Proof of Stembridge's conjecture on stability of Kronecker coefficients

We prove a conjecture of Stembridge concerning stability of Kronecker coefficients that vastly generalizes Murnaghan's theorem. The main idea is to identify the sequences of Kronecker coefficients in question with Hilbert functions of modules over finitely generated algebras. The proof only uses Schur-Weyl duality and the Borel-Weil theorem and does not rely on any existing work on Kronecker coefficients.
Comment: 8 pages, v2: Added references, Remark 4.5, and Section 4.3 on stability result for plethysms