Blobbed topological recursion of the quartic Kontsevich model II: Genus=0 (with an appendix by Maciej Dołęga)

We prove that the genus-0 sector of the quartic analogue of the Kontsevich model is completely governed by an involution identity which expresses the meromorphic differential ω0,n at a reflected point ι z in terms of all ω0,m with m≤ n at the original point z. We prove that the solution of the involution identity obeys blobbed topological recursion, which confirms a previous conjecture about the quartic Kontsevich model.