# Finite symmetric tensor category fiber-functor adapter

Family 208: Finite symmetric tensor categories and the Verlinde tower. First application triage, 9 October 2026 Australia/Brisbane.

## Problem and potential new use

Category-theory software researchers can track a faithful exact monoidal representation in a higher Verlinde category.

## Applicability and commercial boundary

The level depends on the category and need not be effectively bounded; existence is not an efficient functor constructor.

## 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

Inspect explicit level and data representation for a small category.

## 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).

[Fiber functors for finite symmetric tensor categories in positive characteristic](https://github.com/openai/math/blob/fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb/preprints/Fiber-functors-for-finite-symmetric-tensor-categories-in-positive-characteristic-September-24-2026/paper.pdf).