The phrase "are certainly based on" is correct and usable in written English.
You can use it when discussing the foundation or origin of an idea, theory, or argument, emphasizing certainty in that basis.
Example: "The conclusions drawn in this study are certainly based on extensive research and data analysis."
Alternatives: "are undoubtedly founded on" or "are clearly derived from".
Such misunderstandings are certainly based on subtle differences in language, but the term CM is ambiguous, as Seshia et al. [9] and Olesen [10] himself recognized, and surely does not help in overcoming them.
The upregulation of CGRP and nNOS immunoreactivity in rat primary trigeminal afferents six hours after onset of a nitroglycerin infusion at the same dose as in the present study [30] and the increase in NOS-positive second order neurons, which continued during many hours [31, 32], are certainly based on long-term transcriptional effects.
To overcome this problem a bottom-up methodology is proposed, which relies on the basic idea that the system configuration is certainly based on one or more thermodynamic cycles that may share some processes or be combined in a cascade form.
Although to their credit, the recent experiments were certainly "based on the results of animal experimentation".
Van der Waerden believed that "it was certainly based on earlier traditions".
It's certainly based on a bunch of people that I knew in my 20s and probably, I'm sure for some of my friends, I was even a little bit of that type of character -- the friend that asks to crash on your couch and decides to stay a couple of days longer than he should.
I did the same thing with "The Help" -- I hate having a preconceived notion of what it's going to be and then playing to that thing, especially once I heard that it's certainly based on the book, but [with] a series, there's a lot of maneuvering that we have to do.
One of the most striking examples, the "Hindu necklace" commissioned from Cartier by the U.S. heiress and socialite Daisy Fellowes in 1936, was almost certainly based on one the jeweler made in 1935 for the Maharajah of Patna.
A ridiculously specific prediction that was almost certainly based on intercepted Axis crypto-transmissions was de Wohl's announcement, on July 18 , 1941 that the two S.S. field marshals leading the invasion of Russia, General Wilhelm Keitel and General Walter von Brauchitsch, were involved in a plan to assassinate Hitler.
Cases of infanticide between these two wren species were almost certainly based on food resource competition, since nestlings were killed only during a pronounced food shortage.
