Prince Mohammed’s consolidation of power has upended decades of efforts by previous Saudi rulers to build loyalty and consensus within the royal family. And even before the disclosure of the record-breaking purchase in a New York art auction by one of his associates, Prince Mohammed’s extravagance had already raised eyebrows, most notably with the impulse purchase two years ago in the south of France of a Russian vodka titan’s 440-foot yacht, for half a billion dollars.

A spokeswoman for Christie’s, the auction house that sold “Salvator Mundi,” said it did not comment on the identities of any buyers or sellers without their permission. Prince Bader did not respond to a detailed request for comment. But as The Times was pressing for a response on Wednesday, the newly opened branch of the Louvre in Abu Dhabi, in the United Arab Emirates, tweeted that the painting “is coming to Louvre Abu Dhabi.” The Saudi crown prince is a close ally of his counterpart in Abu Dhabi.

Documents provided from inside Saudi Arabia and reviewed by The Times reveal that representatives for the buyer, Prince Bader, did not present him as a bidder until the day before the sale. He was such an unknown figure that executives at Christie’s were scrambling to establish his identity and his financial means. And even after he had provided a $100 million deposit to qualify for the auction, the Christie’s lawyers conducting due diligence on potential bidders pressed him with two pointed questions:

Where did he get the money? And what was his relationship with the Saudi ruler, King Salman?

Real estate, Prince Bader replied, without elaborating. He was just one of 5,000 princes, he told the auction house, according to documents and people involved.

Less than two weeks earlier, on Nov. 4, the crown prince had ordered the crackdown on more than 200 of the richest Saudi princes, businessmen and government officials. The kingdom had been squeezed by years of low oil prices, and Prince Mohammed was seeking to recover hundreds of billions of dollars in alleged illicit gains.

“Salvator Mundi” represented a major prestige purchase in the art world, if a controversial one. Some experts questioned whether the painting was a true Leonardo. Some were simply unimpressed. The painting’s previous owner, Dmitry E. Rybolovlev, is a Russian billionaire who bought a $95 million Florida home from Donald J. Trump nearly a decade ago. Mr. Rybolovlev had paid $127.5 million for the painting in 2013 — less than a third of its sale price last month — and he is still locked in litigation with the dealer who sold it to him over that lofty price, among other transactions.