You're right. I've messed up. The notation here is a bit misleading and I didn't dig as deep here as I should have. I'll fix the website soon.

Thanks for sharing such an insightful article of complex material. Some follow-up showing how this helps optimization (gradient descent, Newton solvers?) would be great.

>> For convenience of notation, we’ll drop the explicit parametrization of the curves and denote this vector shift as [...]

FYI for clarity I wish the explicit parametrization was kept, even though it is more verbose.