Establish a classification-free automorphism-group bound

Prove the upper bound on the logical automorphism group of stabilizer codes without invoking classification results for finite groups, with the aim of exposing the structural origin of the bound and enabling extensions to other code and gate models.

Background

The main extremal theorem shows that, for stabilizer codes encoding at least three logical qubits, automorphism logical groups cannot exceed the Siegel parabolic generated by all addressable logical $S$ and controlled-NOT gates. The proof uses classifications of finite subgroups of binary symplectic groups. The paper identifies replacing these classification-dependent arguments with a structural proof as an unresolved mathematical problem.