The contradiction at the heart of the Islanders’ signing of Julien Gauthier is equal parts compelling and mystifying — enough to act as jet fuel for speculation.

Consider all of these facts:

• The Islanders need to add scoring, and the two readily available options on the market — the Senators’ Alex DeBrincat, to whom they have been connected via trade, and Vladimir Tarasenko, a free agent who, per Sportsnet’s Elliotte Friedman, changed his representation Wednesday to J.P. Barry and Pat Brisson of CAA — each will likely cost in the range of $8 million annually.

• The Islanders have yet to re-sign restricted free agent Oliver Wahlstrom, who should come in at a cost between $900,000 and $1.1 million annually.