Reproduce “Log-Concavity and Kesten–Stigum Tightness for Planted 3-SAT Broadcasts” on OpenResearch
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About this paper
Yan Ru Pei
The authors analyze root reconstruction on a Poisson hypertree modeling planted 3-SAT. They transform signed clause observations into a symmetric channel and track chi-square capacity across tree levels. A second-order coefficient identifies robust behavior at the Kesten–Stigum threshold. Exact-leaf tightness is proved for p0=0–0.0321; reconstruction at p0=0.10 is certified below the threshold, while the intervening exact-leaf boundary remains open.
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