human: Given a hyperedge-centered hypergraph: <hypergraph>, where the center hyperedge is induced by one source paper and its member nodes are the cited papers.

Details of the hypergraph:
Center hyperedge (induced by source paper "information theoretic thresholds from the cavity method"):
  Abstract: Abstract   Vindicating a sophisticated but non-rigorous physics approach called the cavity method, we establish a formula for the mutual information in statistical inference problems induced by random graphs and we show that the mutual information holds the key to understanding certain important phase transitions in random graph models. We work out several concrete applications of these general results. For instance, we pinpoint the exact condensation phase transition in the Potts antiferromagnet on the random graph, thereby improving prior approximate results (Contucci et al., 2013)  [34] . Further, we prove the conjecture from Krzakala et al. (2007)  [55]  about the condensation phase transition in the random graph coloring problem for any number    q  ≥  3    of colors. Moreover, we prove the conjecture on the information-theoretic threshold in the disassortative stochastic block model (Decelle et al., 2011)  [35] . Additionally, our general result implies the conjectured formula for the mutual information in Low-Density Generator Matrix codes (Montanari, 2005)  [73] .

Includes members:
  Member "planting colourings silently":
    also connected through other hyperedges:
      - Hyperedge HE-1 (induced by source paper "charting the replica symmetric phase")
  Member "mutual information in rank one matrix estimation":
    also connected through other hyperedges:
      - Hyperedge HE-2 (induced by source paper "overlap matrix concentration in optimal bayesian inference")
  Member "the condensation phase transition in random graph coloring":
    also connected through other hyperedges:
      - Hyperedge HE-3 (induced by source paper "charting the replica symmetric phase")
  Member "asymptotic mutual information for the two groups stochastic block model":
    also connected through other hyperedges:
      - Hyperedge HE-4 (induced by source paper "the kikuchi hierarchy and tensor pca")
  Member "semidefinite programs on sparse random graphs and their application to community detection":
    also connected through other hyperedges:
      - Hyperedge HE-5 (induced by source paper "computational hardness of certifying bounds on constrained pca problems")
  Member "conditioning and covariance on caterpillars":
    also connected through other hyperedges:
      - Hyperedge HE-6 (induced by source paper "mean field approximation convex hierarchies and the optimality of correlation rounding a unified perspective")
  Member "chasing the k colorability threshold":
    also connected through other hyperedges:
      - Hyperedge HE-7 (induced by source paper "the rate distortion function and excess distortion exponent of sparse regression codes with optimal encoding")
  Member "on the complexity of random satisfiability problems with planted solutions":
    also connected through other hyperedges:
      - Hyperedge HE-8 (induced by source paper "sum of squares meets square loss fast rates for agnostic tensor completion")

Question: Please tell me which class the source paper belongs to. The 40 classes are: cs.NA(Numerical Analysis), cs.MM(Multimedia), cs.LO(Logic in Computer Science), cs.CY(Computers and Society), cs.CR(Cryptography and Security), cs.DC(Distributed, Parallel, and Cluster Computing), cs.HC(Human-Computer Interaction), cs.CE(Computational Engineering, Finance, and Science), cs.NI(Networking and Internet Architecture), cs.CC(Computational Complexity), cs.AI(Artificial Intelligence), cs.MA(Multiagent Systems), cs.GL(General Literature), cs.NE(Neural and Evolutionary Computing), cs.SC(Symbolic Computation), cs.AR(Hardware Architecture), cs.CV(Computer Vision and Pattern Recognition), cs.GR(Graphics), cs.ET(Emerging Technologies), cs.SY(Systems and Control), cs.CG(Computational Geometry), cs.OH(Other Computer Science), cs.PL(Programming Languages), cs.SE(Software Engineering), cs.LG(Machine Learning), cs.SD(Sound), cs.SI(Social and Information Networks), cs.RO(Robotics), cs.IT(Information Theory), cs.PF(Performance), cs.CL(Computation and Language), cs.IR(Information Retrieval), cs.MS(Mathematical Software), cs.FL(Formal Languages and Automata Theory), cs.DS(Data Structures and Algorithms), cs.OS(Operating Systems), cs.GT(Computer Science and Game Theory), cs.DB(Databases), cs.DL(Digital Libraries), cs.DM(Discrete Mathematics). Directly output the class name.

gpt: cs.DM(Discrete Mathematics)