human: Given a node-centered hypergraph: <hypergraph>, where nodes represent papers and hyperedges represent sets of papers co-cited by a source paper.

Details of the hypergraph:
Center node: "circuit complexity proof complexity and polynomial identity testing"
  Abstract: We introduce a new algebraic proof system, which has tight connections to (algebraic) circuit complexity. In particular, we show that any super-polynomial lower bound on any Boolean tautology in our proof system implies that the permanent does not have polynomial-size algebraic circuits (VNP is not equal to VP). As a corollary to the proof, we also show that super-polynomial lower bounds on the number of lines in Polynomial Calculus proofs (as opposed to the usual measure of number of monomials) imply the Permanent versus Determinant Conjecture. Note that, prior to our work, there was no proof system for which lower bounds on an arbitrary tautology implied any computational lower bound. #R##N#Our proof system helps clarify the relationships between previous algebraic proof systems, and begins to shed light on why proof complexity lower bounds for various proof systems have been so much harder than lower bounds on the corresponding circuit classes. In doing so, we highlight the importance of polynomial identity testing (PIT) for understanding proof complexity. #R##N#More specifically, we introduce certain propositional axioms satisfied by any Boolean circuit computing PIT. We use these PIT axioms to shed light on AC^0[p]-Frege lower bounds, which have been open for nearly 30 years, with no satisfactory explanation as to their apparent difficulty. We show that either: a) Proving super-polynomial lower bounds on AC^0[p]-Frege implies VNP does not have polynomial-size circuits of depth d - a notoriously open question for d at least 4 - thus explaining the difficulty of lower bounds on AC^0[p]-Frege, or b) AC^0[p]-Frege cannot efficiently prove the depth d PIT axioms, and hence we have a lower bound on AC^0[p]-Frege. #R##N#Using the algebraic structure of our proof system, we propose a novel way to extend techniques from algebraic circuit complexity to prove lower bounds in proof complexity.

Connected through hyperedge HE-1 (induced by source paper "search problems in algebraic complexity gct and hardness of generator for invariant rings"):
  with members:
    - "operator scaling via geodesically convex optimization invariant theory and polynomial identity testing"
    - "alternating minimization scaling algorithms and the null cone problem from invariant theory"
    - "no occurrence obstructions in geometric complexity theory"
    - "algorithmic and optimization aspects of brascamp lieb inequalities via operator scaling"
    - "a deterministic polynomial time algorithm for non commutative rational identity testing"
    - "geometric complexity theory v efficient algorithms for noether normalization"

Connected through hyperedge HE-2 (induced by source paper "towards an algebraic natural proofs barrier via polynomial identity testing"):
  with members:
    - "succinct hitting sets and barriers to proving algebraic circuits lower bounds"
    - "arithmetic circuits with locally low algebraic rank"
    - "geometric complexity theory and matrix powering"
    - "functional lower bounds for arithmetic circuits and connections to boolean circuit complexity"
    - "no occurrence obstructions in geometric complexity theory"
    - "the chasm at depth four and tensor rank old results new insights"
    - "on minimal free resolutions and the method of shifted partial derivatives in complexity theory"
    - "rectangular kronecker coefficients and plethysms in geometric complexity theory"

Connected through hyperedge HE-3 (induced by source paper "proof complexity lower bounds from algebraic circuit complexity"):
  with members:
    - "functional lower bounds for arithmetic circuits and connections to boolean circuit complexity"
    - "an exponential lower bound for homogeneous depth 5 circuits over finite fields"
    - "identity testing and lower bounds for read k oblivious algebraic branching programs"
    - "subexponential size hitting sets for bounded depth multilinear formulas"
    - "hitting sets for roabp and sum of set multilinear circuits"
    - "deterministic identity testing for sum of read once oblivious arithmetic branching programs"
    - "explicit noether normalization for simultaneous conjugation via polynomial identity testing"
    - "quasipolynomial time identity testing of non commutative and read once oblivious algebraic branching programs"

Connected through hyperedge HE-4 (induced by source paper "algebraic proof complexity progress frontiers and challenges"):
  with members:
    - "functional lower bounds for arithmetic circuits and connections to boolean circuit complexity"
    - "proof complexity lower bounds from algebraic circuit complexity"
    - "a deterministic polynomial time algorithm for non commutative rational identity testing"
    - "generating matrix identities and proof complexity"
    - "short proofs for the determinant identities"
    - "algebraic proofs over noncommutative formulas"
    - "resolution over linear equations and multilinear proofs"

Connected through hyperedge HE-5 (induced by source paper "strong eth breaks with merlin and arthur short non interactive proofs of batch evaluation"):
  with members:
    - "quadratic time hardness of lcs and other sequence similarity measures"
    - "probabilistic polynomials and hamming nearest neighbors"
    - "why walking the dog takes time frechet distance has no strongly subquadratic algorithms unless seth fails"
    - "popular conjectures imply strong lower bounds for dynamic problems"
    - "edit distance cannot be computed in strongly subquadratic time unless seth is false"
    - "time optimal interactive proofs for circuit evaluation"
    - "a satisfiability algorithm for sparse depth two threshold circuits"

Connected through hyperedge HE-6 (induced by source paper "functional lower bounds for arithmetic circuits and connections to boolean circuit complexity"):
  with members:
    - "proof complexity lower bounds from algebraic circuit complexity"
    - "an exponential lower bound for homogeneous depth 5 circuits over finite fields"
    - "on the power of homogeneous depth 4 arithmetic circuits"

Connected through hyperedge HE-7 (induced by source paper "characterizing propositional proofs as non commutative formulas"):
  with members:
    - "generating matrix identities and proof complexity"
    - "algebraic proofs over noncommutative formulas"

Connected through hyperedge HE-8 (induced by source paper "generating matrix identities and proof complexity"):
  with members:
    - "short proofs for the determinant identities"

Question: Please tell me which class the center node 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)