The Fine Structure Constant from Möbius Topology: 1/α_ideal = 24π²/√3 (Paper II of III)

We derive the geometric ideal value of the fine structure constant from Möbius n=3 standing wave topology, without any mass measurements or free parameters: 1/α_ideal = 24π²/√3 = 136.757 250 186... Relative error from CODATA 2018: 0.20%. The correction δ = 0.279 is derived in Paper III. ─── Derivation (two steps) ─────────────────────────────── Step 1 — Wave-particle threshold E/f² = 4π² The Möbius stability condition λ/A = √3 (Schwartz 2024, arXiv:2308.12641) gives the minimum aspect ratio for smooth Möbius embedding. Combined with A² = E/(2πf)², this yields the wave-particle threshold: E/f² = 4π² ≈ 39.48 This is the MAXIMUM energy-frequency ratio for a stable Möbius standing wave. Above this threshold, the aspect ratio λ/A drops below √3, smooth embedding fails, and the fermion must emit a boson to restore stability. The electron sits precisely at this threshold. Step 2 — Threshold fixes the Möbius circumference At the threshold, λ = √3 — the circumference of the equilateral triangle Möbius band (Schwartz 2024, the tightest stable Möbius configuration). The outer double-twist boundary has circumference 2√3. Therefore: 1/α_ideal = 4π² × 2√3 = 24π²/√3 The three factors: • 4π: Möbius double-circuit holonomy (720°) • 1/cos(30°) = 2/√3: equilateral triangle projection (Schwartz 2024) • 3π: three-node phase bandwidth (n=3 mode) ─── What this derivation does NOT use ─────────────────── - No particle masses (mₑ, mₚ, quark masses)- No coupling constants- No free parameters- No dimensional quantities The result is determined entirely by topology (π, √3). ─── Series information ────────────────────────────────── Paper II of III. Published simultaneously with:- Paper I: Overview and main result (1/α = 137.035 999 121, 14.9 ppb)- Paper III: Mass ratio correction and quantum oscillation (mₑ/mₚ and e)