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 "variety membership testing algebraic natural proofs and geometric complexity theory"):
  Abstract: We study the variety membership testing problem in the case when the variety is given as an orbit closure and the ambient space is the set of all 3-tensors. The first variety that we consider is the slice rank variety, which consists of all 3-tensors of slice rank at most $r$. We show that the membership testing problem for the slice rank variety is $\NP$-hard. While the slice rank variety is a union of orbit closures, we define another variety, the minrank variety, expressible as a single orbit closure. Our next result is the $\NP$-hardness of membership testing in the minrank variety, hence we establish the $\NP$-hardness of the orbit closure containment problem for 3-tensors. #R##N#Algebraic natural proofs were recently introduced by Forbes, Shpilka and Volk and independently by Grochow, Kumar, Saks and Saraf. Blaser et al. gave a version of an algebraic natural proof barrier for the matrix completion problem which relies on $\coNP \subseteq \exists \BPP$. It implied that constructing equations for the corresponding variety should be hard. We generalize their approach to work with any family of varieties for which the membership problem is $\NP$-hard and for which we can efficiently generate a dense subset. Therefore, a similar barrier holds for the slice rank and the minrank varieties, too. This allows us to set up the slice rank and the minrank varieties as a test-bed for geometric complexity theory (GCT). We determine the stabilizers of the tensors that generate the orbit closures of the two varieties and prove that these tensors are almost characterized by their symmetries. We prove several nontrivial equations for both the varieties using different GCT methods. Many equations also work in the regime where membership testing in the slice rank or minrank varieties is $\NP$-hard. We view this as a promising sign that the GCT approach might indeed be successful.

Includes members:
  Member "alternating minimization scaling algorithms and the null cone problem from invariant theory":
    also connected through other hyperedges:
      - Hyperedge HE-1 (induced by source paper "rigorous guarantees for tyler s m estimator via quantum expansion")
  Member "barriers for rank methods in arithmetic complexity":
    also connected through other hyperedges:
      - Hyperedge HE-2 (induced by source paper "more barriers for rank methods via a numeric to symbolic transfer")
  Member "succinct hitting sets and barriers to proving algebraic circuits lower bounds":
    also connected through other hyperedges:
      - Hyperedge HE-3 (induced by source paper "implementing geometric complexity theory on the separation of orbit closures via symmetries")
  Member "discovering the roots uniform closure results for algebraic classes under factoring":
    also connected through other hyperedges:
      - Hyperedge HE-4 (induced by source paper "schur polynomials do not have small formulas if the determinant doesn t")
  Member "towards an algebraic natural proofs barrier via polynomial identity testing":
    also connected through other hyperedges:
      - Hyperedge HE-5 (induced by source paper "implementing geometric complexity theory on the separation of orbit closures via symmetries")
  Member "on the complexity of the permanent in various computational models":
    also connected through other hyperedges:
      - Hyperedge HE-6 (induced by source paper "geometric complexity theory and matrix powering")
  Member "the complexity of tensor rank":
    also connected through other hyperedges:
      - Hyperedge HE-7 (induced by source paper "optimal curve straightening is exists mathbb r complete")
  Member "rectangular kronecker coefficients and plethysms in geometric complexity theory":
    also connected through other hyperedges:
      - Hyperedge HE-8 (induced by source paper "the computational complexity of plethysm coefficients")

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)