terms from four to zero, meaning he’ll be able to run for two more six-year terms in 2024 when he otherwise would have had to step aside. Assuming he’s victorious in those races, Putin, who’s been in power for 20 years and would be ruling while in his 80s, would be the longest-ruling leader in Russian history.

The amendments in reality already had been approved by Russia’s parliament and the referendum had little legal force. It was meant to provide a stamp of legitimacy to the changes, however, so authorities sought a high turnout. Before the vote, independent Russian media reported regional authorities had received instructions from Putin’s administration to deliver a resounding result, with a turnout of at least 55%.

That posed a challenge because independent polling showed many Russians were indifferent to the vote, amid a long-term erosion in Putin’s approval ratings. A survey by the state polling agency VTsIOM in May showed fewer than 28% of Russians “trust” Putin, down from over 47% in just two years.

The week of the vote, Denis Volkov, deputy director of the Levada Center, Russia’s only non-government polling agency, told ABC News that his polling suggested Putin’s decision to reset his term limits was highly divisive among Russians, with around 40% supporting it and 30% opposing it. That number shifted in the Kremlin’s favor when looking at those who intended to vote — Volkov said at the time he believed a 55% turnout would be “rather good” for the authorities.

The Kremlin arranged an “ad-hoc” vote, which didn’t meet criteria to make it a legal referendum, meaning it was not obliged to adhere to strict measures intended to prevent fraud. Election monitors said that resulted in a situation where monitoring the vote was impossible.

The referendum was held over seven days, in what authorities said was to facilitate social distancing amid Russia’s worsening coronavirus epidemic. Far more people also were allowed to vote from home or at workplaces, and in Moscow and St. Petersburg online voting was encouraged.

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Election monitors like Udot said those adjustments greatly facilitated fraud. Ballots were kept in polling stations overnight without observers. An election commission member in Moscow told The Associated Press last week he was seeing hundreds more votes being brought from alleged “home voters” than was feasibly possible.

“Their hands were untied,” Udot said, saying he had never seen anything like it.

His organization, Golos said, has received 2,100 reports of violations.

Alongside allegations of ballot stuffing, there were widespread reports of public sector workers being pressured into voting. State companies received instructions directing them to ensure employees voted, according to news outlets including Reuters. Some voters told journalists they had been registered to vote by their employers without their knowledge.

Reuters sent journalists to monitor a polling station in a Moscow suburb for seven days. Its official turnout was 43%. But average turnout for the rest of the suburb where it was located was 83%. And in two polling stations located in the same school building, but where Reuters did not have observers, the turnouts were 87% and 85%.

Those trying to monitor the vote also sometimes encountered resistance, Reuters reported. A journalist in St. Petersburg had his arm broken as police tried to remove him from a polling station where alleged fraud was reported.

As Udot came to meet with ABC News on Thursday he was ambushed by a crew from a pro-Kremlin television channel, NTV. The channel frequently produces highly edited reports smearing Kremlin critics as Western agents. The reporters harassed Udot for an hour, asking him why he was talking with American journalists. Udot said he was forced to call the police to intervene.

Shortly thereafter, NTV published a report falsely suggesting Udot had attacked the network’s own journalist.

“It happens every time after and before elections,” he told ABC News afterwards. “Our phones are tapped — when we agree to a meeting with foreign diplomats or journalists, all of a sudden a TV crew or some stringer will appear.”

“We are showing the truth,” he added. “And that truth destroys their house of cards. That is why we are attacked.”

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