---
title: "The blockwise Alperin weight conjecture"
authors:
  - "OpenAI (internal model)"
year: 2026
venue: "openai/math manuscript collection (GitHub), result family 202; unreviewed"
arxiv: null
doi: null
source: "https://github.com/openai/math/blob/main/preprints/The-Blockwise-Alperin-Weight-Conjecture-September-23-2026/paper.pdf"
topics:
  - "openai-math"
  - "ai-generated-math"
  - "algebra"
  - "unformalized"
seed_rank: 2057
seed_batch: "openai-math-2026-10-07"
reviewed: "2026-10-07"
pool: "maths-foundations"
relevance_score: 7
lineage: ai-mathematical-reasoning
cites:
  - title: "The Blockwise Alperin Weight Conjecture"
    url: "https://github.com/openai/math/blob/main/preprints/The-Blockwise-Alperin-Weight-Conjecture-September-23-2026/paper.pdf"
    year: 2026
    arxiv: null
    doi: null
---

# The blockwise Alperin weight conjecture

## One-sentence takeaway

OpenAI's result family 202 (Algebra) claims: Proves the numerical blockwise Alperin weight conjecture for every prime and every finite group: the number of irreducible Brauer characters in a block equals the number of conjugacy classes of its weights.

## Why it matters here

Pure mathematics with no direct engine use; it is in the library as part of the openai/math corpus, which records what an AI research model claims to have proved. More broadly, every card in this batch is evidence for the `ai-mathematical-reasoning` thread: per the repo README, an unreleased internal OpenAI model produced it, using about three hours of ChatGPT Pro thinking compute per result on average, across roughly 4,000 posed problems.

## Key ideas

- *The Blockwise Alperin Weight Conjecture*: We prove the numerical blockwise Alperin weight conjecture for every finite group and every prime p. For each p-block B, the number of irreducible Brauer characters in B equals the number of conjugacy classes of B-weights.

## Caveats

- Unreviewed: these are AI-generated manuscripts posted to GitHub with no peer review or arXiv deposit. The repo README says results are "at different stages of verification" and that "some of the unformalized results could have issues."
- This card restates the repo's family summary, manuscript abstracts and Lean scope notes. It is not an independent check of the proofs, and the scope of each theorem is exactly as stated there.
- Lean: not formalized. The repo has no Lean development for this family, so the claim rests on the prose manuscript(s) alone.

## Links

- Manuscript: [The Blockwise Alperin Weight Conjecture](https://github.com/openai/math/blob/main/preprints/The-Blockwise-Alperin-Weight-Conjecture-September-23-2026/paper.pdf)
- Family entry: https://github.com/openai/math/blob/main/CONTENTS.md
- Overview PDF: https://github.com/openai/math/blob/main/overview.pdf
- Repo: https://github.com/openai/math