A fixed-point Type IIB string theory framework, previously applied to resolve the vacuum energy problem in cosmology, to design a CNS-penetrant rabies drug candidate, and to predict the quarter-Möbius molecule C12F2, is here applied to a further member of the topological ring molecule series. C16F4, a sixteen-membered all-carbon ring with four fluorine substituents at quarter-point positions, is predicted to be the first eighth-Möbius molecule: topological sector n = 4, phase shift π/8 per ring traversal, sixteen loops required for wavefunction phase return. The sixteen-membered ring carries sixteen π electrons, satisfying the 4n anti-aromatic criterion with n = 4 and placing the highest occupied molecular orbital (HOMO) and lowest unoccupied molecular orbital (LUMO) of the parent ring at exact degeneracy. The fourfold quarter-point substitution geometry reduces the first-order frontier splitting to 0.125ε — substantially smaller than the 0.333ε splitting in C12F2 — making the near-degeneracy and associated pseudo-Jahn-Teller (PJT) instability more robust. Nine topological configurations are predicted, compared with five for C12F2 and three for the confirmed half-Möbius molecule C13Cl2. The predicted switching gap is 18.46 kcal/mol. C16F4 is synthesisable by the scanning tunnelling microscope (STM) and ultra-high vacuum (UHV) technique demonstrated for C13Cl2 and is verifiable by observation of a sixteenfold helical Dyson orbital. The three-molecule series — C13Cl2 (confirmed), C12F2 (predicted), C16F4 (predicted) — constitutes a systematic topological sector ladder derived from a single fixed point τ* = 220.