Arithmetic Unique Ergodicity for Infinite Dimensional Flat Bundles

Both the paper and the candidate solution prove that microlocal lifts of joint Hecke–Maass eigensections equidistribute to Haar/Liouville on the S^3-bundle π* M. The paper proves base equidistribution via Lindenstrauss’s measure rigidity with Hecke recurrence and strong positive entropy, then deduces SU2-Haar on the fiber by a Hopf/Borel-density/Schur argument (e.g., Theorems 6.1–6.5 and the constructions in §§3–5 ). The candidate solution proves the same limit but invokes higher-rank S-arithmetic measure rigidity (EKL) after establishing invariance under A∞ and Hecke operators at several finite places. This is a different, standard route used in Silberman–Venkatesh; both are coherent with the microlocal construction in §3 and the Hecke formalism in §4 of the paper (e.g., (3.8)–(3.9), Theorem 3.1; and (4.8)–(4.12) ).