───Thought Acceleration is our magic.
Fast thinking is only a prerequisite. Thought Acceleration itself is applying that ability to multi−expansion diagrams.

And furthermore, superior alchemists must have multiple sectors in their brains.

If Thought Acceleration is proof of an alchemist, then the number of sectors is proof of their facilities.

Through Thought Partition, a superior alchemist can create between three and five rooms.

I gave the example of dividing one 'thought' into rooms to Shiki, but that would be the limit of a strictly average alchemist.

Superior alchemists may perform first−order tetrations of their 'thought' into rooms.

These 'rooms' are synergistic.
Four Thought Partitions allow 256 thought processes. But, that does not simply mean 256 alchemist calculations can be achieved.

The 256 accelerated intelligences do not work independently, but constantly cycle towards the same goal.