this gave me an idea... since I'm only looking at one quadrant, what if I took the radius of the circle needed to touch both (x,y) and (y,x)...I mean, just the hypotenuse of a right triangle touching either point... plus the sine times cosine of the vector... wouldn't that give a unique identifier?

like...

(x^2+y^2)+( SIN(ATAN(x/y)) * COS(ATAN(x/y)) )

everything right of the decimal point would be descriptive of the vector, unique because of the phase difference and because we're only dealing with one quadrant... everything left of the decimal point would be a whole integer hypotenuse^2...