Problem detail · source-aware
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For an inclusion-free hypergraph on $n$ vertices, a weight assignment $w:[n]\to[d]$ is isolating when a unique edge attains minimum weight. Faber and Harris conjectured that the number of isolating assignments is at least $n\sum_{j=0}^{d-1} j^{n-1}$, attained by the hypergraph of $n$ singleton edges. The bound holds, and extends to a more general class of objective functions.
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.
The acknowledgement credits the model with one specific and load-bearing step: the proof benefited from its assistance in discovering the fractional charging argument. The authors are the pair who stated the conjecture in 2018.
Provider: OpenAI · Prompt public: unknown · Independence: unknown
arXiv preprint; not yet peer-reviewed.
Correctness: unknown · statement fidelity: unaudited · peer review: none
VibeMathed reports this item as resolved. VibeMath preserves that report as a source assertion and has not independently authored a plain-language mathematical explanation.
Source-reported tools: argument.
Independent: unknown · difference confidence: 0
VibeMath has not independently audited the mathematical statement, proof, or novelty claim.