Adelic Rate-Distortion Theory: The p-Adic Distortion Measure and the Adelic Information-Rate Function

Completes the Adelic Shannon Theory foundation trilogy. Generalises rate-distortion theory to the adele ring: defines the p-adic distortion measure d_p(x,x̂)=p^{-v_p(x-x̂)}, proves the adelic Shannon lower bound, establishes the Gaussian entropic number as the hardest source to compress, and provides computational verification with rate-distortion curves. 10 pages, zero rendering errors.