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

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.

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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.