That which the Machaber writes in the first siman of Shulchan Aruch,
יתגבר כארי לעמוד בבוקר לעבודת בוראו, שיהא הוא מעורר השחר
From here could one say that if one doesn’t get up by alos hashachar he is not following what it says in Shulchan Aruch and is being ovar on this Halacha? Or is the Shulchan Aruch simply telling us this is the proper thing to do (however if one wouldn’t do it they wouldn’t be “ovar” on anything.) Is there a proof one way or the other? Putting aside what the Rema adds in that at least a person shouldn’t be ovar the zman tefillah, meaning they shouldn’t get up so late. Unless one would say the Rema is not coming to argue but rather to explain what the Shulchan Aruch means and that this is really only an “etizah tovah”.
Answer:
From all of the commentaries on the Shulchan Aruch, it is clear that this is a virtue, and not a formal halachic obligation.
See the Mishnah Berurah (who discusses the concept of joining night and day with Torah and tefillah), the Taz, the Ben Ish Chai (Vayishlach 2-3), the Gra (who mentions a source from the Yerushalmi concerning David Ha-Melech), and others.
Moreover, this depends on the personal avodah of each person, and there are many, many Torah luminaries who did not get up early, because their schedule was better suited to rising later.
Best wishes.
