An Explicit Windowed Sparsity Bound for Divergent 3x+1 Orbits, with Logarithmic-Floor Exclusion beyond the Harmonic Barrier

Garcia and Tal proved in 1999 that every infinite orbit of the 3x+1 map has Banach density zero. We give a short self-contained proof of an explicit quantitative form: for every infinite aperiodic orbit, the number of orbit points in any window [a, a+X) is at most C X^b log(2X) uniformly in a, for every b > 0.96538..., with the exponent equal to Rozier's critical ones-ratio times log2(3). Three consequences follow for the Syracuse map with valuation drift g_n: every divergent orbit has summable reciprocals; no divergent orbit satisfies g_n <= B log2(n) + O(1) eventually for any B <= 1; and an occupation bound extends the exclusion to every B < 1.03585... This passes the threshold 8/9 recently proved by De Jesus and shown there to be terminal for congruence-packing, and it settles the graded harmonic-thinness requirement of his Open Problem 12.8 in a stronger form than requested. No claim is made on cycles, on the Effective Occupation Conjecture, or on the Collatz conjecture itself.