If your an arbiter, what is your decision in this position

it is over for one of the players (i won't say which :D). but it certainly needs to be played out. it is a decisive outcome. 

actually, i take that back. it is a draw. but, it's certainly not a given. needs accurate play. 

I'd let them play it out.

Who is claiming the win, White or Black?

Step 1: draw a box

Agreed with rooperi. I'd tell them to finish, without even bothering to figure out what is the outcome with best play.

This is a draw, but I would have them play it out. Black needs to find some fairly tough moves to draw. 

Really, doesn't white need to find tough moves to draw? I think every move loses except 1. Kg3 for white.

agreed - white is lucky to draw!

How hard is it for white to just stalk black's king and get the opposition when black captures white's pawn?

To make it easier you can think of it as, every time black goes up a rank white needs to be able to go left 1 file.

In effect this means white wants to go to the low ranks because if the black king can both go up and stop you from going left you lose... this is impossible if you're on a low rank.

Anyway something like this:

@bestovalltime - look up trebuchet -- white loses if he tries to go for the pawn.

Take the white pawn.

If the white king goes to g5 he should lose.  As I said all black needs to do is at some point make sure he goes up and the white king can't go left in response.

Or as in this mainline white falls into a well known lost position.

Black Ka6. White has to move away.

If white ever touched e8 is meant he spent a move not going left.  All back would have to do to win if white goes to e8 is be sure not to stop moving up...

You should make a diagram if you think you see something.

I already showed that line.  Here, your move for white, whats your move.  By the way I premove king takes pawn so take your time lol

Every move loses except 1. Kg3.