The entire framework rests on one eigenvalue spectrum. Here it is in twelve lines of NumPy, no external data. If these numbers don't come out, the framework is wrong — so check them first.
import numpy as np # 14 face normals: 6 squares (±axes) + 8 hexagons (±±± body diagonals) normals = np.vstack([np.eye(3), -np.eye(3), np.array([[i,j,k] for i in [1,-1] for j in [1,-1] for k in [1,-1]])/np.sqrt(3)]) # adjacency: square–hex share an edge (cosθ = 1/√3); hex–hex share an edge (cosθ = 1/3) A = np.array([[1 if (i<6)!=(j<6) and abs(np.dot(normals[i],normals[j])-1/np.sqrt(3))<0.01 else (1 if i>=6 and j>=6 and abs(np.dot(normals[i],normals[j])-1/3)<0.01 else 0) for j in range(14)] for i in range(14)]) L = np.diag(A.sum(1)) - A # face Laplacian: L = D − A print(np.round(np.linalg.eigvalsh(L.astype(float)), 4)) # → [0 2.4384 2.4384 2.4384 4 4 6.5616 6.5616 6.5616 7 7 7 7 9]
Expected output — the spectrum every result is read from:
[-0. 2.4384 2.4384 2.4384 4. 4. 6.5616 6.5616 6.5616
7. 7. 7. 7. 9. ]
The roots 2.4384 and 6.5616 are (9∓√17)/2 — the master equation λ²−9λ+16 = 0. The −0.0 is the floating-point print of the exact zero mode.
Every number in the repository recomputes from the cell integers alone — no fitted constants, no imported data. Both scripts below run in under a minute.
# clone and install git clone https://github.com/WebEnvy/UnifiedFoamFieldTheory cd UnifiedFoamFieldTheory pip install numpy scipy # the full spectrum verification python verification/19079730_UFFT_Spectrum_Verification.py # spectral uniqueness of the Kelvin cell among the 5 Fedorov parallelohedra python streams/education/Mathematics/verify_spectra_v2.py
The second script reproduces all five Fedorov-cell face-Laplacian spectra and the identities that single out the truncated octahedron — the uniqueness the theory depends on.
Every derivation, all 77 parts, the full status table and the eleven predictions.
Open the framework →The self-contained book — 44 chapters, narrative plus theorems, for a careful reader.
Open the book →Every UFFT paper is open-access on Zenodo with a permanent DOI, one per result. Browse the full record by sector.
Browse the papers →Repository: github.com/WebEnvy/UnifiedFoamFieldTheory · Author: Luke Martin, ORCID 0009-0006-3716-5951 · Not yet peer reviewed — independent reproduction invited.