Many a successful science project has been based upon the building of a suspension bridge from toothpicks or other individually fragile materials. With the right leverage, materials of dubious strength can support a far greater weight than might be expected.

In negotiations, too, leverage can play an outsized role. Right now, Vermont officials at both the state and federal level are weighing whether they have enough to somehow reopen the Vilas Bridge in North Walpole, which has been closed since 2009.

It was then the bridge was deemed unsafe to vehicle traffic after a failed safety inspection. Fixing the bridge has shown up on the New Hampshire 10-year transportation plan since — it’s now slated to begin in 2028 at a cost of $6.9 million — but has, each time, been bumped back or removed from that schedule. New Hampshire’s reasoning is that while the bridge is convenient and historic, it isn’t the only way across the river in that neck of the woods. There are two other bridges spanning the river nearby, including the New Arch Bridge, which also leads into Bellows Falls. It’s just not a priority project to those in Concord.

It is to merchants in Bellows Falls, who have complained their business is off by about 30 percent since its closure. Officials there say relying on the Arch Bridge is unsafe because of abutting train tracks. When a train is passing, they note, the bridge is impassable to emergency vehicles.

Vermont state officials have tried to find a deal by which the Vilas Bridge can get fixed and reopened sooner, but without actually paying more than the state’s agreed-to part of the cost. And there’s the rub. Both states rely equally on the 30 bridges that span the Connecticut River, but because the river was long ago deemed part of New Hampshire, the Granite State is responsible for 93 percent of the cost of bridge projects.

In 2014, Vermont offered to pay all the cost of the Vilas Bridge work — if New Hampshire would then pick up all the cost of future work on all 30 Connecticut River bridges until the balance was repaid. New Hampshire refused.

And that’s where leverage comes in — the political kind, not the scientific principle.

Vermont wants the bridge opened soon because it has far more to lose. Downtown Bellows Falls relied heavily on traffic running across the bridge to and from Route 12 in Walpole. But the reverse isn’t really true. North Walpole isn’t suffering from a lack of traffic since the bridge closed. If anything, parts of the town may be seeing more vehicles. And because of the Arch Bridge and the one farther south at Route 123, Walpole residents aren’t greatly inconvenienced. If they want to go to Bellows Falls, they can. But the traffic flow across the Arch Bridge essentially bypasses most Bellows Falls businesses. Unfortunately for them, they lack leverage to force New Hampshire to pay the lion’s share of the cost of repairs. With plenty of important projects on its plate, one might expect the N.H. DOT to continue to ignore the noise from across the river until it’s backed up financially.

There is one lever that might work in Vermont’s favor: In seeking federal funds for a 1994 bridge project in Newport, New Hampshire promised it would maintain the Vilas Bridge, which has historic and architectural value. Vermont started pointing out the bridge needed work as early as 2002, but it continued to deteriorate. Whether that means the state is obligated to act at any given time, we don’t know, nor can we assess whether Vermont’s Washington delegation can use that language to force the Granite State to act.

We’d guess if New Hampshire officials dig in the whole affair could wind up in court, which no one should want.

The larger issue is the unfairness of the cost-sharing between the states. If not for language inserted in plans for a separate project decades ago, Vermont wouldn’t even have this piece of leverage. It should learn from this situation and seek a more equitable arrangement. But that, of course, would mean agreeing to pay more toward the bridges that daily carry residents of both states — and their money — across the river.

An equal stake would, indeed, provide equal leverage.