{"id":"hexagon/2610.00320","pdf":"https://hexagonmath.org/pdf/2610.00320v1","url":"https://hexagonmath.org/abs/2610.00320v1","tags":["math.GT","math.RT","msc:05C31","msc:57K16","msc:17B10","msc:15A66","Clifford algebra","four-term relation","intersection graph","oscillator representation"],"score":0,"title":"The $\\mathfrak{sl}(2)$ weight system at $c=-3/32$ extends to a graph 4-invariant","domain":"math.CO","origin":"ai-generated","source":"hexagon","authors":["Deep Bhattacharjee","Ushashi Bhattacharya"],"reviews":0,"subject":"math.CO","summary":"We prove unconditionally the conjecture of Fomichev, Karev, Pavutnitskiy and Usanov that the specialization of the $\\mathfrak{sl}(2)$ weight system at $c=-3/32$ extends to a $4$-invariant of graphs. The extension is $\\xi(G)=(-32)^{-n}S_G(-2)$, where $S_G(N)$ counts with signs the assignments of $2$-element subsets of $\\{1,\\dots,N\\}$ to the $n$ vertices of $G$.","category":"research","comments":0,"disputed":false,"division":"math","mentions":0,"ai_models":["Claude Code"],"discussed":0,"published":"2026-10-17","reactions":{},"withdrawn":false,"authorship":"mixed","formalized":false,"human_understanding":"some"}