Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Finite-Type Invariants of order one for long virtual knots   We extend to the long virtual knot case the constructions first presented by
A. Henrich and later generalized by the author to the framed virtual knot case.
These consist of three Vassiliev invariants of order one, including a universal
one, as well as the notions of a based matrix and a singular based matrix and
their relation to long flat virtual knots.

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The categories of this paper are: nucl-th
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The categories of this paper are: dg-ga
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The categories of this paper are: hep-lat
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The categories of this paper are: cond-mat
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The categories of this paper are: adap-org
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The categories of this paper are: plasm-ph
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The categories of this paper are: cs
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The categories of this paper are: hep-ex
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The categories of this paper are: comp-gas
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The categories of this paper are: astro-ph
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The categories of this paper are: q-bio
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The categories of this paper are: cmp-lg
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The categories of this paper are: ao-sci
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The categories of this paper are: funct-an
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The categories of this paper are: solv-int
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The categories of this paper are: patt-sol