{
  "annotation_id": "3d39e6aa-7bce-4dae-80be-2089fad4bfcd",
  "date_created": "2026-03-02T18:00:32.073000Z",
  "date_modified": "2026-03-02T18:00:32.073000Z",
  "file_hash": "69cb6131d1d51d316e5dad8f953ca06445fb8db78941884d10b076cf86ae163a",
  "private": false,
  "record": {
    "abstract": "This paper studies the possibility of using the survival function to predict\nlong term stability by extrapolation. The survival function is a function of\nthe initial coordinates and is the number of turns a particle will survive for\na given set of initial coordinates. To determine the difficulties in\nextrapolating the survival function, tracking studies were done to compute the\nsurvival function. The survival function was found to have two properties that\nmay cause difficulties in extrapolating the survival function. One is the\nexistence of rapid oscillations, and the second is the existence of plateaus.\nIt was found that it appears possible to extrapolate the survival function to\nestimate long term stability by taking the two difficulties into account. A\nmodel is proposed which pictures the survival function to be a series of\nplateaus with rapid oscillations superimposed on the plateaus. The tracking\nstudies give results for the widths of these plateaus and for the seperation\nbetween adjacent plateaus which can be used to extrapolate and estimate the\nlocation of plateaus that indicate survival for longer times than can be found\nby tracking.",
    "arxiv_id": "physics/0007008",
    "authors": [
      "G. Parzen"
    ],
    "categories": [
      "physics.acc-ph"
    ],
    "title": "Prediction of long term stability by extrapolation",
    "url": "https://arxiv.org/abs/physics/0007008"
  },
  "schema_id": "dorsal/arxiv",
  "source": {
    "execution_id": "d1b1aa11-c447-4ece-94d6-cd48804a0a09",
    "id": "arXiv Dataset IDs",
    "type": "Model",
    "variant": "snapshot-2026-03-01",
    "version": "0.1.0"
  },
  "user_id": 1000002
}