Math RefereeA uniform influence bound for hypergraph properties
Independent panel assessments · paired prompt comparison
The proposed argument
The proof combines biased Fourier identities, restriction to a vertex block, and a bound on captured low-degree mass. It chooses a block and cutoff to combine this with the Fourier tail uniformly in the bias, and then integrates the influence bound for increasing properties.
This test concerns this manuscript only. Independent human mathematical assessment remains pending.
Reading order
Follow the dependencies
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Your independent assessment
Track the dependence on p, r, and n through restriction and low-degree capture, including cutoffs below one. Check the stated uniformity in p and the separate threshold-width consequence.