Harary–Schwenk–Scott conjecture for locally finite trees

Let $G$ be a locally finite tree. A graph $G$ is reconstructible if every graph hypomorphic to $G$ is isomorphic to $G$, where hypomorphism means that there is a bijection between the vertex sets whose corresponding vertex-deleted induced subgraphs are isomorphic. Harary–Schwenk–Scott conjecture. Every locally finite tree is reconstructible. The conjecture arose after non-reconstructible infinite graphs and locally finite forests were found, and it was proposed as the corresponding positive statement for locally finite trees. The paper constructs a counterexample, so the conjecture is refuted.