Mr. Homann concludes below that:
"These observations clearly indicate that the so-called 'precession of the earth' is NOT a scientific fact, and that the Sirius system has a noticeable gravitational influence on our solar system."
In other words, the solar system according to Homann's interpretation is gravitationally linked to Sirius.
That may mean that Sirius is the sun's dual, Sirius and sun orbiting around a barycenter.
But Sirius already is a binary system, made up of Sirius A and the smaller sirius B:

So, if Homann is right, we woudl have a ternary star system, sirius A, sirius B and Sun.
Another possibility woudl be that the sun has a closer dual, sunB, and that this binary system orbits around the Sirius binary system.
If so, we would have a quadruple star system.
Even though fascinating, the latter hypothesis needs a candidate for sunB, whereas the former (the ternary system) would not need a sunB.