{
  "schemaVersion": 1,
  "id": "linearizability-overlap",
  "kind": "history",
  "title": "Overlapping queue operations and a legal linearization",
  "caption": "Two overlapping operations may be ordered at internal linearization points; a later enqueue must remain after both completed calls in real time.",
  "description": "Three thread lanes share a time axis. Thread P enqueues x from time 0.8 to 4.7 and linearizes at 2.3. Thread Q dequeues x from time 1.6 to 5.9 and linearizes at 3.6. Thread R enqueues y from time 6.2 to 7.7 and linearizes at 6.8. The first two operations overlap; both precede the third in real time. The legal sequential witness is enqueue x, dequeue x, enqueue y.",
  "lanes": [
    { "id": "p", "label": "Thread P" },
    { "id": "q", "label": "Thread Q" },
    { "id": "r", "label": "Thread R" }
  ],
  "operations": [
    {
      "id": "enq-x",
      "lane": "p",
      "call": "enq(x)",
      "start": 0.8,
      "end": 4.7,
      "result": "ok",
      "linearization": 2.3,
      "tone": "primary",
      "object": "queue",
      "note": "publishes x"
    },
    {
      "id": "deq-x",
      "lane": "q",
      "call": "deq()",
      "start": 1.6,
      "end": 5.9,
      "result": "x",
      "linearization": 3.6,
      "tone": "event",
      "object": "queue",
      "note": "observes x"
    },
    {
      "id": "enq-y",
      "lane": "r",
      "call": "enq(y)",
      "start": 6.2,
      "end": 7.7,
      "result": "ok",
      "linearization": 6.8,
      "tone": "inferred",
      "object": "queue",
      "note": "later in real time"
    }
  ],
  "markers": [
    { "time": 6.0, "label": "quiescent cut", "tone": "muted", "pattern": "dashed" }
  ],
  "witnesses": [
    {
      "label": "legal witness",
      "operations": ["enq-x", "deq-x", "enq-y"],
      "tone": "inferred"
    }
  ],
  "precedence": [
    { "from": "enq-x", "to": "enq-y", "label": "real-time precedence", "tone": "primary" },
    { "from": "deq-x", "to": "enq-y", "label": null, "tone": "event" }
  ],
  "horizon": 8.2
}