# Spin-group tensor invariant scale reduction

Family 204: Tensor saturation for even spin groups. First application triage, 9 October 2026 Australia/Brisbane.

## Problem and potential new use

Symbolic representation teams could eliminate common weight dilation when testing type-D tensor invariants under the root-lattice condition.

## Applicability and commercial boundary

This implication is not an efficient invariant finder; input weights, root-lattice membership and existing representation algorithms still matter.

## Initial business decision

Research reference or conditional symbolic/verification engineering. No practical implementation, recurring buyer need or profitability has been demonstrated; a weak business bridge is explicitly deferred.

## Next verification action

Extract a computable tensor multiplicity example and measure whether removing dilation saves work.

## Evidence scope

The catalog statement was individually reviewed. Main-paper proof, construction effectiveness and selected formal scope comparison remain queued. No independent Lean verification was run. Source revision `fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb`. See [source metadata](source.json).

[Tensor saturation for even spin groups](https://github.com/openai/math/blob/fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb/preprints/Tensor-Saturation-for-Even-Spin-Groups-September-24-2026/Tensor-Saturation-for-Even-Spin-Groups-September-24-2026.pdf).