Looking at the damaged piece, the best professionals could not have foreseen this astronomical price. The historical significance of the bust partly explains it. It is the only three-dimensional portrait of Antinous identified as such by an inscription on the piece. Better, the man who commissioned it was the scion of an ancient patrician family from Rome, Lucius Flaccus, whose name is given in Greek form, Lukkios Flakkos.

But the documented history of the sculpture in modern times made it impeccably kosher in Unesco terms. It came to light in the Syrian town of Banias on the Golan Heights and was acquired not later than 1879 by the Chancellor of the French consulate in Beirut, as is established in the journal where its important Greek inscription was published in 1879. In recent years, nothing approaching the attention the bust received in December could be observed as it passed through the hands of famous dealers — Nicolas Koutoulakis of Geneva and Paris, Robin Symes of London, Albrecht Neuhaus of Würzburg and Jean-Luc Chalmin of Paris all handled it — before Mr. Day bought it in 1992. The damage probably turned off many, as did a price that, if set around Sotheby’s “low estimate,” must have been deemed enormous.

The story repeats itself with variations in the case of Mr. Day’s green porphyry sphinx carved in Rome in the Egyptian style possibly at the end of the first century A.D. Looked at from a distance, with its decidedly spoofy touch, the human-headed feline creature could be mistaken for an 18th- or 19th-century poor imitation of the Ancient Egyptian style.

Scholars say it is a Roman attempt at imitating an Egyptian black granite sphinx dating from the reign of Tuthmosis III. The Roman piece is, however, larger and more angular than the Egyptian original. The assumption is that it was recovered in the 19th century, although where and when cannot be ascertained, nor is it clear why it was only published as late as 1972.

However, it is in the sphinxes’ nature to be enigmatic, and 1972 is close enough to 1970. The prospect that it might have come from a temple celebrating the mystery of Isis under the rule of Domitian (81-96 A.D.), who restored the Iseum, added to its tickle. The silent laugh of the human-headed lioness suggests that it was amused at the $5.23 million bill that this month’s buyer had to settle — four times what Sotheby’s thought it might cost.