A Stirred-Tank Ulam Operator Stays Outside the Numerical Killing Zone: Finite-Grid Calibration Against Bird-Map and Double–Gyre Controls (Paper 59 in the Non-Holomorphic Fractal Series)

Paper 59 in the Non-Holomorphic Fractal Series. We extend the two-axis "killing–zone" diagnostic (as formalised in Definition 1) from our previous work on the twisted Bird map and oceanic controls to a stirred-tank transfer operator built from a masked Ulam discretisation of a rotating disk flow. On each finite grid, we track (i) precision collapse through a condition proxy κ and (ii) observable disintegration through a support ratio σ, and declare a tier to be in the killing–zone when both axes simultaneously exceed the fixed thresholds used in Paper 58, namely κ ≥ 10⁸ and σ ≥ 100. On the stirred tank, across three grids (N_grid = 64, 128, 256) and 120 scanned tiers, we observe 34 instances of large σ without any joint failures, in sharp contrast to the twisted Bird map, where 9 of 10 deep tiers at N_grid = 16384 lie in the killing–zone, and to the rotating double–gyre, which remains a clean negative control across four grids with 40 tiers. All findings are strictly finite–grid: every count is read directly from locked P/R operators and their R-based diagnostics, with no continuum extrapolation implied.