Topological recursion for the extended Ooguri–Vafa partition function of colored HOMFLY-PT polynomials of torus knots

We prove that topological recursion applied to the spectral curve of colored HOMFLY-PT polynomials of torus knots reproduces the -point functions of a particular partition function called the extended Ooguri–Vafa partition function. This generalizes and refines the results of Brini–Eynard–Mariño and Borot–Eynard–Orantin.
We also discuss how the statement of spectral curve topological recursion in this case fits into the program of Alexandrov–Chapuy–Eynard–Harnad of establishing the topological recursion for general weighted double Hurwitz numbers partition functions (a.k.a. KP tau-functions of hypergeometric type).