The sl(2) weight system at c = -3/32 extends to a graph 4-invariant: Lean 4 formalization and verification code

Lean 4 formalization of the paper The sl(2) weight system at c = -3/32 extends to a graph 4-invariant by Deep Bhattacharjee and Ushashi Bhattacharya, with the LaTeX source, the paper as a PDF, and independent checks in Python, Julia, C and C++.

The paper proves the conjecture of Fomichev, Karev, Pavutnitskiy and Usanov (arXiv:2607.24217, Section 4) that the specialization of the 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) is the signed count of assignments of 2-element subsets of {1,...,N} to the n vertices of G, with sign (-1)^{|p(x) ∩ p(y)|} on each edge xy. The Lean theorem SL2W.main_theorem states both parts of the conjecture and depends only on the axioms propext, Classical.choice and Quot.sound.