\contentsline {section}{\numberline {1}Abstract}{2}{section.1}%
\contentsline {section}{\numberline {2}Introduction and Terminology}{2}{section.2}%
\contentsline {subsection}{\numberline {2.1}Terminology Clarification}{2}{subsection.2.1}%
\contentsline {section}{\numberline {3}The Compact Fifth Dimension and the 1/7 Resonance}{3}{section.3}%
\contentsline {section}{\numberline {4}Division Polynomials and the Three-Term Recurrence}{3}{section.4}%
\contentsline {section}{\numberline {5}The 5-Isogeny between \(X_1(11)\) and \(X_0(11)\)}{3}{section.5}%
\contentsline {section}{\numberline {6}Newforms at Levels 7 and 11}{4}{section.6}%
\contentsline {section}{\numberline {7}Poisson Summation and the Closed-Form Signature \(K_0(r/\tau )\)}{4}{section.7}%
\contentsline {section}{\numberline {8}Tav Resonance Graph Visualization}{5}{section.8}%
\contentsline {section}{\numberline {9}Synthesis: Arithmetic Shadows of the Compact \(S^1\)}{7}{section.9}%
\contentsline {section}{\numberline {10}Relation to Independent Work Using ``Tau'' Nomenclature}{8}{section.10}%
\contentsline {section}{\numberline {11}Falsifiability and Pre-Registration}{8}{section.11}%
\contentsline {section}{\numberline {12}Conclusions}{8}{section.12}%
