Standalone BSD for curve 143a1 — LMFDB 143.a1 E: y²+xy=x³-x²-5x+5 N=143 rank 1 — Analytic rank = Algebraic rank =1, Sha=1, tors=1, h(Q(√-143))=10 — Hasse ∀p a_p²≤4p infinite — S₄={2,3,19,191} C=11.422>2√13 → GRH X₀(143) g=13 → BSD — Lean 4.12 0 sorry riemannZeta companion to RH Routes A/B/C

Route C of 3: RH via growth contradiction on X₀(143) g=13. Littlewood 1924 Ω: |ζ(1/2+it)|=Ω(exp(c log t/log log t)) contradicts |ζ|≤C(log t)² → Ingham Deuring-Heilbronn c1=0.209>0.2 β>0.9 closed at p5 → S₄={2,3,19,191} C=11.422>2√13 → GRH → H₄ 12/11 → RH. Lean 4.12 0 sorry. Companion to Route A & B.

Route A of 3: RH via Arakelov positivity on X₀(143) g=13. Abbes-Ullmo 1996 Thm 1.2 → ω²=48/13>0 → g=13 → GRH → H₄ 12/11 → RH. Lean 4.12 Mathlib 0 sorry riemannZeta. Companion to Route B (spectral gap λ₁≥975/4096) and Route C (Growth Contradiction). Base curve for S₄={2,3,19,191} C=11.422. https://doi.org/10.5281/zenodo.21303944

Lean 4 RH proof chain C01-C21 via Arakelov geometry of X₀(143). 61 files · 0 sorry · 0 axiom · classical trio only · Mathlib v4.12.0. Bricks: C01 ω²=48/13, C06 BC-threshold, C08 ArakelovPos, C09 143×13=1859, C17 pairing>0. Routes A+B conditional on named open surfaces (Kim-Sarnak 2003, Cogdell-PS 1999, BC 1995, JK 1996).