Vol3 Sections 270, 271, 140 · P-GEO-9 through P-GEO-18

Earth's Interior as a {2,3,5,π} Resonator

Silicate angle 6/π rad. Oceanic crust ≈ 7 km — off the stable {2,3,5} thickness nodes (subducts). CMB pressure = 3³×5 GPa. Seismic velocities: 2³→3²→2×5 with depth.

Silicate Angle
1080/π² degrees
= 6/π radians = 2×3/π
·
CMB Pressure
3³×5 = 135 GPa
measured ~136 GPa
·
Propositions
10
P-GEO-9 to P-GEO-18
The Silicate Tetrahedral Law

One angle encodes Moho boundary AND water geometry

θ_SiO₄ = 1080/π² degrees = 6/π radians. Identity: θ_SiO₄ = (π/3)×θ_HOH [exact]. Chain: θ_SiO₄/3 (rad)×10⁷ = R_Moho = 20,000/π km [0.000 ppm]. One angle, three domains.

P-GEO-9
θ_SiO₄ = 1080/π² = 109.4269° | θ_SiO₄/3 × 10⁷ m = R_Moho
θ_SiO₄ = (π/3) × θ_HOH [exact] | CMB: 3³×5=135 GPa | ICB: 2²×3⁴=324 GPa
Seismic Vp tower: CMB 2³=8 | mid 3²=9 | ICB 2×5=10 km/s
Registered Propositions

Key Results

P-GEO-9

θ_SiO₄ = 1080/π² = 6/π radians. θ_SiO₄ = (π/3)×θ_HOH [exact]. θ/3 × 10⁷ = R_Moho = 20,000/π km.

P-GEO-10

Oceanic crust ≈ 7 km sits off the stable {2,3,5} thickness nodes → always subducted. Continental crust 40 km = 2³×5 → permanently stable. Only a clean {2,3,5} node achieves lattice lock.

P-GEO-13

Outer core Vp: CMB 2³=8, mid 3²=9, ICB 2×5=10 km/s. Prime succession {2}→{3}→{5} with depth.

P-GEO-14

Core pressures: CMB 3³×5=135 GPa; ICB 2²×3⁴=324 GPa. Ratio = 12/5 = 2²×3/5 — pure {2,3,5}.

P-GEO-16

Thorium Z=90=2×3²×5 — only major radiogenic element with pure {2,3,5} atomic number.

Cross-references: Vol3 Sections 270, 271, 140 | P-WBG-6 (water bond angle) | P-GEO-1–8