Recursive Adelic Dynamics

This paper presents a comprehensive framework integrating recursive expansive dynamics, p-adic quantum geometry, adelic number theory, hyperfolding rings, and golden-ratio modulated recursive structures. We derive a new action principle that unifies quantum gravity, cosmology, and algebraic geometry through recursive Lie algebra deformations, recursive entropy scaling, and adelic corrections to gauge theories. Key results include: (i) The Inverse Zero Operator (IZO) as a renormalization tool, stabilizing infinities in gravitational entropy. (ii) Recursive entropy corrections explaining black hole microstates and gravitational wave echoes. (iii) Adelic Gromov-Witten invariants linking p-adic geometry with quantum field theory. (iv) Fractal p-adic correspondence showing that Hausdorff-dimension-modulated structures naturally emerge from adelic cohomology. (v) ϕ-modulated gravitational delays testable in LIGO-Virgo, with predictions for log-periodic cosmological modulations. We explore implications for quantum holography, number-theoretic quantum gravity, and nonlocal field theories, establishing testable predictions and a mathematically rigorous extension of QFT and gravity.