OpenAI · 204-01 · 2026-09-24 · Algebra
Tensor saturation for even spin groups
preprints/Tensor-Saturation-for-Even-Spin-Groups-September-24-2026
Family 204. Tensor saturation for even spin groups.
The authors are OpenAI. This companion does not verify the proof and does not adopt it as a theorem of Ngo Cheung’s series. It is not a premise. O.1 stays NOT_CLOSED. Anti-de Sitter results are not a de Sitter state, not Em02-E’s relational lapse, not XVI-P’s QdS scheme, and not XVI-Q’s sigma-image record. No quantum coefficient is admitted. No compilation is asserted.
Read against the standing problems
Standing problems. No standing problem is named in this text. It was still read against the nine problems and does not close any of them. The authors are OpenAI. The companion does not verify the proof. This is not a premise of a manuscript by Ngo Cheung. O.1 stays NOT_CLOSED. No quantum coefficient is admitted. No compilation is asserted. XVI-P · XVI-N
Proves saturation factor one for , : 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- part of the simply-laced saturation conjecture.
We prove the saturation conjecture for , 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.
Preprint source and Lean scope
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No Lean scope note is in the repository for this family. The preprint source below is still the full manuscript, not only the abstract. No compilation is asserted.