Tensor saturation for even spin groups

What OpenAI claims

Proves saturation factor one for Spin (2n), n ≥ 2: for three dominant integral weights whose sum lies in the root lattice, an invariant at any common positive integral dilation already gives an invariant at the original weights. This resolves the type-D part of the simply-laced saturation conjecture.

Paper

1. Tensor saturation for even spin groups

   24 September 2026 · Preprint, not peer reviewed · PDF

   We prove the saturation conjecture for Spin (2n), n ≥ 2. If three dominant integral weights sum to an element of the root lattice, then the existence of a nonzero tensor invariant after a positive integral dilation implies the existence of one at the original weights.

Status

Preprint. The paper has not been independently reviewed. Treat the result as OpenAI's claim until other mathematicians have checked it. If a video exists, it illustrates the statement; it is not the proof.