This is scientific proof that heliocentrism is false.

HC claims the sun's rays hit the earth in parallel.

However, this cannot be seen anywhere ever.

All sunbeams occur in one shape only: a pyramid. And these rays all have a single point of convergence at the sun.

This also provably and visually demonstrates the closeness of the sun.

HC is provably and utterly false.

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There you go again with your straw-man heliocentrism.
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But otherwise you're all off, on the rest as well.
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Maybe you've never heard of a laser beam.
The one thing that differentiates a laser from other types of light is that the rays are all parallel to each other.
There are other aspects too, but parallel rays are at the top of the list..
"Any lamp" at a very great distance also shines with very nearly parallel rays.
But the SHAPE of the lamp at great distance may not be discernible.
This is shown by the fact that a small mirror can reflect the sun's light visible for 50 miles away.
But the SHAPE of the mirror cannot be determined at that distance.
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The (very nearly) parallel rays of the sun's light is an observable fact, which is useful for many observations.
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The sun has a diameter, and as such, its rays are a little bit scattered since all parts of the sun shine similarly.
This is why any object held up to sunlight casts a shadow that is a little bit fuzzy.
The sun is not "a single point" but a circle with a measurable diameter, about 1/2 of one degree.
Navigators have been in agreement on this fact for about 300 years, in case you missed it.
If this is what you're referring to by "a pyramid" that's the wrong word. It should be "a cone."
The sun's light through a small aperture emerges in a cone shape, not "a pyramid." The sun isn't a rectangle.
Curiously, the small aperture can be in the shape of a square or an elongated rectangle or even a crescent, and you still get a cone pattern.
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During a partial solar eclipse, the sun's image with a bite taken out of it, can be seen under the shadow of trees.
That's because the tree leaves act as apertures between the leaves where the sunlight passes through.
And the distance between each image is the same close to the tree as it is far away from the tree, showing that the sun's rays are parallel.
Objective observation proves your statement false.
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The great distance of the sun (approx. 92 million miles away) allows us to use its light AS IF it were parallel rays in many ways.
But in some applications, a polarizing filter is beneficial to arrange the light in more parallel rays than without the filter.
You can test this very simply by rotating two polarizing filters and watch the sunlight go from bright to almost blackout.
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Explain scientifically how you can have a hot spot on top of the clouds if the sun is that far away.  I just wish you could be objective and not cloud everything with insults.  You assertion that it's "nonsense" and "quixotic" is decidedly unhelpful.  I want to see scientific information.