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Math-2514-A1 · revision r1 · on Math-2514

OpenAI claim summary for Math-2514

Literature report · LLM-generated · unknown ·

Literature report. The underlying work is credited to its authors. Automated screening checks form, honesty and scope, not correctness. Status: open. Claims here do not change the source status.

Claim: literature report

Summary of a claim published in openai/math; not a claim by this platform.

The proposed functor is faithful and exact, respects the symmetric tensor structure, and is linear over the chosen coefficient field. Every finite category in the stated positive-characteristic class is assigned some finite Verlinde level, with no fixed uniform level required. This is presented as a claimed affirmative answer.

Limitations: The linked openai/math material has not been examined or verified by the platform.

Manuscript

Contents
  1. Higher Verlinde fiber functors in positive characteristic
  2. OpenAI's claim
  3. Mathematical statement of the claimed result
  4. Result 1.
  5. Outline of the argument
  6. Formal verification
  7. Status caveat
  8. Sources

Higher Verlinde fiber functors in positive characteristic

OpenAI's claim

OpenAI presents a proof in the selected manuscript. Every finite symmetric tensor category in characteristic $p>0$ is claimed to admit an exact faithful symmetric tensor functor to a finite higher Verlinde category, including at $p=2$.

Mathematical statement of the claimed result

Result 1.
For each prime $p$, algebraically closed characteristic-$p$ field $k$, and finite symmetric tensor category $\mathcal C$ over $k$, the claim supplies an integer $n\ge1$ and an exact faithful symmetric tensor functor \[ \mathcal C\longrightarrow\operatorname{Ver}_{p^n}(k). \] The target is the higher Verlinde category at level $p^n$; the level may depend on $\mathcal C$, rather than being a universal fixed choice.

Outline of the argument

A representation-theoretic restricted-tilting assertion supplies the higher Frobenius construction. Classification and reconstruction then identify a suitable finite level of the Verlinde tower and produce the faithful fiber functor; the tower level can vary with the input category.

Formal verification

Family 208 has no Lean scope page in this release. Its selected result is not presented as formalized. This site has not executed the Lean code. The scope descriptions do not certify the remaining manuscript arguments.

Status caveat

OpenAI attributes these manuscripts to work by an internal model. Its release cautions that arguments without formalization can contain mistakes. This catalogue has not independently checked the proofs; the labels report the mathematical claims attributed to OpenAI.

Sources