The Elessar going with Asenath into the Sawtooth Mountains

The Elessar is a Green Stone in Tolkien's writings.  It was actually Galadriel's gift to Aragorn in Lothlorien, and in my opinion was likely a major reason, if not the source of power, that enabled him to do such feats as confronting Sauron through the Orthanc Stone, walking the Paths of the Dead, and healing Eowyn and Faramir in the Houses of Healing.

He would adopt the name of this Stone as his royal name:  King Elessar.  Actually, Galadriel first called him this in Lothlorien when she gave Aragon the Elessar, and told him, from that hour, to take 'the name that was foretold for you, Elessar, the Elfstone of the House Elendil!'.

It is interesting that we once again have Names and Stones, as an aside.

In any case, Elessar means Elfstone, and it was said to have magical properties.  Here is a brief description from Tolkien Gateway:

After the completion of the jewel, many Elves, including the other Noldor, were astonished by it, for the stone was green as the leaves but had the clear light of the Sun imprisoned within it. It was said that any who looked upon the stone would see withered and aged things as whole and young again. It was also claimed that it granted any who wore the gem the power to heal any hurts of anyone that they touched.

The impact of this Stone was seen immediately by those who looked upon Aragorn after he pinned it on.  Immediately "those who saw him wondered; for they had not marked before how tall and kingly he stood, and it seemed to them that many years of toil had fallen from his shoulders".

Aragorn was young again in the eyes of those around him when he put that Stone on.  Based on that last description of the Stone, in that it granted healing powers, you can see why my guess is that it factored into Aragorn's healing of Eowyn and Faramir.  And not just their healing, by the way, but he labored all that night following the breaking of Gondor's siege to heal as many as he could.

At the doors of the Houses many were already gathered to see Aragorn, and they followed after him; and when at last he had supped, men came and prayed that he would heal their kinsmen or their friends whose lives were in peril through hurt or wound, or who lay under the Black Shadow.  And Aragorn arose and went out, and he sent for the sons of Elrond, and together they laboured far into the night.  And word went through the City: 'The King is come again indeed.'  And they named him Elfstone, because of the green stone that he wore, and so the name which it was foretold at his birth that he should bear was chosen for him by his own people.

So, that is just some background to the Elessar and its importance.

My current, and very recent, guess is that the Elessar was in Asenath's possession when she descended below Williams Peak and confronted the Balrog.  This guess is based on examining some of the dialogue involving The Germans.  It appears that the scope of their mission not only involved finding and rescuing Joseph, but also finding the Elessar (and other artifacts such as the Brass Plates).

As mentioned in an earlier post, The Germans touched down on our world on January 2, 2020.  On January 3, they begin using the Stone, at least according to the 'dialogue' that I picked up from that day.  Here it is again:

Jan. 3, 2020
Gesehen Aus [I think short for Ausir] und auch kinder in stein
Wo ist ein grun stucke
Gross stadt Jorgen sie
Ich bin spielen
Freundebuche suchen

That second line is where we first get mention of a "Green Piece" (I've bolded the line), and should probably end with a question mark.  It would translate into something like "Where is a Green Piece?".  The question to me implying that this is also part of their quest - they need to find this thing.

Just as to what this Piece is remained a mystery to me for quite awhile, and although I am not 100% confident (like everything else), my fairly strong guess is that this is the Elessar.  A dialogue captured on January 23 seems to support this:

Jan. 23, 2020
Sene arwen-u aman mene sar du arnu inis to induce emen/menes (??) tis albano has suen elgemir

Ich habe gamu in stein tele mektu ista ansil gilla eldarinwa stucke afil o estaru

I won't go through all of this here, but the word to key in on intially is that last word in the first line:  elgemir.  This is an example of a word I wrote down wrong, either because I 'misheard' a consonant, or I didn't write it down correctly.  The correct word should be Eldamir.  I just swapped a G for a D, which I think could be a pretty natural mistake if hearing that word - they can seem pretty similar if hearing a word quickly with others.

That word is important because Eldamir is another name for the Elessar, and means the same thing - Elfstone.

Thar first line appears to be some kind of "call" that The Germans heard or saw in their Stone.  That is what they say, at least, in the beginning of the second line ("I have a call/shout in Stone").  They conclude that statement by linking Elfstone with that earlier Stucke word - the Green Piece.  They say something like "Shiniest Elfish Piece, is it not concerning the name?"

The name in question is Eldamir from that first line, I think, and The Germans say that this call regarding Eldamir is about the same thing that they called earlier the Green Piece ("Is this Eldamir not the Green Piece?).

At some point between then and April they must find the Stone.  The next very clear mention of it is on April 9, 2020.  Asenath will arrive, I believe, at the Sawtooth Mountains on or around April 14, but likely 'landed' here before that.   She would have been coming from Valinor, leaving from there on or around April 2 and arriving here, then, potentially on April 8 (6 days of travel).  It may be that April 9 marks when the Stone was first given to her.

This is the reference from April 9:

April 9, 2020

Astensenwend
Green stone

 My translation for that first Elvish word goes something like "Sunlight for free Maiden", and this would be provided by the Green Stone, or Elessar.  The 'free Maiden' (sen-wend) I have in this case as Asenath, given events that will shortly transpire at Sawtooth.

Asenath will descend below the Earth and in the darkness confront the Balrog.  She had a body at this point, like we do, though she is 'free' in that she is not bound to our world and is not subject to death as we are.  The Green Stone is being provided for her to use in this confrontation, perhaps not unlike Frodo carrying the Phial of Galadriel into Shelob's Lair.

It makes sense to me, and I hadn't thought of it before, but working it through a bit, revisiting some of these words, and imagining what just such a confrontation might entail, I think the Elessar was probably a crucial weapon of light for her to have and this would be why one of the first things The Germans mentioned or looked for when that arrived was this Green Stone.

The question is where did they find it?  One thought is that this was also in the keeping of Tom Bombadil, and that The Germans found the Study, and thus found the Stone.  I am still exploring that, though, and there are other possibilities.

The big thing here, though, is to get out that I believe Asenath had the Elfstone on her and that it acted as a source of Ancient Sunlight in whatever her encounter entailed.  I also now believe that this is not the last we will see or hear of this Stone, and that in future events (future for us, I mean) the Stone may also prove to be a blessing.