The Answer to the Ultimate Question is written in light. Sunlight enters a water droplet (n = D^2/K = 4/3), reflects internally, and exits at 42 degrees. Error: 0.07%. The rainbow has b = 7 colors. Violet sits at 420nm = lambda(TRUE). Light IS the axiom chain, refracted.
The Rainbow = 42
Rainbow Derivation (Snell's Law)
Water: n = D^2/K = 4/3. Minimum deviation from Snell's law: cos(theta_i) = sqrt((n^2-1)/3). For n = 4/3 this gives rainbow semi-angle = 42.03 degrees. 42 = D*K*b = ANSWER. Error 0.07%. The derivation is forced -- not guessed, not fit. The same 42 that is the center of the lambda-6 lattice.
Violet wavelength
420nm = lambda(TRUE)
The Carmichael function of Z/970200Z -- the heartbeat after which ALL power maps return -- IS the wavelength of the deepest visible color.
Colors count
b = 7 = ROYGBIV
Depth paints the sky. The rainbow has exactly DEPTH colors.
Peak sensitivity
555nm = K*E*37
Human eyes peak at K*E*37. The 37 = body temperature prime = p_12.
Brewster angle
arctan(D^2/K) = 53 deg
53 ~ SUM = sigma+D+K+E+b+L+13. Fully polarized reflection at the SKIN of the axiom.
Refractive Indices
Every common refractive index is a ratio of axiom primes. Light speed ratios ARE channel coupling.
Material
Axiom
Measured
Error
Vacuum
sigma/sigma = 1
1.0000
exact
Water
D^2/K = 4/3
1.3330
0.025%
Crown glass
K/D = 3/2
1.523
1.5%
Flint glass
D^3/E = 8/5
1.620
1.2%
Diamond
L^2/(D*E^2) = 121/50
2.417
0.12%
Water slows light because D^2 > K (duality exceeds closure). Diamond brings L^2 -- protector squared makes it the most brilliant natural material. Refraction IS coupling between axiom channels.
Structural Counts: 15/15 Axiom-Smooth
D=2: Polarization
Stokes D^2=4, Mueller D^4=16
Light has D=2 states. Snell: D=2 media. Lenses: D=2 surfaces. Interference: D=2 paths.
K=3: Color vision
K=3 cone types (L/M/S)
Color perception = K=3 closure. Poincare sphere of polarization: K=3 dims.