Quantum Vibrational Coherence in Microtubules: Mesoscale Superposition Without Consciousness-Specific Geometry — E8 Intelligence Research

FINDING: Microtubule quantum coherence evidence suggests biological systems may exploit quantum superposition at mesoscale, but the mathematical core remains vibrational mode structure rather than proven consciousness-specific geometry. MATH: - Microtubule lattice: tubulin dimers arranged in 13-protofilament cylinders (13 = Fibonacci-adjacent prime), with 8nm dimer pitch and 4nm longitudinal spacing → helical symmetry group approximates a 3-start/13-start screw axis. - Quantum beat frequencies in cavity QED (arXiv:1401.3218): ω₁ - ω₂ = Δ (detuning), with second-order correlation g⁽²⁾(τ) = 1 + |g⁽¹⁾(τ)|² cos(Δτ) — coherence lifetime τ_c ∝ 1/γ (decoherence rate). - Excitation propagation in simulations: modeled as Fröhlich condensate at ~10¹¹ Hz (terahertz gap), with energy quanta ħω ≈ k_BT at 300K → ħω/k_BT ≈ 0.16 (not a golden ratio). - No published equation yet links quantum beats to 0.618 or 1.618. The 13-protofilament count is the only structural number with Fibonacci res Author: Andrew Stewart Caldin, Independent Researcher, UK. Part of the E8 Intelligence Research series. Platform: e8intelligence.com