What is the documented origin of this famous quote- “Hail Emperor, those who are about to die salute you.”?

“Ave Imperator, morituri te salutant,” is a well known Latin phrase that is translated to mean, “Hail Emperor, those who are about to die salute you.”

It was first reportedly used at an event in 52 AD on Lake Fucinus, located in central Italy. The ‘naumachiarii’ were captives and criminals fated to die fighting during mock naval battles in the presence of the Emperor Claudius (10 BC to 54 AD). Prisoners of war and criminals condemned to die were tasked with enacting naval battles to the death for public entertainment. The phrase in all likelihood was an isolated incident of a mass plea for sympathy or mercy by desperate convicted men.

The lake was surrounded by rafts to prevent a mass breakout and both Roman infantry and cavalry lined the lake protected by ramparts and equipped with catapults and ballistae (bolt throwers considered an ancient missile weapon). Additionally, ships bearing Roman marines were ready as needed.

Source material validating this event comes from three Roman historians, who were all born after the events of 52 AD. Both Suetonius, a Roman historian (c. 69-75 to after 130, probably writing around 121 AD), and Cassius Dio, a Roman consul (around 155-164 to after 229, probably writing around 200-22) wrote about the event and quoted the phrase. A third documented historical source comes from a Roman historian and politician named Tacitus (c. 56-117, writing from around 98 to 117) who wrote about the event in his ‘Annals.’