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: "a formal proof of hensel s lemma over the p adic integers"
  Abstract: The field of p-adic numbers ℚp and the ring of p-adic integers ℤp are essential constructions of modern number theory. Hensel’s lemma, described by Gouvea as the “most important algebraic property of the p-adic numbers,” shows the existence of roots of polynomials over ℤp provided an initial seed point. The theorem can be proved for the p-adics with significantly weaker hypotheses than for general rings. We construct ℚp and ℤp in the Lean proof assistant, with various associated algebraic properties, and formally prove a strong form of Hensel’s lemma. The proof lies at the intersection of algebraic and analytic reasoning and demonstrates how the Lean mathematical library handles such a heterogeneous topic.

Connected through hyperedge HE-1 (induced by source paper "normalizing casts and coercions"):
  with members:
    - "tabled typeclass resolution"
    - "the lean mathematical library"
    - "formalising perfectoid spaces"

Connected through hyperedge HE-2 (induced by source paper "the lean mathematical library"):
  with members:
    - "counting immutable beans reference counting optimized for purely functional programming"
    - "a formalization of forcing and the unprovability of the continuum hypothesis"
    - "formalizing the solution to the cap set problem"
    - "formalising perfectoid spaces"
    - "formalizing computability theory via partial recursive functions"
    - "congruence closure in intensional type theory"
    - "type classes for mathematics in type theory"

Connected through hyperedge HE-3 (induced by source paper "formalizing the solution to the cap set problem"):
  with members:
    - "homotopy type theory in lean"
    - "formal proofs of transcendence for e and pi as an application of multivariate and symmetric polynomials"
    - "type classes for mathematics in type theory"

Connected through hyperedge HE-4 (induced by source paper "formalising perfectoid spaces"):
  with members:
    - "the lean mathematical library"
    - "formalizing the solution to the cap set problem"

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.LO(Logic in Computer Science)