Lipschitz Functions on Sparse Graphs II

Samuel Korsky

For the Lipschitz-function growth constant c(Q_d) of the d-dimensional hypercube, log c(Q_d)≤(3/4+o(1))(log d)/d. The argument compares graph homomorphisms with K_(d,d).

Sources for this record

What was already known

Korsky, Saffat and Aiylam introduced c(G) and earlier sparse-graph bounds. Galvin and Tetali’s graph-homomorphism comparison theorem supplies a prior input.

AI involvement AI-centered

Samuel Korsky credits GPT-5.5 with the hypercube bound mechanism, computations and initial draft. Korsky developed the separate sharp random-graph theorem and presents the hypercube argument.

The model supplied the retained upper-bound mechanism, but the paper’s main random-graph advance is human-origin and the comparison theorem is prior work.

Importance Modest

Provides a distinct upper bound for hypercube growth constants.

Limitations

This is an auxiliary, non-sharp hypercube estimate. The paper’s sharp random-graph constant is Korsky’s human-origin result and is outside this AI contribution; no completed check of the hypercube proof is documented.

Technical verification Reported

A paper proof is present, but no completed check of the hypercube upper-bound argument by a named human or machine is documented.

Human understanding Few

The initial draft and bound mechanism are credited to GPT-5.5; no named human explanation of that mechanism is documented. Few is the evidence default.

Correction and publication history