Rumours have swirled in Beijing in recent weeks that China’s seemingly invincible leader, Xi Jinping, is in trouble, dogged by a protracted trade war with the US, a slowing economy and a public health scandal involving thousands of defective vaccines given to children.

Xi’s name seemed to have disappeared for a while from the cover of the People’s Daily, replaced with articles about his deputy, Li Keqiang, and large portraits of him were said to have been taken down after a young woman filmed herself throwing ink at his image.

No. 1 will rest while Ocean takes over the military Cryptic slogan on internet

On 13 July, online reports claimed there was gunfire in central Beijing as a coup unfolded. A cryptic slogan emerged online: “No. 1 will rest while Ocean takes over the military,” a reference to a rival politician taking power.

For now, Xi remains in full control of the government and party, and mentions of him in state-run media are as frequent as ever, but the hearsay is a sign all is not right with China’s most powerful leader in decades.

“Such rumours may well lack credibility, but they do offer some indication that the disharmony within China’s party elite is increasing ,” the Hong Kong political analyst Lee Yee wrote in in the online journal China Heritage.

This week, an essay by a law professor at Tsinghua University, one of the country’s top schools, made the rounds on Chinese social media. The essay - Our dread now and our hopes - by Xu Zhangrun offered one of the most direct criticisms of the Chinese government under Xi’s direction.

Referring to Xi only as “that official”, Xu accused him of reversing years of reforms, effectively returning China to an era of totalitarian politics and a style of dictatorship last seen under Mao Zedong.

“After 40 years of reform, overnight we’re back to the ancien régime,” he wrote, calling for the return of term limits, abolished under Xi earlier this year, the rehabilitation of those punished for the 4 June pro-democracy protests crushed by the government and an end to the cult of personality surrounding Xi.

“The party is going to great lengths to create a new idol, and in the process it is offering up to the world an image of China as modern totalitarianism,” he wrote.

Xu is one among several intellectuals voicing dissent. Sun Wenguang, a retired professor at Shandong University published an essay in July urging Xi to stop spending money abroad on projects such as the Belt and Road initiative, and spend it at home instead. He was later detained by Chinese security while giving an interview to Voice of America.

“For the first time since Xi Jinping gained power in 2012, he is facing a pushback from within the party, from liberal intellectuals and so forth,” said Willy Lam, a senior fellow at the Jamestown Foundation and adjunct professor at the Center for China Studies at the Chinese University of Hong Kong.

The pushback is also emerging in other ways. A group of alumni from Tsinghua published an open letter on Wednesday calling for the sacking of a professor over his claims China had emerged as the world’s top superpower.

Hu Angang, who claimed in a series of speeches that China had surpassed the US in economic strength and technological know-how, is one of many who have echoed Xi’s claims that China has entered a new era of power on the world stage, reversing his predecessors’ more muted global aspirations.

“[Hu] misleads government policy, confuses the public, causes other countries to be overly cautious about China and for neighbours to be afraid of China. Overall, it does harm to the country and its people,” the former students said, according to images of the letter posted online.

Such criticism is an indirect rebuke of Xi’s more assertive foreign policy, and comes as his opponents use economic troubles and failed trade negotiations with the US as pretext to question him, according to analysts.

That dissent, while very unlikely to push Xi from power, could impede what had appeared to be his absolute hold over the party and the government. “His position is safe,” Lam said. “It’s just his authority has been dented to some extent. His authority has suffered.”