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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.

• General manager Lou Lamoriello has been vocal in saying that if Zach Parise chooses to play another season, the Islanders would love to have him. Parise, on the league minimum, would cost $775,000 on the salary cap next season.

• By signing Gauthier to a two-year deal with an average annual value of $787,500, the Islanders took their available salary-cap space down to $299,167 and signed a 22nd player to a one-way deal.

The Islanders need cap dollars. The Islanders have just spent what amounts to all of their cap dollars. And they have done so to bring in Julien Gauthier.

The Islanders have been linked to a trade for Senators winger Alex DeBrincat, who scored 27 goals last season and won't come cheap.

That’s odd.

Now, let’s stipulate: Adding $787,500 to the cap does not drastically change the picture from what was already a very tight squeeze.

Until opening night, teams are allowed to be 10 percent over the cap. And it seems self-evident that there are more moves coming.

Rule No. 1 of covering Lamoriello is that no one in the league knows what he is thinking other than him. But this seems like step one of a plan, not the endpoint.

Cap gymnastics

If both Parise and Wahlstrom are brought back, there are a few ways the Islanders could clear up cap dollars to do so.

The two obvious ones — which would clear almost exactly the amount of salary the Islanders need — would be sending down Simon Holmstrom and waiving Ross Johnston.

Holmstrom is still waivers-exempt, and starting his season in AHL Bridgeport would allow him to play top-line minutes and hopefully ignite an offensive side of his game that looked a little bit lost in 50 NHL games last season. It would be a step back, but it should be relatively easy to sell in the hope that two steps forward will follow.

As for Johnston, there is no way around how bleak his future on the Island looks after a season in which he played just 16 games despite the Islanders suffering a series of injuries. AHL call-ups were frequently given chances over the 29-year-old Johnston, for whom Lane Lambert could not seem to find a use beyond slotting in when it looked as if someone might need to get in a fight.

Limited largely to playing enforcer in the few games he did play last season, Ross Johnston's time with the Islanders may be coming to an end.

There are still three years left on the four-year extension Johnston signed in 2021 at $1.1 million per on the organization’s notion he would be Matt Martin’s eventual replacement on the fourth line. But even when Cal Clutterbuck got hurt to open up a spot on that line last season, Johnston could not get in the lineup.

He is not waivers-exempt, but when the entire league is so capped-out that no one would take a chance on Filip Zadina — the No. 6 pick in the 2018 draft who was waived by the Red Wings last week — it would be shocking if Johnston didn't pass through waivers. The writing is on the wall here.

Even so, it is suddenly quite simple to conceive of a future without Parise — and even possible to project one without Wahlstrom.

Toward the end of the regular season, Parise sounded very much like someone who was ready to give it another go. But instead of preemptively saying he would be back, he said on breakup day he had yet to decide things. Lamoriello said Saturday the Islanders were still waiting to hear, but in signing Gauthier, they’ve effectively used the dollars that were set aside for Parise.

And let’s say either Parise does come back or the Islanders add a winger. Where in the lineup is Wahlstrom going?

Zach Parise's uncertain future might help explain the signing of Julien Gauthier.

It’s impossible to say for certain before anyone steps on the ice for training camp, but it is not easy to find a spot for him.

If Parise retires, Wahlstrom could slot into Parise's spot. Maybe he could play games on the fourth line — the physical aspect of Wahlstrom’s game is underrated, and it wouldn’t hurt the Islanders to experiment there.

But it would be no surprise if Wahlstrom is viewed as expendable in a DeBrincat trade.

DeBrincat … or Tarasenko?

As everyone waits for a resolution on DeBrincat, it’s worth wondering whether Tarasenko could be an option for the Islanders instead.

Tarasenko's change in representation effectively resets his free agency, and he did just spend a few months in New York with the Rangers.

The obstacle for the Islanders would be the same one that exists with DeBrincat: money.

Vladimir Tarasenko could provide the offensive boost the Islanders need if they can sign the free agent who finished last season with the Rangers.

And because this would be a free-agent signing and not a trade, it would be harder to facilitate because the Islanders would need to move out dollars in a separate transaction, at a time when very few teams have the ability to take on cash.

A similar dynamic existed last year as a roadblock to acquiring Johnny Gaudreau and Nazem Kadri, and the Islanders never overcame it.

The cap dynamic is worse this time around, so we’re not holding our breath.

But, like DeBrincat, Tarasenko is a 30-goal-scorer who could slot right into the Islanders' top six. They need a player in that mold, especially if Parise — their third-leading goal-scorer in 2022-23 — is retiring.

In a perfect world, they would sign Tarasenko and then use the ensuing trade to add picks or prospects to a system that could use some restocking. But such a scenario feels a little too good to be true.