Spectral Verification: Face Adjacency Laplacian of the Truncated Octahedron (UFFT Supplementary)

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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:

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Topics & keywords

Keywords
  • Adjacency list
  • Laplace operator
  • Face (sociological concept)
  • Spectrum (functional analysis)
  • Polynomial
  • Graph
  • Octahedron
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