In case anyone still has some interest in the above, I post this note to say that I have just published a paper on these coins together with Zach Beasley (owner of the 2003 Pannonian hat coin) and Ron Bude:
Full reference: Lars Ramskold, Ronald Bude, Zachary Beasley, 2016: Methods for Authenticating Ancient Bronze Coins: A Case Study of Constantine's "Pannonian Cap" Coin. Niš & Byzantium XIV, pp. 87-121.
Summary: The most discussed and controversial of all ancient bronze coins is the so called Pannonian cap coin, discovered in 2003, showing Constantine I wearing a pillbox cap. We have examined every detail of this coin through stereoscopic wet and dry study, physical probing, iconographical analysis, die matching, and two types of radiological analyses: XEDS and micro-CT scanning. Each individual way of investigation indicates that the coin is ancient, and we are confident that it was produced in 318-319 CE. It shares the obverse die with a second Cap coin, discovered in 2012, which is thus also ancient. We identify the reverse die of the 2003 coin as engraved by an Imperial Mint engraver, and since the two coins share the same obverse die, it is likely but not certain that they were produced at the Imperial Mint of Siscia. Nor is it certain that they were officially sanctioned. We show that headgear seen on early 4th C art - including the porphyry tetrarchs in Venice and Niš; the Arch of Constantine; the great hunt mosaic in the Roman villa at Piazza Armerina; and on numerous palaeochristian sarcophagi - conventionally identified as the "Pannonian cap" of Vegetius, is in fact the headgear of the lictors...the state-paid summoners - at the time. We accordingly identify the pillbox cap on the two coins as that of a lictor.
The full paper is available on Academia.org.
I hope the paper will stimulate further ideas and research.
/Lars Ramskold
