The Climb Past the Closure

A census of band maxima -- for each mass number A', the largest level count attained by any band of a fixed single-particle spectrum as a coupling ranges over [0, 1] -- is continued past the closure at A' = 184, over A' = 185 to A' = 236 with the same machinery. The maximum does not rest at its post-closure value of 198: it climbs to 258 in nine steps (198, 214, 222, 228, 236, 240, 250, 252, 258), each held constant across a run of consecutive mass numbers while the set of couplings attaining it widens at every row without exception. The excess of the maximum over 184 grows in the same stepped rhythm, from 14 to 74. The 184 reach remains complete past its closure: at every row of the span the count 184 is reached at all 1,001 couplings, as are the counts 50, 82 and 126. No closure past 184 is named.