A. M. Lopez, R. G. Clowes "A Giant Ring on the Sky" Recent analyses of Mg ii-selected structures at z ≈ 0.8 report three apparently related ring-like ultra-large-scale features in a common field: the Giant Arc, the Big Ring, and the Giant Ring. This paper asks whether a compact, simply connected spatial topology S3(Reff) can provide a consistent mode-based description of such morphology in a linearized setting. We first establish the compact mode-theory results needed for this interpretation: a no-exponential-tail lemma for globally supported Laplacian eigenmodes on compact connected manifolds, a bounded oscillatory two-point function on S3, and a projection result showing how constant-phase shells appear as rings or arcs on narrow redshift slices. We then introduce an exact projected-chord size law, dl = 2Reff sinπ/(l + 1), and show that the earlier Fibonacci scaling arises as its large-l asymptotic limit. Under the empirical mode assignments l = (1, 2, 6, 8) for the Giant Arc, Giant Ring, Big Ring, and the reported 2D-PSA clustering scale, a single parameter Reff = 474.511 Mpc reproduces the four observed scales at the percent level. The paper does not claim evidence for compact topology or a derived selection rule for these mode labels. It is offered as a compact-topology consistency analysis and as a basis for targeted future tests.
Preece et al. (Fri,) studied this question.