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 "a generalized sylvester gallai type theorem for quadratic polynomials"):
  Abstract: In this work we prove a version of the Sylvester-Gallai theorem for quadratic polynomials that takes us one step closer to obtaining a deterministic polynomial time algorithm for testing zeroness of $\Sigma^{[3]}\Pi\Sigma\Pi^{[2]}$ circuits. Specifically, we prove that if a finite set of irreducible quadratic polynomials $\mathcal{Q}$ satisfy that for every two polynomials $Q_1,Q_2\in \mathcal{Q}$ there is a subset $\mathcal{K}\subset \mathcal{Q}$, such that $Q_1,Q_2 \notin \mathcal{K}$ and whenever $Q_1$ and $Q_2$ vanish then also $\prod_{i\in \mathcal{K}} Q_i$ vanishes, then the linear span of the polynomials in $\mathcal{Q}$ has dimension $O(1)$. This extends the earlier result [Shpilka19] that showed a similar conclusion when $|\mathcal{K}| = 1$. #R##N#An important technical step in our proof is a theorem classifying all the possible cases in which a product of quadratic polynomials can vanish when two other quadratic polynomials vanish. I.e., when the product is in the radical of the ideal generates by the two quadratics. This step extends a result from [Shpilka19]that studied the case when one quadratic polynomial is in the radical of two other quadratics.

Includes members:
  Member "the matching problem in general graphs is in quasi nc":
    also connected through other hyperedges:
      - Hyperedge HE-1 (induced by source paper "equivalence classes and conditional hardness in massively parallel computations")
  Member "reconstruction of real depth 3 circuits with top fan in 2":
    also connected through other hyperedges:
      - Hyperedge HE-2 (induced by source paper "discovering the roots uniform closure results for algebraic classes under factoring")
  Member "progress on polynomial identity testing ii":
    also connected through other hyperedges:
      - Hyperedge HE-3 (induced by source paper "subspace arrangements graph rigidity and derandomization through submodular optimization")
  Member "explicit noether normalization for simultaneous conjugation via polynomial identity testing":
    also connected through other hyperedges:
      - Hyperedge HE-4 (induced by source paper "operator scaling via geodesically convex optimization invariant theory and polynomial identity testing")
  Member "geometric complexity theory v efficient algorithms for noether normalization":
    also connected through other hyperedges:
      - Hyperedge HE-5 (induced by source paper "general linear group action on tensors a candidate for post quantum cryptography")
  Member "algebraic independence and blackbox identity testing":
    also connected through other hyperedges:
      - Hyperedge HE-6 (induced by source paper "polynomial invariant theory and shape enumerator of self dual codes in the nrt metric")
  Member "blackbox identity testing for bounded top fanin depth 3 circuits the field doesn t matter":
    also connected through other hyperedges:
      - Hyperedge HE-7 (induced by source paper "succinct hitting sets and barriers to proving algebraic circuits lower bounds")

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)