Goals and use cases for a system that stores, queries, and manipulates equations

I love the idea, but I am concerned that if run by and for physicists, it will perpetuate the lack of rigor and "shorthands" physicists use to abuse mathematics [1]. I would propose an additional feature: that entries be highlighted in an additional way if they are mathematically false as written (or misleadingly overloaded, or just a huge abuse).

[1] e.g. the sum of natural numbers being -1/12, perpetuated with reckless abandon in this video https://www.youtube.com/watch?v=w-I6XTVZXww to the dismay of mathematicians everywhere. I also have personal gripes with the way physicists use delta functions, and hear many physicists say (about some topic in mathematics), "I don't want to actually do the mathematics here, I just want to get intuition about it."

I wonder what a mashup between this equation store, OEIS, and Wolfram Alpha would look like.