Yes this is a very well corroborated claim, but fundamentally faith based nonetheless.
This entire discussion is predicated on a minimalist set of mathematical axioms being valid, but there isn't even agreement on what that set of axioms is (though it may seem so to a layman). We still manage to get on in the world because we can do highly effective utilitarian reasoning without that being resolved.
> that our perception allows us to interrogate these properties.
That's not about science, that's about logic. Anything that can interact with people can be detected and interrogated. It does not exclude the possibility that other things may exist but there is both no way for us to interact with those things and, as such, they have no relevance to our lives.
Rather, science is an inquiry into what can be learned about the universe under certain limiting assumptions. Like a game, it has certain rules, at least on a tentative basis.
To make an analogy, chess seeks to find out what kinds of tactics can defeat the enemy's King under assumptions about how the Queen can move, but does not imply a belief or faith about Queens.
Science doesn't preclude parallel games or fields of inquiry being played under different rules, such as the theologies of religions, perhaps political ideologies, literature, music, and so forth. Some people play multiple games at once. My parents were educated in theology, but became good scientists. I'm a scientist but also a musician.
In my view, the thing that makes science stick out is not its relationship to religion, but its success. I think that in the 17th century, scholars mostly assumed that science would peter out -- it would run into a brick wall, or merge with theology. That it has done neither of those things could not have been predicted at the time, and inspires a certain amount of awe today, as well as an attraction to curious minds.
This is a really weird statement to me - what is the definition of faith that you are working from?
As someone who grew up in an evangelical environment, "faith" was the belief in God and his plans ("Have faith this will work out, God would only give you what you can handle." type of thing). Outside of that context I've generally understand it to mean "believing without evidence."
A well corroborated claim is the opposite of lacking in evidence and does not require belief in God. This sounds like you are conflating "belief" and "faith," which are not the same. I believe the sun is coming up tomorrow because the preponderance of evidence says it will, that does not require faith.
Also the subject matter is in many cases very different, and even if someone doesn't understand the science behind something they can observe and see a tangible result.
I cannot test whether or not I will go to heaven after I die. This belief requires faith