Emergence of Gravity from Arithmetic Saturation and Two-Time Dynamics

We present a theoretical framework for quantum gravity based on a dynamical dualitybetween two mutually exclusive regimes: the internal structure S (O) (Real Time ϕ, localarithmetic on N) and the external structure S (O^-1) (Complex Time ω, global spectral geometry on C). Spacetime emerges from a stroboscopic process of information saturationgoverned by prime number distribution. The switch boundary acts as a topological horizon, enabling an entropic derivation of Einstein's equations through the demand/supply duality: matter (demand) reduces local entropy, geometry (supply) compensates via horizon ux, recovering the Bekenstein-Hawking coe cient 1/4 and coupling constant κ = 8πG/c3 with nofree parameters. The non-Hermitian transition Hamiltonian with PT symmetry connects thedynamics to the Riemann zeta zeros. Numerical simulations (N = 50, 000) con rm: uniformerror distribution (99. 9%), emergent Heisenberg principle (σxσp ≥ ℏ/2), normalized gapsg/lnp = 1. 006, and 25. 1% gravitational wells. We predict a testable arithmetic holographicnoise signature.