I think there is a very simple key in understanding this problem in the nomenclature. The cataphract, originally, was never a designation of the oven-men Oriential knights or their armoured horses. The term originally meant "bulwarked" or "protected from all sides" and the Greeks, whenever they were about to describe heavy horse organized in serried ranks, capable of melee and extensively armed and armoured, called them "cataphracts". Basically any heavy cavalry, without a known institution to provide for them a name (Or simply of unknown nature) was flatly called "cataphract". Our only relief in this mess is that not too many forces used heavy horse in this manner, nor utilized the knee-to-knee organization. This gives us a pool stretching from Saka-Scythians, Sarmatians, Pergamenes, Seleucids, Armenians, Parthians, Atropatene... And basically any Eastern power that were tugging for the pieces of the once Achaemenid worldly order.
For the optimally armed and armoured super-heavy horse, we begin to see, by the 1st-2nd century CE the rising use of the term "clibanarii/clibanarius", which may have been derived from the Middle Persian "griwa-pana-bara" or "Grîvpânvar", those who bear neck-guards. This is a much more specific criterion, and gave the clibanarius (Oven-man in Roman; Possible cross-transfer back to Middle Persian with "tannûr" meaning oven inspired by the lamellar or combined lamellar-maille-and-plate cuirass, also known as the klibanion or the "oven"). Scholars have for decades been fighting ferociously over the problems in the nomenclature between terms cataphractii/cataphractarii/clibanarii, but during bulk of this period overlooked the significance of the Iranian origins of the word. The Roman jocular reference and the Middle Persian honourary designation do not necessarily conflict each other. In fact, it actually makes some sense: A Roman learns that the ridiculously well-armed Iranian cavalry name themselves "kribanpar" or some other gibberish which sounds humorously like "clibanar...". And it catches on like a rash. Instead we have observed how scholars try to "Sarmatianize" the word for "cataphract" and instead "Partho-Sassanianize" the word for "clibanarius".
The latter term prevailed and along with it its Iranian origins; The Byzantines strictly ascribed their elite cavalry contingents "Klibanophoros/Klibanophoroi", and the royal guard would become the "Athanatoi" or the "Immortals", which draws heavily upon the Sassanian 10,000 strong heavy cavalry, named "Zhâyedân" (Immortals). Ironically, both appear to be a corruption of the Royal Companions of the Achaemenids, whom also numbered 10,000. Herodotus, even in his grave, the same old joker.
The lesson to be learned is to never, ever, ever, ever, ever underestimate the power behind a fucked up nomenclature, especially if it is well established in academia. I can easily slap two more examples: Persia and Parthia. These are two of the largest cans of worms you can open up within the circles of Iranian studies and belong to a greater issue called the "Iranian nation and the eternal name dispute". I refuse. For the sake of sanity, patience and peace of mind.
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