Spectral Verification: Face Adjacency Laplacian of the Truncated Octahedron (UFFT Supplementary)
Abstract
Independent verification that the face adjacency Laplacian of the truncated octahedron has spectrum Spec(L) = {0¹, ((9−√17)/2)³, 4², ((9+√17)/2)³, 7⁴, 9¹} with characteristic polynomial p(λ) = λ(λ²−9λ+16)³(λ−4)²(λ−7)⁴(λ−9). Verified numerically (numpy, max deviation 4.44×10⁻¹⁵) and symbolically (sympy, polynomial identity = True). The √17 is confirmed exact. This result underlies all UFFT predictions depending on √17 — solar neutrino mixing, Higgs/Z mass ratio, PMNS angles. Includes Jupyter notebook and standalone Python script. Dependencies: numpy, sympy only. Runtime: < 30 seconds.
Fields of Study & Subjects
Neutrino Physics Research
Astrophysics and Cosmic Phenomena
Particle physics theoretical and experimental studies
Publication details
- Journal / source
- Zenodo (CERN European Organization for Nuclear Research)
- Publication date
- 18 March 2026
- Language
- EN
- Document type
- Preprint