Some say that the high density EOS is only poorly constrained, but this statement is just like a pump and dump. If you look at the QCD calculations you may find huge uncertainty, but this uncertainty extends to the direction to make the EOS softer below the conformal bound that is already very soft. This implies an intriguing physics picture that interacting nuclear matter quickly approaches the conformal EOS and it is saturated by weakly interacting quark matter after smooth crossover where the speed of sound can have a peak. Such considerations lead us to a well constrained and very likely EOS with quark matter crossover. Then, the question is whether such a smooth change without the frequently-postulated first-order discontinuity can be detectable by the gravitational wave observation or not, and our recent analysis gives a positive answer.