Operations of cumulation-decimation reach the following end states or fixed cycles.

Basin-0 (0): 0 » 0 …

Basin-1 (9): 8 » (36) 9 » (45) 9 … 9 » (45) 9 …

Basin-2 (1): 1 » 1 … 4 » (10) 1 » 1 ... 7 » (28) 1 » 1 …

Basin-3 (3): 2 » 3 » 6 » (21) 3 … 3 » 6 » (21) 3 … 5 » (15) 6 » (21) 3 … 6 » (21) 3 …

Decimal numeracy contains four implicit digital equilibria. Any cumulation-decimation process will fall into one of these, and remain there. They can be framed as abstract *sinks* or *basins of attraction*.

Each exhibits distinctive characteristics.

These can be classified by their power of capture. What – and first of all *how much* – does each *take* beside itself?

The result is an assignment of values, 3, 2, 1, 0.

As a bonus, captivation values can be adopted as ordinal indices.

They then acquire informative (or non-arbitrary) tags.

Their names say what – or at least how much – they do.

Basin-0 captures nothing. From it nothing enters or leaves. Uniquely, it coincides with its own index. Singularity is not unity, but the subtraction of unity from the unit.

Basin-1 brings the octave to novelty. Unity has no place in it, unless in the difference between eight and nine.

Basin-2, finally, reaches unity, in two ways. Four and seven both feed it.

Basin-3, the summit of captivation, draws what it catches into the triad. Two, five, and six arrive there.

In this way decimal number falls into four non-arbitrary categories. Echoes of the Tetraktys might be noted.

Thought you would find this interesting, Vauung: https://claraschelling.substack.com/p/the-history-of-non-numerical-conflict

My name sums to 208. You're 140, correct?