How many classical symbols does it take to imitate a six-dimensional mathematical state space?

This candidate gives an exact answer: three. That means a three-state alphabet, sometimes called a trit. It does not mean three bits.

The state space is a cross-polytope, the higher-dimensional relative of an octahedron. The question concerns every input–output probability allowed by the full affine measurement model. Sender and receiver may use free shared randomness. Under those assumptions, three symbols suffice, and two do not.

Earlier work had narrowed the answer to three or four. The new argument closes that gap and, together with known bounds, identifies dimensions three through six as exactly the three-symbol range.

The proof reduces the problem to finitely many measurements. More than a hundred and thirty-three thousand rooted representatives are classified exactly. They leave two hundred and seventeen valid records, representing forty-nine genuinely different geometric classes. Twenty-eight classes require the more involved certificates.

Each certificate gives a random choice of at most three possible outputs. Crucially, this shared random choice is the same for every input. Only the allocation among those outputs depends on the input.

The package separates checking that no support was missed from checking that every saved simulator works. The result remains an unrefereed, computer-assisted candidate. It does not settle higher dimensions or establish a new general simulation algorithm.

This is the Evidence Press release for the six-dimensional cross-polytope, dated the eleventh of October, twenty twenty-six. The page links the paper and evidence. This AI voice briefing is an explanation, not additional evidence.