[math-fun] How does this function manage to oscillate on the unit interval?

https://www.wolframcloud.com/objects/d4fa673b-0423-42fb-b7b5-0f70a7c14c6e Sidarth Ghoshal has exactly determined the mean value and amplitude of an O(10^-6) ripple in a function whose definition appears nonoscillatory. It graphs like the error in a Remez minimax approximation, even unto the ripples Chebychummying at the endpoints. But unboundedly. Worse, Sid says there are O(10^-13) ripples on the O(10^-6) ripples. Whether or not he discovers their formula, I consider Sid's present formula a breakthrough. —rwg