In animal cells, which structure is thought to produce the spindle fibers that separate the sister chromatids during anaphase

The Centrioles produce the spindle fibers.

for example, no new evidence will demonstrate that the earth does not orbit around the sun (heliocentric theory), or that living things are not made of cells (cell theory), that matter is not composed of atoms, or that the surface of the earth is not divided into solid plates that have moved over geological timescales .