Topological Mass Generation from TT/24: Unifying Chern-Simons Theory with Catalan Geometry

We present KSAU v5.0, a phenomenological framework that models fermion Yukawa couplings as topological partition functions of knotted configurations motivated by Chern‑Simons theory. Introducing a master constant K = T/24, the framework maps nine charged fermions to knots and links from the KnotInfo/LinkInfo census using an automated topology selection algorithm (17,154 entries) and achieves a global mean absolute error of 1.38%. The geometric action combines bulk hyperbolic volume, boundary crossing contributions, and a generational Twist correction. The manuscript introduces three geometric selection rules, documents an unexpected numerical bridge between the Catalan constant and 7T/24, and provides explicit falsifiability criteria including neutrino mass bounds, fourth‑generation exclusion, and a 12‑crossing link prediction. Limitations, parameter counts, and open mathematical questions are discussed.