4 problems

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Non-definability of Gauss diagram realizability in first-order logic with parity quantifiers
Non-definability conjecture. Realizability of Gauss diagrams cannot be defined in first-order logic with a parity quantifier over their interlacement graphs.
Conjectureopenfinite-model-theory gauss-diagrams graph-theoryarXiv posted 2 days ago
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Kosaka's conjecture on virtual bridge number and primary data
Kosaka's conjecture. Virtual knots have the same virtual bridge number if they have the same primary data.
Conjectureopenbridge-number gauss-diagrams virtual-knotsarXiv posted 2 days ago
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Goussarov's realization conjecture for finite type knot invariants
A finite type invariant of classical knots is an invariant obtained from the finite-type filtration of knot invariants. A Gauss diagram formula is a combinatorial formula on Gauss…
Conjectureopenfinite-type-invariants gauss-diagrams knot-theoryarXiv posted 2 days ago
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Polyak's conjecture on Gauss diagram formulas and degenerate diagrams
A Gauss diagram formula for a knot in $\mathbb{S}^3$ is an element of the space of arrow-diagram formulas satisfying the relations coming from Reidemeister moves. Let…
Conjectureopenfinite-type-invariants gauss-diagrams knot-theoryarXiv posted 2 days ago

Non-definability of Gauss diagram realizability in first-order logic with parity quantifiers