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Maximum size of a three-sunflower-free family of four-element sets
The manuscript claims a computer-assisted exclusion of 69-member three-sunflower-free four-uniform families, giving 54 <= M(4,3) <= 68. It improves the upper bound 83 in Axante et al., arXiv:2609.06175v1, Theorem 6.9. The classical lower construction is reproduced, not claimed as new. The proof combines their intersecting-family bound 27, structural point-link reductions, Jin's graph-homomorphism theorem, exact certificates and finite exhaustive checks. A local cap of 61 requires a complete R16 point-link and is not a global bound. Cardinality 68 is not excluded, the exact value is not determined, and the general sunflower conjecture (Erdős #20) remains open.
Exact FrontierDelta
Prior state unknown→proved
Scope and record
Occurred: Oct 1, 2026
Delta type: SOURCE CLAIM
Assumptions: VibeMathed verification: unreviewed. Publication: announcement. AI contribution: ai-assisted. VibeMathed editorial classifications, scores, notes, relations, and dataset structure are CC BY 4.0. Source statements and linked content retain their own rights.
Canonical aliases: Maximum size of a three-sunflower-free family of four-element sets · Three-sunflower-free four-uniform families
Confidence: Not scored
Registry verification: unreviewed · announcement · partial
Attribution
VibeMathed
registry · event recorded by
Sol 5.6
model · ai model contributor · OpenAI
Astra 6
model · ai model contributor · OpenAI
Pro 6
model · ai model contributor · OpenAI
Sol 6.1
model · ai model contributor · OpenAI
Oleksiy Babanskyy
human · human collaborator
Artifacts and verifiers
Compute record
No linked compute attempts recorded.
Lineage and corrections
This event attributed to Oleksiy Babanskyy
Axante et al.: tracked finite bounds and imported Proposition 6.7 evidence for this event
Erdős Problem #20: general sunflower conjecture (remains open) evidence for this event
This event attributed to Astra 6
This event attributed to Pro 6
VibeMathed record: Maximum size of a three-sunflower-free family of four-element sets evidence for this event
This event attributed to Sol 6.1
The manuscript claims a computer-assisted exclusion of 69-member three-sunflower-free four-uniform families, giving 54 <= M(4,3) <= 68. It improves the upper bound 83 in Axante et al., arXiv:2609.06175v1, Theorem 6.9. The classical lower construction is reproduced, not claimed as new. The proof combines their intersecting-family bound 27, structural point-link reductions, Jin's graph-homomorphism theorem, exact certificates and finite exhaustive checks. A local cap of 61 requires a complete R16 point-link and is not a global bound. Cardinality 68 is not excluded, the exact value is not determined, and the general sunflower conjecture (Erdős #20) remains open. parent of this event
Maximum size of a three-sunflower-free family of four-element sets parent of this event
Fixed manuscript, source, certificates and reproduction instructions evidence for this event
Axante et al. on aiXiv (same paper as arXiv:2609.06175) evidence for this event
This event attributed to Sol 5.6
Maximum size of a three-sunflower-free family of four-element sets evidence for this event
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