Paper 14 — Black Circle Hypergeometric Reduction and Cavity Bound

This paper develops the analytic foundations for quasi-normal mode (QNM) analysis of the Black Circle interior — a Cayley–Dickson sedenion-algebraic compact object with de Sitter interior metric.
Starting from the Regge–Wheeler scalar field equation, we perform a hypergeometric reduction of the interior ODE and derive a closed-form QNM condition via Wronskian matching at the Eddington–Finkelstein junction. The cavity bound λGM² < 2.14×10⁻³ is established from the Breitenlohner–Freedman constraint applied to the de Sitter interior. The rough one-loop imaginary part Im(W) = −74.800 r_s⁻¹ is computed from the QNM spectrum; this value is superseded in Paper 18 of the series, which uses the corrected QNM spectrum from Papers 15–17.