Global Cusp Atlas for Ramanujan's Mock Theta Functions - Synthesis of Odd Persistence and Even Compensation with Spectral and Resonance Implications

This paper constructs a modular framework for cusp behavior in Ramanujan’s mock theta functions, synthesizing analytic persistence at odd cusps and exact compensation at even cusps. It introduces a unified twisted L-function encoding both behaviors, proves its meromorphic continuation, and derives a functional equation linking ss and 1−s1 - s. Spectral analysis yields zero-density bounds and invites a conjectural critical-line distribution. A heuristic analogy with Veneziano amplitudes frames cusp divergences as arithmetic resonance structures, suggesting symbolic parallels between automorphic L-functions and scattering poles in physics. The framework embeds mock theta functions within augmented automorphic representations, offering a propagation-ready scaffold for further spectral, arithmetic, and interdisciplinary exploration.