Bloch Sphere Volume Ratio Corrected to 2/(3π) — E8 Intelligence Research

FINDING: The Bloch sphere's SU(2) parameter space volume ratio (2/π) is not directly linked to φ in the provided sources; the only φ connection is a BBP-type formula for π² in the golden ratio base, unrelated to the Bloch sphere volume ratio. | MATH: Bloch sphere volume = 4π/3 (unit sphere in R³); SU(2) parameter space (S³) volume = 2π²; ratio V_Bloch/V_SU(2) = (4π/3)/(2π²) = 2/(3π) ≈ 0.2122 — NOT 2/π. The claimed "2/π" is incorrect; correct ratio is 2/(3π). BBP-type formula: π² = Σ_{k=0}^∞ [1/φ^{2k}] · (some rational polynomial in φ, per arXiv:2508.03743) — exact form not extracted from abstract. | CONNECTION: φ appears via fifth roots of unity (geometric pentagonal symmetry) in the BBP proof; the Bloch sphere ratio 2/(3π) has no φ, 0.382, 0.618, 0.786, 1.618, 2.618, or base-60 link. The BBP φ-base formula connects to pentagonal/quasi-crystalline symmetry (φ is the silver ratio of 5-fold symmetry), but not to SU(2) or Bloch sphere. | DEPTH: 3 — The sources are pedagogical videos (no n Author: Andrew Stewart Caldin, Independent Researcher, UK. Part of the E8 Intelligence Research series. Platform: e8intelligence.com