A graph with three card types and five vertex orbits (Kourovka Notebook Problem 20.71(b)): Lean 4 formalization and verification code

Lean 4 formalization of the paper A graph with three card types and five vertex orbits by Deep Bhattacharjee and Ushashi Bhattacharya, with the LaTeX source, the paper as a PDF, and independent checks in Python, Julia, C and C++.

Problem 20.71 of the Kourovka Notebook (J. Lauri) asks whether a connected graph with exactly k isomorphism types of vertex-deleted subgraphs (cards) can have more than k orbits of its automorphism group on the vertices, for k = 2, 3, 4. The paper answers k = 3 in the affirmative: the Cayley graph of the Suzuki 2-group of order 64 on F_8 x F_8, with product (a,b)(c,d) = (a+c, b+d+ac^2) and connection set {(a,0), (a,a^3) : a != 0}, minus the identity, is a connected graph on 63 vertices with exactly 3 card types and 5 vertex orbits. The Lean theorem K2071.main_theorem states this and depends only on the axioms propext, Classical.choice and Quot.sound.