Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Placeholder Substructures III: A Bit-String-Driven ''Recipe Theory'' for
  Infinite-Dimensional Zero-Divisor Spaces   Zero-divisors (ZDs) derived by Cayley-Dickson Process (CDP) from
N-dimensional hypercomplex numbers (N a power of 2, at least 4) can represent
singularities and, as N approaches infinite, fractals -- and thereby,scale-free
networks. Any integer greater than 8 and not a power of 2 generates a
meta-fractal or "Sky" when it is interpreted as the "strut constant" (S) of an
ensemble of octahedral vertex figures called "Box-Kites" (the fundamental
building blocks of ZDs). Remarkably simple bit-manipulation rules or "recipes"
provide tools for transforming one fractal genus into others within the context
of Wolfram's Class 4 complexity.

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The categories of this paper are: alg-geom
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The categories of this paper are: hep-ex
12
The categories of this paper are: nucl-th
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The categories of this paper are: solv-int
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The categories of this paper are: bayes-an
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The categories of this paper are: q-fin
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The categories of this paper are: plasm-ph
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The categories of this paper are: econ
6
The categories of this paper are: astro-ph
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The categories of this paper are: hep-lat
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The categories of this paper are: comp-gas
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The categories of this paper are: q-alg
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The categories of this paper are: nucl-ex
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The categories of this paper are: quant-ph
9
The categories of this paper are: nlin
7
The categories of this paper are: hep-th