Bounded swaps in pass-and-swap queues. An Evidence Press briefing. Many service systems match jobs with resources that can handle them, such as computing tasks with servers that hold the right data. For some queues, long-run behaviour has a simple formula, called a product form. In a pass-and-swap queue, a job that finishes service hands its place to a later job it is allowed to swap with, and that job passes the turn further back. A swapping graph says which jobs may swap. In 2024, Dorsman and Gardner limited each service to at most a fixed number of swaps, called the cap, a step motivated by redundancy scheduling. They proved the simple formula holds while no chain of swappable jobs is longer than the cap, and conjectured that, under a colouring condition, longer chains always die out. This release proves the conjecture false for every cap of two or more. In the smallest example, five jobs sit in a ring with a cap of two. There are a hundred and eighty arrangements, each with a chain that is too long, which the system can never leave and keeps revisiting. For jobs in a ring, such a trap exists exactly when the number of jobs leaves remainder one on division by twice the cap. Other networks fail too: a computer census of networks with up to seven jobs finds one thousand three hundred and fifty-five failures, none of them bipartite, meaning split into two groups that only swap across groups. For bipartite networks with an odd cap, the release proves the conjecture true, if every position is served. Inside the traps, the natural formula needs equal rates within each queue. The theorems have written proofs, and the counts are checked by exact programs that can be rerun. This is an anonymous, unrefereed candidate, not peer reviewed or independently reproduced. Published on 20 October 2026, its paper and evidence are linked from the Evidence Press release page. This briefing uses an AI-generated voice and is not additional scientific evidence.