Aspden's spacing d = 6.3740e-13 m (2d = 1.2748e-12 m; U16 gives 1.275e-12)

1. Nearest-neighbour cubic relay: modes for 2000 random directions and wavenumbers
   largest relative split between the two transverse modes: 1.1e-15
   largest |lowest eigenvalue| (the static longitudinal mode): 2.7e-15
   [100]: sum k_i^4 = 1.0000; group deficit (kd)^2 x 0.1250; band top along the line 2.0000 hbar c/d = 0.619 MeV for Aspden's d
   [110]: sum k_i^4 = 0.5000; group deficit (kd)^2 x 0.0625; band top along the line 2.8284 hbar c/d = 0.876 MeV for Aspden's d
   [111]: sum k_i^4 = 0.3333; group deficit (kd)^2 x 0.0417; band top along the line 3.4641 hbar c/d = 1.072 MeV for Aspden's d
   path weighting (1+z)^0: 3.2450e+17 s = 10.28 billion light-years
   path weighting (1+z)^1: 4.5809e+17 s = 14.52 billion light-years
   path weighting (1+z)^2: 6.6835e+17 s = 21.18 billion light-years

2. GRB 090510, limit (a), quadratic law: group deficit at 28 GeV below 1.285e-18
   internal resonance (1 - v_g/c = 1.5 (E/E_res)^2): E_res > 3.025e+19 eV (U15: 3.0e19)
   relay spacing along the cube axis: d < 2.260e-26 m; Aspden's d is 2.82e+13 times larger
   relay spacing along the cube diagonal: d < 3.914e-26 m; Aspden's d is 1.63e+13 times larger

3. Crab check (U16): d < 2.382e-19 m along a cube axis

4. Nested lattices (U44: level k has spacing d/s^k and energy s^k x 511 keV)
   s = 2: spacing below 2.26e-26 m from level 45; energy above 3.02e+19 eV from level 46; both from level 46 (spacing 9.06e-27 m, energy 3.60e+19 eV)
   s = 3: spacing below 2.26e-26 m from level 29; energy above 3.02e+19 eV from level 29; both from level 29 (spacing 9.29e-27 m, energy 3.51e+19 eV)
   s = 4: spacing below 2.26e-26 m from level 23; energy above 3.02e+19 eV from level 23; both from level 23 (spacing 9.06e-27 m, energy 3.60e+19 eV)

5. A level's share f, for a level between about 0.2 MeV and 0.7 GeV (limit (f), comoving path):
   f < 1.17e-19
   s = 2: levels 0 to 10 (11 levels) lie in that range
   s = 3: levels 0 to 6 (7 levels) lie in that range
   s = 4: levels 0 to 5 (6 levels) lie in that range

6. n_k/(m_k Omega_k^2), relative to level 0, for s = 3, k = 0..5: ['1.000', '1.000', '1.000', '1.000', '1.000', '1.000']
