What gives a piece the ability to pin? (Improved Edition)

Due to the errors found in the previous topic, this is the fixed edition of the pin theory.
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This is the result of my drinking:

Definition of a pin: An "Attacker" (the one performing the pin) prevents an opponents piece from moving since moving would result in the capture of a more valuable piece (the target)

We know that all pieces can pin except the King, knight and pawn, but why is that?
One might inaccurately say that the aforementioned trio are point-like pieces, while the other pieces are linear (moving in a line or curve) and this what gives them the ability to pin, however, the true reason is a bit more interesting.

In order to demonstrate the rule which determines weather a piece can pin or not, I'm going to create a "super" knight and pawn which will have the pinning ability.

If i want to give that ability to any piece, even if its a piece of your imagination, all what i have to do is create a "double tempo'd" version of that piece.

Definition : a "double tempo'd" piece is a normal piece that can move twice in one turn, while still following the capture rule( a piece has to stop when capturing )

Example 1 : lichess.org/editor/3n4/8/4P3/8/5K2/8/8/8_w_-_-

To give a knight the pinning ability, i create a double tempo'ed version of a knight.
In this position, the knight is double tempo'd, it can for example move d4 in a single move, you can see that the pawn is pinned since its removal will result in a dead king.

Example 2(super pawn): lichess.org/editor/8/8/p7/1P6/2K5/8/8/8_w_-_-

If we give the black pawn double tempo, we see that the white is pinned to its king, since its removal will result in Axb4.

Example 3 ( imaginary piece) : lichess.org/editor/n7/8/8/8/8/8/8/Bk6_w_-_-

You can even make sure that any imaginary piece (a piece not in a normal chess game) have the pinning ability simply by making it double tempo'd, in this position, my imaginary piece is represented by the bishop, this piece can only move to the last square in the opposite end of the board, in this case, BxA8 Is the only legal move.

This imaginary piece is point-like in its movement, therefore it cannot pin, however, by making it double tempo'd, you see that knight is actually pinned.

So why does making a piece double tempo'd ensure its ability to pin? this follows from this theorem which i discovered:

Theorem:
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Let K be any chess piece, imaginary or rea
If K has the ability to Pin , then the following condition must be satisfied for at least one legal move and legal position.

If K can move from square A to square C in a single move, there exist square B which is between A and C in the "path", And A to B is a legal move. *

The attentive student will now realize that by making a piece double tempo'd, it ensures the existence of square B, which in turn ensures a piece its ability to win.

Notes:

1) the converse of the theorem is true, if the condition is satisfied then the piece can pin.

2) the theorem need to be satisfied for only ONE legal position for it to hold, if an imaginary piece satisfies the condition in one position but not in another, the theorem still ensures its pinning ability.

3) if a piece has the ability to pin, then it can also perform a skewer maneuver.

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With my sincere hope that this will advance our understanding of chess.

-Bourbon53

It is.

but i had fun doing it. and im ashamed to say that i did find it interesting...

But it works.

It's beyond pretentious drivel, it's wrong.

In your first example, the pawn is not pinned by your super knight, because the king is in check. The king has to move, so it's just a more complicated check fork.

In your second example, the pawn is not pinned because it can simply capture the black a pawn.

Try again.

The king is not in check, since the pawn will stop the knight from diectly going to the king.

in the second exaple, you are correct, but if we you replace the white pawn with another piece it will be a pin. therefore, a super pawn can pin.

And this is supposed to be funny/interesting so i allow maximum pretentious levels. :)

Furthermore, I just thought of this...the pawn in the second example is also not pinned even if it just moves forward. The pawn can't threaten the king once the white pawn moves because it can't move diagonally once the capture is not an option.

Your fundamental understanding of how a pin works is flawed. A pin occurs IF and ONLY IF a greater piece can be captured if the lesser piece moves. Since a pawn can only threaten the next piece if it captures, since if there is no capture available it may only advance in a direction it can't capture, there is no way for it to threaten 2 pieces in succession, regardless of how many tempos you give it. It can only fork. It's the same for a knight. Thus, the ability to pin does, in fact, require threat linearity.

#6 - How is the knight stopped by capturing if it has 2 tempos? You're adding extra limitations now to your imaginary pieces. The act of giving the piece 2 tempos would then also require a rule in which once a piece with 2 tempos captures a piece it cannot advance its second tempo. It's beyond pretentious, it's poppycock.

Its not a limitation, just like a normal chess piece stops when it hits an opponents pieces, this super knight will be stopped when it hits the pawn . if a normal bishop is blocked by an opponent piece, it cannot step beyond that piece since it will be stopped upon capture, same principle.

I see what you mean, perhaps the term double tempo is confusing, what i meant is increasing the score of the piece as if its moving in two tempo's