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According to the plot of my story, on the territory of one of the ridges of the trans Antarctic mountains, a monument was built of unprecedented scale in comparison with the previous ones. Possibly the last and most enduring mention of us. Which, in which case, like the tombs of ancient civilizations, which they so characterized, will outlive us ... keeping all the knowledge of human civilization, to those who will live after us. Millions and millions of years later.

Most of the complex is underground, while on the surface there is a domed elevation, hollow inside, and is the entrance to the main complex.

And here we come to the essence of my question: from what should we build this complex and what form should it be in order for it to stand as long as possible?

So the granite, which is familiar for durable buildings, will not suit us, because the rate of granite erosion is approximately two centimeters every ten thousand years, because of this, for example, the world famous Rushmore Mountains, with the faces of American presidents carved on them, will completely cease to exist within the next 7,2 million years (which is too little for us), therefore we need something better.

Note: The most important wear factors will be friction (remember that wind speeds in Antarctica can reach several hundred kilometers per hour) and temperature drops.

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    $\begingroup$ Another challenge with this is plate tectonics. You would need to make sure your structure is near the middle of a plate. If it is near the edge it could be pushed into the mantle or destroyed by a newly formed mountain range. $\endgroup$ – JamesFaix Nov 2 '20 at 13:20
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    $\begingroup$ When you use the hard science tag, flag the question for the moderators to add the post notice $\endgroup$ – L.Dutch - Reinstate Monica Nov 2 '20 at 13:40
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    $\begingroup$ I missed the hard science tag. I don't think you'll be able to accomplish this without some form of self healing structure without resorting to unobtainium (hence my bark answer). Even diamond will break and chip under impacts over the millions of years. $\endgroup$ – Ash Nov 2 '20 at 13:56
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    $\begingroup$ I admit this is off-topic, but your question reminds me of Lovecraft's story, "At the Mountains of Madness". $\endgroup$ – llywrch Nov 2 '20 at 16:17
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    $\begingroup$ The level of the ground rises and falls across millions of years, too. An "underground" complex can be exposed, then topple unsupported as the surrounding earth weathers away. Or the crust may sag, burying the dome under dozens of meters of unexpected deposition. Or, since it's Antarctica, unstoppable glaciers may reshape the mountains, carrying away all traces of the complex. If you want it to last for millions of years, consider putting it on the Moon. $\endgroup$ – user535733 Nov 2 '20 at 16:58
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You asked for "hard science", which "Requires answers backed up by equations, empirical evidence, scientific papers, other citations".

Let us stay with empirical evidence. Your "monument" has to be a small mountain. There are mountains that are easily hundreds of millions of years old, and they are still more or less with us. So, we know empirically that granite and similar hard rocks can withstand the passing of the aeons.

You need to minimize damage to the mountain, so you need to build it on a geologically very stable area: smack in the middle of a craton.

Then you need to minimize damage from flooding, weather and ice flows, so you need to build a very high stone base. Over an existing mountain looks good.

And you need to minimize corrosion, so granite doesn't seem to be the best choice as you already noted; but granite is not a homogeneous material, and most of its resistance appears to come from its content of quartz.

Quartz is up to 10x more resistant than granite to mechanical weathering and is resistant to chemical weathering provided the temperature is low enough.

Therefore, a quartz-covered pyramid in a dry, cold, elevated area of Greenland, in the North Atlantic Craton, should have excellent chances of lasting out the next several million years.

The same applies to the Mawson Craton in Antarctica. You want a high place, to avoid possible problems with ice build-up.

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The best I can answer is where to build, and it's not on earth as anywhere on earth there are lots of things that erode down buildings and structures naturally.

In a stable orbit around the sun.

Once you have an object out in a stable object around sol in such a fashion that it will not cross any belts of smaller particles, the item will stay there under Newton's laws. It will stay in this orbit forever. As there is no atmosphere around it and no biosphere to break it, nothing will erode such a construct if no plants are on it. Our choice of orbit was to prevent collisions, so the lifeless satellite will encounter no change until Sol bloats up and swallows it. Due to the positioning, now it is virtually irrelevant what we build the item from - the cold of space will freeze any water, the harsh solar radiation might bleach paints and break down organic material, but beyond that, all non-organic materials will be preserved quite well. With the right setup, the erosion by solar wind will be small enough to keep the object intact and in the right orbit for the required millions... but now you have pretty much built a moon(?).

Obligatory: that's no moon. – Cadence

That is indeed no moon, that's (depending on size) a planet, dwarf planet, asteroid, or meteoroid. – Jann Poppinga

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    $\begingroup$ Obligatory: that's no moon. $\endgroup$ – Cadence Nov 9 '20 at 17:58
  • $\begingroup$ @cesargastonec which is not possible, because that place isn't stable enough. $\endgroup$ – Trish Nov 9 '20 at 21:10
  • $\begingroup$ @Trish Indeed. I'm not sure but I don't think there is any place on earth stable enough for millions and millions of years. It would be the subject for another question. But I think the answer should focus more on original conditions, before starting to propose new conditions that could moving away from the plot of the story. $\endgroup$ – cesargastonec Nov 9 '20 at 21:21
  • $\begingroup$ Orbits are chaotic by nature. Also. Storing knowledge is interesting only if you can retrieve it right? $\endgroup$ – Anderas Nov 10 '20 at 19:16
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    $\begingroup$ That is indeed no moon, that's (depending on size) a planet, dwarf planet, asteroid, or meteoroid. $\endgroup$ – Jann Poppinga Nov 11 '20 at 10:41

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