Growth Constants for Lipschitz Functions on Sparse Random Graphs
Korsky, Saffat and Aiylam bounded the growth constant for integer-valued Lipschitz functions on between and 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
- 9 / 100
- Disclosed cost
- —
- Wikipedia
- No dedicated article
What was actually shown
Resolved the sharp constant (w.h.p.) for random graphs G(n, d/n)
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Single-author arXiv preprint; not yet peer-reviewed.