Using graph mapper isn’t the best choice for this. I adapted version ‘b’ from here to get the sine curve (white group):
And using ‘X’ or ‘Y’ vectors isn’t correct either, the vector needs to be relative to the curve. I used the ‘Y-axis’ vectors from HFrames.
I added the purple group to get multiples of four ‘Cycles’ but that could be skipped. I spent some time adjusting Seam but finally gave up and ripped out that code as it was getting too complex - but it could be explored if you are up to it. 
sine_2024Aug2b.gh (18.4 KB)
P.S. Seam can be adjusted something like this, but I was trying to derive the slider value automagically so it adapts to different values of ‘Cycles’.
