The Erdos-Sos Pairwise-Sums Problem
Let $f_3(N)$ be the least size forcing a set $A \subseteq \{1,\ldots,N\}$ to contain distinct $a,b,c$ with $a+b$, $a+c$ and $b+c$ all in $A$. The upper bound $f_3(N) \le 5N/8 + O(1)$ matches the standard construction $[N/8,N/4] \cup [N/2,N]$, so $f_3(N) = 5N/8 + O(1)$.
Exact FrontierDelta
Scope and record
Occurred: Jun 28, 2026
Delta type: SOURCE CLAIM
Assumptions: VibeMathed verification: lean-verified. Publication: preprint. AI contribution: ai-co-developed. Imported under CC BY 4.0.
Canonical aliases: The Erdos-Sos Pairwise-Sums Problem · Erdos-Sos pairwise sums
Confidence: Not scored
Registry verification: lean verified · preprint · resolved
Attribution
VibeMathed
registry · event recorded by
Ricky Cipollini
human · human collaborator
GPT-5.5 Pro
model · ai model contributor · OpenAI / Harmonic
Aristotle
model · ai model contributor · OpenAI / Harmonic
Lineage and corrections
This event attributed to Ricky Cipollini
This event attributed to Aristotle
This event attributed to GPT-5.5 Pro