On the Diophantine Stability of the Syracuse Map

We present the results of an exhaustive branch locus computation forthe Collatz map on the family of finite tori²ₖ = (/k)², carried out for alln ≤ 10¹¹ across 27 hierarchically nested grid levels(k ∈ \1, 2, 3, …, 19683\). The computation consumed61.5~hours on a 24-core Intel Core Ultra~9 275HX, accumulating25.1 × 10¹² Collatz steps. Eight figures document theprincipal findings: cell saturation, torus heatmaps, Diophantinesignatures, shift-of-finite-type (SFT) forbidden transitions,foliation enrichment collapse, cell-level statistics, convergenceover~N, and transition/shadow analysis. A comparison with theearlier 10¹⁰ run reveals new structure invisible at lower~N:a ``Diophantine ghost island'' of 251~cells at perpendiculardistance~370 from the main branch locus, created by the best rationalapproximant 460/729 ≈ log₃ 2, together with a sharpenedgap in the shadow offset distribution and a new downward-slopingfeature in the foliation-position shadow profile.