  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 $\omega_{0,n}$ at a reflected point $\iota z$ in terms
of all $\omega_{0,m}$ with $m\leq n$ 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.
