The inverse room problem: hold the volume, search the shape. Minimises the widest gap between adjacent axial modes below 200 Hz, over the Bolt (1946, JASA) ratio area, by a compass search seeded on a feasible grid — derivative-free because the objective has genuine jump discontinuities where a mode crosses the 200 Hz window. Axial modes are n*c/(2L) per axis at c = 343 m/s. The volume is a given and never a free variable: unconstrained, the objective is monotone in volume and the answer degenerates to "build a bigger room". The published answer is a BAND recommendation, one shape covering a range of volumes, with the range derived from a covering number rather than chosen. Pure mathematics - nothing is fetched and nothing is recalled.
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