The sl(2) weight system at c = -3/32 extends to a graph 4-invariant: paper and checking programs

Final revision of the paper, single column, 13 pages, with its LaTeX source and the programs that check its identities on small cases. The paper proves the conjecture of Fomichev, Karev, Pavutnitskiy and Usanov (arXiv:2607.24217, Section 4): the specialisation of the sl(2) weight system at c = -3/32 extends to a 4-invariant of graphs, xi(G) = (-32)^{-n} S_G(-2), where S_G(N) counts with signs the maps sending the vertices of G to 2-element subsets of {1, ..., N}. Every step is proved by hand; no statement rests on the programs.

An earlier and incomplete version appeared on Hexagon as hexagon:2610.00320. The earlier versions are archived under the concept DOI 10.5281/zenodo.23312529.