Problem detail · source-aware

Growth Constants for Lipschitz Functions on Sparse Random Graphs

partialconfidence 70%

VibeMathed reports this item as partial. VibeMath preserves that report as a source assertion and has not independently authored a plain-language mathematical explanation.

Precise statement

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

The source statement is reproduced for indexing with attribution. Mathematical correctness requires domain-expert or mechanical review. VibeMath has not independently audited statement fidelity, correctness, priority, or novelty.

What AI did

GPT-5.5

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.

Provider: OpenAI · Prompt public: unknown · Independence: unknown

Verification boundary

unreviewed

Single-author arXiv preprint; not yet peer-reviewed.

Correctness: unknown · statement fidelity: unaudited · peer review: none

Timeline

  1. arXiv:2605.25515 - Lipschitz Functions on Sparse Graphs II

    Resolved the sharp constant (w.h.p.) for random graphs G(n, d/n)

Known method families

argument (source-reported)

Source-reported tools: argument.

Independent: unknown · difference confidence: 0

What remains uncertain

VibeMath has not independently audited the mathematical statement, proof, or novelty claim.

  • VibeMath has not independently verified the mathematical claim.
  • AI-attempt independence and training-data exposure are unknown unless explicitly documented.
  • VibeMath has not independently audited the mathematical statement, proof, or novelty claim.