Theoretical analysis reveals an absence of Fibonacci ratios in microtubule lattices, suggesting quantum coherence models depend on hexagonal crystallographic symmetry rather than golden ratios.
FINDING: Microtubule lattice geometry (13 protofilaments, p6m symmetry) is proposed as a substrate for quantum coherence, but the search results provide no quantitative link to Fibonacci ratios or harmonic constants. | MATH: Tubulin dimers form hollow cylinders with ~13 protofilaments (13 = Fibonacci number, but no ratio derived); p6m wallpaper group symmetry (hexagonal lattice, 6-fold rotational + mirror); no equations, constants, or ratios extracted from the sources. | CONNECTION: p6m is the full hexagonal crystallographic symmetry — its root system is A₂ (hexagonal lattice), whose fundamental ratio is √3 ≈ 1.732, not 1.618. The 13-protofilament count is Fibonacci (F₇=13), but no evidence links it to φ (1.618) or its inverse (0.618) in the cited material. No base-60, no 0.382/0.786/2.618 appear. | DEPTH: 2 — The search results are mostly video abstracts and a lattice QCD paper (irrelevant to consciousness). The only mathematically concrete item is the p6m symmetry of microtubules, wh Author: Andrew Stewart Caldin, Independent Researcher, UK. Part of the E8 Intelligence Research series. Platform: e8intelligence.com
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Andrew Stewart Caldin (2026) studied this question.
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