Proof of the Riemann Hypothesis via hyperbolic scattering theory on PSL(2,Z)\H. The core proof is the scattering Transmission route of §18: from the Riccati expansion of the Dirichlet-to-Neumann operator (Lemma 18.D) and bridge lemmas (18.D.1–18.D.3), Standing Hypotheses (H1)–(H4) are established unconditionally. Theorem 18.H (off-wall exclusion) then yields Corollary 18.I (RH). Wall singularity analysis (Theorem 18.V) remains conditional on (A1)–(A5). v9: English translation added. Consistency fixes in §0, Abstract, and §1.3 to clarify that the off-wall exclusion route (§18.1–18.7, Corollary 18.I) is unconditional while wall analysis (§18.9–18.18, Theorem 18.V) is conditional. リーマン予想の証明。§18 の散乱 Transmission ルートにおいて、補題 18.D(Riccati 展開)および橋補題 18.D.1–18.D.3 により Standing Hypotheses (H1)–(H4) を無条件に確立。定理 18.H(off-wall 排除)→ 系 18.I(RH)。壁上特異点分類(定理 18.V)は条件 (A1)–(A5) に依存。v9: 英語版追加。§0・要旨・§1.3 の整合性修正(off-wall ルートの無条件性を明確化)。

Bilingual: Japanese (primary) and English translation. 日本語(主)+ 英語翻訳版。