Discoveries / analysis

Complete rational classification of fifth-order autocorrelation ambiguities on $U_{30}$

Agulnick and Busick-Warner exhibited a family of fifth-order ambiguities on the exact unit support $U_{30}$ and conjectured that it was not a complete classification because it did not use the full field $\mathbb Q(\zeta_{30})$. This work proves the complete classification. The larger field enlarges the common amplitude $\alpha$, while every relative ambiguity remains a norm-one parameter in $\mathbb Q(\zeta_6)$. The result is a specialization of a theorem for every exact unit support $U_{6m}$. The entry does not claim a complete parametrization for arbitrary supports: on the 255 automorphism-stable supports treated elsewhere in the paper, the broader result is a closing-degree classification. It does not treat noisy data or noncyclic groups, and it makes no novelty, priority, or firstness claim.