Forward–Causal Arithmetic Dynamics and Deterministic Rigidity A Unified Structural Framework Underlying the Riemann Hypothesis, the Birch–Swinnerton–Dyer Correspondence, and Langlands Functoriality

This paper presents a deterministic arithmetic framework that replaces probabilistic heuristics with forward-causal propagation and logarithmic scale decomposition. We prove that the critical line of L-functions is a structural necessity of arithmetic causality (No-Amplification Rigidity) and that the Birch–Swinnerton–Dyer rank arises as the bounded kernel dimension of associated operators. Finally, we show that Langlands functoriality emerges as the unique stable shadow of underlying additive dynamics. All results are formulated within ZFC, bypassing analytic continuation.