Everywhere at any point on this LP, the 1000Hz test tone has been encoded by a perfect cutter lathe. In practice, the stylus tip is just a point on the surface of the LP; it doesn't "know" where it was a fraction of a second before or after any particular event. How can this phenomenon change the fundamental frequency?
The cutter lathe is moving in a straight line.
A pivoted arm is moving in an arc.
They are not congruent.
Does your direct drive turntable speed up and down to bridge the gap on each rotation ?