A Square-Tank RAS Operator Stays Outside the Numerical Killing Zone: Finite-Grid Diagnostics for a Loop-Coupled Filtration System (Paper 61 in the Non-Holomorphic Fractal Series)

This preprint is part of the Non-Holomorphic Fractal Series (Paper 61). We extend the killing-zone diagnostics of Papers 58–60 from cylindrical inlet–drain tanks to a depth-averaged RAS operator on a square-tank footprint coupled to an eight-node filtration loop. On the same finite-grid framework the twisted Bird-map operators still place 9/10 WBA tiers inside the joint precision-and-observability killing zone, while oceanic, double–gyre, and stirred-tank controls remain safe. Here we build a 10×10×1 m square-tank Ulam operator for a generic high-density grow-out tank, with configurable corner versus centre drains and wall jets that model the return flow from a filtration loop. Across N ∈ {64, 128, 256} and all five drain configurations (centre, NE, NW, SE, SW) the square-tank operators stay outside the joint killing zone on all ten WBA tiers; support ratios remain numerically flat (D_geom = 1.0) for both centre and corner drains on these grids. We then model the filtration loop itself as a block Ulam operator with eight stirred-tank nodes (drum, sand, skimmer, UV, biofilter, oxygen cone, trickling filter, submersible bed) and confirm that each node remains outside the killing zone on the executed grids. From the combined support profiles we keep the geometric mixing penalty D_geom from Paper 60 and promote the per-tank revisit inequality to a two-channel form for both dissolved oxygen (DO) and ammonia (NH3) channels. All claims are strictly finite-grid statements tied to locked CSVs; no continuum or asymptotic properties are asserted beyond what is visible at the reported resolutions.