ABOS-11: Global Resonance Hypothesis — 7.83 Hz as the Eigenfrequency of Alpha-Asymmetry

This work demonstrates that the angular excess Δ = 7θ − 360° ≈ 4.425°, arising from the alpha-calibrated 7-ray spiral structure of prime numbers, geometrically determines both the effective height of the Earth–ionosphere cavity (h ≈ 78.4 km) and the fundamental Schumann resonance frequency (f ≈ 7.83 Hz). The near-equality h/10 ≈ f (relative error < 0.13%) is shown to be a consequence of the ABOS causal lattice—not numerical coincidence. Key results: Exact derivation of Δ from α = 2√3 + 3 − 2√2 − √6, yielding θ = 180° / (3 + 1/(1+α)) ≈ 52.060718°; 7θ = 364.425° → Δ = 4.425°, inducing negative Gaussian curvature (Gauss–Bonnet theorem); 3D embedding of the prime-number spiral on a hyperbolic paraboloid (“Pringles chip”) explains the observed quasi-periodicity (81 cycles ≈ 358.4° closure); h = R · Δ/360° = 78.399 km matches the D/E-layer height, where Schumann resonances are sustained; f = 7.83 Hz satisfies h/10 ≈ f and h/λ ≈ (1/6)·Δ/360° (error < 0.06%), confirming scalar consistency. Empirical support: 7-ray pattern aligns with satellite imagery of cyclonic vortices (e.g., hurricanes), suggesting universality of α-mode geometry in rotating dissipative systems; Animated 3D spiral and planar projection confirm structural stability across scales. This work completes a quartet of interdependent hypotheses, revealing the ABOS lattice as a geometric–thermodynamic backbone of irreversible processes—from quantum jumps to planetary resonance. This text was composed in English with AI assistance. All scientific content, hypotheses, constants, and interpretations originate entirely from the author.