Periodicity Is Enough — Every Nonconstant Periodic Function Is Out of EML's Reach

sin was the specific target. It turns out sin was never the point — no finite EML tree can equal ANY nonconstant, continuous, periodic function, full stop. We built genuine Extreme Value Theorem machinery to get there, then found the proof didn't need it: periodicity alone does the work an infimum was supposed to. Honest scope inside.