Growing Alphabets Do Not Automatically Amplify Shuffle Privacy: A Sharp Geometric Dichotomy

Exact compression, universal χ² bound, explicit obstruction family, and sharp diluting/persistent dichotomy for shuffle-model differential privacy on growing output alphabets. Independent of but informed by the trilogy "Universal Shuffle Asymptotics" (arXiv:2602.09029, arXiv:2603.10073, arXiv:2603.13407).