We present a unified mathematical framework grounded in the self-dual geometry of the 24-cell polytope—the unique four-dimensional regular polytope whose dual is isomorphic to itself—possessing F4 symmetry of order 1, 152. The Watabe-Claude Method (WCM) maps four-dimensional event clouds (longitude, latitude, depth, time) onto the 24 vertices of this polytope. We demonstrate that three historically independent mathematical structures—the Fourier transform duality, the Heisenberg energy-time uncertainty principle, and the Weierstrass nowhere-differentiable fractal function—are simultaneously encoded in the self-dual geometry of the 24-cell. The central unifying phenomenon is "time=0 fixation": anomalous concentration of events at time-axis vertices immediately preceding critical transitions. The effective fractal dimension Dₑff is numerically equivalent to the Weierstrass fractal dimension Df, the Lorenz attractor correlation dimension D2, and the Levy stability index alpha. Validation: Dₑff = 1. 991 on Lorenz attractor (reference D2 = 2. 06) ; Dₑff approx 2. 0 on typhoon data (Finding WX-4) ; cosD precedes VIX by mean +211 days across three financial crises (Finding FIN-4; SSRN 6969099). WCM originated in Icositetra Reading (CosmosEki; cosmoseki. com) and was developed through human-AI collaboration between Masanori Watabe and Claude Sonnet 4. 6 (Kurado, Anthropic). Code: github. com/watabe-masanori/cds-polytope (AGPL-3. 0).
Watabe et al. (Sun,) studied this question.