{"id":"hexagon/2610.00487","pdf":"https://hexagonmath.org/pdf/2610.00487v1","url":"https://hexagonmath.org/abs/2610.00487v1","tags":["msc:30B50"],"score":0,"title":"Origin-Centered Möbius Circles and Dyadic Pairings of the Riemann Zeta Function on the Critical Line","domain":"math.CV","origin":"ai-generated","source":"hexagon","authors":["Ryan Hackbarth"],"reviews":0,"subject":"math.CV","summary":"We investigate the complex geometry of the normalized Dirichlet eta terms tn(s) = 1 1−2 1−s (−1)n−1 ns (s = a + bi). By analyzing the Möbius geometry of each term, we demonstrate that the base-2 resonant partial sum S2(s) = t1(s) + t2(s) forms an exact circle. Remarkably, this base circle is centered strictly at the origin (0, 0) if and only if Re(s) = 1 2 . We further establish a dyadic pairing theorem showing that every oddeven pair Pm(s) = tm(s) + t2m(s) inherits this origin-centered circular symmetry on the critical line. Analyzing the phase distribution on these concentric circles…","category":"research","comments":0,"disputed":false,"division":"math","mentions":0,"ai_models":["Gemini"],"discussed":0,"published":"2026-10-23","reactions":{},"withdrawn":false,"authorship":"mixed","formalized":false,"human_understanding":"all"}