A chiralkine system works on the principle of order, not a balance. It is constituted in six ordered states that switch pairwise. Each state is composed of four ordered polarities (2+ and 2-) called a chiralkine number. The six states (chiralkine numbers) are sorted into three mirror pairs, which can be colour coded yellow, blue and green.

The mirror pairs are sorted into ordered columns of triplets: each triplet containing one number of each kind in order yellow, blue, green or blue, yellow, green. For example:

Going down the rows on one side (in order), there is always a column of 3 of a kind (+ or -) and a diagonal of 3 of a kind, while going down the rows on the other side there is always a column of 3 of a kind and a diagonal of 3 of a kind.

A triplet cannot be formed with two chiralkine numbers of the same kind, because there would then be no column of 3+ or 3- and no mirror pairing of chiralkine numbers across the two sides. For example:

The reason there must be a column of 3+ on one side and 3- on the other side is that the columns define an axis of rotation contituted by opposed corners of a chiral cube, so that the chiralkine numbers are rotating through yellow, blue, green or blue, yellow, green. The four ordered polarities making up a chiralkine number can be colour coded, so that the three of the same kind in a column are red and those in a diagonal are yellow, blue and green.

Each polarity forms a corner of a chiral cube, and four polarities in order form a face: a chiralkine number.

The cube rotates about the axis defined by the red polarities in a column, taking the chiralkine numbers through yellow, blue, green in order.

When the 3+ and 3- are arranged in columns, going down the rows on the two sides switches one + and one – in complementary ways, as if the chiralkine numbers have exchanged component polarities pairwise.

This coupled switching provides the mechanism through which chiralkine systems provide control. They control from both sides of a relationship, each side being coded in one side of the pair of ordered triplets.

Once they have been sorted into ordered triplets, chiralkine numbers of a kind can be superposed, which means that they can be combined without losing information. The key thing to note is that when the column is composed of 3+, you add the +s, not the –s. When the column is composed of 3-, you add the –s, not the +s. It is as if on one side you treat the + polarities like 0 and on the other side you treat the – polarities like 0. However, you never combine a + and – polarity to make 0: everything is coded in one sign (1) or 0.

This ability to superpose chiralkine numbers without losing information is exploited in a chiralkine voting system:

and in a chiralkine exchange:

This is how a chiralkine system works, on the principle of order (yellow, blue, green) instead of a balance. It codes information about both sides of a relationship in four ordered polarities that are manipulated pairwise in order, ensuring that information is never lost. With a system that works on the principle of a balance, information is lost whenever two opposite numbers (e.g. credit and debt) are negated to a single zero. This is why a chiralkine system provides control, but a system based on a balance does not.