Over time, he said, he realized that “every level of the government is corrupt” and took his efforts up a notch. Knowing that judges often made their rulings “after a phone call,” he decided to test whether it would actually work. It did — a court ruled in his favor in a case where a court bailiff tried to impose an administrative fine after Mr. Davydov argued with him at the entrance to a court building.

This kind of success prompted him to do more. He started calling judges over random cases to reveal how the system works.

“When he saw how blatantly corrupt our judges were it was as though his eyes opened up,” Sergei N. Klyavin, a friend, said in an interview.

With time and practice, Mr. Davydov trained himself to sound like a true high-ranking judge. He would speak with the commanding voice of a powerful official, exuding superiority. He would cite the precise case number and list the defendant’s name in full. He would use bureaucratic jargon known only to someone inside Russia’s Kafkaesque legal system.

Apart from judges, he called prosecutors and City Hall officials. The result was always the same: Bureaucrats, both large and small, tacitly acknowledged the unwritten rules of the game, exposing how Russia is run by a set of informal practices that tie the power vertical, built by Mr. Putin, into a chain of command.

It was only a matter of time for the system he exposed to strike back.

In 2016, he called Marina N. Zabbarova, the chief investigator in Perm. Mr. Davydov pretended he was deputy head of the investigative committee, the Russian equivalent to the F.B.I. Saying that he was just passing along instructions received from the Kremlin, Mr. Davydov ordered local law enforcement to create favorable conditions for the governing United Russia party in coming parliamentary elections.

“Any provocations against United Russia must be stopped with the full force of the law,” Mr. Davydov told Mrs. Zabbarova.