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 statistical mechanical interpretation of algorithmic information theory iii composite systems and fixed points"):
  Abstract: The statistical mechanical interpretation of algorithmic information theory (AIT, for short) was introduced and developed by our former works [K. Tadaki, Local Proceedings of CiE 2008, pp.425-434, 2008] and [K. Tadaki, Proceedings of LFCS'09, Springer's LNCS, vol.5407, pp.422-440, 2009], where we introduced the notion of thermodynamic quantities, such as partition function Z(T), free energy F(T), energy E(T), and statistical mechanical entropy S(T), into AIT. We then discovered that, in the interpretation, the temperature T equals to the partial randomness of the values of all these thermodynamic quantities, where the notion of partial randomness is a stronger representation of the compression rate by means of program-size complexity. Furthermore, we showed that this situation holds for the temperature itself as a thermodynamic quantity, namely, for each of all the thermodynamic quantities above, the computability of its value at temperature T gives a sufficient condition for T in (0,1) to be a fixed point on partial randomness. In this paper, we develop the statistical mechanical interpretation of AIT further and pursue its formal correspondence to normal statistical mechanics. The thermodynamic quantities in AIT are defined based on the halting set of an optimal computer, which is a universal decoding algorithm used to define the notion of program-size complexity. We show that there are infinitely many optimal computers which give completely different sufficient conditions in each of the thermodynamic quantities in AIT. We do this by introducing the notion of composition of computers into AIT, which corresponds to the notion of composition of systems in normal statistical mechanics.

Includes members:
  Member "a statistical mechanical interpretation of algorithmic information theory":
    also connected through other hyperedges:
      - Hyperedge HE-1 (induced by source paper "distinction graphs and graphtropy a formalized phenomenological layer underlying classical and quantum entropy observational semantics and cognitive computation")
  Member "fixed point theorems on partial randomness":
    also connected through other hyperedges:
      - Hyperedge HE-2 (induced by source paper "a statistical mechanical interpretation of algorithmic information theory")
  Member "a statistical mechanical interpretation of instantaneous codes":
    also connected through other hyperedges:
      - Hyperedge HE-3 (induced by source paper "a statistical mechanical interpretation of algorithmic information theory")
  Member "natural halting probabilities partial randomness and zeta functions":
    also connected through other hyperedges:
      - Hyperedge HE-4 (induced by source paper "a statistical mechanical interpretation of algorithmic information theory")

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.IT(Information Theory)