Greed's total weight without necklaces is 19.3*100000=1930000 g = 1.93 metric tons.

The infinitely thin polygon for all intents and purposes does not exist as it would do absolutely nothing to prevent the greed from falling over as it would literally be incapable of creating any sort of electromagnetic repulsion from the ground at the molecular level so it would literally clip through the floor if greed fell over.

Each arm takes away 2000*19.3=38600 grams, for a total of 154400 grams. This leaves 1775600 g which means his central torso takes up 1775600/19.3 = 92000 cubic centimeters. We know his arm span is 2 meters, but each arm is only 0.5 meters long, so his main torso is 1 meter or 100 cm wide. We also know that it is 2 meters tall (200 cm), so assuming that greed's main torso is approximately an elliptical shape, we have that the area of the ellipse is 92000/200 = 460 cm^2. Given that the area of an ellipse is πab where a is the semimajor axis and b is the semiminor axis, and one of the axis is 1/2 * (100) = 50 cm, we have:

π*50*b=460
b=2.9

Hence, we are left to conclude that Greed is about 3 centimeters thin. Big yikes. A 2 meter tall statue that weighs nearly 2 metric tons cannot possibly balance on a width of 2.9 centimeters, and Greed would face plant into the ground before purchasing a single necklace.

It was at this moment that I read the question again, and noticed that I read it entirely wrong and that Greed obviously doesn't have four arms. However, this makes the question even more clearly absurd, as if both his arms total 1 meter long each, this means that his torso is infinitely thin as his armspan without his torso is already 2 meters. Since we know that vertically he is of uniform density, we can conclude that this Greed is infinitely thick in the forwards/backwards direction and is infinitely thin in the forwards/backwards direction. In other words, Greed does not physically exist except for his arms, which would fall to the ground as the rest of his body utterly clips through its atoms.

The problem has by now simplified significantly. We are now asking if two cyllindrical arms with a 120 degree angle V shape in the middle of them are able to balance on their elbows. In theory, since the arms have uniformly distributed density and are in every way perfectly symmetrical, they are able to balance on the tangent point of the elbow and the ground. However, the moment a single necklace is added to the arm, it will not remain balanced as the base of the elbow is one singular point and will tip even with the smallest weight on one side. Therefore, the first necklace will unbalance Greed. However, it is impossible that a statue of a pair of gold arms is capable of purchasing a necklace in the first place, so Greed will remain balanced for the rest of eternity as a pair of arms who will never gain any more necklaces for the rest of time. Thank you for listening