1. A mathematical model can never represent reality, but only a simplification or an approximation. If the mathematical model predicts a physical barrier and you obviously don't see one in reality, then there is something wrong with the model. So there is no mathematical proof of you and you want to explain the situation by a mirage. This issue is described in this video better than I could (the Fata Morgana (Mirage), reflection and bending). But I know you will not look into it.
https://youtube.com/watch?v=nJenY3zKWLs
2. How can a physical barrier that should conceal an object not be visible and not conceal the object? In this example, the horizon should lie in front of the oil rigs (as in the mathematical diagram) and cover the lower part. In the globe model there should be a visible physical horizon, the reality shows that there is no physical horizon, but an optical convergence of sky and earth.
If „P“ earth has a radius of 3959 miles,
Then „Q“ every geometric horizon can be 1.22 miles x square root of observer height in feet
Not „Q“ We do not have a geometric (physical) horizon at that distance
Not „P“ the earth is not a globe of 3959 miles
3. I had used a different calculator for the calculation, but the video uses the correct one!
I know that this is not the correct angle as the graphic in the calculator is not true to scale. It should just be a diagram for the description. However, it doesn't change the fact that you should experience a curve in the horizon at some point. But no matter how high you go, it's always completely horizontal.
In my opinion, the bases of the oil platforms are clearly visible, the rear platform is optically higher than the front one and you can see more water behind it. No physical barrier to see. This is not a mirage.

However, this discussion is completely pointless and I will not invest any more energy in it. I don't want to be called a liar or anything else.