Zero-Inaccessible Realization and Isometric Theta-Profile Exchange: A CRP/CRD-Relative Critical-Line Theorem

This preprint develops an axiom-relative critical-line theorem for the completed Riemann zeta function within the Complementary Relational Principle and Complementary Relational Dynamics (CRP/CRD) framework. The centered completed zeta function is decomposed into two explicit theta sectors and lifted to a pair of nonvanishing Hilbert-space profiles. The paper proves that equal profile strength, and equivalently isometric exchange of the two profiles, occurs exactly on the critical line Re(s) = 1/2. It then introduces the CRP/CRD xi zero-realization axiom, according to which a formal zero is physically realized as a zero readout of an isometrically exchanged nonvanishing complementary pair. Under this application axiom, an off-axis zero would imply both equal and strictly unequal profile norms, producing a contradiction. The existence of an off-axis zero is therefore the exact falsification condition for the application axiom. The logical boundary is stated explicitly: universal xi zero realization is equivalent to the Riemann hypothesis in this theta-profile representation. Accordingly, the result is an axiom-relative theorem and is not presented as an unconditional proof of the Riemann hypothesis from standard analytic number theory alone. The deposit contains the manuscript in PDF format and accompanying Lean 4 source code distributed as a text file. The Lean source formalizes the logical dependency among universal zero realization, isometric exchange, critical-axis membership, physical-zero classification, and the off-axis falsification condition. It does not yet formalize the completed zeta function, the theta integrals, positivity of the theta kernel, or the analytic proof of the exchange–critical-line equivalence.