The Earth's motion is unverifiable.
Nope. Not only is it verifiable, it has been verified.
It is against Galileo's relativity if it can be proved.
It is therefore self-contradictory.
Care to elaborate on that some more?
Are you sure it isn't just contradicting your understanding of it?
All that relativity states is that the laws of motion are the same in all INERTIAL reference frames.
This does not apply to ROTATING reference frames as they are not inertial reference frames.
The key difference between inertial and non-inertial frames is the existence of inertial or pseudoforces.
Inertial frames have no such forces.
Non-inertial frames do.
A simple thought experiment to show this is to consider a rotating disc with a ball attached which then releases the ball.
First lets consider this in the inertial reference frame. In this frame the disc is rotating, taking the ball with it.
At any point in time the disc is applying a force to the ball to keep it rotating with it, and the ball has a tangential velocity.
When the ball is released, the disc no longer applies a force and the ball thus moves in a straight line, leaving the disc.
Now lets consider what happens in "reality" in the non-inertial reference frame.
Now the disc is stationary and there is a pseudoforce pushing the ball outwards, with the disc resisting this force.
When the ball is released, this pseudo-force pushes the ball outwards, and causes it to follow a curved trajectory.
Now lets consider your hypothetical world where the non-inertial frames are the same as inertial frames.
Now the ball and disc just sit there, with no force needed as the ball and disc are both stationary. This already contradicts reality.
Now the ball is released. As there is no force, the ball continues to sit there, not moving at all. Again, this contradicts reality.
So no, the laws of motion are NOT the same in inertial and non-inertial frames.
They are only the same in inertial frames.
In non-inertial frames additional inertial or pseudoforces need to be used in addition to the normal laws of motion to account for the fact that it isn't an inertial reference frame.
So no, verifying the rotation of Earth is not a violation of relativity (of any form based upon reality).
Foucault pendulum is a fraud.
Even if the pendulum moves, it's not caused by the rotation.
You not liking it doesn't make it a fraud.
The only explanation that matches what is observed for Focault's pendulum is the rotation of Earth.
There is nothing fraudulent about it.
It can even be demonstrated at the small scale with a turntable and pendulum and camera.
It is a result of a rotating system not being an inertial reference frame, causing the pendulum to appear to follow a curved path instead of a straight path.
On Earth, due to the rotation being slow, this curve is so minor you will not see it but will see the effects after enough oscillations.
Allais effect proves it.
The "Allais effect" proves nothing.
It unsubstantiated, self-contradictory nonsense.
In order for you to be able to prove anything using the Allais effect, you would first need to show it is real.
Then you need to demonstrate that it alone accounts for the change in the plane of the pendulum's oscillation, rather than merely being an additional contributing factor. The last part is of special importance because none of those that I have found reporting it (including Allais himself) indicate that it is the route cause of the variation in the plane of oscillation of the pendulum and instead just have it as an additional effect on it.