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The hardware is patentable - it's physical.

The software is not patentable - it's abstract.

If one wants to argue:

But if I built a strictly hardware machine that can do X, I could patent that

Someone could build something different - calculating the same computation - and not infringe because they have a different implementation!

Patenting the abstract = patenting the idea.

This breaks the patent exchange because you're supposed to disseminate the idea to the public for immediate consumption while patenting a specific implementation of the idea!

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