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To bounce off this... What is your educational background in physics? My main comment is I'm wondering about the foundation this is based on. I really am curious.

What's wrong with the theory? It appears to be missing a spool. For the thread to take the shape of a parabola, the spool would be needed to unwind the initial thread and provide the initial involute. If only a portion of the entire involute is considered, it might get conflated with a parabola. The more developed involutes more closely resemble a spiral. Rather than traveling along the thread, what is being described is the endpoint, and the course it makes as it becomes unraveled from the spool, where if properly wound, serves as an excellent example of a helical coil. The specific gravity, in this case, might be derived from the weight granted to the original development in the vacuum of having left out the spool around which the original thread was packaged and subsequently unraveled from thereafter.