Author: Diego Tentor Date: October 2025 Version: 1.0 (Draft) Abstract We present a formal derivation of the quantization-continuity duality observed in fundamental physics, based on the ArXe Axiom which establishes an isomorphism between the logical operation of negation and Planck time. Through exentational recursion, an exponential structure T^k (k ∈ ℤ) is generated that exhibits dual properties: positive exponents generate…