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The Common Core is simply a statement of what children should know.
This may allude to common core standards; Common core is more than standards. Common core is also a series of websites, linked from the official CCSS website, with many implementation directives.

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A challenge with implementing it is that it's mathematically correct
Throughout this thread I have not seen concerns about math standards per se.

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the developers of the Common Core never had any involvement with the textbook companies, nor did they "support" them. Plus, the textbook companies never had any influence over the Common Core.
There are complex interrelations over time, including funding. We do not need to agree. Some may see it as a chick-or-egg situation, and that is ok, too. Funding and interrelationships between different entities is a bit of a side issue; On this forum, I prefer to focus on the impacts of common core on gifted learners and gifted education.