As I see it Kujonai may still be developing his format.

I would pose the question:

Are you attempting to generalize sign?

If so then I believe it is important to first accept that the real number is two-signed and that its elemental format is

s x

where s is one of two signs; either - or +, and x is a magnitude. Thus a three-signed number can reuse this format with the addition of a new sign. I have chosen to remain consistent with the real number, though in higher sign systems the meaning of '+' then changes. Still, the mnemonic meaning of the signs is consistent, with the number of strokes it takes to draw each sign consistent with its modulo mechanics under product:

-, +, *, #, ...

with one stroke, then two strokes, then three strokes, then four strokes, and then I run out of symbols, but this is acceptable, since upon getting that far it becomes apparent that a general component form can take over:

( 1.1, 1.2, 1.45, 2.34, 0.23 )

being a five-signed number in its most concrete instance. The position of the components are the sign positions. Heading back down to the real number we see that:

( 1, 1 ) = 0

which is simply stating that

- 1 + 1 = 0

and it is this property; the balance of the signs; which yields dimension since the next form (P3, the three-signed numbers) takes the behavior

( 1, 1, 1 ) = 0

such that a simple expression in P3 as

- 1.2 + 2.3

does not any longer cancel as did a real valued( two-signed; P2) expression. Hence the three-sign numbers are two-dimensional.

The four-signed numbers are three dimensional. P3 are the complex numbers, entirely consistent with the definition of the reals, merely up one in sign. Someone who comprehends this should be able to appreciate polysign, even just in the context of definition of real and complex numbers. They are united through polysign. The simplex coordinate system is natural to polysign. There is no need of any cartesian product construction. The generalization of sign immediatley yields dimensional behavior.

I see Kujonai somewhat taking a more complicated approach which may have some validity as the embedding of say a two-sign system within a three-sign system is as appropriate as embedding a line in a plane. Still, I would argue that the fundamental layout that I've presented lays beneath such an approach and will aid in the construction of that higher level concept.

- Tim