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 "ppp completeness with connections to cryptography"):
  Abstract: Polynomial Pigeonhole Principle (PPP) is an important subclass of TFNP with profound connections to the complexity of the fundamental cryptographic primitives: collision-resistant hash functions and one-way permutations. In contrast to most of the other subclasses of TFNP, no complete problem is known for PPP. Our work identifies the first PPP-complete problem without any circuit or Turing Machine given explicitly in the input, and thus we answer a longstanding open question from [Papadimitriou1994]. Specifically, we show that constrained-SIS (cSIS), a generalized version of the well-known Short Integer Solution problem (SIS) from lattice-based cryptography, is PPP-complete. #R##N#In order to give intuition behind our reduction for constrained-SIS, we identify another PPP-complete problem with a circuit in the input but closely related to lattice problems. We call this problem BLICHFELDT and it is the computational problem associated with Blichfeldt's fundamental theorem in the theory of lattices. #R##N#Building on the inherent connection of PPP with collision-resistant hash functions, we use our completeness result to construct the first natural hash function family that captures the hardness of all collision-resistant hash functions in a worst-case sense, i.e. it is natural and universal in the worst-case. The close resemblance of our hash function family with SIS, leads us to the first candidate collision-resistant hash function that is both natural and universal in an average-case sense. #R##N#Finally, our results enrich our understanding of the connections between PPP, lattice problems and other concrete cryptographic assumptions, such as the discrete logarithm problem over general groups.

Includes members:
  Member "on the polynomial parity argument complexity of the combinatorial nullstellensatz":
    also connected through other hyperedges:
      - Hyperedge HE-1 (induced by source paper "on the complexity of modulo q arguments and the chevalley warning theorem")
  Member "consensus halving is ppa complete":
    also connected through other hyperedges:
      - Hyperedge HE-2 (induced by source paper "consenus halving does it ever get easier")
  Member "cls new problems and completeness":
    also connected through other hyperedges:
      - Hyperedge HE-3 (induced by source paper "unique end of potential line")
  Member "a converse to banach s fixed point theorem and its cls completeness":
    also connected through other hyperedges:
      - Hyperedge HE-4 (induced by source paper "spectral inference networks unifying deep and spectral learning")
  Member "local max cut in smoothed polynomial time":
    also connected through other hyperedges:
      - Hyperedge HE-5 (induced by source paper "node max cut and computing equilibria in linear weighted congestion games")
  Member "integer factoring and modular square roots":
    also connected through other hyperedges:
      - Hyperedge HE-6 (induced by source paper "the classes ppa k existence from arguments modulo k")
  Member "settling the complexity of computing approximate two player nash equilibria":
    also connected through other hyperedges:
      - Hyperedge HE-7 (induced by source paper "complexity theory game theory and economics the barbados lectures")
  Member "number balancing is as hard as minkowski s theorem and shortest vector":
    also connected through other hyperedges:
      - Hyperedge HE-8 (induced by source paper "equal subset sum faster than the meet in the middle")

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.CC(Computational Complexity)