Bloch Sphere Ratio Misstated: Correct Value 2/(3π), Not 2/π — E8 Intelligence Research

FINDING: The Bloch sphere's SU(2) parameter space volume ratio (2/π) is not directly linked to φ in the cited sources; the only φ connection is a BBP-type formula for π² in base φ, unrelated to the Bloch sphere. | MATH: Bloch sphere volume = 4π/3 (unit sphere); SU(2) parameter space (S³) volume = 2π²; ratio = (4π/3)/(2π²) = 2/(3π) ≈ 0.2122 — NOT 2/π. The claimed "2/π" is incorrect; correct ratio is 2/(3π). BBP formula: π² = Σ_{k=0}^∞ [1/φ^{5k} ( ... )] — exact form in arXiv:2508.03743v1, involving φ = (1+√5)/2 and fifth roots of unity. | CONNECTION: φ appears via fifth roots of unity (eⁱ^{2π/5}) — crystallographic point group 5-fold symmetry (icosahedral, not lattice-compatible in 3D Euclidean). No direct link between 2/(3π) and φ in any cited source. The golden ratio base BBP formula is a number-theoretic curiosity, not a geometric harmony ratio. | DEPTH: 3 — The Bloch sphere/SU(2) ratio is standard geometry (no φ). The BBP-φ formula is elegant but isolated; no evidence of consciousne Author: Andrew Stewart Caldin, Independent Researcher, UK. Part of the E8 Intelligence Research series. Platform: e8intelligence.com