{
 "id": "source/jia-xian-mactutor",
 "class": "source",
 "slug": "jia-xian-mactutor",
 "label": {
  "ar": "جيا شيان — ماكتوتر",
  "en": "Jia Xian — MacTutor",
  "ur": "جیا شیان — میک ٹیوٹر"
 },
 "summary": {
  "ar": "سيرة تعرض المثلث الصيني المفقود والشاهد اللاحق عند يانغ هوي سنة1261.",
  "en": "Biography describing the lost Chinese triangle account and Yang Hui's1261 witness.",
  "ur": "گم شدہ چینی مثلث کے بیان اور یانگ ہوئی کے1261 والے شاہد کی سوانح۔"
 },
 "stub": false,
 "wings": [],
 "regions": [],
 "periods": [],
 "tags": [],
 "aliases": [],
 "themes": [],
 "data": {
  "kind": "secondary",
  "type": "article",
  "title": "Jia Xian",
  "author": [
   {
    "family": "O'Connor",
    "given": "J. J."
   },
   {
    "family": "Robertson",
    "given": "E. F."
   }
  ],
  "publisher": "MacTutor History of Mathematics, University of St Andrews",
  "language": "en",
  "URL": "https://mathshistory.st-andrews.ac.uk/Biographies/Jia_Xian/",
  "open_access": true,
  "reliability_note": "Actual biography section on lost books, Yang Hui1261, coefficients through sixth power and adjacent-addition rule read; final root-extraction comparison and footer subsequently read. It leaves independent discovery versus Chinese transmission to al-Samawal unresolved. Neither direction nor root-extraction details are imported as Karaji achievements. No China-to-Baghdad diffusion or exact birth/death asserted.",
  "provenance": {
   "generated_by": "github-copilot",
   "model": "unknown",
   "run": "inventions-p3-b98",
   "source": "Direct scholarly biography and footer, not original Chinese texts or cited Chemla paper. Source definition, not a derivative of Karaji's biography."
  },
  "status": {
   "review": "published",
   "completeness": 3
  }
 },
 "prose": {},
 "degree": 0,
 "contemporaries": [],
 "updated": "2026-11-07",
 "connections": [],
 "related": [],
 "license": {
  "prose": "CC BY-SA 4.0",
  "data": "CC0 1.0"
 }
}