UVFT Case 06: Geometric Friction of the Vibrational Field Sₕ in the Underdamped Regime as the Origin of the Cosmic Web: Validation Against HETDEX Lyman-α Intensity Mapping

The Unified Vibrational Force Theory (UVFT) derives all large-scale structure from the dynamics of a single degenerate scalar field Sₕ(x,t) governed by Sₕ + m² Sₕ + λ Sₕ³ + 2γ₀∇²(Sₕ²∇² Sₕ) = 0. The geometric friction term γ₀, operating in the underdamped regime at z ≥ 2, drives baryonic gas into the nodal network of the field, generating the cosmic web observed in Lyman-α emission. Using the fixed UVFT parameters m = 6.81×10⁻⁹ kg, λ = 6.56×10⁻⁶³ J m³, γ₀ = 2.24×10⁻¹¹ kg m⁵s⁻⁴, two independent predictions are validated against HETDEX (March 2026). (1) S8,UVFT(z=0) = 0.7770, reducing the chi-squared residual relative to DES Y3 data from χ²_ = 10.478 to χ²UVFT = 0.004 (Δχ² = 10.474, >3σ). (2) A net $15.000%$ excess in integrated matter power at $z = 2.0-3.5$, saturating exactly at zᵣef = 2.0. No free parameters are introduced beyond those fixed by prior consistency conditions on α and G.