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 "implementing geometric complexity theory on the separation of orbit closures via symmetries"):
  Abstract: Understanding the difference between group orbits and their closures is a key difficulty in geometric complexity theory (GCT): While the GCT program is set up to separate certain orbit closures, many beautiful mathematical properties are only known for the group orbits, in particular close relations with symmetry groups and invariant spaces, while the orbit closures seem much more difficult to understand. However, in order to prove lower bounds in algebraic complexity theory, considering group orbits is not enough. #R##N#In this paper we tighten the relationship between the orbit of the power sum polynomial and its closure, so that we can separate this orbit closure from the orbit closure of the product of variables by just considering the symmetry groups of both polynomials and their representation theoretic decomposition coefficients. In a natural way our construction yields a multiplicity obstruction that is neither an occurrence obstruction, nor a so-called vanishing ideal occurrence obstruction. All multiplicity obstructions so far have been of one of these two types. #R##N#Our paper is the first implementation of the ambitious approach that was originally suggested in the first papers on geometric complexity theory by Mulmuley and Sohoni (SIAM J Comput 2001, 2008): Before our paper, all existence proofs of obstructions only took into account the symmetry group of one of the two polynomials (or tensors) that were to be separated. In our paper the multiplicity obstruction is obtained by comparing the representation theoretic decomposition coefficients of both symmetry groups. #R##N#Our proof uses a semi-explicit description of the coordinate ring of the orbit closure of the power sum polynomial in terms of Young tableaux, which enables its comparison to the coordinate ring of the orbit.

Includes members:
  Member "on geometric complexity theory multiplicity obstructions are stronger than occurrence obstructions":
    also connected through other hyperedges:
      - Hyperedge HE-1 (induced by source paper "the computational complexity of plethysm coefficients")
  Member "the complexity of factors of multivariate polynomials":
    also connected through other hyperedges:
      - Hyperedge HE-2 (induced by source paper "algebraic branching programs border complexity and tangent spaces")
  Member "succinct hitting sets and barriers to proving algebraic circuits lower bounds":
    also connected through other hyperedges:
      - Hyperedge HE-3 (induced by source paper "variety membership testing algebraic natural proofs and geometric complexity theory")
  Member "towards an algebraic natural proofs barrier via polynomial identity testing":
    also connected through other hyperedges:
      - Hyperedge HE-4 (induced by source paper "variety membership testing algebraic natural proofs and geometric complexity theory")
  Member "membership in moment polytopes is in np and conp":
    also connected through other hyperedges:
      - Hyperedge HE-5 (induced by source paper "efficient algorithms for tensor scaling quantum marginals and moment polytopes")
  Member "on vanishing of kronecker coefficients":
    also connected through other hyperedges:
      - Hyperedge HE-6 (induced by source paper "the computational complexity of plethysm coefficients")
  Member "geometric complexity theory and matrix powering":
    also connected through other hyperedges:
      - Hyperedge HE-7 (induced by source paper "the computational complexity of plethysm coefficients")
  Member "no occurrence obstructions 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)