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---------- CVD_3PT_GROWTH_FORMULA_V1 ---------------
Date: 2026-01-12
Theorem: phi^3 = curl(Psi · grad Psi)
Growth Basis Vectors:
g1 = nucleation vector (seed plane normal)
g2 = extension vector (phi * g1)
g3 = termination vector (phi^2 * g1)
Constraint: g1 + g2 + g3 = 0
Magnitude Ratio: |g1| : |g2| : |g3| = 1 : phi : phi^2
Resonance Frequencies (Schumann-harmonic):
f1 = 7.83 Hz (fundamental)
f2 = phi * f1 ≈ 12.67 Hz
f3 = phi^2 * f1 ≈ 20.50 Hz
Temporal Phases:
t1 = nucleation (0 ≤ t < τ/3)
t2 = extension (τ/3 ≤ t < 2τ/3)
t3 = termination (2τ/3 ≤ t ≤ τ)
Diamond Growth Integral:
D(r,t) = ∫[∑_{i=1}^3 (g_i · exp(2πi f_i t) / |r - r_i|)] dt
Boundary: |r - r_i| ≥ λ_i where λ_i = c / f_i
CVD Process Control Functions:
Q(t) = Q₀ · sin(2π f₂ t) [Microwave power]
T(t) = T₀ + ΔT · cos(2π f₃ t) [Temperature]
P(t) = P₀ · exp(-phi · t / τ) [Pressure]
Gas Ratio: CH₄/H₂ = phi/100
3‑Point Reflection Geometry:
Points: r1, r2, r3 forming equilateral triangle
Reflection planes: Π₁, Π₂, Π₃ with normals n_i = g_i
Symmetry: C₃v (120° rotational + vertical reflection)
Growth continuity: ∇·D = 0 at all t
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