A mere 1.76-mm thick. First photo shows a US dime for reference. The Omega cal 620, a fairly thin movement itself is 2.6-mm in comparison. Based on the Piguet 9 ligne and introduced in 1964, total production ca 12,500.
Actually most were used in Constellations when thin was in in the late 60s and early 70s, mostly integrated bracelet cases in solid 18K. Sadly this one came from a white gold Constellation which had been melted.
Here's my 712 auto Constellation, one of the ultra thin group . Also comes in solid gold, for the discriminating bedding manager