Errantum: Petersen graph has branchwidth 4

In my doctoral thesis [1], I claimed a proof that the branchwidth of the Petersen graph had branchwidth 5 and proceeded to prove that it was a member of the obstruction set for graphs with branchwidth at most 4. I have stated this claim in Hicks [2] and Hicks et al. [4]. There was, however, an error in the construction of the tangle used to prove the claim. The branchwidth of the Petersen graph is 4. Figure 1 offers an optimal branch decomposition for the Petersen graph of width 4 that was computed using my tangle basis code [3] and the branchwidth of the Petersen graph is at least 4 since it contains K5 as minor [5].