This document serves as the official research roadmap and project manual for the Generative Fluctuation Arithmetic (GFA) program. The manual provides a complete overview of the development of GFA from its foundational generative structures through recursive arithmetic, structural mathematics, recursive prime theory, zeta structures, spectral theory, critical-line stability, bridge consistency, transfer frameworks, and formal verification objectives. The document organizes the entire research program into five major phases: • Phase 1 – Foundations of Generative Mathematics• Phase 2 – Recursive Prime Mathematics• Phase 3 – GFA Zeta Program and Riemann Hypothesis Architecture• Phase 4 – Strengthening and Formalization Frameworks• Phase 5 – Lean 4 Formal Verification Program For each phase, the manual records the corresponding research papers, their logical dependencies, and their role within the broader GFA framework. The document is intended to function as a navigation guide for readers, researchers, reviewers, and future formalization efforts. It provides a unified view of the complete GFA program, clarifies the progression of ideas across the project, and outlines the pathway from foundational generative mathematics to the formal verification of the GFA-RH and GFA–Classical RH transfer frameworks. This release represents the organizational and architectural summary of the current GFA research program prior to Lean 4 formalization and verification.