why CTS require a separate step?

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Strange question, why you need to fix the timing?
Well the cts is needed to reduce the clock time arrival to all leaf element and to facilitate the hold time fixing after that.
I means a good skew should give a very hold time fixing ( few buffer added).
To reduce the impact the local skew should be preferred instead global skew (usual).
 

all steps before CTS, the clock tree is perfect, means the clock arrives to each leaf elements at the same time, no delay due to clock tree, then after the CTS, the setup need to be fix before the hold time.
 

before CTS, the clock is defined as set_ideal_clock (something like this), and the set_propagated_clock is false, means the clock path is null for all clock pin of each element.
After CTS, the real clock path with real timing is used to know when the CK pin is stimulated.
 

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