Topological Universality of α = 6/5 in Microtubule Lattice Spectra
Abstract
The fractional diffusion index α = 6/5, derived as an exact eigenvalue of the Sephirotic graph Laplacian, universally converges in the normalized Laplacian spectra of biologically accurate microtubule lattice graphs. GPU-accelerated eigendecomposition on lattices with up to 9,150 nodes across five protofilament architectures (11-15 PF) shows |λ - 6/5| < 3×10⁻⁴. The associated eigenvector is perfectly bilateral (r = +1.000) with alternating protofilament phases. Universality confirmed across eight helical topologies and fractal gel graphs. 100,000-graph null test: p = 0.058. Honest negatives reported for dynamical tests (Kramers, spectral gap, transport), establishing the connection as topological rather than dynamical.
Fields of Study & Subjects
Graph theory and applications
Spectral Theory in Mathematical Physics
Complex Network Analysis Techniques
Publication details
- Journal / source
- Zenodo (CERN European Organization for Nuclear Research)
- Publication date
- 11 March 2026
- Language
- EN