This paper introduces and develops the Base-24 = 2³×3 mixed-radix arithmetic system as a natural computational framework for the Inverted Hypersphere Cosmology (IHC) series. The base-24 system arises because 24 = 2³×3 is the minimal radix that provides exact terminating representations for all quantities whose prime factorisation involves only 2 and 3 — precisely the quantities that appear in the IHC geometric structure (N=33, M=11, Z₃ colour classes, Z₈ fermion classes, Fibonacci bridge F₁₂=144=2⁴×3²). Key results include: exact base-24 decomposition of all IHC GUT quantities; the Fibonacci bridge identity F₁₂=144=2⁴×3² as the unique quantisation of the 5-dimensional SO(5) geometry into binary-ternary arithmetic; the identity k_GUT=272=8×(N+1) in base-24 form; and the three-generation structure as 3×Z₈=3×2³. The cosmological constant suppression ratio S=1.1407×10⁻¹²³ is derived with zero fitted parameters. Validation scripts and figures are included in the uploaded ZIP. Companion papers: IHC GUT paper (Zenodo: https://doi.org/10.5281/zenodo.19211056) and main IHC preprint (Zenodo: https://doi.org/10.5281/zenodo.19135785, under review as ijt-4241652).