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ZENODO
Preprint . 2026
License: CC BY
Data sources: ZENODO
ZENODO
Preprint . 2026
License: CC BY
Data sources: Datacite
ZENODO
Preprint . 2026
License: CC BY
Data sources: Datacite
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On the Sunflower Conjecture: Computational Bounds and an Unsuccessful Proof Attempt

Authors: Mitchell, Cody; Claude, Opus;

On the Sunflower Conjecture: Computational Bounds and an Unsuccessful Proof Attempt

Abstract

CORRECTION NOTICE (v2, January 15, 2026): Version 1 claimed a proof of the Sunflower Conjecture. This claim is RETRACTED. Mathematician Thomas Bloom identified a fundamental error: Lemma 4.2 incorrectly bounds the piercing number independently of r, which is known to be impossible. The main theorem does not follow. --- This paper documents an unsuccessful attempt to prove the Sunflower Conjecture of Erdős and Rado (1960). What remains valid: - Computational results for m(n,3) up to n=6 - Structural definitions and observations - Detection applications (as heuristic methods) What is retracted: - Theorem 1.2 (Main Result) - Theorem 4.1 (Universal Piercing Bound) - Lemma 4.2 - Any claim to have proved the Sunflower Conjecture The Sunflower Conjecture remains OPEN. We publish this correction transparently to acknowledge the error, credit Thomas Bloom for identifying it, and document the failed approach for educational purposes. Supplementary verification code included.

Keywords

combinatorics, extremal set theory, delta-system, sunflower conjecture, Erdős-Rado

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selected citations
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This is an alternative to the "Influence" indicator, which also reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).
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popularity
This indicator reflects the "current" impact/attention (the "hype") of an article in the research community at large, based on the underlying citation network.
BIP!Popularity provided by BIP!
influence
This indicator reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).
BIP!Influence provided by BIP!
impulse
This indicator reflects the initial momentum of an article directly after its publication, based on the underlying citation network.
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