Tuesday, September 29, 2026

SGC-0010

Tier under review: an upstream claim has changed and the tier of this claim is being reviewed.
SGC-0010 Theorem External theorem

Proper classes (in the project's sense: circular self-embedding structures) have their mathematical home in terminal coalgebras νF ≅ F(νF).

Scope 全项目唯一贯穿诸文档的定理级锚点。只有固有类/非良基集合↔νF 为定理级;与分形、旋机、阴阳互生的等同为结构推论或阐释级。νF 是道的诸像之一,不是道本身。 English translation pending
Sources 第十四章 循环识别与固有类;第十五章 旋机吸引子系统的形式化
External anchor Aczel, Non-Well-Founded Sets (1988); Rutten, Universal coalgebra (2000)

Premises and dependents

No published premises or dependents.

Related corrections

  • SGX-002 νF 即道;νF 是无根世界唯一的地基 / 共同的最抽象数学本体 → νF 是道的诸像之一,不是道本身;是固有类的数学家园
  • SGX-003 固有类、非良基集合、分形、旋机、阴阳互生「五名同一」为精确等同 → 仅固有类/非良基集合↔νF 为定理级;其余为结构推论或阐释级

Cite

Claim template
〔定理级〕固有类(在本项目意义上的循环自嵌套结构)以终余代数 νF ≅ F(νF) 为数学家园。——李旭彤《生之科学》(第十四章 循环识别与固有类),问道研究所,2026。
Chinese
李旭彤:〈SGC-0010〉固有类(在本项目意义上的循环自嵌套结构)以终余代数 νF ≅ F(νF) 为数学家园〔定理级〕,载《生之科学》第十四章 循环识别与固有类,问道研究所,2026。https://reresearch.org/claim/sgc-0010/
English
Li, Xutong (2026). SGC-0010 [Theorem]: Proper classes (in the project's sense: circular self-embedding structures) have their mathematical home in terminal coalgebras νF ≅ F(νF). In: Science of Generation, 第十四章 循环识别与固有类. Reasoning Research Institute. https://reresearch.org/en/claim/sgc-0010/
BibTeX
@misc{SGC-0010,
  author = {Li, Xutong},
  title = {{SGC-0010}: Proper classes (in the project's sense: circular self-embedding structures) have their mathematical home in terminal coalgebras νF ≅ F(νF).},
  howpublished = {Science of Generation Portal},
  organization = {Reasoning Research Institute},
  year = {2026},
  url = {https://reresearch.org/en/claim/sgc-0010/},
  note = {Epistemic tier: Theorem. Source: 第十四章 循环识别与固有类}
}