A microcanonical phase transition for the Collatz affine random model

We introduce a microcanonical framework for the Syracuse affine random model of Tao (Forum Math. Pi, 2022) by conditioning on S_n = s. Under this conditioning the multiplicative phase becomes deterministic, and the affine Fourier coefficient at hard frequencies reduces to a primitive ternary Bernoulli-bridge transform on a real-line perpetuity. Combining ensemble equivalence, Brémont's Rajchman classification for contracting-on-average affine IFS, and an exact suffix self-similarity,we prove a sharp phase transition for the resonant hard frequency at the entropy line h_* = 2 log_3 2 - 1 ≈ 0.262: subcritical decay below, supercritical obstruction above. We further prove density-one and fiberwise flattening for all hard frequencies via pair-switch averaging, forcing any HFBD-violating sequence onto a positive-codimension 3-adic exceptional tree.