Carry Dynamics, Fourier Obstructions, and a Conditional Normality Reduction for the Fibonacci Concatenation

This paper develops a rigorous conditional framework for studying the normality of the concatenation of the positive Fibonacci numbers in base 32. The argument begins with the Fourier characterization of normality and follows a possible persistent Fourier defect through the exact carry dynamics of Fibonacci addition. Boundary contributions are shown to be asymptotically negligible because the number of concatenation boundaries grows linearly, whereas the total digit length grows quadratically. The central result is a conditional normality criterion based on two explicit hypotheses: Forgetting of old order: order inherited through earlier carry states has vanishing macroscopic influence. No permanently effective novelty: newly generated structured interior contributions have vanishing normalized nontrivial Fourier mass. Under these hypotheses, together with the stated carry-history decomposition and the boundary estimate, the Fibonacci concatenation is normal to base 32. The implication is deductive once the hypotheses are assumed; the hypotheses themselves are not proved in this paper. The paper further analyzes carry recurrences, Cassini-type restrictions, recurrent carry structures, exact block transport, and the resulting terminal obstruction. These arguments clarify the possible mechanisms by which non-normality could persist. Two complete Python scripts are included as appendices. They provide finite plausibility checks for the two hypotheses, with an adjustable parameter N, progress and runtime reporting, CSV output, and all required library information. For N=20,000, the scripts reproduce the numerical results reported in the paper. The work is therefore presented as a rigorous conditional research framework with empirical plausibility evidence, not as an unconditional proof of normality.