{
  "abstract": "Human sleep is organized into a small number of cycles per night: deep sleep dominates early cycles, REM lengthens toward morning, and light sleep clusters at cycle boundaries. These regularities have long been described qualitatively but never distilled into closed-form laws from large-scale data. A total of 1,106 nights (Sleep-EDF 153 + SHHS 953) are segmented into REM-anchored cycles, and four cycle-indexed statistics follow simple closed-form equations: cycle length declines nearly linearly (R^2=0.996), REM duration follows an inverted U (R^2=0.873), deep-sleep (N3) run length decays exponentially (R^2=0.987) with a time constant of 2.94 cycles, consistent with the homeostatic Process S of the two-process model, and light-sleep (N1) run length follows a U shape (R^2=0.956), confirming a \"long-short-long\" pattern across the night. The laws are reproduced by per-night differentiable fitting (142/142 and 773/773 nights converge), by unconstrained symbolic regression (PySR), and by a 500-night generative synthesizer built from them. Their robustness is established against the two main methodological threats: bootstrap CIs computed by resampling whole nights (1,000 replications) exclude zero for every shape term, and a five-level scan of the REM-merge segmentation threshold preserves every qualitative form. These appear to be the first closed-form laws governing the macro-structure of sleep, distilled and tested across an age-mixed sample (healthy young adults and community-based older adults).",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2611.00550",
  "author_total": 1,
  "authors": [
    {
      "name": "Junhui Gao"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/19x4tgc8jy8vy.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2611.00550",
  "fulltext_url": null,
  "id": "19x4tgc8jy8vy",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2611.00550",
  "language": null,
  "licence": "CC-BY-4.0",
  "licence_label": "CC BY 4.0",
  "licence_source": "article",
  "licence_url": "http://creativecommons.org/licenses/by/4.0/",
  "metadata_licence": "CC0-1.0",
  "native_subjects": [
    [
      "arxiv",
      "cs.AI"
    ],
    [
      "arxiv",
      "q-bio.QM"
    ]
  ],
  "openalex": null,
  "pdf_url": "https://arxiv.org/pdf/2611.00550",
  "pmcid": null,
  "pmid": null,
  "published": "2026-11-01",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/19x4tgc8jy8vy.ris",
  "sources": [
    {
      "first_seen": "2026-11-03T12:21:15Z",
      "native_id": "2611.00550",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2611.00550"
    }
  ],
  "subjects": [
    {
      "field": "biology",
      "origin": "arxiv:q-bio.QM",
      "subfield": "bioinformatics"
    }
  ],
  "title": "Governing Equations of Human Sleep Macro-Structure:Symbolic Discovery from 1,106 Nights",
  "title_text": "Governing Equations of Human Sleep Macro-Structure:Symbolic Discovery from 1,106 Nights",
  "type": "preprint",
  "updated_at": "2026-11-05T15:20:29Z",
  "url": "https://research.draconitic.com/paper/19x4tgc8jy8vy",
  "venue": "arXiv",
  "versions": []
}