The inverse pairs

The pairing of the inverse hexagrams between the circles:

From now on, this is merely speculation. There are some hidden connections between the received circles, the inverse pairs, and the final sequence.
5 and 8 are the most perfect pair: they are neighbors and inverse pairs too.

There are some 'jumps' between the pairs and inverse pairs:

And so on. Clearly, this is not a solution, but maybe something, that will bring us closer to the method of creating the sequence. Or just a tricky dead end, I don't know. If someone can figure out the logic behind this, then we will be a step closer to the solution.

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