There is a newer version of the record available.

Published January 15, 2026 | Version v1-retracted
Preprint Open

RETRACTED: A Proof of the Sunflower Conjecture

Authors/Creators

  • 1. independent researcher
  • 2. Anthropic

Description

RETRACTED VERSION. The proof claim in this version is invalid. A fundamental error confused matching number with piercing number and does not support the claimed r-independent bound. The Sunflower Conjecture remains open.

This record is preserved as an audit trail and must not be cited as a proof. Use the corrected version, doi:10.5281/zenodo.18260198, or the concept DOI doi:10.5281/zenodo.18256088, which resolves to the latest version.

The retained computational values for m(n,3) through n = 6 and heuristic applications are separate from the retracted proof claim.

Files

SUNFLOWER_PROOF.pdf

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Additional details

Software

Repository URL
https://github.com/SproutSeeds/sunflower-conjecture
Programming language
Python
Development Status
Active

References

  • P. Erdős, R. Rado, Intersection theorems for systems of sets, J. London Math. Soc. 35 (1960), 85-90.
  • R. Alweiss, S. Lovett, K. Wu, J. Zhang, Improved bounds for the sunflower lemma, Ann. Math. 194 (2021), 795-815.