P-MOHO-1 · The Moho as a Tau-Register Transition
The Moho discontinuity marks the G0/G1 Tau-register boundary in Earth's interior. Below it: the dense G0 mantle/core lattice. Above it: the open G1 crust, ocean, and atmosphere. The seismic velocity jump at the Moho is the direct observational signature of this register transition.
P-MOHO-2 · Earth Radius = 20,000/π km
The FOT Tau-lattice assigns Earth a canonical radius of exactly 20,000/π kilometres — the radius of a sphere whose circumference is precisely 40,000 km. This is the value encoded into the SI metre by the 1791 French Académie definition.
P-MOHO-3 · Seismic Velocities as Pure {2,3} Values
At the Moho, compressional and shear wave velocities fall on the {2,3} sub-lattice of the FOT prime lattice. Observed centre values lie within 220 ppm of the exact lattice values — within the canonical Radian Veil band.
| Wave type | FOT exact (km/s) | Observed range (km/s) | Centre PPM |
|---|---|---|---|
| P-wave (Vp) | 8.000 | 7.6 – 8.1 | ~60 ppm |
| S-wave (Vs) | 4.500 | 4.0 – 4.7 | ~220 ppm |
| Ratio Vp/Vs | 1.7778 (16/9) | 1.72 – 1.78 | within band |
P-MOHO-4 · Vp/Vs = 16/9 as a Tau-Lattice Fraction
The ratio 16/9 = (4/3)² is a fundamental Tau-lattice fraction — the square of the perfect fourth musical interval. It recurs across acoustic, harmonic, and molecular domains, confirming it as a primary Tau-coupling constant.
P-MOHO-5 · Sidereal Year = Moho Year × 730/729
The FOT derivation of the sidereal year proceeds through the Moho orbital period — the characteristic oscillation time of the G0/G1 register boundary. The correction factor 730/729 = (3⁶ + 1)/3⁶ introduces the sixth power of prime 3.
P-MOHO-6 · The 1/(5π) Equalisation Factor
The factor 1/(5π) is the coupling constant at the G0/G1 register boundary — the only {2,3,5,π} value that equates the orbital Tau-wave period with the radial seismic wave period at R = 20,000/π km.
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