Helical Fibonacci Anyon Monodromy and Sub-Landauer Decoherence Invariance in 13-Protofilament Microtubule Networks [Physical Review Letters Edition]

Topological Quantum Error Correction in Orch-OR: Helical Fibonacci Lattices, Non-Abelian Anyon Braiding, Flat Hodge Memory, and Optomechanical Diósi–Penrose Reduction [Physical Review Letters Edition] Author: Dimitar Stavrev Prodromov (ORCID: 0009-0004-8070-1348) Affiliation: AETERNA Research Laboratories, Pomorie, Bulgaria MSC-2020: 81P68, 81P15, 81T45, 81V80, 83C45 | arXiv Classes: quant-ph, physics.bio-ph, cond-mat.mes-hall Letter Abstract (APS REVTeX 4-2 Specification) We establish a closed-form mathematical framework for room-temperature topological quantum coherence in cylindrical bio-macromolecular and synthetic optomechanical lattices. Addressing thermal decoherence in warm condensed-matter environments, we prove that a 13-protofilament cylindrical lattice of tubulin heterodimers constitutes a topological quantum error-correcting network governed by Fibonacci helical windings (k ∈ {1, 3, 5, 8}). Introducing a Peierls chiral gauge phase of π/2 on inter-helical tunnelings maps the system to a 13 × 13 skew-Hermitian Hamiltonian Ĥ = iA, whose topological zero mode E6 ≡ 0.00000000 is unconditionally guaranteed by Jacobi's theorem on odd-dimensional skew-symmetric operators within a zero-mode excitation gap |E±1| = 0.9064 t0 ≈ 1578 K. Non-Abelian Fibonacci anyon braiding is mediated by the unitary monodromy B = FRF in SU(2)3 Chern–Simons theory with golden ratio quantum dimension dτ = φ ≈ 1.61803399. Non-dissipative memory is formalized via flat connections and integer Aharonov–Bohm holonomies on the 13-fold punctured torus H1(Xpunct, ℤ), proving strictly zero Prigogine entropy production (diS / dt ≡ 0.00000000). Furthermore, we eliminate the post-selection probability bottleneck of weak values via Grover amplitude amplification Ĝ = (2|Ψ⟩⟨Ψ| − 𝕀)(𝕀 − 2|Φ⟩⟨Φ|), achieving Ptotal = 99.9913% within k = 39 cycles (ε = 0.02), regularized by a Breit–Wigner denominator. Finally, coupling optical modes to a 1 pg suspended Si3N4 optomechanical nanobeam under nuclear-scale spatial smearing (R0 ≈ 3 fm) yields gravitational self-energy EG = 1.241257 × 10−33 J and objective reduction timescale τn = 84.96 ms ≈ 11.77 Hz, matching the human electroencephalographic alpha rhythm. ⚖️ PROPRIETARY SOVEREIGN RESEARCH LICENSE (PSRL v2.0) © 2026 Dimitar Stavrev Prodromov / AETERNA Research Laboratories, Pomorie, Bulgaria. ALL RIGHTS RESERVED. 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