Halcyonic Systems

This document has been withdrawn.

It was an early write-up of the common-core result for the systems-science foundations project, circulated in mid-2026 to get reactions. It did that, and the reactions were useful. It is down because one of its central claims turned out to be false.

The document said the walking arrow 2 was the maximal structure common to the encoded traditions, and that nothing larger was shared. That is wrong. Compared as free categories, a three-object shape embeds into every one of them, because in a free category every path counts as a morphism. It gets in through a composite that no tradition actually asserts. The counterexample is machine-checked in the repository as free_category_maximality_fails.

The repaired result is narrower and, I think, better. Comparing the traditions by what each one directly states rather than what its closure entails, the only dependency all of them assert is a single one, and it is forced by two of the traditions rather than chosen by me. Existence of the embeddings is proved. Maximality, as originally stated, is not, and is not true.

The source, the counterexample, and the corrected statement are public in the repository. Nothing has been deleted; the earlier version of this page remains in its git history. If you read the original and want the current statement, the repository is the place to look.