Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Presto! Digitization, Part I: From NKS Number Theory to "XORbitant"
  Semantics, by way of Cayley-Dickson Process and Zero-Divisor-based
  "Representations"   The objects of the great Nonlinear Revolutions - Catastrophes and Chaos in
the 1960s-70s (henceforth, CT); and, small-world and scale-free Network Theory
(NT), emerging quite recently - will be spliced together by a New Kind of
Number Theory, focused on digitizations (i.e., binary strings). NT nodes then
become feature-rich representations (nodules in a "rhizosphere") of CT
contents. The "Box-Kite" formalism of zero-divisors (ZD's) - first showing in
the 16-D Sedenions, then in all higher 2^N-ions derived from Imaginaries by
Cayley-Dickson Process (CDP) - can model such "enriched" nodules. Its
(bit-string XOR-ing vs. matrix-multiplying) operations unfold into
"representations" of the objects linked in CT with "partitions of Nullity":
Singularities. The route from here to fractals and Chaos, via CDP extensions to
2^N-ions for growing N, will involve us in graphics of higher-dimensional
"carry-bit overflow," as manifest in the mandala-like patterns of "emanation
tables" (the rough equivalent, for ZD's, of group theorists' Cayley Tables).
I'll lead into this with a quote about "Hjelmslev's Net" (which I'll claim is
the CDP manque') from a famous postmodern text, Deleuze and Guattari's "A
Thousand Plateaus" (where "rhizosphere" imagery arose). With strong assists
from the CT-based structuralism of Jean Petitot, Algirdas Greimas's "Semiotic
Square" will show us how to explicitly link CT to semiotic foundations via ZD
"representations," while the infinite-dimensional ZD meta-fractal or "Sky"
where Box-Kites fly - first appearing in the 32-D Pathions and incorporating
the higher 2^N-ions - will provide sufficient lebensraum for Levi-Strauss's
"Canonical Formula" of mythwork to unfurl in. (These results serve to extend my
NKS 2004 paper, available at the Wolfram Science website.)

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The categories of this paper are: gr-qc
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The categories of this paper are: patt-sol
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The categories of this paper are: q-alg
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The categories of this paper are: chao-dyn
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The categories of this paper are: atom-ph
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The categories of this paper are: chem-ph
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The categories of this paper are: funct-an
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The categories of this paper are: ao-sci
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The categories of this paper are: plasm-ph
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The categories of this paper are: hep-ex
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The categories of this paper are: hep-th
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The categories of this paper are: hep-lat
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The categories of this paper are: physics
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The categories of this paper are: cs
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The categories of this paper are: q-fin
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The categories of this paper are: astro-ph