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
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
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
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
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
First report of the hypercube upper bound.
Read this published revision