I studied Hegel for about 4 years in Germany and wrote my master thesis about the Science of Logic. I agree with most of what you are saying although I have the feeling you are simplyfying some things.

For example: Hegel did the basic work for the late science of the logic already in the encyclopedia of the philosophical sciences. In here he layed the ground work for what later became famous as the trinity of thesis, antithesis and synthesis.

It is called the "three moments of the logic-realistic" and contains a reasonable moment ("thesis"), the dialectical moment ("antithesis") and the speculative moment ("synthesis").

I strongly recommend reading these in order to truly understand what Hegel's dialectic is all about. Dialectic thinking means to negate a negation. It means to having not truly experienced an idea, but to have at least experienced it in one of its determinations. The act of speculation (the way to the "antithesis") means to deny the actual possibility to beeing able to recognize something solely by reasonable thinking, but to acknowledge that the idea beeing researched about is differentiated within itself.

I do not agree on the last paragraph. Can you give a reference please where Hegel speaks about the synthesis of spirit and matter?

I am asking, because in a commented copy of the "Science of Logic" we used in university, Hegel writes:

The physical nature is such Other according to its determination; it is the Other of the mind. But since the spirit is the true Something and the nature for itself is only what it is in opposite of the spirit, therefore, insofar it is looked upon as itself, its quality is beeing exactly this: beeing the Other in opposite to itself, beeing out of itself.

(Source: Georg Wilhelm Friedrich Hegel: Werke in 20 Bänden mit Registerband, herausgegeben von Eva Moldenhauer und Karl Markus Michel, Band 5: 127)

(Original: Solches seiner Bestimmung nach Andere ist die physische Natur; sie ist das Andere des Geistes… Aber indem der Geist das wahrhafte Etwas und die Natur daher an ihr selbst nur das ist, was sie gegen den Geist ist, so ist, insofern sie für sich genommen wird, ihre Qualität eben dies, das Andere an ihr selbst, das Außer-sich-Seiende … zu sein.).

In my view Hegel clearly speaks of a hierarchy here. He is putting the mind above the matter. The mind is "the true something" and the nature is "only what it is in opposite of the spirit". Or did I misunderstand this?

I always thought Hegel thought strictly dualistical as Platon did. Maybe I am wrong. Therefore I am asking you for reference.