Conditional Reduction of the Selberg Spectral Gap to Langlands Symmetric Power Functoriality

The Selberg Eigenvalue Conjecture asserts that the first non-trivial Laplacian eigenvalue on a congruence surface satisfies λ₁ ≥ 1/4. The best unconditional bound gives λ₁ ≥ 975/4096, and the argument breaks down precisely because the automorphy of Symᵏ π for Maass forms is unproven when k ≥ 5. We present a mechanized conditional reduction in Lean 4: assuming the existence of symmetric power lifts and the Jacquet-Shalika unitarity bounds, no exceptional eigenvalue λ₀ < 1/4 can exist. The reduction does not prove the conjecture unconditionally; it identifies the precise functoriality degree $k=5$, i.e., a $GL(6)$ lift where any proof must eventually do its hardest work.