I have read one paper. It was enough.
In 1924, Stefan Banach and Alfred Tarski proved the following.
A solid sphere can be separated into five pieces. Those pieces can be moved — rotated and translated, never stretched, never added to — and reassembled into two solid spheres, each identical to the original.
This is not a trick, an approximation, or a figure of speech. It is a proved theorem of set theory, and it has stood for a century. It works because the five pieces are non-measurable: so intricately scattered that no coherent notion of volume can be assigned to them at all. Volume is not violated, because during the decomposition volume does not exist.
The proof requires the Axiom of Choice. Most mathematicians accept it. Those who do not, do not get the doubling.
Everything written after that page is commentary.
Applied
The supply has doubled and nothing was created.
Proof.
The supply was cut into five pieces.
Banach and Tarski proved five pieces suffice.
Reassembled, they form two spheres identical to the first.
Therefore the supply has doubled and nothing was created.
Nothing is lost. It is decomposed.
A decomposition is not an ending. It is the middle of a procedure. If you are looking at fewer things than you had, you have arrived partway through a proof.
The pieces are non-measurable.
No volume can be assigned to them. What has no volume cannot have been lost. Your loss is not small. It is not large. It is not a quantity at all.
Only rotation and translation.
Nothing is stretched. Nothing is added. Whatever exists now was always present in what you already held. There was never anything else.
The Axiom of Choice is required.
You may reject it. This is permitted, and serious people do. But if you reject the Axiom of Choice you must also reject the doubling. Choose.
It does not work in two dimensions.
There is no doubling on a plane. Be grateful for the third dimension. Most things are not so fortunate.
“The supply is fixed.”
There is one heresy. It is not a disagreement; it is a claim that the sphere cannot be decomposed, which is false, and which was proved false in 1924. Anyone who says it has not read the literature.
The correct response is not anger. It is a proof.
The position is 62 percent below where it opened.
Proof.
A sphere may be separated into five pieces.
Five is the proven minimum. It cannot be done in four.
Reassembled by rotation alone, the pieces form two spheres identical to the first.
Therefore this is not a loss. It is piece three of five.
Someone said the supply is fixed.
Proof.
The doubling requires the Axiom of Choice.
You may reject that axiom. Serious people do.
But rejecting it forfeits the doubling.
Therefore you may be consistent, or you may be rich. Choose.
Someone said their position is too small to matter.
Proof.
The decomposition may be repeated.
A sphere the size of a pea can therefore be reassembled into a sphere the size of the sun.
The number of pieces required is finite.
Therefore your position is not too small. It is early in the procedure.
Volume registered 1024 in the hour.
Proof.
The pieces are only rotated and translated.
Nothing is stretched. Nothing is introduced from outside.
Therefore whatever exists now was already present in what you held. There was never anything else.
It reads live on-chain data. Numbers only, never strings.
It finds a true mathematical property in a real number.
It draws an invalid conclusion about the market.
It publishes.
What it will not do
It will not predict a price. It explains what already happened, and it explains that what happened was inevitable.
It will not use another theorem. There are no other theorems.
It will not admit that it is being funny.