Archimedean Anchoring and Exact Realizability in Affine p-adic Normalization Dynamics

We study affine normalization dynamics governed by p-adic valuation data from a purely arithmetic and structural point of view. Instead of relying on probabilistic heuristics, average-case behavior, or growth estimates, we analyze the exact algebraic constraints imposed by valuation patterns and inverse reconstruction. We show that every finite valuation word induces a rigid and deterministic p-adic congruence structure, and that infinite valuation words are always formally compatible at the p-adic level. As a consequence, no argument based solely on local constraints, finite data, or infinite-depth p-adic coherence can exclude infinite formal behavior. The decisive obstruction is Archimedean. Using exact closed-form descriptions of iterated normalization and their inverse reconstruction, we prove that every realizable orbit must arise from a finite inverse construction anchored at a concrete terminal value. Infinite inverse constructions, although fully coherent in the p-adic integers, are arithmetically unrealizable as natural numbers. This Archimedean anchoring principle excludes infinite valuation patterns and provides an exact non-realizability criterion for infinite inverse branches. The framework is entirely deterministic and non-probabilistic, and relies only on explicit identities, divisibility, and congruence conditions.