Signed numbers perform action under product.

The spin 1/2 concept is declared in the context of real numbers isn't
it?
So that this particle goes through (-1)(-1)(-1)(-1) or twice around to
get back where it started.

The two-signed numbers are limited to two positions and so it is
claimed that one needs a half spin particle. This is like trying to get
half of a sign.

four-signed numbers propose a more consistent paradigm.

In the four-signed domain one can travel (-1)(-1)(-1)(-1) and wind up
at the same point without having gone around twice. The positions are:

... -, + , * , #, -, +, *, #, ...

This model remove the paradoxical twice around action that has been
maintained.

There are some natural consequences if one generalizes this concept.
There are four elemental types of sign here.
One of them (+ ) jumps two positions and so would be the traditional
spin 1 model.
i.e. the ... (+)(+)(+) ... operation yields the following patterns:
... -, *, -, *, ...
... +, #, +, #, ...
(*) generates an inverse of (-) :
... -, #, *, +, -, #, *, +, ...
(#) generates a neutral pattern:
..., -, -, -, -, ...
..., +, +, +, +, ...
... *, *, *, *, ...
... #, #, #, #, ...

So altogether there are eight patterns generated.
Two of them are inverses.
four of them are what might be called neutral.
Depending on what context you are working in the quantity of observed
four-signed actions might be eight, four, three, or two.
Tossing out the neutrals would make sense since there is no action in
them.
Distinguishing between -,+,*,#,- and its inverse might be difficult or
impossible to do.
Equivalently the two forms of the + operation may not be readily
distinguishable.
These eliminations leave two types of distinguishable actions.
The validity of these eliminations are based on the symmetry of the
geometry of the coordinate system of the four-signed numbers. That is
to say, because the system is perfectly symmetrical there is no way to
tell what the actual sign is. The pattern of sign changes is all that
we have to go on.

There are only two dynamic patterns.
This is consistent with the standard spin model.
I wish that someone would refute this so that I can understand the
standard model better.
Note that the populations of the two types may be different in the
four-signed paradigm.

If you are not familiar with sign generalization please see:
http://bandtechnology.com/PolySigned/PolySigned.html

-Tim