VibeMathedMath problems solved by AI

Growth Constants for Lipschitz Functions on Sparse Random Graphs

Korsky, Saffat and Aiylam bounded the growth constant c(G)c(G) for integer-valued Lipschitz functions on G(n,d/n)G(n,d/n) between 1/(2d)1/(2d) and 4log2d/d4\log^2 d/d up to lower-order terms. The random-graph side is sharpened.

Result
Proved(see note)
Status
Partial result
AI contribution
AI co-developed
Method
Argument
Field
Combinatorics
Posed by
Samuel Korsky, Saffat Saffat, Dhroova Aiylam
Year posed
Years open
Solved
2026-05-25
Model
GPT-5.5
Vendor
OpenAI
Collaborators
Samuel Korsky
Verification
Unreviewed
Publication
Preprint
Significance
10 / 100
Disclosed cost
Wikipedia
No dedicated article

What was actually shown

sharpens the previous bounds rather than closing the gap

What the AI did

The acknowledgement is unusually direct about scope: the author credits GPT-5.5 with producing fully the mechanism of the upper bound for the hypercube graph. The author is one of the three who set the original bounds.

Verification

Single-author arXiv preprint; not yet peer-reviewed.

Source

arXiv:2605.25515 - Lipschitz Functions on Sparse Graphs II

Discussion