Let me first say that ever since I found and subsequently devoured every word a 1st edition copy of The Silmarillion in a box of old books in our basement as a 15 year old, I have longed to be able to converse about the intricacies and mysteries of Middle-earth history with someone without them looking at me like I was crazy. So I'm glad I found this site.
As for the Arkenstone=Silmaril debate, here are some of my thoughts on the theories put forth in this thread:
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The Lonely Mountain being a volcano - Many people have claimed at volcanos can't be conical with a pointy peak. This is not true at all. There are three types of volcanos, Cinder Cones, Composite Volcanos, and Shield Volcanos. The make up an appearance of these are quite different from each other based entirely on the type of eruptions that form them. Shield volcanos are not conical at all and are formed entirely by continuous lava seepage and cooling (think parts of Hawaii). There is very little pressure release in this type of volcanic eruption due to the proximity of the magma chambers to the earths surface, therefore there isn't very much ash or particulates released into the atmosphere. But the other two types, Cinder Cones and Composite volcanos, are characterized by violent eruptions due to the pressure and magma having to breaking through dense rock covering the magma chambers. This causes lots of particulate and ash to be flung into the atmosphere and settle along the slopes. Over many eruptions and coupled with lava flows, this causes a very conical mountain to rise. Then, as the volcano goes dormant, the ash and particulate weather faster that the solid, cooled magma lining the central vent, giving the appearance of a chimney at the top. So it is very much is possible for the Lonely Mountain to be a volcano.
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Gems can't form in volcanos- plenty of crystallization forms in magma chambers and is then pushed to the surface in eruptions. Some examples are diamonds and obsidian. Furthermore, there are enough heat and pressure in there that many metals such as gold and silver can be refined. Who knows, maybe even mithril
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My overall thinking after spending the better part of the past two evenings reading through all these theories and looking back at the books is that I am almost certain the Arkenstone as it stands in the Hobbit is not a Silmaril. Too many characters would have recognized it as such. Galadriel (Fëanors niece), Gandalf and Thranduil to name a few. Galadriel may have been content to leave it be considering her experience with the pain it caused. I doubt Gandalf would try to take it seeing as he generally takes a hands off approach when it comes to influencing the destiny of middle earth, preferring to assist and observe rather than take direct action himself. Thranduil's reaction could range anywhere from strong desire (he may not have seen it in the past, but would surely know what a Silmaril should look like) to outright lust to get from the dwarves. Certainly though, if it was a Silmaril, it wouldn't be regarded with the seeming apathy that it is from these three characters.
However, I have an inkling that had JRRT been given the opportunity to solidify, refine and publish his own version of the Silmarillion, the Arkenstone would have become a Silmaril. The Hobbit was published when JRRT was still formulating his Silmarillion mythos and as such he probably didn't have the Silmarils' qualities or fates set in stone (pun not necessarily intended). So the Arkenstone and the Silamarils could have grown out of the same place in his mind. I think had he been given more time to really distill his world into a cohesive canon, I have no doubt that is where the Arkenstone was heading.
But, as of now, let me introduce my own theory on the origin of the Arkenstone:
Fëanor, being the perfectionist he was, had to go through many inferior versions before he was able to create the three final Silmarils. One of those versions just wasn't quite indestructible, didn't have quite enough of the light of he trees, wasn't quite the right size for his tastes. So he threw it in the trash. Some Maia probably saw it, thought it would fetch a pretty penny, and hawked it to one of those rube Avarian elves still hanging out near lake Cuiviénen. Over the ages, it got lost among the markets and pawn shops of the Sindar until one Lorien elf dropped it on a weekend hiking trip and it fell into the caldera of the lonely mountain. Fast forward to the dwarves digging it up, naming it the Heart of the Mountain, and proclaiming that there is no other one like it. Thus, it becomes another example of the "little-man" syndrome that the dwarves harbor (passed down to them even from their very creation by Aulë) in their relationship with the elves: Their great gem that bestows a divine right to rule is just a cheap knock off of the real deal.
Sorry for the long windedness and thanks for bearing with me.