Hohoho

So no evidence then?

All that is needed to prove it is a square inside a square.

The outer square has side lengths of a+b

The inner square has side lengths of c.

It touches the outer square such that it divides the edge of the outer square into a length of a and a length of b.

This produces 4 right angle triangles with side lengths a, b and c.

The area of the inner square is c^2. The area of a single triangle is a*b/2, so the are of the 4 triangles is 2*a*b.

The are of the outer square must be the sum of those areas, i.e. c^2+2*a*b. Its area is also (a+b)^2=a^2+b^2+2*a*b.

That means a^2+b^2+2*a*b = c^2+2*a*b

And thus a^2+b^2 = c^2.

There is no way out of this and no experimental error as it is pure math.

Any experiment you try and do which produces just a little bit more or less requires you to determine the experimental accuracy and if that little bit more or less is just due to experimental error.