Killing-Zone Diagnostics and Geometric Mixing Penalties for a Recirculating Aquaculture Ulam Operator: Finite-Grid Calibration Against Bird-Map, Double-Gyre, and Stirred-Tank Controls (Paper 60 in the Non-Holomorphic Fractal Series)

This preprint is part of the Non-Holomorphic Fractal Series (Paper 60). It extends the finite-grid "killing-zone" diagnostic for Ulam transfer operators, developed in Papers 58–59, to a recirculating aquaculture system (RAS) inlet–drain tank operator motivated by high-density African catfish production. On the executed grids, the RAS operator shows zero joint killing-zone tiers but exhibits nontrivial support-ratio (σ-only) stress in dead zones, in contrast to the twisted Bird map's pathological behaviour and the well-behaved oceanic and stirred-tank controls. From the eigenmode support ratios the paper defines a conservative geometric mixing penalty D_geom and a Nyquist-style per-tank revisit inequality that bounds how frequently a mobile sensing platform must revisit each tank relative to oxygen and ammonia time scales. 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.