So, I shoudl really do a re-read, but I was reminded of this poem from the first book.

"On his first hand he wore rings of stone,Iron, amber, wood, and bone.There were rings unseen on his second hand.One was blood in a flowing band.One of air all whisper thin,And the ring of ice had a flaw within.Full faintly shone the ring of flame,And the final ring was without name."

Most of these are easy enough to understand, they mean Kvothe learned the name of each substance, with the final ring likely being copper. Further, what were the "rings unseen", the narrator pretty quickly describe them visually, so expect for the ring of air and the final one, what where the unseen ones? Were they ones Kvothe carried INSIDE his hand (blood and bone)? Finally, the flaw within the ring of ice, what is that a nod to? if he learned the name of something why would anything he made of it be flawed? A part of me wonders if a) whoever saw the ring didn't understand what they saw, b) Kvothe was pulling a fast one and made rings the old fashioned way as a way to up his esteem, which would explain how he made one of copper and c) it's actually two rings, one of ice and another "unseen" substance within it.